{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:U2TXMNSWIA4Q5WONEYK4O2GHLY","short_pith_number":"pith:U2TXMNSW","canonical_record":{"source":{"id":"1110.4796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-21T14:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"226e0ee0a341b8e48cbcb2868e932a76b7530da82529b8e378953f8bbd0e44a6","abstract_canon_sha256":"4d222d7eb544fb2848e1175868cf44216857411fdc6df8ff9bc09d1740a8171d"},"schema_version":"1.0"},"canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","source":{"kind":"arxiv","id":"1110.4796","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4796","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4796v2","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4796","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"pith_short_12","alias_value":"U2TXMNSWIA4Q","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2TXMNSWIA4Q5WON","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2TXMNSW","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:U2TXMNSWIA4Q5WONEYK4O2GHLY","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4796","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-21T14:03:53Z","cross_cats_sorted":[],"title_canon_sha256":"226e0ee0a341b8e48cbcb2868e932a76b7530da82529b8e378953f8bbd0e44a6","abstract_canon_sha256":"4d222d7eb544fb2848e1175868cf44216857411fdc6df8ff9bc09d1740a8171d"},"schema_version":"1.0"},"canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:05.064659Z","signature_b64":"uS7J407RCpf8OxprqH2GJtriYpg7SyPXr+FN8NfmtMvqVgZqEPYJkbKy3WoCzXXbO6L0k8/LDjhy8QIanzCtBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","last_reissued_at":"2026-05-18T04:07:05.063975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:05.063975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4796","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fJ7ona8R37/DimQUrviST6RcNlHhdroRksyif644np3Lmw6C1PARTfBXW/PC8qU/agivqRwtqQDyAumNpfQ9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:59:48.696393Z"},"content_sha256":"9c266254dabcdea32d38bddcb74085f15f7e7211ec1c57cdf5cb880b33fb6920","schema_version":"1.0","event_id":"sha256:9c266254dabcdea32d38bddcb74085f15f7e7211ec1c57cdf5cb880b33fb6920"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:U2TXMNSWIA4Q5WONEYK4O2GHLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Antoine Lemenant (LJLL), Antonin Chambolle (CMAP)","submitted_at":"2011-10-21T14:03:53Z","abstract_excerpt":"Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution $u$ of a Neumann problem near a crack in dimension 2. We consider non smooth cracks $K$ that are merely closed and connected. At any point of density 1/2 in $K$, we show that the blow-up limit of $u$ is the usual \"cracktip\" function $\\sqrt{r}\\sin(\\theta/2)$, with a well-defined coefficient (the \"stress intensity factor\" or SIF). The method relies on Bonnet's monotonicity formula \\cite{b} together with $\\Gamma$-convergence techniques."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4796","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnbGPCAYHCGS97nOAQJT5viy5lrjs8Ooc47ik2I/Ff4/5k2K6xKq1se85d3Ml0VAGylDoguMAFxyFwmHP4s2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:59:48.696757Z"},"content_sha256":"6afdfb68da9ad09eb8cb9f091f6634b63cfad99d2330bac6a177eb42d582e0f7","schema_version":"1.0","event_id":"sha256:6afdfb68da9ad09eb8cb9f091f6634b63cfad99d2330bac6a177eb42d582e0f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/bundle.json","state_url":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T04:59:48Z","links":{"resolver":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY","bundle":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/bundle.json","state":"https://pith.science/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U2TXMNSWIA4Q5WONEYK4O2GHLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:U2TXMNSWIA4Q5WONEYK4O2GHLY","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":"4d222d7eb544fb2848e1175868cf44216857411fdc6df8ff9bc09d1740a8171d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-21T14:03:53Z","title_canon_sha256":"226e0ee0a341b8e48cbcb2868e932a76b7530da82529b8e378953f8bbd0e44a6"},"schema_version":"1.0","source":{"id":"1110.4796","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4796","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4796v2","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4796","created_at":"2026-05-18T04:07:05Z"},{"alias_kind":"pith_short_12","alias_value":"U2TXMNSWIA4Q","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"U2TXMNSWIA4Q5WON","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"U2TXMNSW","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:6afdfb68da9ad09eb8cb9f091f6634b63cfad99d2330bac6a177eb42d582e0f7","target":"graph","created_at":"2026-05-18T04:07:05Z","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":"Motivated by some questions arising in the study of quasistatic growth in brittle fracture, we investigate the asymptotic behavior of the energy of the solution $u$ of a Neumann problem near a crack in dimension 2. We consider non smooth cracks $K$ that are merely closed and connected. At any point of density 1/2 in $K$, we show that the blow-up limit of $u$ is the usual \"cracktip\" function $\\sqrt{r}\\sin(\\theta/2)$, with a well-defined coefficient (the \"stress intensity factor\" or SIF). The method relies on Bonnet's monotonicity formula \\cite{b} together with $\\Gamma$-convergence techniques.","authors_text":"Antoine Lemenant (LJLL), Antonin Chambolle (CMAP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-21T14:03:53Z","title":"The Stress-Intensity Factor for nonsmooth fractures in antiplane elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4796","kind":"arxiv","version":2},"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":"sha256:9c266254dabcdea32d38bddcb74085f15f7e7211ec1c57cdf5cb880b33fb6920","target":"record","created_at":"2026-05-18T04:07:05Z","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":"4d222d7eb544fb2848e1175868cf44216857411fdc6df8ff9bc09d1740a8171d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2011-10-21T14:03:53Z","title_canon_sha256":"226e0ee0a341b8e48cbcb2868e932a76b7530da82529b8e378953f8bbd0e44a6"},"schema_version":"1.0","source":{"id":"1110.4796","kind":"arxiv","version":2}},"canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6a776365640390ed9cd2615c768c75e0252c96531a4e2172ba5d7ef6f99a496","first_computed_at":"2026-05-18T04:07:05.063975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:05.063975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uS7J407RCpf8OxprqH2GJtriYpg7SyPXr+FN8NfmtMvqVgZqEPYJkbKy3WoCzXXbO6L0k8/LDjhy8QIanzCtBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:05.064659Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4796","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c266254dabcdea32d38bddcb74085f15f7e7211ec1c57cdf5cb880b33fb6920","sha256:6afdfb68da9ad09eb8cb9f091f6634b63cfad99d2330bac6a177eb42d582e0f7"],"state_sha256":"d98af68dfe56075d8e9d561a10c8b263427818f22ffd1864963cd6ea51c53ac3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QnwujGm04kmwlmSCbmSv/3zn4Q2xuvy62i0S0G9y0ZJFAHv1lGXmSZLlvKLoSz0+t+GQJdY42HdA0pNbhqmVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T04:59:48.698834Z","bundle_sha256":"e283630c5ced795a17d98afe4676a8346733da73254822b83f817a96de2d9671"}}