{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3ZQRPIWRNINZ5UBTZWUI4C5QYM","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":"d3600fbafd725d797ae28fdbe7e69833da5e8d06d816d7a93b9bcbde72daa0ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T15:22:43Z","title_canon_sha256":"9ed27e20fde03aa468c5d9ea6a0fbd0310b4cdf331af705205390c4880af1d42"},"schema_version":"1.0","source":{"id":"1401.6373","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6373","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6373v1","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6373","created_at":"2026-05-18T03:01:12Z"},{"alias_kind":"pith_short_12","alias_value":"3ZQRPIWRNINZ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3ZQRPIWRNINZ5UBT","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3ZQRPIWR","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:53e8c32a067a2f90823968836faa9c2ede3f1078885ed3b7b41be7cb98f71b12","target":"graph","created_at":"2026-05-18T03:01:12Z","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":"Let (M,g) be a compact Riemannian manifold without boundary. Let D be a compact subdomain of M with smooth boundary. We examine the heat content asymptotics for the heat flow from D into M where both the initial temperature and the specific heat are permitted to have controlled singularities on the boundary of D. The operator driving the heat process is assumed to be an operator of Laplace type","authors_text":"M. van den Berg, P. Gilkey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T15:22:43Z","title":"Heat content with singular initial temperature and singular specific heat"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6373","kind":"arxiv","version":1},"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":"sha256:9d01897166f7a666387865ea8ce8eb738b882734f201b402371ba8a915f9a79b","target":"record","created_at":"2026-05-18T03:01:12Z","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":"d3600fbafd725d797ae28fdbe7e69833da5e8d06d816d7a93b9bcbde72daa0ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-01-24T15:22:43Z","title_canon_sha256":"9ed27e20fde03aa468c5d9ea6a0fbd0310b4cdf331af705205390c4880af1d42"},"schema_version":"1.0","source":{"id":"1401.6373","kind":"arxiv","version":1}},"canonical_sha256":"de6117a2d16a1b9ed033cda88e0bb0c32f81f814e7987f9b8ca2a93af326a98d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de6117a2d16a1b9ed033cda88e0bb0c32f81f814e7987f9b8ca2a93af326a98d","first_computed_at":"2026-05-18T03:01:12.302686Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:12.302686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tlxZE8uIZRE1MyKl8lRAnQrgKZgYhKwMOuPnvtjkYhetKDbhaG/HIpwo39eDJwmknwKoPSV4tvTEHbzDivIXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:12.303476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6373","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d01897166f7a666387865ea8ce8eb738b882734f201b402371ba8a915f9a79b","sha256:53e8c32a067a2f90823968836faa9c2ede3f1078885ed3b7b41be7cb98f71b12"],"state_sha256":"f23812398db1ad7604dc18617acf586479dc34e9729ae6b06e27af062aa60e80"}