{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:7DZWAZGTSOYSKH66ZR5PLSYC72","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":"749aa2dc349e433c8133a21c691db6db9e334e2088a58674facd86a7a4ab4af5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-06T05:12:59Z","title_canon_sha256":"5602156ea7fb1cdbc904b60a2afcdbd98109a0a1dc8b0f23ce938451f10e4d24"},"schema_version":"1.0","source":{"id":"2207.02441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.02441","created_at":"2026-07-05T06:03:55Z"},{"alias_kind":"arxiv_version","alias_value":"2207.02441v1","created_at":"2026-07-05T06:03:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.02441","created_at":"2026-07-05T06:03:55Z"},{"alias_kind":"pith_short_12","alias_value":"7DZWAZGTSOYS","created_at":"2026-07-05T06:03:55Z"},{"alias_kind":"pith_short_16","alias_value":"7DZWAZGTSOYSKH66","created_at":"2026-07-05T06:03:55Z"},{"alias_kind":"pith_short_8","alias_value":"7DZWAZGT","created_at":"2026-07-05T06:03:55Z"}],"graph_snapshots":[{"event_id":"sha256:1c17d961fde81a3d754764cdc34a271cf6464566829fbe8e80e25b1b0f8d2ce1","target":"graph","created_at":"2026-07-05T06:03:55Z","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/2207.02441/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose inverse problems of crack propagation using the phase-field models. First, we study the crack propagation in an inhomogeneous media in which fracture toughness varies in space. Using the two phase-field models based on different surface energy functionals, we perform simulations of the crack propagation and show that the $J$-integral reflects the effective inhomogeneous toughness. Then, we formulate regression problems to estimate space-dependent fracture toughness from the crack path. Our method successfully estimates the positions and magnitude of tougher regions. We also demonstr","authors_text":"Natsuhiko Yoshinaga, Yueyuan Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-06T05:12:59Z","title":"Inverse problems of inhomogeneous fracture toughness using phase-field models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.02441","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":"sha256:0d09d520197ae7b8a5861005b3afd062f6415c0fcd3941577f607f1c74396f62","target":"record","created_at":"2026-07-05T06:03:55Z","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":"749aa2dc349e433c8133a21c691db6db9e334e2088a58674facd86a7a4ab4af5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2022-07-06T05:12:59Z","title_canon_sha256":"5602156ea7fb1cdbc904b60a2afcdbd98109a0a1dc8b0f23ce938451f10e4d24"},"schema_version":"1.0","source":{"id":"2207.02441","kind":"arxiv","version":1}},"canonical_sha256":"f8f36064d393b1251fdecc7af5cb02fe8fd08a248395bd2ba39c081739987457","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f8f36064d393b1251fdecc7af5cb02fe8fd08a248395bd2ba39c081739987457","first_computed_at":"2026-07-05T06:03:55.487002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:03:55.487002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YL98MV3I2/TfPc81G+/aB4p700u7M669p6tmJUOnEIYqSuhuRvVSbXq7PXlczaL0iWvmpwgq86F+eL1J9Qg0DA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:03:55.487407Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.02441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d09d520197ae7b8a5861005b3afd062f6415c0fcd3941577f607f1c74396f62","sha256:1c17d961fde81a3d754764cdc34a271cf6464566829fbe8e80e25b1b0f8d2ce1"],"state_sha256":"471d27de1af78d83c0f743425c51d0390ff27d20ea7090ff55a18476ae0b22c6"}