{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:5VZQHNIES2YEXD3EQC7KH7SSLQ","short_pith_number":"pith:5VZQHNIE","canonical_record":{"source":{"id":"math/0606045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-06-02T08:17:54Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"c2f64edb267d0f3ecc24e384d70fa8edc810d0b58fd606fc64e1c2ed4d52c119","abstract_canon_sha256":"0e85ca943236ef2297343cfb399de24af4515af1d4bb5affd87645c83df3ddde"},"schema_version":"1.0"},"canonical_sha256":"ed7303b50496b04b8f6480bea3fe525c02c52bee005bc03f57cd74d07f4e1352","source":{"kind":"arxiv","id":"math/0606045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606045","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606045v1","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606045","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"5VZQHNIES2YE","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_16","alias_value":"5VZQHNIES2YEXD3E","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_8","alias_value":"5VZQHNIE","created_at":"2026-06-03T22:06:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:5VZQHNIES2YEXD3EQC7KH7SSLQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0606045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AP","submitted_at":"2006-06-02T08:17:54Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"c2f64edb267d0f3ecc24e384d70fa8edc810d0b58fd606fc64e1c2ed4d52c119","abstract_canon_sha256":"0e85ca943236ef2297343cfb399de24af4515af1d4bb5affd87645c83df3ddde"},"schema_version":"1.0"},"canonical_sha256":"ed7303b50496b04b8f6480bea3fe525c02c52bee005bc03f57cd74d07f4e1352","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T22:06:19.816219Z","signature_b64":"hWbq305PXllqGLkzYsRUXuxj8MIrPd6DBo4g+ZuyY7mPxdOXu2PtwweqZHnb/5UVln2fyJPn5Ir4lSzxZJIlDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed7303b50496b04b8f6480bea3fe525c02c52bee005bc03f57cd74d07f4e1352","last_reissued_at":"2026-06-03T22:06:19.815791Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T22:06:19.815791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0606045","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":"2026-06-03T22:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EdiuPML0N0FhVmsZ0dXatbPptYvGFym3KQLn1UG/He6TjK+yZ4x040UUh3p3cEZBJACiUfcXDXD7t5laaeLeBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:00:23.279703Z"},"content_sha256":"4423d63911fece648664370d3d033f4322dc8e096419072138a95a773ee70b22","schema_version":"1.0","event_id":"sha256:4423d63911fece648664370d3d033f4322dc8e096419072138a95a773ee70b22"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:5VZQHNIES2YEXD3EQC7KH7SSLQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Dual Mesh Method for a Non-Local Thermistor Problem","license":"","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.AP","authors_text":"Abderrahmane El Hachimi, Delfim F.M. Torres, Moulay Rchid Sidi Ammi","submitted_at":"2006-06-02T08:17:54Z","abstract_excerpt":"We use a dual mesh numerical method to study a non-local parabolic problem arising from the well-known thermistor problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606045","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0606045/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T22:06:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hFA1HNGJxuxw23/bMFmBG9brQ5KrREk6pUGGwBbEdPR9R17fyeaiX1+ApOlLmoWfyShxWjsxWZheiRKV1LwADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:00:23.280288Z"},"content_sha256":"50e49fa9ab3ac98ced78cf446e1680a5802a2235ed173ae95f26f6fde3e99375","schema_version":"1.0","event_id":"sha256:50e49fa9ab3ac98ced78cf446e1680a5802a2235ed173ae95f26f6fde3e99375"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ/bundle.json","state_url":"https://pith.science/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ/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":"2026-06-21T08:00:23Z","links":{"resolver":"https://pith.science/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ","bundle":"https://pith.science/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ/bundle.json","state":"https://pith.science/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5VZQHNIES2YEXD3EQC7KH7SSLQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:5VZQHNIES2YEXD3EQC7KH7SSLQ","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":"0e85ca943236ef2297343cfb399de24af4515af1d4bb5affd87645c83df3ddde","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AP","submitted_at":"2006-06-02T08:17:54Z","title_canon_sha256":"c2f64edb267d0f3ecc24e384d70fa8edc810d0b58fd606fc64e1c2ed4d52c119"},"schema_version":"1.0","source":{"id":"math/0606045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0606045","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0606045v1","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0606045","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"5VZQHNIES2YE","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_16","alias_value":"5VZQHNIES2YEXD3E","created_at":"2026-06-03T22:06:19Z"},{"alias_kind":"pith_short_8","alias_value":"5VZQHNIE","created_at":"2026-06-03T22:06:19Z"}],"graph_snapshots":[{"event_id":"sha256:50e49fa9ab3ac98ced78cf446e1680a5802a2235ed173ae95f26f6fde3e99375","target":"graph","created_at":"2026-06-03T22:06:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0606045/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use a dual mesh numerical method to study a non-local parabolic problem arising from the well-known thermistor problem.","authors_text":"Abderrahmane El Hachimi, Delfim F.M. Torres, Moulay Rchid Sidi Ammi","cross_cats":["cs.NA","math.NA"],"headline":"","license":"","primary_cat":"math.AP","submitted_at":"2006-06-02T08:17:54Z","title":"A Dual Mesh Method for a Non-Local Thermistor Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0606045","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":"sha256:4423d63911fece648664370d3d033f4322dc8e096419072138a95a773ee70b22","target":"record","created_at":"2026-06-03T22:06:19Z","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":"0e85ca943236ef2297343cfb399de24af4515af1d4bb5affd87645c83df3ddde","cross_cats_sorted":["cs.NA","math.NA"],"license":"","primary_cat":"math.AP","submitted_at":"2006-06-02T08:17:54Z","title_canon_sha256":"c2f64edb267d0f3ecc24e384d70fa8edc810d0b58fd606fc64e1c2ed4d52c119"},"schema_version":"1.0","source":{"id":"math/0606045","kind":"arxiv","version":1}},"canonical_sha256":"ed7303b50496b04b8f6480bea3fe525c02c52bee005bc03f57cd74d07f4e1352","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ed7303b50496b04b8f6480bea3fe525c02c52bee005bc03f57cd74d07f4e1352","first_computed_at":"2026-06-03T22:06:19.815791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:19.815791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hWbq305PXllqGLkzYsRUXuxj8MIrPd6DBo4g+ZuyY7mPxdOXu2PtwweqZHnb/5UVln2fyJPn5Ir4lSzxZJIlDg==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:19.816219Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0606045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4423d63911fece648664370d3d033f4322dc8e096419072138a95a773ee70b22","sha256:50e49fa9ab3ac98ced78cf446e1680a5802a2235ed173ae95f26f6fde3e99375"],"state_sha256":"272a959895526796062b99a90b6a4ca28a2c8c73ddd66885d7eb10ea005bf750"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8FMvctXijhy035nW04X4iqyp9iux00mO8zF/qhW4JWZo5MpOs6XKozbLVPXui6uxpeiKTDk9SuadeE0wu6z5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:00:23.282246Z","bundle_sha256":"42b6483ce44d2bb55f5667a7db5ae95fdd980da6f92965eb55f38f3e49a7b1d3"}}