{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MDSYUFJ73VE2LLOWUKUWSX3VYC","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":"e0b851a48caebc6255f486c92cfb3af27353eeae9c9c5b730e87abead89d1c38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-18T16:00:24Z","title_canon_sha256":"41a590248250b0b2fce380b757a21a8efc64beab2f26e1c9e35383c0c2be341d"},"schema_version":"1.0","source":{"id":"1107.3485","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.3485","created_at":"2026-05-18T04:18:03Z"},{"alias_kind":"arxiv_version","alias_value":"1107.3485v1","created_at":"2026-05-18T04:18:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.3485","created_at":"2026-05-18T04:18:03Z"},{"alias_kind":"pith_short_12","alias_value":"MDSYUFJ73VE2","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MDSYUFJ73VE2LLOW","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MDSYUFJ7","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:7ac7db85459335a868f6dc421e933ae421c700a745a0a7042d384a3ba2694ea3","target":"graph","created_at":"2026-05-18T04:18:03Z","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 deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first one is deduced from a balance law for entropy and it describes the evolution of the absolute temperature; the other one is an equilibrium equation for microforces and it regulates the behaviour of a scalar phase parameter. Moreover, the second equation shows a time-relaxation coefficient related to the time-derivative of the phase parameter.\n  We prove well-posedness of solution to the given system, using a","authors_text":"Manuela Girotti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-18T16:00:24Z","title":"Time relaxation of a phase-field model with entropy balance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.3485","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":"sha256:4ba7692c3b0c24cb0143e63a0098b6f6521be6634b8365bd074d888791ef38e0","target":"record","created_at":"2026-05-18T04:18:03Z","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":"e0b851a48caebc6255f486c92cfb3af27353eeae9c9c5b730e87abead89d1c38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-18T16:00:24Z","title_canon_sha256":"41a590248250b0b2fce380b757a21a8efc64beab2f26e1c9e35383c0c2be341d"},"schema_version":"1.0","source":{"id":"1107.3485","kind":"arxiv","version":1}},"canonical_sha256":"60e58a153fdd49a5add6a2a9695f75c0a8f24786378e661850f4db7507b1a36a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60e58a153fdd49a5add6a2a9695f75c0a8f24786378e661850f4db7507b1a36a","first_computed_at":"2026-05-18T04:18:03.016394Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:03.016394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZWr+sNcSDgnmy4TTW/7jae0dUfn1KBTbAIXw8rjCf6BC5AvnVe2cO5mKcjcV/86YzEWN9dgJpnHOFFHRpKSVBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:03.018915Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.3485","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ba7692c3b0c24cb0143e63a0098b6f6521be6634b8365bd074d888791ef38e0","sha256:7ac7db85459335a868f6dc421e933ae421c700a745a0a7042d384a3ba2694ea3"],"state_sha256":"f481390e0ab51884cbf6dfc5cca1a88518a39e7007bac91d2e22cccb986e9a0f"}