{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:EBY4X2LKMFVGFA5X5344KORFO6","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":"e90fbe1e24a92a63e4cb1a4b03f39ed20a3ae3710d4b1ae49c537ae6158946da","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-24T20:21:02Z","title_canon_sha256":"38d465bf6525e32a2aca6b3d10613cad9f908d274dd86ba004d5b9746610c0c1"},"schema_version":"1.0","source":{"id":"0812.4529","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4529","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4529v5","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4529","created_at":"2026-05-18T02:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"EBY4X2LKMFVG","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"EBY4X2LKMFVGFA5X","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"EBY4X2LK","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:5435ac9e2bb20a083ca97801db3e304a1f4b87c8e7a7425c02330e60ec808a3c","target":"graph","created_at":"2026-05-18T02:15:03Z","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":"In this paper we address the vector problem of a 2D half-plane interfacial crack loaded by a general asymmetric distribution of forces acting on its faces. It is shown that the general integral formula for the evaluation of stress intensity factors, as well as high-order terms, requires both symmetric and skew-symmetric weight function matrices. The symmetric weight function matrix is obtained via the solution of a Wiener-Hopf functional equation, whereas the derivation of the skew-symmetric weight function matrix requires the construction of the corresponding full field singular solution. The","authors_text":"A.B. Movchan, A. Piccolroaz, G. Mishuris","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-24T20:21:02Z","title":"Symmetric and skew-symmetric weight functions in perturbation models of 2D interfacial cracks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4529","kind":"arxiv","version":5},"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:c3881e8b649adb71d7ba948cb5fa4da835da09112bd5d2f79f6048f925f86701","target":"record","created_at":"2026-05-18T02:15:03Z","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":"e90fbe1e24a92a63e4cb1a4b03f39ed20a3ae3710d4b1ae49c537ae6158946da","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2008-12-24T20:21:02Z","title_canon_sha256":"38d465bf6525e32a2aca6b3d10613cad9f908d274dd86ba004d5b9746610c0c1"},"schema_version":"1.0","source":{"id":"0812.4529","kind":"arxiv","version":5}},"canonical_sha256":"2071cbe96a616a6283b7eef9c53a2577850ae195477b55ba29eeefa5ef384ba1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2071cbe96a616a6283b7eef9c53a2577850ae195477b55ba29eeefa5ef384ba1","first_computed_at":"2026-05-18T02:15:03.874630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:15:03.874630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M32O40YMG6gBgxRtG05wMewLQEL1jWBTJTmCHL+xwaHq6bH8y2iqZqth4K1nysW6PS+5Bjk9VO1UnehuHMzzCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:15:03.875009Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4529","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3881e8b649adb71d7ba948cb5fa4da835da09112bd5d2f79f6048f925f86701","sha256:5435ac9e2bb20a083ca97801db3e304a1f4b87c8e7a7425c02330e60ec808a3c"],"state_sha256":"e908d48e0d29ef43914b388f7e5f40e0b11c3941cd953473e44d5572e71677c6"}