{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YVMRUPSVFHZ66NIVDAVBBPCABH","short_pith_number":"pith:YVMRUPSV","canonical_record":{"source":{"id":"1403.0443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-03T14:32:28Z","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"title_canon_sha256":"c330de9bf77c3a028193c7ffb8330a1d30481e24d617adaf621f5f1a64cf3c8d","abstract_canon_sha256":"ddf5d12e3d3a830532a1701f51168e92ad4726300e72ce07c1785318291ecfb2"},"schema_version":"1.0"},"canonical_sha256":"c5591a3e5529f3ef3515182a10bc4009d1a349b41cfee07cbfa7470c58d385d9","source":{"kind":"arxiv","id":"1403.0443","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0443","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0443v1","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0443","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"YVMRUPSVFHZ6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YVMRUPSVFHZ66NIV","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YVMRUPSV","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YVMRUPSVFHZ66NIVDAVBBPCABH","target":"record","payload":{"canonical_record":{"source":{"id":"1403.0443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-03T14:32:28Z","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"title_canon_sha256":"c330de9bf77c3a028193c7ffb8330a1d30481e24d617adaf621f5f1a64cf3c8d","abstract_canon_sha256":"ddf5d12e3d3a830532a1701f51168e92ad4726300e72ce07c1785318291ecfb2"},"schema_version":"1.0"},"canonical_sha256":"c5591a3e5529f3ef3515182a10bc4009d1a349b41cfee07cbfa7470c58d385d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:24.864554Z","signature_b64":"kOJvripBNeHc7Ka9xmXOPM2aw1yhkgWyW4M0PY3gf6ohInYrULBFvWgZsMzzGsKmSj6ELfgPAysa9Js4s0EaDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5591a3e5529f3ef3515182a10bc4009d1a349b41cfee07cbfa7470c58d385d9","last_reissued_at":"2026-05-18T02:57:24.863763Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:24.863763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.0443","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":"2026-05-18T02:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"68KwzyW1iUuMTa3/TXPC+1YQbhxLdvzxroci0JlYQuwO4WhNFdQaA258zxGS3nRSFbPLhWBqwSpDTvdL7DcPBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:13:06.402820Z"},"content_sha256":"3d7b6d75f69ca85d6ef404e3a1641a183ef05982617e1f62dc5bd235e1bc5d77","schema_version":"1.0","event_id":"sha256:3d7b6d75f69ca85d6ef404e3a1641a183ef05982617e1f62dc5bd235e1bc5d77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YVMRUPSVFHZ66NIVDAVBBPCABH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Bernd Schmidt, Manuel Friedrich","submitted_at":"2014-03-03T14:32:28Z","abstract_excerpt":"We consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either homogeneous elastic deformations or configurations that are completely cracked generically along a crystallographic line. As applications we discuss cleavage properties of strained crystals and an effe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0443","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":"2026-05-18T02:57:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QW61XdCgSMXcWk9qspsv+Eh9lid3z3tlvpzlavk3Qrr+9iKzxuyqMMGG55XWPALlAoOVx7fLv322xWpc/DYGBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:13:06.403445Z"},"content_sha256":"23eeb1fcf00987f4d937ec5a2aac1c4add9173fa2328c48c93c98c6ad638a746","schema_version":"1.0","event_id":"sha256:23eeb1fcf00987f4d937ec5a2aac1c4add9173fa2328c48c93c98c6ad638a746"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YVMRUPSVFHZ66NIVDAVBBPCABH/bundle.json","state_url":"https://pith.science/pith/YVMRUPSVFHZ66NIVDAVBBPCABH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YVMRUPSVFHZ66NIVDAVBBPCABH/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":"2026-06-07T16:13:06Z","links":{"resolver":"https://pith.science/pith/YVMRUPSVFHZ66NIVDAVBBPCABH","bundle":"https://pith.science/pith/YVMRUPSVFHZ66NIVDAVBBPCABH/bundle.json","state":"https://pith.science/pith/YVMRUPSVFHZ66NIVDAVBBPCABH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YVMRUPSVFHZ66NIVDAVBBPCABH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YVMRUPSVFHZ66NIVDAVBBPCABH","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":"ddf5d12e3d3a830532a1701f51168e92ad4726300e72ce07c1785318291ecfb2","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-03T14:32:28Z","title_canon_sha256":"c330de9bf77c3a028193c7ffb8330a1d30481e24d617adaf621f5f1a64cf3c8d"},"schema_version":"1.0","source":{"id":"1403.0443","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.0443","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"arxiv_version","alias_value":"1403.0443v1","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.0443","created_at":"2026-05-18T02:57:24Z"},{"alias_kind":"pith_short_12","alias_value":"YVMRUPSVFHZ6","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YVMRUPSVFHZ66NIV","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YVMRUPSV","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:23eeb1fcf00987f4d937ec5a2aac1c4add9173fa2328c48c93c98c6ad638a746","target":"graph","created_at":"2026-05-18T02:57:24Z","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 consider a two-dimensional atomic mass spring system and show that in the small displacement regime the corresponding discrete energies can be related to a continuum Griffith energy functional in the sense of Gamma-convergence. We also analyze the continuum problem for a rectangular bar under tensile boundary conditions and find that depending on the boundary loading the minimizers are either homogeneous elastic deformations or configurations that are completely cracked generically along a crystallographic line. As applications we discuss cleavage properties of strained crystals and an effe","authors_text":"Bernd Schmidt, Manuel Friedrich","cross_cats":["cond-mat.mtrl-sci","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-03T14:32:28Z","title":"On a discrete-to-continuum convergence result for a two dimensional brittle material in the small displacement regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.0443","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":"sha256:3d7b6d75f69ca85d6ef404e3a1641a183ef05982617e1f62dc5bd235e1bc5d77","target":"record","created_at":"2026-05-18T02:57:24Z","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":"ddf5d12e3d3a830532a1701f51168e92ad4726300e72ce07c1785318291ecfb2","cross_cats_sorted":["cond-mat.mtrl-sci","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-03T14:32:28Z","title_canon_sha256":"c330de9bf77c3a028193c7ffb8330a1d30481e24d617adaf621f5f1a64cf3c8d"},"schema_version":"1.0","source":{"id":"1403.0443","kind":"arxiv","version":1}},"canonical_sha256":"c5591a3e5529f3ef3515182a10bc4009d1a349b41cfee07cbfa7470c58d385d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5591a3e5529f3ef3515182a10bc4009d1a349b41cfee07cbfa7470c58d385d9","first_computed_at":"2026-05-18T02:57:24.863763Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:24.863763Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kOJvripBNeHc7Ka9xmXOPM2aw1yhkgWyW4M0PY3gf6ohInYrULBFvWgZsMzzGsKmSj6ELfgPAysa9Js4s0EaDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:24.864554Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.0443","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d7b6d75f69ca85d6ef404e3a1641a183ef05982617e1f62dc5bd235e1bc5d77","sha256:23eeb1fcf00987f4d937ec5a2aac1c4add9173fa2328c48c93c98c6ad638a746"],"state_sha256":"8743cb8a1febde28dee00a57ef1095552bd917edd233cdc954e113eaf2cf995d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BPP1h+eDMebriMv7gy5izv7bqcKdHVf2GLp3j8+EdGLKtqgB9cCkgaARxYyNGwc0A5YhFSMUHViQCKC27uOAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:13:06.406660Z","bundle_sha256":"311ff28b466167d2885443ea94158c694af048bd060c4c655419b9fa45545486"}}