{"as_of":"2026-08-10T18:21:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:3d47fa506f163d7aab9a94ce534ba611673b4a93b2cda42c406a6845a85e65ce","coverage":[{"denominator":131,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-30T12:43:24.600460Z","state":"measured"},{"denominator":101,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":101,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-10T06:31:04.303077+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T04:16:34.393827Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-10T04:16:34.526216Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"cited_work":{"arxiv_id":"2607.27049","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.27049","snapshot_observed_at":"2026-08-10T04:16:34.526216Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","venue":"math.NA","work_id":"6860018d-9f20-431d-ac0e-149a4ec2eb83","year":2026},"citing_paper":{"arxiv_id":"2608.06642","last_updated":"2026-08-06T23:20:39Z","snapshot_observed_at":"2026-08-10T18:10:28.500154Z","submitted_at":"2026-08-06T23:20:39Z","title":"The error estimate of entropy-stable discontinuous Galerkin methods for hyperbolic conservation laws","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-10T04:16:34.393827Z"},"links":{"cited_paper":"/paper/2607.27049","citing_paper":"/paper/2608.06642"},"observation_digest":"sha256:12eb1ad404a7d6f10ce0171f6b6feed30d799ab6a63a70c17979dfe2603c3248","observation_id":"546a0071-dc7b-40e3-a853-fcf6ec303178","resolution":{"observed_at":"2026-08-10T04:16:34.532134Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.27049/citation-record","integrity":"/paper/2607.27049/integrity","json":"/paper/2607.27049/citation-record.json","paper":"/paper/2607.27049"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"1711.10358","last_updated":"2018-06-11T14:26:19Z","snapshot_observed_at":"2026-07-06T06:11:38.247679Z","submitted_at":"2017-11-27T09:08:03Z","title":"A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1711.10358","snapshot_observed_at":"2026-07-30T12:43:19.069755Z","title":"A general framework to construct schemes satisfying additional conservation relations.Applicationtoentropyconservativeandentropydissipativeschemes","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.069755Z"},"links":{"cited_paper":"/paper/1711.10358","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:6b407cf33f471fbaed87c1f28a29414765871e4a766c3f58a11861ae71a6b7fc","observation_id":"8133d7eb-f668-4b5b-bfd8-52fa33fa2564","resolution":{"observed_at":"2026-07-30T12:43:19.069755Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1912.08108","last_updated":"2021-04-19T15:10:47Z","snapshot_observed_at":"2026-08-08T15:55:20.904481Z","submitted_at":"2019-12-17T16:01:32Z","title":"Analysis of the SBP-SAT Stabilization for Finite Element Methods Part I: Linear Problems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1912.08108","snapshot_observed_at":"2026-07-30T12:43:19.169515Z","title":"AnalysisoftheSBP-SATStabilization for Finite Element Methods Part I: Linear problems","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.169515Z"},"links":{"cited_paper":"/paper/1912.08108","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:f36925827b6cdc5f933e832da4b5a5403d495dc145efc1b49fc856edafea1fc7","observation_id":"c9562c16-9073-4db9-85dc-9b7b942474fa","resolution":{"observed_at":"2026-07-30T12:43:19.169515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:19.230655Z","title":"Reinterpretation and Extension of Entropy Correc- tion Terms for Residual Distribution and Discontinuous Galerkin Schemes: Application to Structure Preserving Discretization","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.230655Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:ce168d9eb42e4fba9112939871c8f9522581d031c5bcfd10294731ce7b79912f","observation_id":"76ca98bf-d9bf-46b4-8fad-edb94e7ca096","resolution":{"observed_at":"2026-07-30T12:43:19.230655Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:19.276457Z","title":"A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.276457Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:05cd33987c8ebddf0c7d1f991e52126880905e046cc4ac21ef68342225499a88","observation_id":"c536a526-522b-481f-a8b1-433f7c7e2fa3","resolution":{"observed_at":"2026-07-30T12:43:19.276457Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2019.02.007","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Encapsulated high order difference operators on curvilinear non-conforming grids","venue":"Journal of Computational Physics","work_id":"c3afef5c-778c-4113-a9ba-31ac2af0f6ae","year":2019},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.373513Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:11eb94fd0b89128bd84b0d3e5a4d77c3ba176c783f90a5f0822a4d8e40612643","observation_id":"4ae06f53-004f-4e64-bb79-4569f3f79e01","resolution":{"observed_at":"2026-07-30T12:46:01.408765Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2603.27421","last_updated":"2026-08-03T17:24:56Z","snapshot_observed_at":"2026-08-06T23:37:34.221988Z","submitted_at":"2026-03-28T21:45:40Z","title":"Error analysis of an asymptotic-preserving, energy-stable finite volume method for barotropic Euler equations","version":3},"cited_work":{"arxiv_id":"2603.27421","doi":"10.48550/arxiv.2603.27421","metadata_source":"pith","pith_arxiv_id":"2603.27421","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Error analysis of an asymptotic-preserving, energy-stable finite volume method for barotropic Euler equations","venue":"math.NA","work_id":"70fb1e10-5a87-4b5f-9318-87ba431a0345","year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.439216Z"},"links":{"cited_paper":"/paper/2603.27421","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:fae6bcfda1e0e0cb012a89f207f3e7b0136d814317ffcd46c9139a0c25e59b8e","observation_id":"132f2fb8-ad69-4844-ac15-82ad2945c270","resolution":{"observed_at":"2026-07-30T12:46:01.104838Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0036142902420436","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Stability and Convergence of a Class of Finite Element Schemes for Hyperbolic Systems of Conservation Laws","venue":"SIAM Journal on Numerical Analysis","work_id":"c9430666-6328-4278-a9e6-e9efed517ee3","year":2004},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.504973Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:1a0aa097df5fe0f177ff1c0d1f5b566e68685b476128de8f81f93832b7439106","observation_id":"6d6a68e1-0760-4b0c-847d-e6a3f78a44b5","resolution":{"observed_at":"2026-07-30T12:46:00.946497Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.22195","last_updated":"2025-07-29T19:45:28Z","snapshot_observed_at":"2026-08-09T19:18:08.109801Z","submitted_at":"2025-07-29T19:45:28Z","title":"An entropy-stable and kinetic energy-preserving macro-element HDG method for compressible flows","version":1},"cited_work":{"arxiv_id":"2507.22195","doi":"10.48550/arxiv.2507.22195","metadata_source":"pith","pith_arxiv_id":"2507.22195","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"An entropy-stable and kinetic energy-preserving macro-element HDG method for compressible flows","venue":"cs.CE","work_id":"96c082bd-17a3-4b24-b5f9-e0d7acdb0aa3","year":2025},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.603664Z"},"links":{"cited_paper":"/paper/2507.22195","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:dd3956a261f580854d69eb8a0b9a8505d7de50187a5cc29d64d06cae43be25b2","observation_id":"b7005e2b-0bec-4d64-adf7-f9cb583bec6c","resolution":{"observed_at":"2026-07-30T12:46:00.716715Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.11068","last_updated":"2026-07-11T09:45:50Z","snapshot_observed_at":"2026-08-08T08:02:32.204853Z","submitted_at":"2025-07-15T08:01:26Z","title":"Stability of the Active Flux Method in the Framework of Summation-by-Parts Operators","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.11068","snapshot_observed_at":"2026-07-30T12:43:19.704493Z","title":"Sta- bility of the Active Flux Method in the Framework of Summation-by-Parts Operators","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.704493Z"},"links":{"cited_paper":"/paper/2507.11068","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:7831592b6c29436e0befc5129b391acc06700bbb273d6036b4a42e8287ab4ce8","observation_id":"a4d8addb-a578-48e7-a97c-d3145dde8616","resolution":{"observed_at":"2026-07-30T12:43:19.704493Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/978-3-642-58535-7_5","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Numerical methods for gasdynamic systems on unstructured meshes","venue":"Lecture notes in computational science and engineering","work_id":"f2763dba-30d7-4cd5-9402-aee4803506ea","year":1999},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.770113Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:cbe9ace6e563a34999932c9f993b733c416af7775458f5280cc87f334b4ad8fb","observation_id":"52c30cb7-fdf8-4203-91db-a778dd5eff9b","resolution":{"observed_at":"2026-07-30T12:46:00.599444Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1411.1607","last_updated":"2015-07-19T19:58:28Z","snapshot_observed_at":"2026-08-09T11:52:37.906502Z","submitted_at":"2014-11-06T13:39:40Z","title":"Julia: A Fresh Approach to Numerical Computing","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1411.1607","snapshot_observed_at":"2026-07-30T12:43:19.867047Z","title":"Julia:AFreshApproachtoNumer- ical Computing","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.867047Z"},"links":{"cited_paper":"/paper/1411.1607","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:fea990fda35cc45afe9add51145aa3ed73b17ac634b026f4ea801059a2fa6ae7","observation_id":"7c94d319-f4bb-49a9-9f4d-e8abbf6b5a9d","resolution":{"observed_at":"2026-07-30T12:43:19.867047Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:19.964340Z","title":"Boyd and L","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:19.964340Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:f779fcc5ef91c97ff7992e407ac4b85d95462cd59b004819be9e40053df5ad3c","observation_id":"b8a77048-3ddd-4767-b88d-a37e0707204b","resolution":{"observed_at":"2026-07-30T12:43:19.964340Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1602.02128","last_updated":"2016-02-05T19:29:47Z","snapshot_observed_at":"2026-07-06T04:45:18.334893Z","submitted_at":"2016-02-05T19:29:47Z","title":"Error estimate for time-explicit finite volume approximation of strong solutions to systems of conservation laws","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1602.02128","snapshot_observed_at":"2026-07-30T12:43:20.029226Z","title":"Error Estimate for Time-Explicit Finite Volume Approximation of Strong Solutions to Systems of Conservation Laws","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.029226Z"},"links":{"cited_paper":"/paper/1602.02128","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:8004a30fe4cf1a19df891041af221f55af5cb2999a47139bbc6747e614c1c840","observation_id":"8e59a433-26ee-49ec-af69-94d280f300f1","resolution":{"observed_at":"2026-07-30T12:43:20.029226Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/130946873","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Superconvergence of discontinuous Galerkin methods for linear hyperbolic equations","venue":"SIAM Journal on Numerical Analysis","work_id":"66ae9ed1-154b-4edb-926f-528a41dc4963","year":2014},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.118416Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:d28cf4514213230047672aa9a5013b0f647a1f4c6fc1cf6be1b281b1327c7e93","observation_id":"65c18e3c-2719-4e38-9332-e0e3a485d4a0","resolution":{"observed_at":"2026-07-30T12:46:00.365191Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1088/1742-6596/3173/1/012034","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Efficient Compressible Turbulent Flow Simulations: Entropy Projection and Correction for an ILES in a Discontinuous Galerkin solver","venue":"Journal of Physics Conference Series","work_id":"533de5e6-5380-497e-8591-c7322413eea0","year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.212863Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:ac8019d41a36cd9c9ada68127bed6ce9f1dbddc3fe74644d0aeecec985e508dc","observation_id":"0ff61685-d59a-4c51-a859-3a2083a31fcb","resolution":{"observed_at":"2026-07-30T12:46:00.046003Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.276231Z","title":"Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.276231Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:95473064f3295340b36dad23c3cbf2fef909c36606718c686ec5a6cb4a26d1d6","observation_id":"2ddec7e5-c0c6-412f-ae3b-3b02f1e39646","resolution":{"observed_at":"2026-07-30T12:43:20.276231Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.377064Z","title":"Time-Stable Boundary Conditions for Finite-Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Schemes","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.377064Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:bb4accd711999274547474260fa738eac0efbd574de5a127f4da48d082678695","observation_id":"787d96f4-e6bb-40de-aa27-fe2a1c5e3085","resolution":{"observed_at":"2026-07-30T12:43:20.377064Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.441442Z","title":"An artificial viscosity approach to high order entropy stable discontinuous Galerkin methods","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.441442Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:62b3b624b42002022cd85a4a2e0259d03d82028d235221b142d12a04e67907ab","observation_id":"a72f49da-ab7e-4df1-9271-ad086080f4b5","resolution":{"observed_at":"2026-07-30T12:43:20.441442Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5281/zenodo.19906078","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":null,"venue":"Zenodo (CERN European Organization for Nuclear Research)","work_id":"03b21229-cd40-4988-b6c7-0f690d630bcd","year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.631586Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:061d765903689983c47b33d04faf7ae1f68bf05796b0c9dc9a87c8f7dba536d0","observation_id":"864a8bf3-d1d1-462f-bd8b-185d9f5802a7","resolution":{"observed_at":"2026-07-30T12:45:59.827943Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.699258Z","title":"Ontheentropy projectionandtherobustnessofhighorderentropystablediscontinuousGalerkinschemes for under-resolved flows","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.699258Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:1d66db407fc6bebd92edd7d0b0994f67c1cbea1b87b1e0d628c81c50dbbe4ab8","observation_id":"73be8fed-5bdd-44cc-8c64-4ceae16b3e3e","resolution":{"observed_at":"2026-07-30T12:43:20.699258Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.768497Z","title":"Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes forCompressibleEulerandNavier-StokesEquations","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.768497Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:68020a486c910bbf715c682e55a0c67ca179669cbb6f588e92c5c2d7bdeb3d00","observation_id":"d9a5b05a-8100-4d12-8cfc-eb2332c67b60","resolution":{"observed_at":"2026-07-30T12:43:20.768497Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.2307/30044201","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Means Generated by an Integral","venue":"Mathematics Magazine","work_id":"067dc17a-aab2-4d79-af0d-945a07646a64","year":2005},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.830794Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:0f47b24e0d60953b71913eadce3ca5d94930adc625736f97e6eff65576617a07","observation_id":"b90eb704-a35b-435b-8e33-52c67ee6bd62","resolution":{"observed_at":"2026-07-30T12:45:59.647598Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.894884Z","title":"Entropy stable high order discontinuous Galerkin methods with suitable quadrature rules for hyperbolic conservation laws","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.894884Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:486dafb7634be445ce0261a87148a47b749b7557c1ab8ce942161025d92cbdb2","observation_id":"637c0a9d-36c0-427a-8ffb-c2abdb728684","resolution":{"observed_at":"2026-07-30T12:43:20.894884Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:20.946080Z","title":"Review of Entropy Stable Discontinuous Galerkin Methods for Systems of Conservation Laws on Unstructured Simplex Meshes","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:20.946080Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:a1dded478facb6cdedb5bcbb8068b220036953c61c6733426cecdada4cf48baf","observation_id":"fb899bb5-3ff4-4f09-8d59-2fc47e84e5a2","resolution":{"observed_at":"2026-07-30T12:43:20.946080Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/090747701","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Superconvergence of discontinuous Galerkin and local discon- tinuous Galerkin schemes for linear hyperbolic and convection-diffusion equations in one space dimension","venue":"SIAM Journal on Numerical Analysis","work_id":"53bac6b4-3587-4b83-88d1-429ab5db20da","year":2010},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.008954Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:5d57dfae0cd08d7b606f7be4e36cd6949ab544ea950034863744470665d96ed8","observation_id":"6fcae958-06ff-41e5-9220-8811fe79e71a","resolution":{"observed_at":"2026-07-30T12:45:59.477619Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.219109Z","title":"Berlin Heidelberg: Springer, 2016.doi:10","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.219109Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:d0ccdec74cb2447600b3f8b00926f7366b33a52f37ba461316c8885a8bcbdaab","observation_id":"f96e0fa0-43a4-4ed6-9ab0-48fa8966a6e2","resolution":{"observed_at":"2026-07-30T12:43:21.219109Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.303430Z","title":"TheSecondLawofThermodynamicsandStability","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.303430Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:a14c4ec2c0cdf8b5334084c707bdfae1328e6a35d701392d5ca844861e76745a","observation_id":"860deebc-a220-4180-aa2e-04d89219aeb6","resolution":{"observed_at":"2026-07-30T12:43:21.303430Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1510.05430","last_updated":"2015-10-19T11:34:56Z","snapshot_observed_at":"2026-07-06T04:33:30.469495Z","submitted_at":"2015-10-19T11:34:56Z","title":"A posteriori analysis of fully discrete method of lines DG schemes for systems of conservation laws","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1510.05430","snapshot_observed_at":"2026-07-30T12:43:21.396567Z","title":"A Posteriori Analysis of Fully Discrete Method of Lines Discontinuous Galerkin Schemes for Systems of Conservation Laws","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.396567Z"},"links":{"cited_paper":"/paper/1510.05430","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:5546c3a27465c3c02882442eafcedbf2b2b9186c11d6e8c645d9b2f056b825d5","observation_id":"1cfa9b3b-2a7c-4544-9f48-a0c9284880d2","resolution":{"observed_at":"2026-07-30T12:43:21.396567Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.453576Z","title":"Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.453576Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:4e730c3faecab4fab10c6d76ae84b598eacc84a5b40ecdb07cfe21d050c9cc71","observation_id":"f39279ef-3434-4dd6-9f61-76ca24fc20c4","resolution":{"observed_at":"2026-07-30T12:43:21.453576Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/0711052","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Two methods of Galerkin type achieving optimum𝐿2 rates of convergence for first order hyperbolics","venue":"SIAM Journal on Numerical Analysis","work_id":"baa41ff8-561e-4d49-b19c-5578ae714bf9","year":1974},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.524208Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:bc50a642d0bea89e1ac25a4bd6da016c38e9af6a357f3ad1a3f595c27ea06f5f","observation_id":"8c9fa640-3050-4cc1-9559-bf9ea79bf0e0","resolution":{"observed_at":"2026-07-30T12:45:59.380362Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.593556Z","title":"Uniqueness of Solutions to Hyperbolic Conservation Laws","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.593556Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:ff339aa3660080c4218299fc62044f7581e5beac29c0e95810c85aa0c90d084e","observation_id":"ee8d4bef-85d2-419e-8a39-324525d6c9f4","resolution":{"observed_at":"2026-07-30T12:43:21.593556Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.674175Z","title":"Doehring, J","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.674175Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:e9fcfc2836a036ce614ab8d8b63dade35c993247d236ec61bf0eb987dc424cfd","observation_id":"65150e57-90f4-44b6-8adb-3670a2a21b34","resolution":{"observed_at":"2026-07-30T12:43:21.674175Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/0710074","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Galerkin methods for first order hyperbolics: An example","venue":"SIAM Journal on Numerical Analysis","work_id":"81a4c2fc-ae63-47d9-8884-8641e0a9119d","year":1973},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.761109Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:28adf3f72690da389fe8ddae554f04cff07ca5e149fcc3a6c32becfb4e4df5f9","observation_id":"76d0b968-da00-44e7-9d9c-ca85695fecf6","resolution":{"observed_at":"2026-07-30T12:45:58.994739Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.848399Z","title":"Conservative correction procedures utilizing artificial dissipation operators","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.848399Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:0da7d6de93b5ce11db602a7715f43d423ce04fa4d3797f731314277436070ab0","observation_id":"a444d8b8-00fc-4f52-b66e-cd3b2d2e6b42","resolution":{"observed_at":"2026-07-30T12:43:21.848399Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.889482Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.889482Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:249e9a18d967c9f27d64bde6cfc35f4febe3f5c92144b48188c9401b2b6835f2","observation_id":"66e884a0-8e02-4b34-bcff-bc52180f0f57","resolution":{"observed_at":"2026-07-30T12:43:21.889482Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.923715Z","title":"High-order entropy stable finite difference schemes for nonlinearconservationlaws:Finitedomains","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.923715Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:c1048c9e674141433fe02747a61a872a68a3439f610a7ba912cd9ef4ba43d8d3","observation_id":"ccc85a45-6306-48c0-b37a-13b9a9257a82","resolution":{"observed_at":"2026-07-30T12:43:21.923715Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:21.960545Z","title":"Construction of Approximate Entropy Measure-Valued Solutions for Hyperbolic Systems of Conservation Laws","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:21.960545Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:2ef7e0737f3ae7c8ae17f8dd69995a7ae9529957aeac845f68c6c86cf6f0768a","observation_id":"ca195cee-7726-426c-84a1-d0a08aa1b4a3","resolution":{"observed_at":"2026-07-30T12:43:21.960545Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.033616Z","title":"EnergyPreservingandEnergyStableSchemes for the Shallow Water Equations","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.033616Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:2cd3b01058f35a006b38e69bb24c3fc58cd95a00876c59c7960419bede6728bf","observation_id":"b1705617-d3f4-4bac-9856-889e30dccaad","resolution":{"observed_at":"2026-07-30T12:43:22.033616Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.jcp.2011.03.042","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Well-balanced and energy stable schemes for the shallow water equations with discontinuous topography","venue":"Journal of Computational Physics","work_id":"851a8317-82ac-4845-96fa-764f70f3e319","year":2011},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.097737Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:64636ed04236a7ec9f49b9f93020f9dd30c321a571627ac4f54c75413a99c14b","observation_id":"b896426a-e045-4110-ac2b-9086c52e98cd","resolution":{"observed_at":"2026-07-30T12:45:58.652284Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/110836961","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"ArbitrarilyHigh-OrderAccurateEntropyStable Essentially Nonoscillatory Schemes for Systems of Conservation Laws","venue":"SIAM Journal on Numerical Analysis","work_id":"84070a8d-272c-44a4-9e41-9264a759c3c4","year":2012},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.128990Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:ba3693f245f388aa8ab7bc8bbc6edb22833daa6af6fb8cf0d620fa71319ef1b3","observation_id":"cb811fa5-7dc9-4673-9caf-c7978ff483cc","resolution":{"observed_at":"2026-07-30T12:45:58.444736Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.186527Z","title":"Systems of Conservation Equations with a Convex Ex- tension","venue":null,"work_id":null,"year":1971},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.186527Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:dbb0b6548e3187c492a34cd6fe1068d61aabb8b5e538e79d4e0532de3fe3c9b8","observation_id":"8e45a6b7-1910-4e4a-9b66-62b95812acd4","resolution":{"observed_at":"2026-07-30T12:43:22.186527Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1093/imanum/drv028","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Error estimates for a numerical ap- proximation to the compressible barotropic Navier-Stokes equations","venue":"IMA Journal of Numerical Analysis","work_id":"4dbfb5c3-28f2-4552-8ede-af017c601282","year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.258056Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:3c050396a743a0fa7a2c11f7ffba0617bddd9a42f3f7530a75da42e87d483612","observation_id":"cc7f2844-5c26-444b-9d7f-49b920ee799f","resolution":{"observed_at":"2026-07-30T12:45:58.246616Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.09026","last_updated":"2021-11-05T14:58:06Z","snapshot_observed_at":"2026-08-04T20:25:30.182311Z","submitted_at":"2020-07-17T14:41:41Z","title":"Stability issues of entropy-stable and/or split-form high-order schemes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.09026","snapshot_observed_at":"2026-07-30T12:43:22.296674Z","title":"Stability Issues of Entropy-Stable and/or Split-form High-order Schemes","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.296674Z"},"links":{"cited_paper":"/paper/2007.09026","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:b026fcf3469b1ee90f9f0ded0679a189370d424121a7df249c6ada51f9cd7376","observation_id":"111e7239-18b8-40cc-b540-d9c3e21a3ec3","resolution":{"observed_at":"2026-07-30T12:43:22.296674Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.339714Z","title":"A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.339714Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:09df8f0411e92c3ce7bb71944d313c3dd2d48e7e313897a7bd207f634f2187aa","observation_id":"e813df60-748b-4e47-ae7c-2f133aa008e2","resolution":{"observed_at":"2026-07-30T12:43:22.339714Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.374794Z","title":"Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.374794Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:7fd39ee22306b01943882bd2291081db0336b71d196a092b714ceb6054fbd52d","observation_id":"63b43d8c-1c20-47e5-af94-8daa47785945","resolution":{"observed_at":"2026-07-30T12:43:22.374794Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.406812Z","title":"ASkew-SymmetricDiscontinuousGalerkinSpectralElementDiscretization and Its Relation to SBP-SAT Finite Difference Methods","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.406812Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:7fcd46a1769913ade91ea6585f229ca56921386e1f83d360080b39a50c244b1c","observation_id":"4f50d0fd-f27f-4ff5-8406-e29ac4a0c48e","resolution":{"observed_at":"2026-07-30T12:43:22.406812Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.438512Z","title":"Awellbalancedandentropyconservative discontinuous Galerkin spectral element method for the shallow water equations","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.438512Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:fb311f547e6168318f4793d874c470b9bd42d8d32357be2a5dffc23eced899b3","observation_id":"36639488-5c8d-48dc-8af7-c60af747893d","resolution":{"observed_at":"2026-07-30T12:43:22.438512Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00574-016-0144-z","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"RelativeentropybasederrorestimatesfordiscontinuousGalerkinschemes","venue":"Bulletin of the Brazilian Mathematical Society New Series","work_id":"e5af897c-58d7-4b6e-8a7c-7c4dd7ab09e3","year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.497597Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:71b3e1d0fead8ab091c0da664f0a07a319274e97fed6dda118724a95eb8acfa3","observation_id":"9299d151-ef7f-46f2-b39a-399b950a70b7","resolution":{"observed_at":"2026-07-30T12:45:58.116098Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1405.7616","last_updated":"2014-05-29T17:02:44Z","snapshot_observed_at":"2026-07-06T03:44:59.966841Z","submitted_at":"2014-05-29T17:02:44Z","title":"A posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1405.7616","snapshot_observed_at":"2026-07-30T12:43:22.533673Z","title":"A Posteriori Analysis of Discontinuous Galerkin Schemes for Systems of Hyperbolic Conservation Laws","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.533673Z"},"links":{"cited_paper":"/paper/1405.7616","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:d0913252be549dde29eafdad04a5463fd51ccff9432d273b35de88592a24fa4a","observation_id":"a2fc4e37-1bc5-4753-9052-8931b179209e","resolution":{"observed_at":"2026-07-30T12:43:22.533673Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.579713Z","title":"Convergence of hyperbolic approximations to higher- order PDEs for smooth solutions","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.579713Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:df1b1c2347c86ee039827fa44623e171eb87fb4911b8078ac2ca4c0b779303b1","observation_id":"97e3b17d-37d7-48e2-aa1c-8b2d9fe02b2a","resolution":{"observed_at":"2026-07-30T12:43:22.579713Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.613514Z","title":"Glaubitz, A","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.613514Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:96c30511a84288468f2c34ee9ed96ad0954dc075032544cf6d0c0f0b3300606a","observation_id":"fb87833d-2442-4eea-9c52-b7ec8d85c6aa","resolution":{"observed_at":"2026-07-30T12:43:22.613514Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.650849Z","title":"An interesting class of quasi-linear systems","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.650849Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:6d296760ad605ff160ecb52167d5077615f8e513d80b7c55f54125c5416e7186","observation_id":"e6079e8d-3c0a-421b-a697-61872cc35dd9","resolution":{"observed_at":"2026-07-30T12:43:22.650849Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.732109Z","title":"Theconvergenceratefordifferenceapproximationstomixedinitialbound- ary value problems","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.732109Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:054dff9b84cb918e2c1e27534de38fa818cfa5f9005f13bfbe0db1c93e686838","observation_id":"5f4d6230-d6d1-4bd8-aa06-499e698c3083","resolution":{"observed_at":"2026-07-30T12:43:22.732109Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.768600Z","title":"Gustafsson, H.-O","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.768600Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:189b876e129b09fcee491b1e6cf58285d99818752214d767dbe3bcf883dd84b1","observation_id":"9c67aadb-3c43-4858-8f41-62bd3b0952ab","resolution":{"observed_at":"2026-07-30T12:43:22.768600Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.834187Z","title":"On the symmetric form of systems of conservation laws with entropy","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.834187Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:7904d818035d56f0918faf5e8339c799df589d9618340de6df2cfdc8982e6250","observation_id":"3a2ceda6-02f0-4b82-802d-01945cf1aefc","resolution":{"observed_at":"2026-07-30T12:43:22.834187Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.893626Z","title":"A provably entropy stable subcell shock capturing approach for high order split form DG for the compressible Euler equations","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.893626Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:16dca716a99d7ddab57c643bee8076bdd95ae6b7817ccdf2809eb257e69928d3","observation_id":"8ae9a334-1a8e-41de-9a62-ff7ed289b393","resolution":{"observed_at":"2026-07-30T12:43:22.893626Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.944032Z","title":"Constructing stable, high-order finite-difference operators on point clouds over complex geometries","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.944032Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:e04777e7d8eb8c60a7bf7af6b403734cf1dc0968de9d81be697c3e2450033e02","observation_id":"746a2506-54b4-4b1a-a0b3-62efa2b82b6a","resolution":{"observed_at":"2026-07-30T12:43:22.944032Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:22.984292Z","title":"Entropy-stable, high-order summation-by-parts discretizations without in- terfacepenalties","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:22.984292Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:fde2783b05b81e906f7c11111879da3cc8c9958488d01c76951eee0a38b19932","observation_id":"3e9a577a-ac10-4069-b612-3cefc50db448","resolution":{"observed_at":"2026-07-30T12:43:22.984292Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.039611Z","title":"MultidimensionalSummation-By- Parts Operators: General Theory and Application to Simplex Elements","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.039611Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:5d79df0169b843c6d6d8bd075d3c263644a7f16138ba0dcdf8924a25fd57b817","observation_id":"89f589d6-d2e5-4f61-862c-edeed5f5ddd7","resolution":{"observed_at":"2026-07-30T12:43:23.039611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.077385Z","title":"Entropy stable spacetime discontinuous Galerkin methods for the two-dimensional compressible Navier–Stokes equations","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.077385Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:a6dfe4a507c143293f7005773391feceb94441a749fdc6d223291582e3bf976e","observation_id":"af2fc73a-1a33-445b-a315-a45de7fb54b8","resolution":{"observed_at":"2026-07-30T12:43:23.077385Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s00211-013-0558-0","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Entropy stable shock capturing space-time discontinuous Galerkinschemesforsystemsofconservationlaws","venue":"Numerische Mathematik","work_id":"5fe56b5e-99fb-431f-9f6e-a64a98020fb4","year":2014},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.111878Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:2c883f5b65acc2add5d0133cf8b08198336abba81a382f81dc2a9dcbc075dd50","observation_id":"6408c5df-04a0-458c-b94b-513b10803ed0","resolution":{"observed_at":"2026-07-30T12:45:57.794256Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1002/num.22089","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Error estimates to smooth solutions of semi-discrete discontin- uous Galerkin methods with quadrature rules for scalar conservation laws","venue":"Numerical Methods for Partial Differential Equations","work_id":"5a05bb71-edd6-4067-bddd-2e43c02dd434","year":2017},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.147307Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:df2d7de7228cfa9c96b3ecc0c026eef04efdcc31d8c88cc8f2535c9076b1666c","observation_id":"027db58d-f945-4711-b512-4eccced94d68","resolution":{"observed_at":"2026-07-30T12:45:57.594744Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0045-7825(86)90127-1","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A new finite element formulation for compu- tational fluid dynamics: I. Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics","venue":"Computer Methods in Applied Mechanics and Engineering","work_id":"fbbe7608-6b43-41a8-8599-5cefd5cfbedd","year":1986},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.254207Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:caf25ecf38127d2f5524766101ba69ece76b398be6e32f9e8680446f2b8db8e4","observation_id":"b4273996-24b4-4538-9f19-7008a367d9f3","resolution":{"observed_at":"2026-07-30T12:45:57.398773Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.298225Z","title":"A Flux Reconstruction Approach to High-Order Schemes Including Dis- continuous Galerkin Methods","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.298225Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:069ae1e4b3de09f093c1dc794effe9260c205fa5eef8ced4a34f2c647504a481","observation_id":"3580aa64-551d-4eb1-9f8b-9123197cd2ac","resolution":{"observed_at":"2026-07-30T12:43:23.298225Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.332975Z","title":"Affordable, entropy-consistent Euler flux functions II: Entropy productionatshocks","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.332975Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:93d49bae2b70567406d7e0d435c24a9ad8fddfdceb8ee8891596fd9dff6cb488","observation_id":"565af070-e46a-42b0-aa59-6cd02ada11c5","resolution":{"observed_at":"2026-07-30T12:43:23.332975Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.378203Z","title":"On a cell entropy inequality for discontinuous Galerkin meth- ods","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.378203Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:73c9b66eaf665d531fccef026dface8f6865594bfd7c200f6b51c6c49eea609b","observation_id":"913d2cb4-d63d-4f96-9723-4ec79dbef1b2","resolution":{"observed_at":"2026-07-30T12:43:23.378203Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/s0025-5718-1986-0815828-4","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation","venue":"Mathematics of Computation","work_id":"31018cb0-e676-438b-ab71-2391ef3d22bb","year":1986},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.437767Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:df2e03f32d107f5e540e30e0e6a781e0c6f85ecffaf11ac7ca08c31291c51800","observation_id":"53cf54f1-8c63-4be7-a50d-de2ab82e0cf7","resolution":{"observed_at":"2026-07-30T12:45:57.228681Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/s0036142903438136","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"ErrorEstimatesforFiniteVolumeApproximationsofClassical SolutionsforNonlinearSystemsofHyperbolicBalanceLaws","venue":"SIAM Journal on Numerical Analysis","work_id":"2f5f2806-b69b-4ec2-8bc0-de2beef95781","year":2006},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.484251Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:a975b68e745163c534b333a02baeb13238527d9a2770e452ef23907238911296","observation_id":"247cfd98-fd41-4886-8ae6-f81a29f8e90b","resolution":{"observed_at":"2026-07-30T12:45:57.014739Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1905.09847","last_updated":"2019-05-23T18:02:02Z","snapshot_observed_at":"2026-07-06T07:55:03.097133Z","submitted_at":"2019-05-23T18:02:02Z","title":"Relaxation Runge-Kutta Methods: Conservation and stability for Inner-Product Norms","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.09847","snapshot_observed_at":"2026-07-30T12:43:23.523106Z","title":"Relaxation Runge-Kutta Methods: Conservation and Stability for Inner- Product Norms","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.523106Z"},"links":{"cited_paper":"/paper/1905.09847","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:19d89208d9f391eb9f3959b440183d6893b956ea31915d84ee8be31a6259cc1b","observation_id":"eb41e22c-6d38-4bf8-b2d9-9a5ff0eae85b","resolution":{"observed_at":"2026-07-30T12:43:23.523106Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.577089Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.577089Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:ba6b320297e22b57859d836e81268bfa1e54f5f6681359f574b36cd6d715860e","observation_id":"8f76ed39-cf1f-488d-b406-32e4e10e3ba6","resolution":{"observed_at":"2026-07-30T12:43:23.577089Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.617300Z","title":"MetricIdentitiesandtheDiscontinuousSpectralElementMethodonCurvi- linear Meshes","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.617300Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:b432739a718c2674483268e79872400b56cfc5a24a265ceed237e4082a0a61e1","observation_id":"f87dfc70-c0d7-414d-b7ea-5154867ab872","resolution":{"observed_at":"2026-07-30T12:43:23.617300Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.697876Z","title":"FiniteElementandFiniteDifferenceMethodsforHyperbolic PartialDifferentialEquations","venue":null,"work_id":null,"year":1974},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.697876Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:00e05f5893ab0955af72e3997e5be4fb42c6240e27dbcdbe82e3498c7c3d9e72","observation_id":"73bd58ca-867f-4d3b-8c29-5429d3958b47","resolution":{"observed_at":"2026-07-30T12:43:23.697876Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.790795Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.790795Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:bfa12cf794109aa349cfdf0accbb407fa64796ce90ba567633bbf79041ea33fa","observation_id":"65e588ab-4bc0-457f-b027-9d53b92f8914","resolution":{"observed_at":"2026-07-30T12:43:23.790795Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.799414Z","title":"A robust first order meshfree method for time-dependent nonlinear conservationlaws","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.799414Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:46e7a10c4c20f795d589731cd169adf92a921811926250a3e096ec4f3a0926fb","observation_id":"9f58a6d4-5c64-46c8-b3a9-e467dcc5229d","resolution":{"observed_at":"2026-07-30T12:43:23.799414Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:23.943481Z","title":"FullyDiscrete,EntropyConservativeSchemes of Arbitrary Order","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:23.943481Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:22604532805dcf7660dd249395796507091d20bd0486efe824a9527b23f0b6da","observation_id":"540e744c-3a11-457a-b354-5171d1da5120","resolution":{"observed_at":"2026-07-30T12:43:23.943481Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.13221","last_updated":"2025-06-20T08:31:43Z","snapshot_observed_at":"2026-08-07T00:34:26.184748Z","submitted_at":"2025-06-16T08:20:41Z","title":"Conditional a priori error estimates of finite volume and Runge-Kutta discontinuous Galerkin methods with abstract limiting for hyperbolic systems of conservation laws in 1D","version":2},"cited_work":{"arxiv_id":"2506.13221","doi":"10.48550/arxiv.2506.13221","metadata_source":"pith","pith_arxiv_id":"2506.13221","snapshot_observed_at":"2026-08-05T02:49:54.815029Z","title":"Conditional a priori error estimates of finite volume and Runge-Kutta discontinuous Galerkin methods with abstract limiting for hyperbolic systems of conservation laws in 1D","venue":"math.NA","work_id":"75303464-f2dd-4870-8c28-192c9006036e","year":2025},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.003539Z"},"links":{"cited_paper":"/paper/2506.13221","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:e0d8350cbe483aef7c3c5eec7e3f9e1acd42bc9c8dced6f72f4d335106cf323a","observation_id":"01516815-48b8-4e2c-9264-fa22da5d3c9c","resolution":{"observed_at":"2026-07-30T12:45:56.830662Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/17m1139333","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"On the order of accuracy of finite difference operatorsondiagonalnormbasedsummation-by-partsform","venue":"SIAM Journal on Numerical Analysis","work_id":"3e5f9485-ef7f-4b2f-a1db-17e7e428783d","year":2018},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.112993Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:86212c2488af4c7f045d6d70ccb22903590caf577f1c00b8f9feb3d1cf056be1","observation_id":"1e4596d2-ac3e-4be6-bec6-bad62fd991d4","resolution":{"observed_at":"2026-07-30T12:45:56.576291Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.4208/jcm.2002-m2019-0305","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Sub-optimal convergence of discontinuous Galerkin methods with central fluxes for linear hyperbolic equations with even degree polynomial approximations","venue":"Journal of Computational Mathematics","work_id":"49ca95b4-9839-4584-86b5-e4435b0710ea","year":2021},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.279714Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:c3f0c0a5b739df658db8bee21c7ceae962b23e1b877d67d48d05fa67a9a4652e","observation_id":"a000e7f5-a10c-4a5f-b27b-392032c2d3e4","resolution":{"observed_at":"2026-07-30T12:45:56.413983Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.454172Z","title":"ConvergenceofDiscontinuousGalerkinSchemesfor the Euler Equations via Dissipative Weak Solutions","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.454172Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:f78c18f25a94cc118a222e602d682196e843ebeba758448ce7dd5ad44565384d","observation_id":"122705ce-af83-46ff-a6ba-dd10509e9fbb","resolution":{"observed_at":"2026-07-30T12:43:24.454172Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s10915-022-01843-6","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Error Estimates of the Godunov Method fortheMultidimensionalCompressibleEulerSystem","venue":"Journal of Scientific Computing","work_id":"af812463-7a44-4747-99f1-63aae21275a5","year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.542413Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:c16200df4f40187c2eea62ece8a9fc840845836d1d12903c91bd5e37e501a7a1","observation_id":"bc5e009f-d21a-44d5-a6dd-bc2c88e71ad1","resolution":{"observed_at":"2026-07-30T12:45:56.289210Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/mcom/3022","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Optimal error estimates for discontinuous Galerkin methods based on upwind-biased fluxes for linear hyperbolic equations","venue":"Mathematics of Computation","work_id":"a7910b0a-bdb1-42b3-ba39-b3a13f441bfc","year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.547950Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:12b0de6fff04b03f5cca60cf61f011d7280306d9e174f62b5cf75e1d6e7e20c1","observation_id":"90440ec2-64c1-411b-a66c-819121f8e0e4","resolution":{"observed_at":"2026-07-30T12:45:55.894742Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/0022-0396(80)90089-3","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Systemsofconservationlawsofmixedtype","venue":"Journal of Differential Equations","work_id":"6a5cde11-0269-42d8-a51f-19a8f3ed4077","year":1980},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.550393Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:852e7f8ffc22301490f58958d1c6ecdab5df71c53d2e9ec962c6c4d20d0e2ec3","observation_id":"fc38c5ac-8625-4106-9958-f135335e5086","resolution":{"observed_at":"2026-07-30T12:45:55.705139Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.553280Z","title":"Finite volume approximations and strict stability for hyper- bolic problems","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.553280Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:d74c381cbb69ba6b8932bd8635147637035822fc0368ed8cd1e6259d442dfd7f","observation_id":"deea9c23-a172-4a45-ae05-88360f2b6f57","resolution":{"observed_at":"2026-07-30T12:43:24.553280Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/15m1043510","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"EntropyStableStaggeredGrid Discontinuous Spectral Collocation Methods of any Order for the Compressible Navier- Stokes Equations","venue":"SIAM Journal on Scientific Computing","work_id":"efd5dca6-40b8-4c01-9fae-9bc618b779af","year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.555440Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:41e94e938858716e611dad5b9478d9c24938cc2da20f5a0423cb1982b2f6906e","observation_id":"94cadcc5-d450-4c82-9c8b-303950c1baa2","resolution":{"observed_at":"2026-07-30T12:45:55.594971Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.557583Z","title":"OnpositivitypreservingfinitevolumeschemesforEulerequa- tions","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.557583Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:81313829efccfbab52fca04df2bbed8c65796be33678f1ccae2ad1c7410ba8aa","observation_id":"92a7b139-689c-48e5-8508-604664f93548","resolution":{"observed_at":"2026-07-30T12:43:24.557583Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1137/0728006","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"A note on the convergence of the discontinuous Galerkin method for a scalarhyperbolicequation","venue":"SIAM Journal on Numerical Analysis","work_id":"bb3e1e8b-c4ff-4c68-8fbf-fcb1d31cfbed","year":1991},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.559944Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:dd08c6c909befcd8d0544f8dfb308fe13b25849302beb3920b63812d5250ea27","observation_id":"ccbdf782-0307-48b9-afb8-965b28384ce6","resolution":{"observed_at":"2026-07-30T12:45:55.264749Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.562261Z","title":"Petri, S","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.562261Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:67df9e695d4e2f765cf23a58d60dfc016a895605a096e411ef24970a334a4ab2","observation_id":"6b5dfbf0-756a-4879-a15b-3ea27fac6eaf","resolution":{"observed_at":"2026-07-30T12:43:24.562261Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.564410Z","title":"DifferentialEquations.jl–aperformantandfeature-richecosys- temforsolvingdifferentialequationsinJulia","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.564410Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:e9bf803f933ce58c64f7667355f5798656010156eb4d3a0ed5529f78f7fb488a","observation_id":"0b7773a0-f7a1-4b8b-9597-6e2aa6ec759a","resolution":{"observed_at":"2026-07-30T12:43:24.564410Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.567557Z","title":"ANoteonNumericalFluxesConservingaMemberofHarten’sOne-Parameter Family of Entropies for the Compressible Euler Equations","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.567557Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:04900d9d35c6792527bc9788fe13f229ed20a730100dba837613938ed55326ce","observation_id":"1484c323-040a-4f8a-9f3f-1046a9de95a5","resolution":{"observed_at":"2026-07-30T12:43:24.567557Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1701.02264","last_updated":"2017-11-21T16:52:36Z","snapshot_observed_at":"2026-08-05T16:58:37.634532Z","submitted_at":"2017-01-09T17:19:06Z","title":"Comparison of some Entropy Conservative Numerical Fluxes for the Euler Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1701.02264","snapshot_observed_at":"2026-07-30T12:43:24.570309Z","title":"Comparison of Some Entropy Conservative Numerical Fluxes for the Euler Equations","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.570309Z"},"links":{"cited_paper":"/paper/1701.02264","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:b7e6ee3b9d1daa2e2941709402fdab7176e1d13989a1abcb146674ea1f516ac0","observation_id":"cec89f64-520a-4c67-a60e-be129642aa32","resolution":{"observed_at":"2026-07-30T12:43:24.570309Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.5281/zenodo.21672279","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:45:54.953577Z","title":"Convergence of entropy-conservative summation-by- partsdiscretizationstosmoothsolutionsofhyperbolicconservationlaws","venue":null,"work_id":"47b264e5-ae09-4352-b9f6-a1f21008e819","year":2026},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.572876Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:204bc5b9d81c3a1c7961496a36ec2f88b67baa90182478066a2540733b71cd56","observation_id":"dc51e459-2e50-45d8-ae52-f7a622c72a12","resolution":{"observed_at":"2026-07-30T12:45:54.973736Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1609.08029","last_updated":"2016-12-11T15:17:07Z","snapshot_observed_at":"2026-07-06T05:12:14.251446Z","submitted_at":"2016-09-26T15:44:41Z","title":"Shallow water equations: Split-form, entropy stable, well-balanced, and positivity preserving numerical methods","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.08029","snapshot_observed_at":"2026-07-30T12:43:24.576298Z","title":"Shallowwaterequations:Split-form,entropystable,well-balanced,andposi- tivitypreservingnumericalmethods","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.576298Z"},"links":{"cited_paper":"/paper/1609.08029","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:104c982c8fdfea322b9ba165c2fddfa596ee4eef1aa623c583006c0ab8c9dfc0","observation_id":"cc02eb56-7086-413a-a552-14e8e28f2b6b","resolution":{"observed_at":"2026-07-30T12:43:24.576298Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-30T12:43:24.579914Z","title":"SummationByPartsOperators.jl: A Julia library of provably stable discretiza- tion techniques with mimetic properties","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.579914Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:8509b11b5083aa7b2a009c8ab0e4978188d1d90ed070698f5d793e59b41ce692","observation_id":"b40f07ab-a7fb-4414-9d9c-35dbb9cbe684","resolution":{"observed_at":"2026-07-30T12:43:24.579914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1007/s42967-021-00159-w","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-05T02:28:24.338817Z","title":"Optimized Runge-Kutta meth- ods with automatic step size control for compressible computational fluid dynamics","venue":"Communications on Applied Mathematics and Computation","work_id":"98ccb8ef-3afb-44b9-9e44-c1f9c7f9b14e","year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.582753Z"},"links":{"citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:15bfe059c9a649ee61655c2b294e1f4081de59848d8804249b169d882edbaecc","observation_id":"acc21f62-fa28-4513-b057-8310c86dc43b","resolution":{"observed_at":"2026-07-30T12:45:54.901595Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2009.13139","last_updated":"2021-06-09T15:31:13Z","snapshot_observed_at":"2026-08-08T05:37:18.077853Z","submitted_at":"2020-09-28T08:38:28Z","title":"Preventing pressure oscillations does not fix local linear stability issues of entropy-based split-form high-order schemes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.13139","snapshot_observed_at":"2026-07-30T12:43:24.587288Z","title":"PreventingPressureOscillationsDoesNotFixLocalLinear Stability Issues of Entropy-Based Split-Form High-Order Schemes","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.587288Z"},"links":{"cited_paper":"/paper/2009.13139","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:2bfea369159fb8bd0ece6cea4e1db941119aa21622401a5a12fe123f58afa554","observation_id":"35ac3bd5-5b78-46f4-be86-476a14ef28a0","resolution":{"observed_at":"2026-07-30T12:43:24.587288Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.03012","last_updated":"2020-10-25T10:50:48Z","snapshot_observed_at":"2026-08-07T18:30:40.669069Z","submitted_at":"2020-03-06T02:56:03Z","title":"General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.03012","snapshot_observed_at":"2026-07-30T12:43:24.590123Z","title":"General Relaxation Methods for Initial-Value Problems with Application to Multistep Schemes","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.590123Z"},"links":{"cited_paper":"/paper/2003.03012","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:4b7fe1b25f4a06c53b1631d5984ed6df762c482639ba11b1a5ce3f630f866559","observation_id":"a465688b-18bb-4513-a8ea-6b342e87021d","resolution":{"observed_at":"2026-07-30T12:43:24.590123Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.14802","last_updated":"2020-11-10T04:12:22Z","snapshot_observed_at":"2026-07-06T09:32:58.317099Z","submitted_at":"2020-06-26T05:12:59Z","title":"A Broad Class of Conservative Numerical Methods for Dispersive Wave Equations","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.14802","snapshot_observed_at":"2026-07-30T12:43:24.592859Z","title":"ABroadClassofConservativeNumerical Methods for Dispersive Wave Equations","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.592859Z"},"links":{"cited_paper":"/paper/2006.14802","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:fb998bc898d328a2220a32a201ecb627b990a129cc48516b24fd70d638f49e32","observation_id":"217a4ab0-2e1c-4e68-a1cf-1cac34372e04","resolution":{"observed_at":"2026-07-30T12:43:24.592859Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1511.02052","last_updated":"2016-02-12T05:48:05Z","snapshot_observed_at":"2026-07-06T04:35:35.923583Z","submitted_at":"2015-11-06T12:44:42Z","title":"Summation-by-parts operators for correction procedure via reconstruction","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1511.02052","snapshot_observed_at":"2026-07-30T12:43:24.595666Z","title":"Summation-by-parts operators for correction proce- dure via reconstruction","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":101,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.595666Z"},"links":{"cited_paper":"/paper/1511.02052","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:6ccecc50d54d9587bc5bf70aa23360e739bc2d72d42a8287b9ea61fa9d698d41","observation_id":"d6cda027-ba64-42f8-9fe2-e51565ca7170","resolution":{"observed_at":"2026-07-30T12:43:24.595666Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.09129","last_updated":"2019-11-23T05:33:52Z","snapshot_observed_at":"2026-07-06T07:54:40.999741Z","submitted_at":"2019-05-22T13:34:01Z","title":"Relaxation Runge-Kutta Methods: Fully-Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-Stokes Equations","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.09129","snapshot_observed_at":"2026-07-30T12:43:24.598284Z","title":"RelaxationRunge-Kutta Methods: Fully Discrete Explicit Entropy-Stable Schemes for the Compressible Euler and Navier-StokesEquations","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":102,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.598284Z"},"links":{"cited_paper":"/paper/1905.09129","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:71522124c7f056640c89179a225844d946bb8dc023e46f72e8c0a6ca770400b2","observation_id":"62c4f7fb-a064-4361-ba8b-179defeb65cf","resolution":{"observed_at":"2026-07-30T12:43:24.598284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2112.10517","last_updated":"2023-09-19T06:55:12Z","snapshot_observed_at":"2026-08-10T02:22:23.720110Z","submitted_at":"2021-12-20T13:25:37Z","title":"Efficient implementation of modern entropy stable and kinetic energy preserving discontinuous Galerkin methods for conservation laws","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2112.10517","snapshot_observed_at":"2026-07-30T12:43:24.600460Z","title":"Efficient Implementation of Modern Entropy Stable and Kinetic Energy Preserving Discontinuous Galerkin Methods for Conservation Laws","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws","version":1},"reference_index":103,"source":"pdf_text","source_observed_at":"2026-07-30T12:43:24.600460Z"},"links":{"cited_paper":"/paper/2112.10517","citing_paper":"/paper/2607.27049"},"observation_digest":"sha256:90d2b66ceb52c9fa2921cc3f8985d6aa7acbb543b41591d5b4d71cd45c8a67f4","observation_id":"57098d7a-a633-481e-ad41-5b85cfccca34","resolution":{"observed_at":"2026-07-30T12:43:24.600460Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.27049","last_updated":"2026-07-29T15:39:54Z","latest_version":1,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T16:18:49.531230Z","submitted_at":"2026-07-29T15:39:54Z","title":"Convergence of entropy-conservative summation-by-parts discretizations to smooth solutions of hyperbolic conservation laws"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":12,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":57,"verified_exact":31,"verified_fuzzy":0},"total_outbound_references":131},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 100 of 131 outbound references and 1 inbound Pith citation observation for arXiv:2607.27049."}