{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:FMNDTB33RXE2IQSTANJIYZIUI6","short_pith_number":"pith:FMNDTB33","canonical_record":{"source":{"id":"1110.3612","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T08:57:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4689daefa766b7da7b82e363c143c4421d04e75c9c7bc9745fdbd97ec9d5e161","abstract_canon_sha256":"6f40896c80896185ecc0e59a7c13b53aae2adbe1208965987740cc6ed0f90267"},"schema_version":"1.0"},"canonical_sha256":"2b1a39877b8dc9a4425303528c651447b7c9ea25d7a8a059960401908cbc577f","source":{"kind":"arxiv","id":"1110.3612","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3612","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3612v3","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3612","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"FMNDTB33RXE2","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMNDTB33RXE2IQST","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMNDTB33","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:FMNDTB33RXE2IQSTANJIYZIUI6","target":"record","payload":{"canonical_record":{"source":{"id":"1110.3612","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T08:57:19Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"4689daefa766b7da7b82e363c143c4421d04e75c9c7bc9745fdbd97ec9d5e161","abstract_canon_sha256":"6f40896c80896185ecc0e59a7c13b53aae2adbe1208965987740cc6ed0f90267"},"schema_version":"1.0"},"canonical_sha256":"2b1a39877b8dc9a4425303528c651447b7c9ea25d7a8a059960401908cbc577f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:15.049601Z","signature_b64":"KA/RFjESegH3OqFnsMXSKi4YqsifKXzIjRIJfYRbberIcZwCLDIUtIqebkMoNlA+ihVx8rEnLdSed/FJLSOkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b1a39877b8dc9a4425303528c651447b7c9ea25d7a8a059960401908cbc577f","last_reissued_at":"2026-05-18T03:54:15.049042Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:15.049042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.3612","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8Z3x+LreIo+YmoIlRlSaMeG4BO1cCtZHTfrMt+Ni/5iZFryb1eI06BLUbpDGwlxPuQlmzg7IL1LC/HUGk6dtDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:48:07.638902Z"},"content_sha256":"ba0c8e04c4bad7ae2abe6b4e75ff87c09c95f8cb706fcaba1e6b4fac022977c9","schema_version":"1.0","event_id":"sha256:ba0c8e04c4bad7ae2abe6b4e75ff87c09c95f8cb706fcaba1e6b4fac022977c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:FMNDTB33RXE2IQSTANJIYZIUI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral identities for a semi-infinite interfacial crack in 2D and 3D elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Andrea Piccolroaz, Gennady Mishuris","submitted_at":"2011-10-17T08:57:19Z","abstract_excerpt":"The paper is concerned with the problem of a semi-infinite crack at the interface between two dissimilar elastic half-spaces, loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity (Betti formula), we formulate the elasticity problem in terms of singular integral equations relating the applied loading and the resulting crack opening. Such formulation is fundamental in the theory of elasticity and extensively used to solve several problems in linear elastic fracture mechanics (for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3612","kind":"arxiv","version":3},"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":"2026-05-18T03:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dG53DHRZMzBPlyACR+HOIawSv2+SxMPlAzjG1IUJvq3M583blsqnWr1FL3/b983EqOseNplDMK40609U73G8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T04:48:07.639259Z"},"content_sha256":"201442ca58019e50070b5d854e8daa9bfe78bbdd77ff31ec84341c4c5faf6793","schema_version":"1.0","event_id":"sha256:201442ca58019e50070b5d854e8daa9bfe78bbdd77ff31ec84341c4c5faf6793"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FMNDTB33RXE2IQSTANJIYZIUI6/bundle.json","state_url":"https://pith.science/pith/FMNDTB33RXE2IQSTANJIYZIUI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FMNDTB33RXE2IQSTANJIYZIUI6/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":"2026-06-01T04:48:07Z","links":{"resolver":"https://pith.science/pith/FMNDTB33RXE2IQSTANJIYZIUI6","bundle":"https://pith.science/pith/FMNDTB33RXE2IQSTANJIYZIUI6/bundle.json","state":"https://pith.science/pith/FMNDTB33RXE2IQSTANJIYZIUI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FMNDTB33RXE2IQSTANJIYZIUI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FMNDTB33RXE2IQSTANJIYZIUI6","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":"6f40896c80896185ecc0e59a7c13b53aae2adbe1208965987740cc6ed0f90267","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T08:57:19Z","title_canon_sha256":"4689daefa766b7da7b82e363c143c4421d04e75c9c7bc9745fdbd97ec9d5e161"},"schema_version":"1.0","source":{"id":"1110.3612","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3612","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3612v3","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3612","created_at":"2026-05-18T03:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"FMNDTB33RXE2","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FMNDTB33RXE2IQST","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FMNDTB33","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:201442ca58019e50070b5d854e8daa9bfe78bbdd77ff31ec84341c4c5faf6793","target":"graph","created_at":"2026-05-18T03:54:15Z","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":"The paper is concerned with the problem of a semi-infinite crack at the interface between two dissimilar elastic half-spaces, loaded by a general asymmetrical system of forces distributed along the crack faces. On the basis of the weight function approach and the fundamental reciprocal identity (Betti formula), we formulate the elasticity problem in terms of singular integral equations relating the applied loading and the resulting crack opening. Such formulation is fundamental in the theory of elasticity and extensively used to solve several problems in linear elastic fracture mechanics (for ","authors_text":"Andrea Piccolroaz, Gennady Mishuris","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T08:57:19Z","title":"Integral identities for a semi-infinite interfacial crack in 2D and 3D elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3612","kind":"arxiv","version":3},"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:ba0c8e04c4bad7ae2abe6b4e75ff87c09c95f8cb706fcaba1e6b4fac022977c9","target":"record","created_at":"2026-05-18T03:54:15Z","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":"6f40896c80896185ecc0e59a7c13b53aae2adbe1208965987740cc6ed0f90267","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-10-17T08:57:19Z","title_canon_sha256":"4689daefa766b7da7b82e363c143c4421d04e75c9c7bc9745fdbd97ec9d5e161"},"schema_version":"1.0","source":{"id":"1110.3612","kind":"arxiv","version":3}},"canonical_sha256":"2b1a39877b8dc9a4425303528c651447b7c9ea25d7a8a059960401908cbc577f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b1a39877b8dc9a4425303528c651447b7c9ea25d7a8a059960401908cbc577f","first_computed_at":"2026-05-18T03:54:15.049042Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:15.049042Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KA/RFjESegH3OqFnsMXSKi4YqsifKXzIjRIJfYRbberIcZwCLDIUtIqebkMoNlA+ihVx8rEnLdSed/FJLSOkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:15.049601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3612","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba0c8e04c4bad7ae2abe6b4e75ff87c09c95f8cb706fcaba1e6b4fac022977c9","sha256:201442ca58019e50070b5d854e8daa9bfe78bbdd77ff31ec84341c4c5faf6793"],"state_sha256":"93ba3beb2954d11218c20ca74dec1c2db8977e3454040d989a4a68701cfd8801"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f0enB1Q+eyPdlUGeg5Q3DWGryD1XK/gOY5dlzILeE9V/TzkovlJ/LW5gZTNClCKHrzLlPoLN5L2mF6GPQjvcDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T04:48:07.641493Z","bundle_sha256":"ddc12534cdd156e2b9e1c8d45a3ef00aec508f1f37ad032647cfc844f2fc4a9e"}}