{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O2PT4GBNWGU6MFUQW3QQDNI6BZ","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":"92df5ebfc89b964e0b4390ca0455b74ca3daf55eb993f9d911b38059a1e3e734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-21T06:50:40Z","title_canon_sha256":"8a5e293a05a4bff8618956d2b5413a4c4c779c7d07334a27b398a5d951b3d872"},"schema_version":"1.0","source":{"id":"1804.07902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.07902","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"1804.07902v1","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.07902","created_at":"2026-05-18T00:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"O2PT4GBNWGU6","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"O2PT4GBNWGU6MFUQ","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"O2PT4GBN","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:dc4768f1c7c72773057d4f3f51839cb708fe517d104754269a455169ec8a7701","target":"graph","created_at":"2026-05-18T00:07:07Z","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 present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio-Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of","authors_text":"Giuliano Lazzaroni, Marita Thomas, Riccarda Rossi, Rodica Toader","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-21T06:50:40Z","title":"Rate-independent damage in thermo-viscoelastic materials with inertia"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.07902","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":"sha256:89319e729534a0e1d6d5685b9a5a8eb523b3b7aff95230924cf5e4fbc3010264","target":"record","created_at":"2026-05-18T00:07:07Z","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":"92df5ebfc89b964e0b4390ca0455b74ca3daf55eb993f9d911b38059a1e3e734","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-21T06:50:40Z","title_canon_sha256":"8a5e293a05a4bff8618956d2b5413a4c4c779c7d07334a27b398a5d951b3d872"},"schema_version":"1.0","source":{"id":"1804.07902","kind":"arxiv","version":1}},"canonical_sha256":"769f3e182db1a9e61690b6e101b51e0e476f9a8323e785323a247e6569c2f8f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769f3e182db1a9e61690b6e101b51e0e476f9a8323e785323a247e6569c2f8f0","first_computed_at":"2026-05-18T00:07:07.669746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:07.669746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Bj+KTYfpbasm1KW9gso16XStv4wNN7ls3Md5Cx41ltKauAQxpvb6rz3ylovAj7EP5MIP3S4kMFYvjgLIPhmbDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:07.670395Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.07902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89319e729534a0e1d6d5685b9a5a8eb523b3b7aff95230924cf5e4fbc3010264","sha256:dc4768f1c7c72773057d4f3f51839cb708fe517d104754269a455169ec8a7701"],"state_sha256":"a56b2d131f21f3f9479ede966931456d12c5132285e0cf769edfd407dc518821"}