{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XWMTTOQWZIY2HU4OIAYK7KJTDR","short_pith_number":"pith:XWMTTOQW","canonical_record":{"source":{"id":"1206.6315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-27T15:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"ce45c81faf49544431e86b1b7e9e272ea2734ae5963e6dae45659afc76f85651","abstract_canon_sha256":"3025e3a3d71e95df71d4cb5fd36fd7a57b63579178c3bd45f0b090995bf9e910"},"schema_version":"1.0"},"canonical_sha256":"bd9939ba16ca31a3d38e4030afa9331c4c77cd8bc1f568bb199f2991dbd8bd02","source":{"kind":"arxiv","id":"1206.6315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6315","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6315v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6315","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"XWMTTOQWZIY2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XWMTTOQWZIY2HU4O","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XWMTTOQW","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XWMTTOQWZIY2HU4OIAYK7KJTDR","target":"record","payload":{"canonical_record":{"source":{"id":"1206.6315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-27T15:54:00Z","cross_cats_sorted":[],"title_canon_sha256":"ce45c81faf49544431e86b1b7e9e272ea2734ae5963e6dae45659afc76f85651","abstract_canon_sha256":"3025e3a3d71e95df71d4cb5fd36fd7a57b63579178c3bd45f0b090995bf9e910"},"schema_version":"1.0"},"canonical_sha256":"bd9939ba16ca31a3d38e4030afa9331c4c77cd8bc1f568bb199f2991dbd8bd02","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:27.010718Z","signature_b64":"++Gg0FIofLjVAJC62ia+HDTMy9JBpeOYospijJIxuTl8ADW4iepN4v02uxRVid1jOVMtDb/4bgYLJ0Td4sxODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd9939ba16ca31a3d38e4030afa9331c4c77cd8bc1f568bb199f2991dbd8bd02","last_reissued_at":"2026-05-18T03:52:27.009859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:27.009859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.6315","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":"2026-05-18T03:52:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U9no8zB+k8CFG45kkbXYLuxxHlfXJl21nSCExzu7a15Zxz9Ei9k4oME/zU+Hx+JDkconEG7UVje+rNt7Mw2tAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:21:14.879142Z"},"content_sha256":"d13a6aedaac62f71f3a33865cf71534f170121dbc9db4ad05edebfdb728d0e58","schema_version":"1.0","event_id":"sha256:d13a6aedaac62f71f3a33865cf71534f170121dbc9db4ad05edebfdb728d0e58"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XWMTTOQWZIY2HU4OIAYK7KJTDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary perturbations due to the presence of small linear cracks in an elastic body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Habib Ammari, Hyeonbae Kang, Hyundae Lee, Jisun Lim","submitted_at":"2012-06-27T15:54:00Z","abstract_excerpt":"In this paper, Neumann cracks in elastic bodies are considered. We establish a rigorous asymptotic expansion for the boundary perturbations of the displacement (and traction) vectors that are due to the presence of a small elastic linear crack. The formula reveals that the leading order term is \\epsilon^2 where \\epsilon is the length of the crack, and the \\epsilon^3-term vanishes. We obtain an asymptotic expansion of the elastic potential energy as an immediate consequence of the boundary perturbation formula. The derivation is based on layer potential techniques. It is expected that the formu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6315","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":"2026-05-18T03:52:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkVtVm8yDSe8+wocet35WvwELxFIqyeMI0bb8dcoNW3t/OSKYugJ7so29U+iiT70U/xK1tsM2cPEzSecowqWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T11:21:14.879848Z"},"content_sha256":"39af9b03e7f32486011176d2d191ed4dc09ab5f8e995cd13c076479fa2100229","schema_version":"1.0","event_id":"sha256:39af9b03e7f32486011176d2d191ed4dc09ab5f8e995cd13c076479fa2100229"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR/bundle.json","state_url":"https://pith.science/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR/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":"2026-05-27T11:21:14Z","links":{"resolver":"https://pith.science/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR","bundle":"https://pith.science/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR/bundle.json","state":"https://pith.science/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XWMTTOQWZIY2HU4OIAYK7KJTDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XWMTTOQWZIY2HU4OIAYK7KJTDR","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":"3025e3a3d71e95df71d4cb5fd36fd7a57b63579178c3bd45f0b090995bf9e910","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-27T15:54:00Z","title_canon_sha256":"ce45c81faf49544431e86b1b7e9e272ea2734ae5963e6dae45659afc76f85651"},"schema_version":"1.0","source":{"id":"1206.6315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.6315","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"arxiv_version","alias_value":"1206.6315v1","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.6315","created_at":"2026-05-18T03:52:27Z"},{"alias_kind":"pith_short_12","alias_value":"XWMTTOQWZIY2","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XWMTTOQWZIY2HU4O","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XWMTTOQW","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:39af9b03e7f32486011176d2d191ed4dc09ab5f8e995cd13c076479fa2100229","target":"graph","created_at":"2026-05-18T03:52:27Z","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, Neumann cracks in elastic bodies are considered. We establish a rigorous asymptotic expansion for the boundary perturbations of the displacement (and traction) vectors that are due to the presence of a small elastic linear crack. The formula reveals that the leading order term is \\epsilon^2 where \\epsilon is the length of the crack, and the \\epsilon^3-term vanishes. We obtain an asymptotic expansion of the elastic potential energy as an immediate consequence of the boundary perturbation formula. The derivation is based on layer potential techniques. It is expected that the formu","authors_text":"Habib Ammari, Hyeonbae Kang, Hyundae Lee, Jisun Lim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-27T15:54:00Z","title":"Boundary perturbations due to the presence of small linear cracks in an elastic body"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6315","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:d13a6aedaac62f71f3a33865cf71534f170121dbc9db4ad05edebfdb728d0e58","target":"record","created_at":"2026-05-18T03:52:27Z","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":"3025e3a3d71e95df71d4cb5fd36fd7a57b63579178c3bd45f0b090995bf9e910","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-27T15:54:00Z","title_canon_sha256":"ce45c81faf49544431e86b1b7e9e272ea2734ae5963e6dae45659afc76f85651"},"schema_version":"1.0","source":{"id":"1206.6315","kind":"arxiv","version":1}},"canonical_sha256":"bd9939ba16ca31a3d38e4030afa9331c4c77cd8bc1f568bb199f2991dbd8bd02","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd9939ba16ca31a3d38e4030afa9331c4c77cd8bc1f568bb199f2991dbd8bd02","first_computed_at":"2026-05-18T03:52:27.009859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:27.009859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"++Gg0FIofLjVAJC62ia+HDTMy9JBpeOYospijJIxuTl8ADW4iepN4v02uxRVid1jOVMtDb/4bgYLJ0Td4sxODg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:27.010718Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.6315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d13a6aedaac62f71f3a33865cf71534f170121dbc9db4ad05edebfdb728d0e58","sha256:39af9b03e7f32486011176d2d191ed4dc09ab5f8e995cd13c076479fa2100229"],"state_sha256":"6859d81add1db41027de903d17693954736fa98d7b1a9735285dfbb6e95503f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A/9zgPqHak4pWEASndB6gD5BOBkuRVgnSIe+K+TBVFzFpLgjsTKhBw0OI8JILMg2H5hjT+JBojrronojSwroCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T11:21:14.883700Z","bundle_sha256":"11d3155936f6300bc881e4254a02629a56ba46287d0e3eecec88cb3f40de16ca"}}