{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SQYY76QZ3HTG4H54U3LKAV2UTB","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":"f55f8dcd58eecba73d4c80aacdf337b6acb791d387c2b883d35479ac9ca6fe2c","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-24T17:02:51Z","title_canon_sha256":"0295f55750293ca8406ed486bed7a75b558d0cdf598f98cfc0441d00b80f2649"},"schema_version":"1.0","source":{"id":"1602.07594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.07594","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"arxiv_version","alias_value":"1602.07594v1","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07594","created_at":"2026-05-18T01:20:02Z"},{"alias_kind":"pith_short_12","alias_value":"SQYY76QZ3HTG","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SQYY76QZ3HTG4H54","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SQYY76QZ","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:1f8ba3f25111595b5faccf769d1c778e0fb79721a670ffff50e022e31b5e80b5","target":"graph","created_at":"2026-05-18T01:20:02Z","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 study a planar thin brittle beam subject to elastic deformations and cracks described in terms of a nonlinear Griffith energy functional acting on $SBV$ deformations of the beam. In particular we consider the case in which elastic bulk contributions due to finite bending of the beam are comparable to the surface energy which is necessary to completely break the beam into several large pieces. In the limit of vanishing aspect ratio we rigorously derive an effective Griffith-Euler-Bernoulli functional which acts on piecewise $W^{2,2}$ regular curves representing the midline of the beam. The e","authors_text":"Bernd Schmidt","cross_cats":["cond-mat.mtrl-sci"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-24T17:02:51Z","title":"A Griffith-Euler-Bernoulli theory for thin brittle beams derived from nonlinear models in variational fracture mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07594","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":"sha256:5739d209cd50b58b9cd9cd1f4d41f9d69ddf090fc603c8aa3a38e7f66ae2d7dc","target":"record","created_at":"2026-05-18T01:20:02Z","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":"f55f8dcd58eecba73d4c80aacdf337b6acb791d387c2b883d35479ac9ca6fe2c","cross_cats_sorted":["cond-mat.mtrl-sci"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-02-24T17:02:51Z","title_canon_sha256":"0295f55750293ca8406ed486bed7a75b558d0cdf598f98cfc0441d00b80f2649"},"schema_version":"1.0","source":{"id":"1602.07594","kind":"arxiv","version":1}},"canonical_sha256":"94318ffa19d9e66e1fbca6d6a05754984cae59a4f1a9e93abd3149a013796c4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94318ffa19d9e66e1fbca6d6a05754984cae59a4f1a9e93abd3149a013796c4a","first_computed_at":"2026-05-18T01:20:02.547272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:02.547272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W3tQVfLfWViT16WjJnd/TrsYYlYfKAUQelppmIJ/X2pFidXJ7hxyrq6U62RCwRABGZVKNwWf2UaX9YYdiuB+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:02.547850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.07594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5739d209cd50b58b9cd9cd1f4d41f9d69ddf090fc603c8aa3a38e7f66ae2d7dc","sha256:1f8ba3f25111595b5faccf769d1c778e0fb79721a670ffff50e022e31b5e80b5"],"state_sha256":"0965f32cde2d269a899504a96f5c1b20bf7655aa57f2c8f0a3cf4650cee643c0"}