{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TC7EK7HMBWQAMZOMRXS7D56HLF","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"306eb2eb318c5201220bc53c9e1f2687aa8a1d1cb456434b52fc3543cfadca93","cross_cats_sorted":["math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-12T14:41:26Z","title_canon_sha256":"a0a3e3c099553d2dd24c0b75911cf8c9ded919345ed1cd977502afca90bbc441"},"schema_version":"1.0","source":{"id":"1104.2233","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2233","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2233v2","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2233","created_at":"2026-05-18T04:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"TC7EK7HMBWQA","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TC7EK7HMBWQAMZOM","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TC7EK7HM","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:613bf38538b597de0d86529b0dc9449a2da48004cf9dd7d9b49e4fd782ebda61","target":"graph","created_at":"2026-05-18T04:22:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove a 2-terms Weyl formula for the counting function N(mu) of the spectrum of the Laplace operator in the Euclidean disk with a sharp remainder estimate O(mu^2/3).","authors_text":"Yves Colin De Verdi\\`ere (IF)","cross_cats":["math.CA","math.MP","math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-12T14:41:26Z","title":"On the remainder in the Weyl formula for the Euclidean disk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2233","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2550eb48c552f4ed1bcaa838b14fbb584c7baed67d6f03731c54c169b89ac02f","target":"record","created_at":"2026-05-18T04:22:31Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"306eb2eb318c5201220bc53c9e1f2687aa8a1d1cb456434b52fc3543cfadca93","cross_cats_sorted":["math.CA","math.MP","math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-12T14:41:26Z","title_canon_sha256":"a0a3e3c099553d2dd24c0b75911cf8c9ded919345ed1cd977502afca90bbc441"},"schema_version":"1.0","source":{"id":"1104.2233","kind":"arxiv","version":2}},"canonical_sha256":"98be457cec0da00665cc8de5f1f7c7595bff89baf6f0866180f495c7e22529f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98be457cec0da00665cc8de5f1f7c7595bff89baf6f0866180f495c7e22529f8","first_computed_at":"2026-05-18T04:22:31.699884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:31.699884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wYzkTedpr2AZYaDxKSP8ksXj+ocfGd7S5+CbbT32R52gHIAbE0rkYNWR/a9GqEp7YHoN/F/e1D+UylZF7mppCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:31.700383Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2233","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2550eb48c552f4ed1bcaa838b14fbb584c7baed67d6f03731c54c169b89ac02f","sha256:613bf38538b597de0d86529b0dc9449a2da48004cf9dd7d9b49e4fd782ebda61"],"state_sha256":"db5daa6039cd236cc3a926521a2d006a9b7b543e11f726c15b4ec90438afdc88"}