{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YN4XRNRVC2BBPDG3KXYHROXPM4","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":"2db49ae572dd3a65ad5f287636bd5eb27ed2b93e3715404a0d2bbd851994e893","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-06T11:57:23Z","title_canon_sha256":"5974680b9461788a57727f5e0fd5b8955c06703c54e078518be0b2fd66927c6c"},"schema_version":"1.0","source":{"id":"1312.1835","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.1835","created_at":"2026-05-18T02:39:25Z"},{"alias_kind":"arxiv_version","alias_value":"1312.1835v2","created_at":"2026-05-18T02:39:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.1835","created_at":"2026-05-18T02:39:25Z"},{"alias_kind":"pith_short_12","alias_value":"YN4XRNRVC2BB","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YN4XRNRVC2BBPDG3","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YN4XRNRV","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:9a7adc15ba9f6b040be7cdf393954beb31e6b6451f7eecf68d0ecee6b9775df3","target":"graph","created_at":"2026-05-18T02:39:25Z","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 two-term quasi-classical trace asymptotic formula for the functions of multi-dimensional Wiener-Hopf operators with discontinuous symbols. The discontinuities occur on the surfaces which are assumed to be piece-wise smooth. Such a two-term formula was conjectured by H. Widom in 1982, and proved by A. V Sobolev for smooth surfaces in 2009.","authors_text":"A. V. Sobolev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-06T11:57:23Z","title":"Wiener-Hopf operators in higher dimensions: the Widom conjecture for piece-wise smooth domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.1835","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":"sha256:020338f5d58a077ec53cb30eaafaf84f5a623cc938d673aacedb6e5b6792b9ce","target":"record","created_at":"2026-05-18T02:39:25Z","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":"2db49ae572dd3a65ad5f287636bd5eb27ed2b93e3715404a0d2bbd851994e893","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-12-06T11:57:23Z","title_canon_sha256":"5974680b9461788a57727f5e0fd5b8955c06703c54e078518be0b2fd66927c6c"},"schema_version":"1.0","source":{"id":"1312.1835","kind":"arxiv","version":2}},"canonical_sha256":"c37978b6351682178cdb55f078baef671397f0ca71049fc4c808c3f5d4e7a0fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c37978b6351682178cdb55f078baef671397f0ca71049fc4c808c3f5d4e7a0fb","first_computed_at":"2026-05-18T02:39:25.614831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:25.614831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VMhya1Qy2qu1xtTtSxVK2+X/3K+FFFTmC7+gHlRrZ/cn9zUUeM4dBOsIR8+zuaEftt4d5OzcjKa1tiXBOslKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:25.615450Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.1835","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:020338f5d58a077ec53cb30eaafaf84f5a623cc938d673aacedb6e5b6792b9ce","sha256:9a7adc15ba9f6b040be7cdf393954beb31e6b6451f7eecf68d0ecee6b9775df3"],"state_sha256":"82aa456785d27e6f4eaaf81052f59e7e88a4e38f4b1c318ca12d0e30d303c918"}