{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:KFHETBASZMWTEH3O2HSWN7XISQ","short_pith_number":"pith:KFHETBAS","schema_version":"1.0","canonical_sha256":"514e498412cb2d321f6ed1e566fee89425e0bca62e0b8ff4df363cfbc2e53fed","source":{"kind":"arxiv","id":"2408.03776","version":1},"attestation_state":"computed","paper":{"title":"An elliptic approximation for phase separation in a fractured material","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kerrek Stinson, Solveig Wittig","submitted_at":"2024-08-07T14:01:26Z","abstract_excerpt":"We consider a free-boundary and free-discontinuity energy connecting phase separation and fracture in an elastic material. The energy excludes the contribution of phase boundaries in the cracked region, providing a heuristic approximation of the interfacial energy in the current material configuration. Our primary result shows that the sharp energy may be recovered via Gamma-convergence from a modified Cahn-Hilliard energy coupled with an Ambrosio-Tortorelli-type approximation of the (linear) elastic and fracture energy."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2408.03776","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-08-07T14:01:26Z","cross_cats_sorted":[],"title_canon_sha256":"bb93f4062223da9cc75f91ec439d0f52fb159f98030ea072658867ccf621b757","abstract_canon_sha256":"9677ae760b8140d7c195d68baafbcdd5184f8fe5abaa16824709ba67dc86a888"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:53:11.000651Z","signature_b64":"FTweDUjM6i+8Rp8BW5AwKGZAXLRaLPkXh3bwTJnXzTtzPKAqHBxIUsn0PK3CqOFuICo234zzT2885TdQD4xEAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"514e498412cb2d321f6ed1e566fee89425e0bca62e0b8ff4df363cfbc2e53fed","last_reissued_at":"2026-07-05T08:53:11.000266Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:53:11.000266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An elliptic approximation for phase separation in a fractured material","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kerrek Stinson, Solveig Wittig","submitted_at":"2024-08-07T14:01:26Z","abstract_excerpt":"We consider a free-boundary and free-discontinuity energy connecting phase separation and fracture in an elastic material. The energy excludes the contribution of phase boundaries in the cracked region, providing a heuristic approximation of the interfacial energy in the current material configuration. Our primary result shows that the sharp energy may be recovered via Gamma-convergence from a modified Cahn-Hilliard energy coupled with an Ambrosio-Tortorelli-type approximation of the (linear) elastic and fracture energy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.03776","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/2408.03776/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2408.03776","created_at":"2026-07-05T08:53:11.000322+00:00"},{"alias_kind":"arxiv_version","alias_value":"2408.03776v1","created_at":"2026-07-05T08:53:11.000322+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.03776","created_at":"2026-07-05T08:53:11.000322+00:00"},{"alias_kind":"pith_short_12","alias_value":"KFHETBASZMWT","created_at":"2026-07-05T08:53:11.000322+00:00"},{"alias_kind":"pith_short_16","alias_value":"KFHETBASZMWTEH3O","created_at":"2026-07-05T08:53:11.000322+00:00"},{"alias_kind":"pith_short_8","alias_value":"KFHETBAS","created_at":"2026-07-05T08:53:11.000322+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.16308","citing_title":"Compactness for $GSBV^p$ via concentration-compactness","ref_index":17,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ","json":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ.json","graph_json":"https://pith.science/api/pith-number/KFHETBASZMWTEH3O2HSWN7XISQ/graph.json","events_json":"https://pith.science/api/pith-number/KFHETBASZMWTEH3O2HSWN7XISQ/events.json","paper":"https://pith.science/paper/KFHETBAS"},"agent_actions":{"view_html":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ","download_json":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ.json","view_paper":"https://pith.science/paper/KFHETBAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2408.03776&json=true","fetch_graph":"https://pith.science/api/pith-number/KFHETBASZMWTEH3O2HSWN7XISQ/graph.json","fetch_events":"https://pith.science/api/pith-number/KFHETBASZMWTEH3O2HSWN7XISQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ/action/storage_attestation","attest_author":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ/action/author_attestation","sign_citation":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ/action/citation_signature","submit_replication":"https://pith.science/pith/KFHETBASZMWTEH3O2HSWN7XISQ/action/replication_record"}},"created_at":"2026-07-05T08:53:11.000322+00:00","updated_at":"2026-07-05T08:53:11.000322+00:00"}