{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:J47YH3U6JWIGL7C2IIHTXVNEIJ","short_pith_number":"pith:J47YH3U6","canonical_record":{"source":{"id":"1410.6194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-22T21:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"0987d253df398bc60d59675825842d65e021ef1203b792fddf05d4353ca21d65","abstract_canon_sha256":"b503c0a82e3ccc3c43854d281bb8bc06ee81203506aa6b9a21b95f55d3d5b4ba"},"schema_version":"1.0"},"canonical_sha256":"4f3f83ee9e4d9065fc5a420f3bd5a4425dfaca18e13b8db872c1689a33b37570","source":{"kind":"arxiv","id":"1410.6194","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6194","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6194v1","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6194","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"J47YH3U6JWIG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J47YH3U6JWIGL7C2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J47YH3U6","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:J47YH3U6JWIGL7C2IIHTXVNEIJ","target":"record","payload":{"canonical_record":{"source":{"id":"1410.6194","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-22T21:21:13Z","cross_cats_sorted":[],"title_canon_sha256":"0987d253df398bc60d59675825842d65e021ef1203b792fddf05d4353ca21d65","abstract_canon_sha256":"b503c0a82e3ccc3c43854d281bb8bc06ee81203506aa6b9a21b95f55d3d5b4ba"},"schema_version":"1.0"},"canonical_sha256":"4f3f83ee9e4d9065fc5a420f3bd5a4425dfaca18e13b8db872c1689a33b37570","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:42.488022Z","signature_b64":"EMYOJtZDz0U4tRELvKuLDj+jKHlEmxeSg7XLkw82RajZCkGYuhDQHpaPGdJMx8VBb63NMcPch8YdXhpqKMH8BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f3f83ee9e4d9065fc5a420f3bd5a4425dfaca18e13b8db872c1689a33b37570","last_reissued_at":"2026-05-17T23:39:42.487350Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:42.487350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.6194","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":"2026-05-17T23:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PnXXfLIQxUD3LpQ2iSM7YrMYvnYKoaMxaQjIXy0TONsQQ6qLB600XJAOpIkbdy7qp0rvdgT4zvPJG0B+RhuPDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:01:23.725025Z"},"content_sha256":"b16856aeb2f8c779692876d78bc9a7363fb5ef7381215e88125fcb6c3453e6d8","schema_version":"1.0","event_id":"sha256:b16856aeb2f8c779692876d78bc9a7363fb5ef7381215e88125fcb6c3453e6d8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:J47YH3U6JWIGL7C2IIHTXVNEIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability analysis for linear heat conduction with memory kernels described by Gamma functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Corrado Mascia","submitted_at":"2014-10-22T21:21:13Z","abstract_excerpt":"This paper analyzes heat equation with memory in the case of kernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of hyperbolic type. Stability is studied in details by analyzing the corresponding dispersion relation, providing sufficient stability condition for the general case and sharp instability thresholds in the case of linear combination of the first three Gamma functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6194","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":"2026-05-17T23:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mbd+fZ2Y/kqQtGxu5gaPHqG5MnvOxO2wwL1gtYHOKFveTgnLKhmwtAMqAmkz5dF3AjfAP+PBbqesnZ58g+NRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T23:01:23.725685Z"},"content_sha256":"64314ea70485ca3fdfbcc7913accd95ad575c8c1197983cc7dd916c27df272c2","schema_version":"1.0","event_id":"sha256:64314ea70485ca3fdfbcc7913accd95ad575c8c1197983cc7dd916c27df272c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ/bundle.json","state_url":"https://pith.science/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ/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":"2026-05-22T23:01:23Z","links":{"resolver":"https://pith.science/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ","bundle":"https://pith.science/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ/bundle.json","state":"https://pith.science/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J47YH3U6JWIGL7C2IIHTXVNEIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:J47YH3U6JWIGL7C2IIHTXVNEIJ","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":"b503c0a82e3ccc3c43854d281bb8bc06ee81203506aa6b9a21b95f55d3d5b4ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-22T21:21:13Z","title_canon_sha256":"0987d253df398bc60d59675825842d65e021ef1203b792fddf05d4353ca21d65"},"schema_version":"1.0","source":{"id":"1410.6194","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.6194","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"1410.6194v1","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.6194","created_at":"2026-05-17T23:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"J47YH3U6JWIG","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"J47YH3U6JWIGL7C2","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"J47YH3U6","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:64314ea70485ca3fdfbcc7913accd95ad575c8c1197983cc7dd916c27df272c2","target":"graph","created_at":"2026-05-17T23:39:42Z","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":"This paper analyzes heat equation with memory in the case of kernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of hyperbolic type. Stability is studied in details by analyzing the corresponding dispersion relation, providing sufficient stability condition for the general case and sharp instability thresholds in the case of linear combination of the first three Gamma functions.","authors_text":"Corrado Mascia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-22T21:21:13Z","title":"Stability analysis for linear heat conduction with memory kernels described by Gamma functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6194","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:b16856aeb2f8c779692876d78bc9a7363fb5ef7381215e88125fcb6c3453e6d8","target":"record","created_at":"2026-05-17T23:39:42Z","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":"b503c0a82e3ccc3c43854d281bb8bc06ee81203506aa6b9a21b95f55d3d5b4ba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-10-22T21:21:13Z","title_canon_sha256":"0987d253df398bc60d59675825842d65e021ef1203b792fddf05d4353ca21d65"},"schema_version":"1.0","source":{"id":"1410.6194","kind":"arxiv","version":1}},"canonical_sha256":"4f3f83ee9e4d9065fc5a420f3bd5a4425dfaca18e13b8db872c1689a33b37570","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f3f83ee9e4d9065fc5a420f3bd5a4425dfaca18e13b8db872c1689a33b37570","first_computed_at":"2026-05-17T23:39:42.487350Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:42.487350Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EMYOJtZDz0U4tRELvKuLDj+jKHlEmxeSg7XLkw82RajZCkGYuhDQHpaPGdJMx8VBb63NMcPch8YdXhpqKMH8BQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:42.488022Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.6194","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b16856aeb2f8c779692876d78bc9a7363fb5ef7381215e88125fcb6c3453e6d8","sha256:64314ea70485ca3fdfbcc7913accd95ad575c8c1197983cc7dd916c27df272c2"],"state_sha256":"253d40a884849a79b9e9e08055568874e10b3a24929732c2a1e9964d89f9593a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzGOnSHumKXKtfnqomva/J5ssoMLo0wCcym1C1LpHACpXfAE9vt26TVJryjYCcITa/LuOvqpuGzOoePxnvmeCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T23:01:23.729188Z","bundle_sha256":"5503bdfb23bdb586ead12980f45173cde8d3943ca98ca49e16c381359cf00c36"}}