{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ST3V6GPHAVOE5IGU323HTHV6F5","short_pith_number":"pith:ST3V6GPH","canonical_record":{"source":{"id":"1411.4609","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T19:55:53Z","cross_cats_sorted":[],"title_canon_sha256":"a79c1dbdeee57feb813f040177c24577011b327f0edcaa479ab51bad380db11c","abstract_canon_sha256":"503fc74f9e9fb9273f90baba4450909c08759f4f29ad5b7feb6e53ca278e9ff1"},"schema_version":"1.0"},"canonical_sha256":"94f75f19e7055c4ea0d4deb6799ebe2f67d7ef38b21a54154432745cf164c387","source":{"kind":"arxiv","id":"1411.4609","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4609","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4609v5","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4609","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"pith_short_12","alias_value":"ST3V6GPHAVOE","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"ST3V6GPHAVOE5IGU","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"ST3V6GPH","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ST3V6GPHAVOE5IGU323HTHV6F5","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4609","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T19:55:53Z","cross_cats_sorted":[],"title_canon_sha256":"a79c1dbdeee57feb813f040177c24577011b327f0edcaa479ab51bad380db11c","abstract_canon_sha256":"503fc74f9e9fb9273f90baba4450909c08759f4f29ad5b7feb6e53ca278e9ff1"},"schema_version":"1.0"},"canonical_sha256":"94f75f19e7055c4ea0d4deb6799ebe2f67d7ef38b21a54154432745cf164c387","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:02.024485Z","signature_b64":"rd2QDWlcu6kyv60oqMtjfYBxVUa2+C3ROkRgfyXF//albZmsUiDtNo0nQixqXh2E3/Rel6fxONCcge3mdIjxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"94f75f19e7055c4ea0d4deb6799ebe2f67d7ef38b21a54154432745cf164c387","last_reissued_at":"2026-05-18T01:37:02.023999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:02.023999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4609","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:37:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"581/g0UzCLUEyDcTfjZ9znJ8TAqR8i/S3/ahC9jjaAxNWipirdg7WzRpA62Pr6Ar2NdoF34KrfnRructsp48AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:16:32.045670Z"},"content_sha256":"f11d42152e9b0ea8b4b5c72629ca59a4ac4c2703d924f230627454012b3edd45","schema_version":"1.0","event_id":"sha256:f11d42152e9b0ea8b4b5c72629ca59a4ac4c2703d924f230627454012b3edd45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ST3V6GPHAVOE5IGU323HTHV6F5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cohesive Dynamics and Brittle Fracture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Robert Lipton","submitted_at":"2014-11-17T19:55:53Z","abstract_excerpt":"We formulate a nonlocal cohesive model for calculating the deformation state inside a cracking body. In this model a more complete set of physical properties including elastic and softening behavior are assigned to each point in the medium. We work within the small deformation setting and use the peridynamic formulation. Here strains are calculated as difference quotients. The constitutive relation is given by a nonlocal cohesive law relating force to strain. At each instant of the evolution we identify a process zone where strains lie above a threshold value. Perturbation analysis shows that "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4609","kind":"arxiv","version":5},"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":"2026-05-18T01:37:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AXi1pvweXH5rPekjrcidQt9g9wmgNlXz9seKV+qzLP0/2HvYKbr17uTnNA/fCqYibQ3doVOD+ZS0PnL9zno+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:16:32.046372Z"},"content_sha256":"1e231b5a6b54ee1ddd700d23893c465c8285a1280ec6ba0bb1ef409592e5ae96","schema_version":"1.0","event_id":"sha256:1e231b5a6b54ee1ddd700d23893c465c8285a1280ec6ba0bb1ef409592e5ae96"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ST3V6GPHAVOE5IGU323HTHV6F5/bundle.json","state_url":"https://pith.science/pith/ST3V6GPHAVOE5IGU323HTHV6F5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ST3V6GPHAVOE5IGU323HTHV6F5/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":"2026-06-09T07:16:32Z","links":{"resolver":"https://pith.science/pith/ST3V6GPHAVOE5IGU323HTHV6F5","bundle":"https://pith.science/pith/ST3V6GPHAVOE5IGU323HTHV6F5/bundle.json","state":"https://pith.science/pith/ST3V6GPHAVOE5IGU323HTHV6F5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ST3V6GPHAVOE5IGU323HTHV6F5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ST3V6GPHAVOE5IGU323HTHV6F5","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":"503fc74f9e9fb9273f90baba4450909c08759f4f29ad5b7feb6e53ca278e9ff1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T19:55:53Z","title_canon_sha256":"a79c1dbdeee57feb813f040177c24577011b327f0edcaa479ab51bad380db11c"},"schema_version":"1.0","source":{"id":"1411.4609","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4609","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4609v5","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4609","created_at":"2026-05-18T01:37:02Z"},{"alias_kind":"pith_short_12","alias_value":"ST3V6GPHAVOE","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"ST3V6GPHAVOE5IGU","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"ST3V6GPH","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:1e231b5a6b54ee1ddd700d23893c465c8285a1280ec6ba0bb1ef409592e5ae96","target":"graph","created_at":"2026-05-18T01:37:02Z","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 formulate a nonlocal cohesive model for calculating the deformation state inside a cracking body. In this model a more complete set of physical properties including elastic and softening behavior are assigned to each point in the medium. We work within the small deformation setting and use the peridynamic formulation. Here strains are calculated as difference quotients. The constitutive relation is given by a nonlocal cohesive law relating force to strain. At each instant of the evolution we identify a process zone where strains lie above a threshold value. Perturbation analysis shows that ","authors_text":"Robert Lipton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T19:55:53Z","title":"Cohesive Dynamics and Brittle Fracture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4609","kind":"arxiv","version":5},"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:f11d42152e9b0ea8b4b5c72629ca59a4ac4c2703d924f230627454012b3edd45","target":"record","created_at":"2026-05-18T01:37:02Z","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":"503fc74f9e9fb9273f90baba4450909c08759f4f29ad5b7feb6e53ca278e9ff1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-17T19:55:53Z","title_canon_sha256":"a79c1dbdeee57feb813f040177c24577011b327f0edcaa479ab51bad380db11c"},"schema_version":"1.0","source":{"id":"1411.4609","kind":"arxiv","version":5}},"canonical_sha256":"94f75f19e7055c4ea0d4deb6799ebe2f67d7ef38b21a54154432745cf164c387","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94f75f19e7055c4ea0d4deb6799ebe2f67d7ef38b21a54154432745cf164c387","first_computed_at":"2026-05-18T01:37:02.023999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:02.023999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rd2QDWlcu6kyv60oqMtjfYBxVUa2+C3ROkRgfyXF//albZmsUiDtNo0nQixqXh2E3/Rel6fxONCcge3mdIjxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:02.024485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4609","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f11d42152e9b0ea8b4b5c72629ca59a4ac4c2703d924f230627454012b3edd45","sha256:1e231b5a6b54ee1ddd700d23893c465c8285a1280ec6ba0bb1ef409592e5ae96"],"state_sha256":"8a7fcc9c2c77407fe030fcb19e72e224afbdc3ad7be123fd5a01a303ddc4ac6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EzbNB+mIMSC1SjZWE0aqx5cdSHxSTM0rRhxBTaTcK+AvCcq6RuevyHeFrOG1R58Do403bH2HDQ1T00QS0E9DCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:16:32.050182Z","bundle_sha256":"02aab5a5758cb6c0125ddfa13ef988555100c821310406fd9f7ed7d3b935e37f"}}