{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ATTTAX34HM4HHHH75EVJJ25V77","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":"f8647cb9ce8aca1df86d7c4297e2064af2e7b6e1727f2b9af64c9e38e6bcac06","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-07T07:02:37Z","title_canon_sha256":"8946586642749184fdbd300b9fc86d454cd91dc368245ce9a5a5d6895a4d8a6a"},"schema_version":"1.0","source":{"id":"1612.02129","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.02129","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"arxiv_version","alias_value":"1612.02129v2","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02129","created_at":"2026-05-18T00:28:25Z"},{"alias_kind":"pith_short_12","alias_value":"ATTTAX34HM4H","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ATTTAX34HM4HHHH7","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ATTTAX34","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:8f77dc397375d48b10334024cc523ef043b356933f995d35e6d8fffc9a00940d","target":"graph","created_at":"2026-05-18T00:28:25Z","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 study inverse boundary problems for a one dimensional linear integro-differential equation of the Gurtin--Pipkin type with the Dirichlet-to-Neumann map as the inverse data. Under natural conditions on the kernel of the integral operator, we give the explicit formula for the solution of the problem with the observation on the semiaxis $t>0.$\n  For the observation on finite time interval, we prove the uniqueness result, which is similar to the local Borg--Marchenko theorem for the Schr\\\"odinger equation.","authors_text":"J. M. Wang, S.A. Avdonin, S.A. Ivanov","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-07T07:02:37Z","title":"Inverse Problems for the Heat Equation with Memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02129","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":"sha256:1883b56825ed16a1b2a8af7040572a88951b03be919dbdb8669f8695f0601339","target":"record","created_at":"2026-05-18T00:28:25Z","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":"f8647cb9ce8aca1df86d7c4297e2064af2e7b6e1727f2b9af64c9e38e6bcac06","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-12-07T07:02:37Z","title_canon_sha256":"8946586642749184fdbd300b9fc86d454cd91dc368245ce9a5a5d6895a4d8a6a"},"schema_version":"1.0","source":{"id":"1612.02129","kind":"arxiv","version":2}},"canonical_sha256":"04e7305f7c3b38739cffe92a94ebb5ffee2661d1f32654171649b86656ccc08c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04e7305f7c3b38739cffe92a94ebb5ffee2661d1f32654171649b86656ccc08c","first_computed_at":"2026-05-18T00:28:25.904716Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:25.904716Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PTcWjz1vf/C207QQXUeRqNjrqim2L5MoeMZuyUEssTyqR9VQgIfwZonKGQawa1r4Gn9JUi+Xu87HKoo0dOINCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:25.905356Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.02129","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1883b56825ed16a1b2a8af7040572a88951b03be919dbdb8669f8695f0601339","sha256:8f77dc397375d48b10334024cc523ef043b356933f995d35e6d8fffc9a00940d"],"state_sha256":"4a8d0bb2cf75c0c72fe9fb03c2a7839f5580ef94d1bb6aacf97c6266ecda16c8"}