{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:57CCRF6FZQWU62FQ3INI3XYKWV","short_pith_number":"pith:57CCRF6F","canonical_record":{"source":{"id":"1212.1400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-06T18:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"6115e8afe12f3eb3f30e71a641cf5ac64e937e533b0154a34f7099311a2988a8","abstract_canon_sha256":"7dd4f467e5f324baaf53360f0efa4f1056b9d63c13e7e8f15cd2d96da39cb570"},"schema_version":"1.0"},"canonical_sha256":"efc42897c5cc2d4f68b0da1a8ddf0ab5434f8116a7eaab07c8b453aab995faf4","source":{"kind":"arxiv","id":"1212.1400","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1400","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1400v1","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1400","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"57CCRF6FZQWU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"57CCRF6FZQWU62FQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"57CCRF6F","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:57CCRF6FZQWU62FQ3INI3XYKWV","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1400","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-06T18:04:06Z","cross_cats_sorted":[],"title_canon_sha256":"6115e8afe12f3eb3f30e71a641cf5ac64e937e533b0154a34f7099311a2988a8","abstract_canon_sha256":"7dd4f467e5f324baaf53360f0efa4f1056b9d63c13e7e8f15cd2d96da39cb570"},"schema_version":"1.0"},"canonical_sha256":"efc42897c5cc2d4f68b0da1a8ddf0ab5434f8116a7eaab07c8b453aab995faf4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:04.058858Z","signature_b64":"6bH+qfPTvpzXpGrLH1vgsAiL1Lu82SiDCWs0nvU1aQUXjAqh2ObWxX4pI/MZUPvmLUMBERzNqBGnpUM2t7qrAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efc42897c5cc2d4f68b0da1a8ddf0ab5434f8116a7eaab07c8b453aab995faf4","last_reissued_at":"2026-05-18T03:39:04.058278Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:04.058278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1400","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MY/1qf9BKsh4jAZ1XA1GmDjTrp9w2pSu0pArjtXCPgxRbSO/3DdqLljxRpsdodE5cNZFgalDttI0iBBjlW4FDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:36:28.248666Z"},"content_sha256":"ced07e9b74bb2da8f1c4f0095ce5c3283ca76759b4e4a7f349acd6f6efa62461","schema_version":"1.0","event_id":"sha256:ced07e9b74bb2da8f1c4f0095ce5c3283ca76759b4e4a7f349acd6f6efa62461"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:57CCRF6FZQWU62FQ3INI3XYKWV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Neumann heat content asymptotics with singular initial temperature and singular specific heat","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"H. Kang, M. van den Berg, P. Gilkey","submitted_at":"2012-12-06T18:04:06Z","abstract_excerpt":"We study the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail as are recursion relations among the coefficients and the relationship between the Dirichlet and Robin settings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1400","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w0l0Xl6he14QG4he1s0vcgPGwcAuCyqy7tYno8wSUwPB+HRUdCcyN5RAgfPcNl9IrzQ6NSkZnHzLLVcpz74FAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:36:28.249249Z"},"content_sha256":"0560b493305fb9b5bf593d3a72efac6a4a2d5516b9b99ea150d1fb638d232fac","schema_version":"1.0","event_id":"sha256:0560b493305fb9b5bf593d3a72efac6a4a2d5516b9b99ea150d1fb638d232fac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/57CCRF6FZQWU62FQ3INI3XYKWV/bundle.json","state_url":"https://pith.science/pith/57CCRF6FZQWU62FQ3INI3XYKWV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/57CCRF6FZQWU62FQ3INI3XYKWV/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T20:36:28Z","links":{"resolver":"https://pith.science/pith/57CCRF6FZQWU62FQ3INI3XYKWV","bundle":"https://pith.science/pith/57CCRF6FZQWU62FQ3INI3XYKWV/bundle.json","state":"https://pith.science/pith/57CCRF6FZQWU62FQ3INI3XYKWV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/57CCRF6FZQWU62FQ3INI3XYKWV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:57CCRF6FZQWU62FQ3INI3XYKWV","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":"7dd4f467e5f324baaf53360f0efa4f1056b9d63c13e7e8f15cd2d96da39cb570","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-06T18:04:06Z","title_canon_sha256":"6115e8afe12f3eb3f30e71a641cf5ac64e937e533b0154a34f7099311a2988a8"},"schema_version":"1.0","source":{"id":"1212.1400","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1400","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1400v1","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1400","created_at":"2026-05-18T03:39:04Z"},{"alias_kind":"pith_short_12","alias_value":"57CCRF6FZQWU","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"57CCRF6FZQWU62FQ","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"57CCRF6F","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:0560b493305fb9b5bf593d3a72efac6a4a2d5516b9b99ea150d1fb638d232fac","target":"graph","created_at":"2026-05-18T03:39:04Z","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 the asymptotic behavior of the heat content on a compact Riemannian manifold with boundary and with singular specific heat and singular initial temperature distributions imposing Robin boundary conditions. Assuming the existence of a complete asymptotic series we determine the first three terms in that series. In addition to the general setting, the interval is studied in detail as are recursion relations among the coefficients and the relationship between the Dirichlet and Robin settings.","authors_text":"H. Kang, M. van den Berg, P. Gilkey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-06T18:04:06Z","title":"Neumann heat content asymptotics with singular initial temperature and singular specific heat"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1400","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:ced07e9b74bb2da8f1c4f0095ce5c3283ca76759b4e4a7f349acd6f6efa62461","target":"record","created_at":"2026-05-18T03:39:04Z","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":"7dd4f467e5f324baaf53360f0efa4f1056b9d63c13e7e8f15cd2d96da39cb570","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-12-06T18:04:06Z","title_canon_sha256":"6115e8afe12f3eb3f30e71a641cf5ac64e937e533b0154a34f7099311a2988a8"},"schema_version":"1.0","source":{"id":"1212.1400","kind":"arxiv","version":1}},"canonical_sha256":"efc42897c5cc2d4f68b0da1a8ddf0ab5434f8116a7eaab07c8b453aab995faf4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efc42897c5cc2d4f68b0da1a8ddf0ab5434f8116a7eaab07c8b453aab995faf4","first_computed_at":"2026-05-18T03:39:04.058278Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:04.058278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6bH+qfPTvpzXpGrLH1vgsAiL1Lu82SiDCWs0nvU1aQUXjAqh2ObWxX4pI/MZUPvmLUMBERzNqBGnpUM2t7qrAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:04.058858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1400","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ced07e9b74bb2da8f1c4f0095ce5c3283ca76759b4e4a7f349acd6f6efa62461","sha256:0560b493305fb9b5bf593d3a72efac6a4a2d5516b9b99ea150d1fb638d232fac"],"state_sha256":"e61ce42a346cb1b9202f2d76138dd482f11c45c28051a9e8fce5591ee94ddf9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MaKfeVew4WIHhUexFMER0h4NSR2Z9bJIeS7pFzKF+HIkBGN8h+An0/36GZqyW140eom4YXecmYcbIapb7oB0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:36:28.251867Z","bundle_sha256":"236bf671fd9c55aad2adf5fd3d7be9882971423040a7de59fa1823fc9935947a"}}