{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PQXBVICDZO5SPIXTTYRHUGAR36","short_pith_number":"pith:PQXBVICD","canonical_record":{"source":{"id":"1406.6981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-26T18:52:21Z","cross_cats_sorted":[],"title_canon_sha256":"eb831554c50ff70eecf9a6c5dd7a8377208b875a168cb9181fa86f869ba53e58","abstract_canon_sha256":"a4fba2a749107b82be38528ec7d8dfd5b2e18cc77d601d7ecc655fd06f1540fb"},"schema_version":"1.0"},"canonical_sha256":"7c2e1aa043cbbb27a2f39e227a1811df8f7c89f7063bcd17fa983694b3e718d3","source":{"kind":"arxiv","id":"1406.6981","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6981","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6981v1","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6981","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"PQXBVICDZO5S","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQXBVICDZO5SPIXT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQXBVICD","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PQXBVICDZO5SPIXTTYRHUGAR36","target":"record","payload":{"canonical_record":{"source":{"id":"1406.6981","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-26T18:52:21Z","cross_cats_sorted":[],"title_canon_sha256":"eb831554c50ff70eecf9a6c5dd7a8377208b875a168cb9181fa86f869ba53e58","abstract_canon_sha256":"a4fba2a749107b82be38528ec7d8dfd5b2e18cc77d601d7ecc655fd06f1540fb"},"schema_version":"1.0"},"canonical_sha256":"7c2e1aa043cbbb27a2f39e227a1811df8f7c89f7063bcd17fa983694b3e718d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:55.357511Z","signature_b64":"gBDkaUmP8F2VTjYX2K861uxoHFIt55FyFjE8N5NIYAkKC+XFLzpdZl4RcSS5N8+fr8rpAh0qC3gPr4LZJmsnCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c2e1aa043cbbb27a2f39e227a1811df8f7c89f7063bcd17fa983694b3e718d3","last_reissued_at":"2026-05-18T02:48:55.356980Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:55.356980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.6981","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6lF9ymLR+AkHoiRSxhMSI4v9AXCcGcIG1LnKbMTVXsW032PxN6dEOlu9lRe6X21FIwk+6BIkWVHiW/YRTfMwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:01:55.552017Z"},"content_sha256":"7551c2863f8367fddb3fa660daf9858646381384e0427e73d472d63ac86da207","schema_version":"1.0","event_id":"sha256:7551c2863f8367fddb3fa660daf9858646381384e0427e73d472d63ac86da207"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PQXBVICDZO5SPIXTTYRHUGAR36","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Energy release rate for non smooth cracks in planar elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antoine Lemenant (LJLL), Antonin Chambolle (CMAP), Jean-Fran\\c{c}ois Babadjian (LJLL)","submitted_at":"2014-06-26T18:52:21Z","abstract_excerpt":"This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density $1/2$ at the tip. First, the blow-up limit of the displacement is analyzed, and the convergence to the corresponding positively $1/2$-homogenous function in the cracked plane is established. Then, the energy release rate is obtained as the derivative of the elastic energy with respect to an infinitesimal additional crack increment."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6981","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":""},"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":"2026-05-18T02:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R7u+51USFOIWhMengoCDhiikPUyURES05YcZVLCq7e7bwAP138qvm03GlysWs9jGg+MnhBEawmxYo2ZHfkiBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:01:55.552363Z"},"content_sha256":"067a20d26e24681454ad5e704ee71cd1dc3977a9911b072ffc90604685119c74","schema_version":"1.0","event_id":"sha256:067a20d26e24681454ad5e704ee71cd1dc3977a9911b072ffc90604685119c74"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQXBVICDZO5SPIXTTYRHUGAR36/bundle.json","state_url":"https://pith.science/pith/PQXBVICDZO5SPIXTTYRHUGAR36/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQXBVICDZO5SPIXTTYRHUGAR36/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":"2026-06-21T06:01:55Z","links":{"resolver":"https://pith.science/pith/PQXBVICDZO5SPIXTTYRHUGAR36","bundle":"https://pith.science/pith/PQXBVICDZO5SPIXTTYRHUGAR36/bundle.json","state":"https://pith.science/pith/PQXBVICDZO5SPIXTTYRHUGAR36/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQXBVICDZO5SPIXTTYRHUGAR36/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PQXBVICDZO5SPIXTTYRHUGAR36","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":"a4fba2a749107b82be38528ec7d8dfd5b2e18cc77d601d7ecc655fd06f1540fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-26T18:52:21Z","title_canon_sha256":"eb831554c50ff70eecf9a6c5dd7a8377208b875a168cb9181fa86f869ba53e58"},"schema_version":"1.0","source":{"id":"1406.6981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6981","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6981v1","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6981","created_at":"2026-05-18T02:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"PQXBVICDZO5S","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQXBVICDZO5SPIXT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQXBVICD","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:067a20d26e24681454ad5e704ee71cd1dc3977a9911b072ffc90604685119c74","target":"graph","created_at":"2026-05-18T02:48:55Z","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"},"paper":{"abstract_excerpt":"This paper is devoted to the characterization of the energy release rate of a crack which is merely closed, connected, and with density $1/2$ at the tip. First, the blow-up limit of the displacement is analyzed, and the convergence to the corresponding positively $1/2$-homogenous function in the cracked plane is established. Then, the energy release rate is obtained as the derivative of the elastic energy with respect to an infinitesimal additional crack increment.","authors_text":"Antoine Lemenant (LJLL), Antonin Chambolle (CMAP), Jean-Fran\\c{c}ois Babadjian (LJLL)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-26T18:52:21Z","title":"Energy release rate for non smooth cracks in planar elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6981","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":"sha256:7551c2863f8367fddb3fa660daf9858646381384e0427e73d472d63ac86da207","target":"record","created_at":"2026-05-18T02:48:55Z","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":"a4fba2a749107b82be38528ec7d8dfd5b2e18cc77d601d7ecc655fd06f1540fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-06-26T18:52:21Z","title_canon_sha256":"eb831554c50ff70eecf9a6c5dd7a8377208b875a168cb9181fa86f869ba53e58"},"schema_version":"1.0","source":{"id":"1406.6981","kind":"arxiv","version":1}},"canonical_sha256":"7c2e1aa043cbbb27a2f39e227a1811df8f7c89f7063bcd17fa983694b3e718d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c2e1aa043cbbb27a2f39e227a1811df8f7c89f7063bcd17fa983694b3e718d3","first_computed_at":"2026-05-18T02:48:55.356980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:55.356980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gBDkaUmP8F2VTjYX2K861uxoHFIt55FyFjE8N5NIYAkKC+XFLzpdZl4RcSS5N8+fr8rpAh0qC3gPr4LZJmsnCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:55.357511Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7551c2863f8367fddb3fa660daf9858646381384e0427e73d472d63ac86da207","sha256:067a20d26e24681454ad5e704ee71cd1dc3977a9911b072ffc90604685119c74"],"state_sha256":"00c57aeb9978715be0d4b8e94d61b960f72224711d2769293e8353e0e3b1ee37"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fAuUjdMJkJTtKD4LbJFcxRV1uX6tXtNrXBiiL/UvDRpDgtPv1YX83YlgU1R03w2jExK5+KxITXyrS82nTmklCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:01:55.554223Z","bundle_sha256":"ea39df5be950b18dbe2d6d3c5ec41ea8970d6ce40cf03e25a0601539e13bbba9"}}