{"as_of":"2026-08-12T21:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:42a7ce4e36b612f12c003dce24e4eee86ea8a2092a2fa09429aad4ce7db1807f","coverage":[{"denominator":10,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":10,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-29T15:04:30.866341Z","state":"measured"},{"denominator":10,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":10,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2605.27065/citation-record","integrity":"/paper/2605.27065/integrity","json":"/paper/2605.27065/citation-record.json","paper":"/paper/2605.27065"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-06-29T15:04:30.866341Z","title":"Decoupling, exponential sums and the Riemann zeta function.J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:56ccb8d8bf463c63770e5fdd1e085c18bb890159eea9ea52125cdf581b298c90","observation_id":"86617f23-fb95-4d3a-bebc-10bbddf2457a","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","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":"2026-06-29T15:04:30.866341Z","title":"The proof of thel2 decoupling conjecture.Ann","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:b820fb54f2bebe5992fee1bd5c538ad25d9866ef452b980f3a2e0ee443fca9ad","observation_id":"2c0f78d1-95b8-407a-968e-28eef973904c","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","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":"2026-06-29T15:04:30.866341Z","title":"Proof of the main conjecture in Vinogradov’s mean value theorem for degrees higher than three.Ann","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:b7bd592c49c03c5e61605d65effc802045fd46d15c85b9445cfd3197b73f9b71","observation_id":"506b54ce-d7b8-49fd-98f2-76b6fe7f5f2f","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","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":"2026-06-29T15:04:30.866341Z","title":"Cambridge University Press, Cambridge, 2020","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:323b0d1bd95193399790115c3b78ac263d0cc36b48ac2663d856203dd29076ab","observation_id":"c5950264-4807-4823-bd37-b6ed4ac3bb5d","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","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":"2026-06-29T15:04:30.866341Z","title":"OnL12 square root cancellation for exponential sums associated with nondegen- erate curves inR4.Trans","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:a45a9e6b09aa857137503787bb3435efd7ec87a2c1bd0e05840e93f2605d2fba","observation_id":"f3301881-a420-4a1f-94d7-5ffa83d602f9","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","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":"2026-06-29T15:04:30.866341Z","title":"Small cap decouplings.Geom","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:d3d4c9155e7347b05621950bce028590eca014704dc5676e2a6bb1da6899b961","observation_id":"d8955df4-cb22-4c06-a035-e626a8aa042c","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2206.01093","last_updated":"2022-08-13T19:14:03Z","snapshot_observed_at":"2026-08-10T05:00:02.726741Z","submitted_at":"2022-06-02T15:20:13Z","title":"Amplitude dependent wave envelope estimates for the cone in $\\mathbb{R}^3$","version":2},"cited_work":{"arxiv_id":"2206.01093","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2206.01093","snapshot_observed_at":"2026-06-29T15:13:31.608059Z","title":"Amplitude dependent wave envelope estimates for the cone inR 3.https://arxiv.org/abs/2206.01093, 2022","venue":null,"work_id":"63feeda0-05c6-4b93-8e4d-d621851271d0","year":2022},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"cited_paper":"/paper/2206.01093","citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:d42bd5af7000f29165207c5767f9810dc02056df09969f3d18db313b73be4abf","observation_id":"37683a17-4321-4e35-b385-4778526796cf","resolution":{"observed_at":"2026-06-29T15:13:31.609602Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-29T15:04:30.866341Z","title":"Small cap decoupling for the moment curve inR3.Anal","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:6ac09b1ec18e5e6ac1b5357e061fa64cca20745d925b2b2c61d1377ae2782609","observation_id":"4fe42129-669a-4968-a92a-a5ec265d2a49","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18016","last_updated":"2024-11-27T03:17:08Z","snapshot_observed_at":"2026-08-12T11:34:00.339362Z","submitted_at":"2024-11-27T03:17:08Z","title":"On the small cap decoupling for the moment curve in $\\mathbb{R}^3$","version":1},"cited_work":{"arxiv_id":"2411.18016","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2411.18016","snapshot_observed_at":"2026-06-29T15:13:31.610729Z","title":"On the small cap decoupling for the moment curve in R3.https://arxiv.org/abs/2411.18016, 2024","venue":null,"work_id":"b629f1fc-1680-43ff-b258-405bac0533f7","year":2024},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"cited_paper":"/paper/2411.18016","citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:f4e6a2115a1edcb3b68856c8128aff3079901bdda16bdd01b038b8150ebada7e","observation_id":"d57eda4f-d01c-42f1-a5c0-dc14f7a01d7e","resolution":{"observed_at":"2026-06-29T15:13:31.612200Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+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":"2026-06-29T15:04:30.866341Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-06-29T15:04:30.866341Z"},"links":{"citing_paper":"/paper/2605.27065"},"observation_digest":"sha256:44b4eccc408ad6c82dfde19a37a7118c2358ad40edce5394452c1da16a12cd9b","observation_id":"68f59ffe-62ec-4e02-bdb6-8124d9246376","resolution":{"observed_at":"2026-06-29T15:04:30.866341Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2605.27065","last_updated":"2026-05-26T14:16:06Z","latest_version":1,"primary_category":"math.CA","snapshot_observed_at":"2026-08-07T08:57:03.344831Z","submitted_at":"2026-05-26T14:16:06Z","title":"A Continuum of Small-cap Decouplings and Exponential Sums for the Moment Curve in $\\mathbb{R}^4$"},"reference_resolution":{"displayed":10,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":8,"verified_exact":2,"verified_fuzzy":0},"total_outbound_references":10},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2605.27065."}