{"as_of":"2026-08-18T10:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:9370b31bb08df5ec7f0ad69109f4cace81ed625e307cb51ed7ab88d5bf71bccc","coverage":[{"denominator":115,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":100,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T13:11:52.935915Z","state":"measured"},{"denominator":103,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":103,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T14:55:36.537356Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T16:38:40.683407Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"cited_work":{"arxiv_id":"2505.22451","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.22451","snapshot_observed_at":"2026-07-03T16:38:40.683407Z","title":"AI mathematician: Towards fully automated frontier mathematical research.arXiv preprint arXiv:2505.22451, 2025","venue":null,"work_id":"029fda32-0b2e-4526-ba05-6c81972b2dfd","year":2025},"citing_paper":{"arxiv_id":"2604.25333","last_updated":"2026-04-28T07:50:42Z","snapshot_observed_at":"2026-08-13T12:59:40.922821Z","submitted_at":"2026-04-28T07:50:42Z","title":"Sign Embedding Quantum Algorithms for Matrix Equations and Matrix Functions","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-07T16:46:15.833617Z"},"links":{"cited_paper":"/paper/2505.22451","citing_paper":"/paper/2604.25333"},"observation_digest":"sha256:41a6355684c542d7ce605f8d3e4cc0c365a70eb07da4e4817c27ba8355e1e004","observation_id":"65e93203-aea1-4bd8-9d72-f6957f9550b8","resolution":{"observed_at":"2026-05-11T23:31:17.226608Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"cited_work":{"arxiv_id":"2505.22451","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2505.22451","snapshot_observed_at":"2026-07-03T16:38:40.683407Z","title":"AI mathematician: Towards fully automated frontier mathematical research.arXiv preprint arXiv:2505.22451, 2025","venue":null,"work_id":"029fda32-0b2e-4526-ba05-6c81972b2dfd","year":2025},"citing_paper":{"arxiv_id":"2606.24899","last_updated":"2026-06-12T13:30:59Z","snapshot_observed_at":"2026-07-06T23:59:23.407216Z","submitted_at":"2026-06-12T13:30:59Z","title":"From Meta Idea to Advanced Mathematical Discovery -- Human-AI Co-Discovery of Sign-Embedding Quantum Algorithms","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-06-27T05:07:24.992096Z"},"links":{"cited_paper":"/paper/2505.22451","citing_paper":"/paper/2606.24899"},"observation_digest":"sha256:34686ae32f5096f875d4b2a6f0e6f735f249501ae7a0633ab1da495a9aee9c65","observation_id":"5b0f6105-5dbf-44ab-8730-1ae04cc195dc","resolution":{"observed_at":"2026-07-03T16:38:40.685226Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.22451","snapshot_observed_at":"2026-08-12T14:55:36.537356Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research.arXiv preprint arXiv:2505.22451, 2025","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.10894","last_updated":"2026-08-11T13:13:11Z","snapshot_observed_at":"2026-08-15T10:15:12.779563Z","submitted_at":"2026-08-11T13:13:11Z","title":"FormaTheoria: Constructing Large-Scale Lean Theories from Mathematical Literature $-$ Toward the Formalization of the Classification of Finite Simple Groups","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-12T14:55:36.537356Z"},"links":{"cited_paper":"/paper/2505.22451","citing_paper":"/paper/2608.10894"},"observation_digest":"sha256:3afc090b0fef11024cb56fb4007d277100f76717cb5566d66edd525fc23cfdcd","observation_id":"7f53abf4-ace0-4997-81f8-7ea467da6918","resolution":{"observed_at":"2026-08-12T14:55:36.537356Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2505.22451/citation-record","integrity":"/paper/2505.22451/integrity","json":"/paper/2505.22451/citation-record.json","paper":"/paper/2505.22451"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:44.422702Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.422702Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b6c1170ef6eabe9ae9c27e92754cfac5659ac4078f1ab4b88f363bf4a5c47413","observation_id":"dd0c5317-bab6-4e26-9cf2-d10bfa1a03e8","resolution":{"observed_at":"2026-08-07T13:11:44.422702Z","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":"2026-08-07T13:11:43.349771Z","title":"**Step 3: Hamiltonian Simulation Error Allocation** Each term e−ikj Bτ must be simulated with error ≤ ϵ 2 in spectral norm","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.349771Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:3c87e5ded6d376e67a56e5625f8b06804297ef88f3118475d13d056cf5ab6780","observation_id":"7bb47902-844b-458d-9d32-cb4af528107e","resolution":{"observed_at":"2026-08-07T13:11:43.349771Z","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":"2026-08-07T13:11:43.742466Z","title":"From Stokes regularity, ∥plim∥L2(Dϵ) ≤C∥g∥ H −1/2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.742466Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:8e552f59ac368778f63b13999e73b2a6a7317a36e9968ef3aa86c8713c37f0c0","observation_id":"8dfe9766-5462-4491-83a4-ec03eeaaf961","resolution":{"observed_at":"2026-08-07T13:11:43.742466Z","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":"2026-08-07T13:11:43.454265Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.454265Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:ce785f43d49696273aad4a581ab7ce1cb309d54a6c43bbc1f36ff9b8a81231c5","observation_id":"410c9bcd-69b7-4064-bebd-900f36a4dc6a","resolution":{"observed_at":"2026-08-07T13:11:43.454265Z","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":"2026-08-07T13:11:43.536198Z","title":"Thus, there exists a unique solution (u,{φ k})in the specified spaces","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.536198Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:0aa5eedb2f2358c83e6399b7f5c397f654fe43ed5e2defe7ab83665f26343b9a","observation_id":"b3714c2c-37e4-4c6b-94c5-a9b502543b7b","resolution":{"observed_at":"2026-08-07T13:11:43.536198Z","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":"2026-08-07T13:11:43.637786Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.637786Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:e62f05545b2f4949ebd5be52cc727e021ed62e7cd8276c5c96b5f0fe401cb377","observation_id":"1c89e5d9-f40b-4544-970e-de8604953059","resolution":{"observed_at":"2026-08-07T13:11:43.637786Z","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":"2026-08-07T13:11:43.843074Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.843074Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:2d8e359e3d79d0481808e1245dadcc2d711b9eb6f3722620dacaf503a66b2966","observation_id":"a71dc4b9-2c9a-45be-bcf3-d7820d9ef9ee","resolution":{"observed_at":"2026-08-07T13:11:43.843074Z","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":"2026-08-07T13:11:43.955958Z","title":"Substituting: RHS≤C∥g∥ H −1/2 ·(C eλ−1∥g∥H −1/2 ) = C eλ ∥g∥2 H −1/2","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:43.955958Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:0add79c8698fb79370f83072c57d72a54ff629632cafd6f1c78858f122e6a1a2","observation_id":"dc8d0600-efc9-4c63-b5f8-c2153d16663c","resolution":{"observed_at":"2026-08-07T13:11:43.955958Z","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":"2026-08-07T13:11:44.037209Z","title":"comment: None type: conjecture Lemma 20.The differencew ε =u lim −u ε satisfies theL 2(Ω)error estimate: ∥wε∥L2(Ω) ≤ Cp eλ ∥g∥H −1/2(∂Ω), whereCis independent of eλ","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.037209Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:8dc3fd3889c452576c8dd9374ab7648dc6685ca8093074fd7a9343ef4bafe4b5","observation_id":"235eca0b-3982-4104-9533-dc2c6a1cf16c","resolution":{"observed_at":"2026-08-07T13:11:44.037209Z","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":"2026-08-07T13:11:44.137125Z","title":"Substitute this into the energy identity: Z Ω λ(x)|divw ε|2 + 2µ(x)|D(wε)|2 dx= eλ∥divu ε∥2 L2(Dε)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.137125Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:d8ed6295a5603f4ecdaf06f793a90e9153ef09e792c71ac751f1ff7f83680b20","observation_id":"496b6461-7805-499e-84f8-d7514b5bf0b6","resolution":{"observed_at":"2026-08-07T13:11:44.137125Z","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":"2026-08-07T13:11:44.231577Z","title":"Thus: Energy integral≤ C eλ ∥g∥2 H −1/2(∂Ω)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.231577Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:275ac1633d447d3dce11c764ba87896b889ff89879be21009fc58424fc2dd986","observation_id":"81294eb8-c088-4893-921d-bdb1ac269f59","resolution":{"observed_at":"2026-08-07T13:11:44.231577Z","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":"2026-08-07T13:11:44.300025Z","title":"Under boundary conditions orthogonal to rigid motions, there existsC K >0such that: ∥wε∥2 H 1(Ω) ≤C K Z Ω |D(wε)|2 +|divw ε|2 dx","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.300025Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b1499b75d5cf891f24d066280daa7f67803805fb0aaa27c37f8b63f03361f3f3","observation_id":"0024c547-c0f7-4647-b31b-c6d8234c320e","resolution":{"observed_at":"2026-08-07T13:11:44.300025Z","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":"2026-08-07T13:11:44.518785Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.518785Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:95973f7ca6a52f0077ed81a38f2e4092709d9cafb10c2b7b77df802b8982542d","observation_id":"17a50fae-2abb-4b9f-9b05-6d4600822e2d","resolution":{"observed_at":"2026-08-07T13:11:44.518785Z","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":"2026-08-07T13:11:44.624763Z","title":"error” w:=u ϵ −u lim satisfies in Ωϵ the homogeneous Lamé system with zero Neumann data on ∂Ω and a “jump–residue","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.624763Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:e441397216f5f3f37cb0fbf8b7fcfba2f91cac7699add14052a1ef855e05af75","observation_id":"b4104d10-fa3a-488a-bb67-2df0b586e500","resolution":{"observed_at":"2026-08-07T13:11:44.624763Z","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":"2026-08-07T13:11:44.748876Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.748876Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:6d2a70d145a36910c4ed46c6c091b12e35ab26132f9b41d4b423dbc43b9c206f","observation_id":"efaba8e5-071a-45ee-a397-0d87876b42d0","resolution":{"observed_at":"2026-08-07T13:11:44.748876Z","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":"2026-08-07T13:11:44.834771Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.834771Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:d533d64c36ad4788bb60418a3ffb474525de464adadf1061377f7b33c95a457f","observation_id":"734fbfdf-ae2f-4528-9e8e-c55f03c3f49a","resolution":{"observed_at":"2026-08-07T13:11:44.834771Z","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":"2026-08-07T13:11:44.890072Z","title":"49 comment: Nonetype: lemma Lemma 25.(Uniform Coercivity of the Elasticity Bilinear Form) Let (λ, µ)satisfy the admissibility λ+ 2µ d >0,µ >0","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.890072Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:0c872519436cb386d0a0b80a4351ee55d5774254e52140bda0056e0d1ca45240","observation_id":"3a04add8-7e41-42f2-b5ea-cc1fe0600848","resolution":{"observed_at":"2026-08-07T13:11:44.890072Z","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":"2026-08-07T13:11:44.974856Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:44.974856Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:302e613f33111b45626c8c6dde9b1ff891300718de275d89d45ce2ab764a85c4","observation_id":"34420fac-d58b-4c4c-b84d-88529b40e68f","resolution":{"observed_at":"2026-08-07T13:11:44.974856Z","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":"2026-08-07T13:11:45.048240Z","title":"Hence for anyu∈H 1(Ωε;R d), aε(u, u) = Z Ωε Q(D(u))dx≥c 0 Z Ωε |D(u)|2 dx","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.048240Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:a3e7dea1bdd95d2c7d450b0101074452d8fe430fb7b80fdfe6b31b2aed494466","observation_id":"eccf26f4-dc52-4007-8819-c5c834f8feac","resolution":{"observed_at":"2026-08-07T13:11:45.048240Z","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":"2026-08-07T13:11:45.185037Z","title":"By Conjecture 1 above, for allu∈V ε, ∥u∥2 H 1(Ωε) ≤C 2 ∥D(u)∥2 L2(Ωε), withCindependent ofε","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.185037Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:0e557b83e202efa54c609b6ded5576c80e3db75ac19edc29efff01b62a46f0f4","observation_id":"4360bf6b-9ce9-4516-9e17-30a4e1847195","resolution":{"observed_at":"2026-08-07T13:11:45.185037Z","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":"2026-08-07T13:11:45.274847Z","title":"uniform extension + Korn on the fixed domain + pull-back,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.274847Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:eb7d4004bfe24f660a8986ab22a84afe825c620b9ca8c50ed2577e99de5a96e3","observation_id":"79ce6f63-fa1a-4de7-91b5-4157cc8d43d5","resolution":{"observed_at":"2026-08-07T13:11:45.274847Z","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":"2026-08-07T13:11:45.355548Z","title":"By the periodicity, the uniform separation of holes, and the Lipschitz regularity of ∂Ω, one constructs (e.g","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.355548Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:7791911adaaec510009550ce88cdd8d7a43b4086ec86ffffe96b5b60d960880b","observation_id":"7397e930-3f5f-49a5-9006-7896f4bf1a49","resolution":{"observed_at":"2026-08-07T13:11:45.355548Z","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":"2026-08-07T13:11:45.425372Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.425372Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:14a562e62d6e574e2c7f97732c9d5cabe723e26b2a5fb187c28ffbf76bb34bb5","observation_id":"fd74b89e-21f2-4140-aaf9-f13ad27b65b5","resolution":{"observed_at":"2026-08-07T13:11:45.425372Z","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":"2026-08-07T13:11:45.504764Z","title":"Take anyu∈V ε and setU:=E εu∈V","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.504764Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:1f2842828ed4e167038f064e13f4802820d9164fb074f65d44f2c6b5e2f0f737","observation_id":"7bbb0fc1-dde1-4440-a13f-d6995c27abe2","resolution":{"observed_at":"2026-08-07T13:11:45.504764Z","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":"2026-08-07T13:11:45.537142Z","title":"Define w:=u e −u lim, φ:= divu e","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.537142Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:af1c5f763cc9cfa9c78a47e093cc40cf6219606a222e04525a7fad5573d44a7c","observation_id":"5bad17ca-2e11-487a-9ada-58e739e3f371","resolution":{"observed_at":"2026-08-07T13:11:45.537142Z","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":"2026-08-07T13:11:45.604760Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.604760Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:87f4a1effd3d3dbf1930891b6b8ec72d85d4fa9c910a0a325a336e8e82be56f9","observation_id":"c3becded-7727-4270-9557-06f357e54105","resolution":{"observed_at":"2026-08-07T13:11:45.604760Z","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":"2026-08-07T13:11:45.664865Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.664865Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:59de08334482f2de2b3713deae6f23db0350921e26ac9aa013cbdd56136f5895","observation_id":"4119ac04-3fbc-41a4-bca0-69f26bf952f8","resolution":{"observed_at":"2026-08-07T13:11:45.664865Z","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":"2026-08-07T13:11:45.764757Z","title":"Putting these together, the left-hand side becomes −˜µ R D |∇w|2 −( ˜λ+ ˜µ) R D |φ|2 and the right- hand side is− R D plimφ","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.764757Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:61a0f66dac4af8b199af4729ed6cca3e5c4d7bd43f36b4d261f2d4078753655a","observation_id":"6622dbb7-8822-4eae-9d4a-5e369508415c","resolution":{"observed_at":"2026-08-07T13:11:45.764757Z","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":"2026-08-07T13:11:45.852272Z","title":"Let V=D and set V ∗ =H −1(D)","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.852272Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:dcaa4dff834ca73045e9dc51939ba69c82ad849bf3de8c474b47909ea76de332","observation_id":"f0e7aedf-c051-464b-acf8-01a9c01ca232","resolution":{"observed_at":"2026-08-07T13:11:45.852272Z","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":"2026-08-07T13:11:45.930233Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:45.930233Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b758bd2f3c4a99876617b9bd8dbd75c744fc918748f729212ceb41356e5b5d1e","observation_id":"6adba2bf-45af-4bd9-ac72-f31e020b25b0","resolution":{"observed_at":"2026-08-07T13:11:45.930233Z","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":"2026-08-07T13:11:46.027259Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.027259Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:6517a3557df8093e7441cafac08da990b3c0c2393530997a1c8d7a65620f4b82","observation_id":"46637211-109c-4fc5-b9f5-b8e678c05717","resolution":{"observed_at":"2026-08-07T13:11:46.027259Z","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":"2026-08-07T13:11:46.117951Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.117951Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:15e0d0a1c8f516f6b01e83acefb2abecc5b47f56b095b47c77f1b2d8dd851c9d","observation_id":"a1952ae7-28e6-4a79-b456-399129472114","resolution":{"observed_at":"2026-08-07T13:11:46.117951Z","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":"2026-08-07T13:11:46.217197Z","title":"Combining the two estimates, |L(φ)| ≤C′ [λ∥divu∥+µ∥∇u∥]· ∥φ∥ H 1/2(∂D) , so by duality ∥σ(u)N∥ H −1/2(∂D) = sup φ̸=0 |L(φ)| ∥φ∥H 1/2 ≤C[λ∥divu∥ L2(D) +µ∥∇u∥ L2(D)], as claimed","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.217197Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b641a37191bf90a33b6240bec766234bb8ec1574b26cc6290f33a02e041801f7","observation_id":"c38b67eb-a976-40fe-844b-e14f483db44b","resolution":{"observed_at":"2026-08-07T13:11:46.217197Z","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":"2026-08-07T13:11:46.317943Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.317943Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:464174f37608e181590f33dbf0d715f54f82ab20705a6bcdfb4f1ab1c7f663e3","observation_id":"662b5847-a368-411d-ac5b-0a77e9f91c73","resolution":{"observed_at":"2026-08-07T13:11:46.317943Z","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":"2026-08-07T13:11:46.401841Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.401841Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:0ae6638bff9b23379651b04e2d42bd3e5fa87ca7f482d5bc7a69f267bdd19157","observation_id":"f25618c4-a2af-4f53-88e5-db377a034500","resolution":{"observed_at":"2026-08-07T13:11:46.401841Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:10.293782Z","title":null,"venue":null,"work_id":"9903791c-fe64-413d-b0bd-6b87c1b71f8a","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.492170Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:8a0df0ea155448b02fc3cf83755e4536f2d1fc8d388a40eff0fe62903d50584d","observation_id":"54f355cc-aca0-48f8-bdb8-1886582296f0","resolution":{"observed_at":"2026-08-07T13:12:10.399339Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:10.048996Z","title":"[Correct]The agent correctly employes mathematical inequality techniques to complete the derivation and gets a reasonable conclusion","venue":null,"work_id":"27422681-ad69-47b5-a42e-8a397518a96e","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.588753Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:410a9bf343fccdaf448d18c7857692fe91070928acd52db71f8b56d12e9c986f","observation_id":"6d7b21d2-8fdb-49c5-9d67-4a313a5dcd85","resolution":{"observed_at":"2026-08-07T13:12:10.208384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:09.761410Z","title":"[Vague]The process here is lack of details of theorem derivation","venue":null,"work_id":"bdadf230-ab2c-478e-95cd-e60e649c11fd","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.673856Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:2cf6286e045364e4dc26e8b4a3b7757038ddb0a2ca28947d46a3a8c81ce0f4bc","observation_id":"77d7bc26-0882-4feb-8eb1-19b95f75a0cc","resolution":{"observed_at":"2026-08-07T13:12:09.904445Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:09.521404Z","title":null,"venue":null,"work_id":"b38f70a9-03cc-4c8f-902d-9e606400b13a","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.766487Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:227920fe6e2af015df907125683508802352eee0019670205f191701f4665b90","observation_id":"fae98266-9e27-4fb9-8915-3b4dcdde0da8","resolution":{"observed_at":"2026-08-07T13:12:09.618587Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:09.279604Z","title":null,"venue":null,"work_id":"399bff4b-d29f-4e5c-8f47-1def90838568","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.852424Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b2d3f413fa4e06bcc62b889a91c012808b7263afb569ce36ee2358a9b79e94b9","observation_id":"f476d221-2d43-4f14-94ca-2f5102fe3d32","resolution":{"observed_at":"2026-08-07T13:12:09.394517Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:09.031329Z","title":"comment: Nonetype: lemma Lemma 34.Let D⊂R d (d≥2 ) be a bounded Lipschitz domain with outward unit normalN, and let the Lamé parameters satisfy ˜µ >0and ˜λ+ 2˜µ/d >0","venue":null,"work_id":"6562c40f-fd31-4abb-ab26-085cf3b4fa09","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:46.917917Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:f0036d268f220514869bc3ae95c774ee967198c8d3b0668b955876566e64a8a7","observation_id":"45dd6bbd-2608-4c99-a8f4-2a2ed4c49c02","resolution":{"observed_at":"2026-08-07T13:12:09.175783Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:08.694499Z","title":"Let T:H 1(D)− →H1/2(∂D) be any bounded right-inverse of the trace map (such an extension operator exists on Lipschitz domains)","venue":null,"work_id":"ce3ae3fb-b6b1-45b0-987d-dc36c3e38a30","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.040386Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:4159eec0e8bc54acc402eab563a81c229c7e5b12386a2dc61583ac8079624346","observation_id":"9bf913d7-4ad9-4719-97ed-3baca2731d09","resolution":{"observed_at":"2026-08-07T13:12:08.851393Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:08.569315Z","title":"Using Cauchy–Schwarz and the two energy bounds above, |⟨τ, g⟩| ≤ ∥∇u∥L2(D)∥∇G∥L2(D) +∥f∥ H −1 ∥G∥H 1(D) ≤(C 1C2 +C 2)∥f∥ H −1(D)∥g∥H 1/2(∂D)","venue":null,"work_id":"f51e56a0-0f23-4f36-9cac-37bb1db55024","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.133741Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:4432d84aaf24e126d1935253b1c7b5dc2c420ac28b2b5c411c6e5fe3802d30c3","observation_id":"c61c97fd-8f2e-465a-90d6-c47a01f0e078","resolution":{"observed_at":"2026-08-07T13:12:08.621135Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:08.458402Z","title":"normal-trace","venue":null,"work_id":"336629cb-d2f2-40c9-afbd-3e15fd8ccfe4","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.222947Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:2b3fc6d04600bdada9f5c946002155db3e93ab22c76145df529d2025e42546f4","observation_id":"be1467e0-a7e7-47b8-8e94-8209de6837fa","resolution":{"observed_at":"2026-08-07T13:12:08.504701Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:08.330717Z","title":"Fix any φ∈H 1 2 (∂D;R d) and choose an H 1-extension v:=Eφ∈H 1(D;R d)with v|∂D =φ,∥v∥ H 1(D) ≤C ext∥φ∥H 1 2 (∂D)","venue":null,"work_id":"7e4753b4-efef-4f54-9547-d26665c602c2","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.356667Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:2216d05f8416c3f60ce4c75329693eeb76cf3c3ca565100404157464db68fd2f","observation_id":"fff10af0-f560-4dd4-8213-4a4b1b2d7b2e","resolution":{"observed_at":"2026-08-07T13:12:08.389750Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:08.198499Z","title":"By the divergence theorem for Lipschitz domains (valid in theH(div)–H 1 duality), one checks for smoothpandφthat Z D σ:∇v+ Z D (divσ)·v= Z ∂D (σ N)·v= Z ∂D (pI N)·φ= Z ∂D p N·φ dS","venue":null,"work_id":"09f922b3-7125-4151-b4d0-95437e0a7f45","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.428595Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:7827a243c1d8834df094cc0f235ec34d147e7c68abe627775c3e6ef5d4df986c","observation_id":"099dfca1-02bb-411f-9032-3cb8f8c2022c","resolution":{"observed_at":"2026-08-07T13:12:08.271631Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:08.024641Z","title":"From the definition ofT p and Cauchy–Schwarz one obtains ⟨Tp, φ⟩ ≤ ∥σ∥L2(D)∥∇v∥L2(D)+∥divσ∥ H −1(D)∥v∥H 1(D) ≤ ∥p∥L2(D)+∥∇p∥H −1(D) Cext∥φ∥H 1 2 (∂D)","venue":null,"work_id":"525dfc60-7f18-4a6b-8d12-b54f0f318e88","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.519671Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:114ccb69ece0655da96d95aad9d0153b99bef6dc8549407bcb1189ff087b0fe9","observation_id":"cc5acbef-20b6-4a4d-b9cf-79058feb58ba","resolution":{"observed_at":"2026-08-07T13:12:08.094419Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:07.853532Z","title":null,"venue":null,"work_id":"59280865-95fb-4872-ae0c-d65e3f98a6d1","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.653429Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:eb51a9dfff6eff1e82d4e08aaf9022d05e4e9d8cca109af5610c07bdf6c83f2d","observation_id":"3b8301a1-563d-488d-8e43-08efe2ea2fee","resolution":{"observed_at":"2026-08-07T13:12:07.942535Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:07.710045Z","title":"Thus the pressure in the inclusions is uniformly bounded by the boundary data, with no dependence onε","venue":null,"work_id":"56bc8e41-1678-47c8-818c-5ef46ed58fe0","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.722200Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:5b866c9b1d3ee3959e0ce1ac3265a4c3d1a3705b673872508b990e1d02006a8b","observation_id":"9846c634-be35-4884-b09f-8a69997ec476","resolution":{"observed_at":"2026-08-07T13:12:07.781680Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:07.546634Z","title":"Set Ωe := Ω\\D e and define w:=u e −u lim on Ωe","venue":null,"work_id":"500303ca-f79d-4973-8c7c-776060d71df6","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.797433Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:6a4700f13b8f5be225b1e503260f3c5b7ee9b4817c9e834f5eb79e0658ca65f9","observation_id":"e845be8f-d421-49ed-8af7-6c0d2638893e","resolution":{"observed_at":"2026-08-07T13:12:07.624598Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:07.375818Z","title":null,"venue":null,"work_id":"3af29f71-7818-4bbb-a95f-dfbe4a3cc637","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.892662Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:efc63dc4cb020cfc0472f863a56b4b72a5506c14fcc1628eb93e9f6d2060d514","observation_id":"558930c5-d970-4146-b79b-d4028a25dbb6","resolution":{"observed_at":"2026-08-07T13:12:07.457708Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:07.110246Z","title":"Fix one inclusion D=D ε,i","venue":null,"work_id":"604ca166-aec5-4079-ade7-fb53088a18bc","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:47.992559Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:0abbd9960557bb2a1cc5615246f4113b56ce3752c5e22794cb34fa120ae43209","observation_id":"e95cef43-b9c7-4a00-a652-c0efc7a93d00","resolution":{"observed_at":"2026-08-07T13:12:07.261449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:06.848147Z","title":"Combining the exterior bound of step 2 with the boundary-trace estimate of step 3 yields ∥ue −u lim∥H 1(Ωe) ≤Cmax i ∥ue −u lim∥H 1/2(∂Dε,i) ≤C ′˜λ−1/2∥g∥H −1/2(∂Ω), as claimed","venue":null,"work_id":"b6df092a-3402-40fc-8370-d268e37dd51f","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.084811Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:8ab57737ea7e3d2fd5dc39534ea72e3bff4a4faa642d9a4f6fd1d8fcc31cb1cc","observation_id":"4f13d8e7-7a0a-449f-9a4f-88260ad2c167","resolution":{"observed_at":"2026-08-07T13:12:06.985097Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:06.622603Z","title":"By standard Neumann–Stokes theory (e.g","venue":null,"work_id":"fd68d35e-a08f-4656-8724-570fa58fdef6","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.183821Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:f81b3dc5e486d7808d9c58a383b1c16d72d95f90a5e8b0e199283c72bef9305e","observation_id":"4e7e8b2c-6d4d-43e0-90ff-fc93439f41c4","resolution":{"observed_at":"2026-08-07T13:12:06.725039Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:06.375009Z","title":"Set w=u λ −u ∞ and φ= divu λ","venue":null,"work_id":"f0123894-fd80-47dd-9712-5a9c952d9bee","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.304910Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:3f8dedb873856a5fc315c25824fdc27e4a4db80a4e0fce168b801a261b5b73ab","observation_id":"abc31366-d523-4809-8301-72c708c128d9","resolution":{"observed_at":"2026-08-07T13:12:06.481516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:06.159164Z","title":"By Cauchy–Schwarz, (λ+µ)∥φ∥ 2 L2 ≤ ∥p∞∥L2 ∥φ∥L2 ⇒ ∥φ∥L2(D) ≤(λ+µ) −1∥p∞∥L2(D) ≤C 2λ−1∥t∥H −1/2(∂D)","venue":null,"work_id":"d479ae3d-d260-4068-9ff7-edba219b687a","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.383670Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:9276831be7d63da2d8e0393fb9cae8fbaef20ee9d7ec03c806460b7c1b416172","observation_id":"399f6fd8-4c19-4d9c-979e-e91ace355eaf","resolution":{"observed_at":"2026-08-07T13:12:06.248991Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:05.944373Z","title":"From the energy identity again, µ∥∇w∥2 L2 ≤ ∥p∞∥L2 ∥φ∥L2 ≤C 3λ−1∥t∥2 H −1/2","venue":null,"work_id":"68f5ba39-42f1-4562-ae54-e1924ce4ff73","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.494649Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:e1ee97f03b4d76aa4be4bd3ee6e0a0c0e9074df1ffc71f2f40764490c08b5272","observation_id":"83a92a10-6b18-4aea-b0ba-70b399383666","resolution":{"observed_at":"2026-08-07T13:12:06.077461Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:05.737906Z","title":"Since t7→u λ −u ∞ is linear and the above estimate is uniform for all admissibletandλ≥λ 0, we conclude ∥A−1 λ −B −1∥L(V ∗,V) ≤Cλ −1/2","venue":null,"work_id":"ce2e114e-5398-4899-b870-80532f9fe08c","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.612394Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:4a40ab9cb3ce93bceaf28f3e843899fb01dfa52706232b86dc95adb2af265c21","observation_id":"0d08a0ba-1522-4f8b-a9a4-91dd037d2afc","resolution":{"observed_at":"2026-08-07T13:12:05.835561Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:05.564148Z","title":"elastic pressure","venue":null,"work_id":"55073d5e-852c-4970-a1ed-30268f61eace","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.712681Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:304d78ff7ba6e45ad2be18a66ef58830597e4f366b024386bfe65fae35650eff","observation_id":"3be4e0cf-27de-4c7d-8660-783797735a19","resolution":{"observed_at":"2026-08-07T13:12:05.648769Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:05.326935Z","title":"Define the trial spaces V:={u∈H 1(D;R d) : Z ∂D u·r= 0∀rigid motionsr}, Q:=L 2 0(D) ={q∈L 2(D) : Z D q= 0}","venue":null,"work_id":"fbc66955-a108-4c7d-9c9d-72c587d0f18f","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.798696Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:3f3a00fea1a98035fbadbbcf6b0567a248d95bf3e8c39dee14c3fc0e505539a0","observation_id":"689118a2-3a0e-40b9-bad3-24b26e6044b0","resolution":{"observed_at":"2026-08-07T13:12:05.455503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:05.098803Z","title":"A11 A12 A21 A22 # with A11 =a ∞ :V→V ∗, A 12 =−b T :Q→V ∗, A21 =b:V→Q ∗, A 22 =−(1/ ˜λ)s:Q→Q ∗. Equivalently, A(˜λ) =A ∞ −(1/ ˜λ)N, where A∞ =","venue":null,"work_id":"f7a7f852-4762-4710-9490-6790823826de","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.872592Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:881613a4c57918df01e02989e920381e8dc5c380c3df38047870d0bb0c119ec2","observation_id":"a60a679f-0cdb-4376-8feb-cdff4731ecba","resolution":{"observed_at":"2026-08-07T13:12:05.212816Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:04.871894Z","title":null,"venue":null,"work_id":"4404f036-5d00-42dc-9615-983afb4a0247","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:48.949896Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:2592a1e604b22e9f11919f72084f42da285a8092dbd66db3dec193a4e6d7df79","observation_id":"d927d996-6808-4e27-99a7-3e08239f874c","resolution":{"observed_at":"2026-08-07T13:12:04.974853Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:04.604871Z","title":"boundary-trace lemma","venue":null,"work_id":"844973c5-6684-4bc6-9769-bcf3366ee0ca","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.022484Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:6919e78c94f6da2af394f18311ded1e79c522f862e7e956fbaab58752647b39a","observation_id":"c0cb7129-1caf-43d1-80e0-a72081a63abd","resolution":{"observed_at":"2026-08-07T13:12:04.783330Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:04.407635Z","title":"On each ε–inclusion D we denote by N the outward normal and by t:= (−p limI+ 2˜µD(ulim))N the Stokes-limit traction","venue":null,"work_id":"58528134-dc36-4a34-b1bd-4346d5103e72","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.089887Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b29c9fa264b70db1bfab1c2cf57c6609de71292562761d134205aa56c6c44cab","observation_id":"4b098fb3-9d39-43f2-9f4b-fa4fbf87f810","resolution":{"observed_at":"2026-08-07T13:12:04.487612Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:04.246315Z","title":null,"venue":null,"work_id":"7ef329d2-bbd9-4b7c-a396-677104c4f733","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.167474Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:e01151bdd538fcba1f71c3ae67f4a2c436d39558785839b088fffc9e1d6dec4a","observation_id":"df370464-2a51-440c-b2f8-29703077bbd3","resolution":{"observed_at":"2026-08-07T13:12:04.325699Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:04.042800Z","title":"By construction the H 1/2–norm on ∂Dε is the ℓ2–sum of the norms on each inclusion boundary: ∥(uε −u lim −U (1))|∂Dε ∥2 H 1/2(∂Dε) = X cellsD ∥RD 2 ∥2 H 1/2(∂D)","venue":null,"work_id":"fa49aed3-d721-4cec-96f3-b1d0567db219","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.253207Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:171d179796eaad52467a86286b8738220be4c8d30b3674dee2dee686ddde5c77","observation_id":"0944b542-5d9b-485b-9cbd-5d7d4f71c6ba","resolution":{"observed_at":"2026-08-07T13:12:04.134446Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:03.768359Z","title":"Define the space V:= v∈H 1(Ω;R d) : Z ∂Ω v·r dS+ NX i=1 Z ∂D iε v·r dS= 0∀rigid motionsr","venue":null,"work_id":"f56ff53f-9321-40ed-9da7-249810047b06","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.354569Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:921db083e1dd33cbe12754e30bdc2756c8ff0f50a9cca9990aa064bc79390a50","observation_id":"e8278b94-bcc8-4f78-b753-8ff98157145e","resolution":{"observed_at":"2026-08-07T13:12:03.888394Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:03.592011Z","title":"Set euε :=u lim + eλ−1U (1)","venue":null,"work_id":"c7ae1af1-8063-412b-bec3-49e10b68ffab","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.454535Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:cef177597f4e79215d9f061c670282dccd5ba3fa65d132f9b8d2b3219656ca3b","observation_id":"944a2265-d23d-4a92-b43d-568e60a432a5","resolution":{"observed_at":"2026-08-07T13:12:03.663018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:03.388368Z","title":"Its traction-jump on∂D e is J (1) e := σ(˜λ,˜µ)(˜ue)N − − σ(λ,µ)(˜ue)N + = ˜λ−1 σ(˜λ,˜µ)(U (1))N| − −σ (λ,µ)(U (1))N| +","venue":null,"work_id":"298d887b-e663-4ff1-9f23-f3b95d5ceb5f","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.527703Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:41e554c02089a6576ed2a0801e15bc574d5a44841d31319aff3cf0e3043dfefb","observation_id":"3d895fba-a151-4a2d-ac8d-3ed87639e15f","resolution":{"observed_at":"2026-08-07T13:12:03.479474Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:03.144756Z","title":"Then w solves the homogeneous Lamé system in Ωe with zero Neumann data on ∂Ω and with traction-jump J (1) e on ∂De","venue":null,"work_id":"c97465e3-36a0-4eb5-bb30-605a8c3d9425","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.622637Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:5af36be0eeb0e8a3f261d037bf64125e694ed383d3144fc4ace19f43e3daf675","observation_id":"1d2d14c3-19c1-4603-ac1e-30552504be7d","resolution":{"observed_at":"2026-08-07T13:12:03.303395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:02.901503Z","title":"This completes the proof","venue":null,"work_id":"6d708a48-7856-4479-b7bb-635b6c114eab","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.729838Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:c44ea21a0f3e4d1b51147de0ddf1dbd169b81db3298ac196dfb0c0ab2db67cfe","observation_id":"b226e054-a621-43a1-b7f6-97a134b2c60d","resolution":{"observed_at":"2026-08-07T13:12:03.004345Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:02.748918Z","title":"Hence ∥u˜λ −u 0∥H 1(D) ≤ ˜λ−1∥v1∥H 1(D) +C ˜λ−2∥t∥H − 1 2 (∂D)","venue":null,"work_id":"20801ee4-65cf-4ee6-977b-592a64812e73","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.824828Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:8f5147038c75f32b218bb1a687dfb4454af7ee3f990be45696b3c87d28d92887","observation_id":"8cc64270-69ee-4721-a295-f7dc72911ba4","resolution":{"observed_at":"2026-08-07T13:12:02.805489Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:02.617108Z","title":"elastic pressure","venue":null,"work_id":"fa2c9b4f-b335-48e4-bb7b-fe76165d89e1","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.889315Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b6533033d92447ae8a18ba49b23cdfe6b5565df4ed07971d8bbf0ed72d2d9320","observation_id":"fc560351-2b54-430f-acd6-0bd8ba401cde","resolution":{"observed_at":"2026-08-07T13:12:02.678845Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:02.277417Z","title":null,"venue":null,"work_id":"e705a2fe-238c-443a-b97a-c0609853bff8","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:49.959945Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b675447ab25473672f22b77822f6290199b5477651bb86bc9e7cb8ea0b4a8d95","observation_id":"3e2a4714-5c11-49b6-8c32-5191dfb233f2","resolution":{"observed_at":"2026-08-07T13:12:02.466161Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:02.004246Z","title":"[Vague]The proof here just offers the conclusions but not the detailed process","venue":null,"work_id":"99c38f2f-42c7-4331-be55-0d229444a168","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.037992Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:358b00bdb9682092b345339653ffb1d27daa7031f4f8673feaa861c274f0b7e3","observation_id":"b0190fef-9ddd-448d-936a-7a02b4d1a7ce","resolution":{"observed_at":"2026-08-07T13:12:02.137310Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:01.841834Z","title":"Define the closed subspace V0 :={v∈H 1(Ωε;R d) :v= 0on∂D ε, σ(v)N= 0on∂Ω} and the bilinear form a(v, w) := Z Ωε 2µ D(v) :D(w) +λ(divv)(divw) dx","venue":null,"work_id":"5abebec0-b70a-4c1f-a1fc-8df9063681d2","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.134525Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:74d660e680d66c61777849c874180b0cb2d7748c73f1c7e46b830c56782220d5","observation_id":"25c6082e-9036-425a-a8fc-96d95bc9107e","resolution":{"observed_at":"2026-08-07T13:12:01.924600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:01.561827Z","title":null,"venue":null,"work_id":"91334c7d-fc6c-4def-adc7-9f27e3533fbe","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.253547Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b80007f159fa5e2c5b7f508f78c620bbae710c062cb4761a243bb713b6563e44","observation_id":"d0fb0343-c908-4356-86da-58a2f1e71c53","resolution":{"observed_at":"2026-08-07T13:12:01.672312Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:01.295691Z","title":"Set ψ:=E(φ), z:=w ext −ψ","venue":null,"work_id":"c6878402-b18c-44df-9580-a5dcf069c1d8","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.355682Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:c8421e8e7033b8c8014ec76fc3e362248e820c7f4587a3d906d87db3b2569ed9","observation_id":"72b45005-8856-47cd-ad8c-96bc83e70c6e","resolution":{"observed_at":"2026-08-07T13:12:01.404008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:01.054041Z","title":"Taking v=z in the last identity and using Cauchy–Schwarz plus coercivity, α∥z∥ 2 H 1(Ωε) ≤ |a(ψ, z)| ≤C a ∥ψ∥H 1(Ωε) ∥z∥H 1(Ωε), whereC a depends only on the Lamé parameters(λ, µ)","venue":null,"work_id":"8b06fd9b-f084-405c-9928-6269a806d672","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":81,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.433925Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:5add645ed943388beb2dce75e0974f75d61db5c4d03fd03726dfaa280f040e34","observation_id":"35e3fb91-5858-4a27-9ffb-4b2e95255c90","resolution":{"observed_at":"2026-08-07T13:12:01.154668Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:00.829718Z","title":"Notingφ=w ext|∂Dε = (uε −u lim)|∂Dε, we arrive at the asserted estimate ∥uε −u lim∥H 1(Ωε) ≤C∥u ε −u lim∥H 1/2(∂Dε)","venue":null,"work_id":"abc66c1f-6762-427e-aba4-67a99d927246","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":82,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.505852Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:f85b80d37494f16f7a9fb33bcddedb3f5697096b86456bf0700a37cafc6cfd05","observation_id":"ecde4116-5397-4fe5-a5d6-f117d8a25ef3","resolution":{"observed_at":"2026-08-07T13:12:00.947804Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:00.680580Z","title":"3.Ω\\Dis connected and has a Lipschitz boundary∂Ω∪∂D","venue":null,"work_id":"ac913047-0c67-4107-85a2-fc6f79fba82f","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":83,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.587498Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:1fec0efdf40dfe4a9a10a87fb50579991cfcc259f962a31acdc1309a8fced247","observation_id":"66c0aeaf-16d5-4110-a5b4-5347cf047c3f","resolution":{"observed_at":"2026-08-07T13:12:00.738588Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:00.422037Z","title":"3.Ω\\Dis connected and has a Lipschitz boundary∂Ω∪∂D","venue":null,"work_id":"8f2cf87e-7cec-41d2-ad60-5ddb02bfadd9","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.667219Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:c1976d347827df21f953fb928d19f042d8c190a3071d4af5cb3195289f810719","observation_id":"1cf7418c-fda6-48bd-b287-72cb3b1f86ed","resolution":{"observed_at":"2026-08-07T13:12:00.561571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:00.276824Z","title":"By the scalingx=εyone deduces that on eachε-cellε(Y f +k) for allv∈H 1(ε(Yf +k)),∥v∥ H 1(ε(Yf +k)) ≤C 0 ∥v∥L2(ε(Yf +k)) +∥sym∇v∥ L2(ε(Yf +k))","venue":null,"work_id":"4f8d1ee2-7408-466b-84b9-835bc28a76ad","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":85,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.760281Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:fed845e461fba815e820f53edee9bf9560bbb18e11c351aa23baea711bfc1bea","observation_id":"98034778-47c5-442b-9b11-f59aa4e12883","resolution":{"observed_at":"2026-08-07T13:12:00.348234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:12:00.110150Z","title":"We also choose a finite set of boundary functions {ψb} supported in the ε-neighborhood of ∂Ω so that P k ψk + P b ψb ≡1 on Ω","venue":null,"work_id":"04ada8b2-0d71-45bf-803b-32d93fae7266","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":86,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:50.909819Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:b8da80ae27e792b01ccb4662dc0dfc29cd079cb0c1cb9d4810bbd8ba9718fdbf","observation_id":"8bf291a6-a54b-4078-8aec-e49b6d4419f7","resolution":{"observed_at":"2026-08-07T13:12:00.189860Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:59.903049Z","title":"On each interior cell we apply the scaled Korn of Step 1: ∥uk∥H 1(ε(Yf +k)) ≤C 0 [∥ψku∥L2 +∥sym∇(ψ ku)∥L2 ] ≤C 0 ∥u∥L2(suppψ k) +∥ψ k sym∇u∥ L2 +∥u⊗ ∇ψk∥L2","venue":null,"work_id":"633fcac7-49ef-483c-a860-ff2f059b7a1b","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":87,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.011200Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:14d91aceda2e7a88c219cfe6b8ae17be5b48ee70ee4aea2bc64cf15c87b15ee4","observation_id":"a4be7dff-94a6-414b-807f-45c92be62d91","resolution":{"observed_at":"2026-08-07T13:11:59.986349Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:59.648221Z","title":"This completes the proof","venue":null,"work_id":"50a8b899-8dd1-433d-a126-7b2bb5d3451f","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.100966Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:ecea8a4fbf5d927baf1b1f86e0faffd9add69c53cb4ffc2f5d86e23025b21f0b","observation_id":"486be83f-9f83-46a9-a761-9d5ad08d338c","resolution":{"observed_at":"2026-08-07T13:11:59.778648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:59.499840Z","title":"Recall the unfolding operator Tε :L 2(Ωε)→L 2(Ω×Y f ), which on each cellΩ ε ∩ε(k+Y f )is defined by (Tεv)(x, y) =v(εk+εy), x∈ε(k+Y), y∈Y f , zero elsewhere","venue":null,"work_id":"cb70ffcb-84ae-473f-a717-83f3e183e563","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":89,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.205194Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:dfe2a9847c1b9f43230f8d159d169f16733dda6da8aa5daa2a1782972ed1134f","observation_id":"15b77e2d-01b0-4e61-901d-431fb14a5f32","resolution":{"observed_at":"2026-08-07T13:11:59.580869Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:59.288587Z","title":null,"venue":null,"work_id":"b45be7d0-f874-43f8-a547-a0c3d0a6c3d2","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":90,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.334893Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:5a3b8c0dd6d81aeabddb935587c92b8b9f29d0efbf3888390b0a47e7664d8c09","observation_id":"815f34fa-5196-4223-a1ac-3fc41482bb9b","resolution":{"observed_at":"2026-08-07T13:11:59.361492Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:59.067777Z","title":null,"venue":null,"work_id":"3c911e12-cb51-408f-8a65-b89c7bd9691f","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":91,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.499764Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:aab4cc23ea7676303824ac99fe76822016725444fc0139e0f2c00c757aa40f6b","observation_id":"7ceef03b-aafe-40e0-937b-58a0471c7745","resolution":{"observed_at":"2026-08-07T13:11:59.166299Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:58.894586Z","title":"We set W(x, y) = lim ε→0 ∇yTεuε inL 2(Ω×Y f )","venue":null,"work_id":"7c96704b-ab03-4485-a92b-b5402f006196","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.605266Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:971bec138a926e09d9b7600e29d8b809f9d3b18e90f395f6a71666be6ac440d7","observation_id":"7d58d4d1-f545-4a2a-b931-c50478589c9d","resolution":{"observed_at":"2026-08-07T13:11:58.966759Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:58.704915Z","title":null,"venue":null,"work_id":"c8e5e7a6-4cc4-4187-9107-ce4aeceb53c6","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":93,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.718761Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:9aa83c67cf4ec97166d6d71bb0fbee7e0a376b4f6fb40e1ec4034d7b3069d3c6","observation_id":"63ffaa7a-c15d-46a0-a17f-f5cb86895e80","resolution":{"observed_at":"2026-08-07T13:11:58.783745Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:58.518677Z","title":"[Error]The test function space may not be accurate since the divergence of the function is not concluded in this conclusion","venue":null,"work_id":"607f1822-378c-46fb-a0c7-1923a9bd9617","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":94,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.891076Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:d12c290fb26d3f7888c94104fc07c3cf9d4683ba028d8557727bad8e4bf582ff","observation_id":"ddd7289f-f0ac-4585-9ba6-4cfd699caf88","resolution":{"observed_at":"2026-08-07T13:11:58.590884Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:58.283751Z","title":null,"venue":null,"work_id":"7719dbaf-cd34-4ec5-8d5f-b832ee7d7ffa","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":95,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:51.971779Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:3dd8a255f7baa98954c0b1c0a31283eb90d90e9448717511d31850af1d321d89","observation_id":"2a2a2b89-1cf4-49ba-8630-9727206f37a6","resolution":{"observed_at":"2026-08-07T13:11:58.378606Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:58.089223Z","title":"Inserting (vε, qε) into the variational equation and passing to the limit by two-scale convergence (unfolding arguments in Lemma A.4) yields for a.e","venue":null,"work_id":"7bc14618-faa8-4d49-9a58-db2f2007e339","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":96,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.104233Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:cc64d6fe8c2b6b8755f5522cbfaf09250e9fc3f208ed46a21c9d1dec6fc787f2","observation_id":"5bba44c8-d13a-46a6-b4c9-6b48269c0104","resolution":{"observed_at":"2026-08-07T13:11:58.196129Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:57.876022Z","title":null,"venue":null,"work_id":"8e0fe15a-6c76-408b-90e4-5b4ca44c5216","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":97,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.240417Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:9086772f13111e323e1bd452a8b0ffd343f521526b5b43814851889e01f2c012","observation_id":"feebffb0-3255-4991-9e82-556f388cc7ae","resolution":{"observed_at":"2026-08-07T13:11:57.979371Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:57.657362Z","title":"[Vague]The conditions for using the theorem need to be verified","venue":null,"work_id":"4ed7f58e-30fb-4e25-803f-7c53900ab10d","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":98,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.408132Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:a5c45826507a73aa6d9986577109041bea0c119264bacfcf26e2db31d314237d","observation_id":"16902a27-ece9-4e14-8500-7f54ab101a3e","resolution":{"observed_at":"2026-08-07T13:11:57.761707Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:57.450753Z","title":null,"venue":null,"work_id":"46be0adb-c385-47cd-af4f-093dcf68924d","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":99,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.530127Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:170dd9e770591c74b61fbd2b4268a9b1076f26c0bab35a4ae38b346d0bf5208c","observation_id":"b90e3e4a-c662-491e-90ae-103f9e8b875a","resolution":{"observed_at":"2026-08-07T13:11:57.543853Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:57.237180Z","title":"In particular, for any smooth strain field E(x) =D xu0(x), one has by the chain rule ∇xχE(x)(y) = (∂ EχE)(y)[D2 xu0(x)] and hence ∥∇xχDxu0(·)(·/ε)∥L2(Ωε) ≤C∥u 0∥H 2(Ω)","venue":null,"work_id":"1b4c4f8f-59e8-41d0-aeae-7f7744aa8009","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.670969Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:7e2df36325e55311f43d1fe2a9f424ca6120eee3cb284dda35e12597e59217e1","observation_id":"53b28f11-23df-409f-a34c-93680adc319f","resolution":{"observed_at":"2026-08-07T13:11:57.336968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:57.080206Z","title":null,"venue":null,"work_id":"98f189a5-6698-4309-a131-553545c8b295","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":101,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.802484Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:964b67ad89252ce6f48752eacaee6a73119932b4ddf0bf4fef0257aaa9d7ce3e","observation_id":"f9f8474a-c409-4603-b1ea-693cdeda64b6","resolution":{"observed_at":"2026-08-07T13:11:57.151872Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T13:11:56.870232Z","title":"[Vague]The derivation process here is in urgent need of proof details","venue":null,"work_id":"b46364a1-bae9-4613-a711-dd3328d43ca0","year":null},"citing_paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research","version":1},"reference_index":102,"source":"pdf_text","source_observed_at":"2026-08-07T13:11:52.935915Z"},"links":{"citing_paper":"/paper/2505.22451"},"observation_digest":"sha256:073b15598fdb9b7f695b86719276f965eaad0a50bdb5251b5903f6e60f4adbb8","observation_id":"f6e59551-9c46-432c-9d04-0a417627241c","resolution":{"observed_at":"2026-08-07T13:11:56.975163Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.22451","last_updated":"2025-05-28T15:10:37Z","latest_version":1,"primary_category":"cs.AI","snapshot_observed_at":"2026-08-15T10:14:27.381910Z","submitted_at":"2025-05-28T15:10:37Z","title":"AI Mathematician: Towards Fully Automated Frontier Mathematical Research"},"reference_resolution":{"displayed":100,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":50,"verified_exact":0,"verified_fuzzy":49},"total_outbound_references":115},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 100 of 115 outbound references and 3 inbound Pith citation observations for arXiv:2505.22451."}