{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7Y4Y7SGGN23EOZ7QJHYD7FIROQ","short_pith_number":"pith:7Y4Y7SGG","canonical_record":{"source":{"id":"1502.05492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-19T08:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"de9712dee5ec5cbc13812f654e9a0c8e1af158984114708fb1d4217d0847a91e","abstract_canon_sha256":"ee97fce67cff97dd02aa872441e4aeb39c1ec6a9fb39616e0b3fb84c4d700e68"},"schema_version":"1.0"},"canonical_sha256":"fe398fc8c66eb64767f049f03f9511743950404b8c5e475b463d1b409b87a4ac","source":{"kind":"arxiv","id":"1502.05492","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05492","created_at":"2026-05-18T02:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05492v2","created_at":"2026-05-18T02:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05492","created_at":"2026-05-18T02:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"7Y4Y7SGGN23E","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7Y4Y7SGGN23EOZ7Q","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7Y4Y7SGG","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7Y4Y7SGGN23EOZ7QJHYD7FIROQ","target":"record","payload":{"canonical_record":{"source":{"id":"1502.05492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-19T08:14:50Z","cross_cats_sorted":[],"title_canon_sha256":"de9712dee5ec5cbc13812f654e9a0c8e1af158984114708fb1d4217d0847a91e","abstract_canon_sha256":"ee97fce67cff97dd02aa872441e4aeb39c1ec6a9fb39616e0b3fb84c4d700e68"},"schema_version":"1.0"},"canonical_sha256":"fe398fc8c66eb64767f049f03f9511743950404b8c5e475b463d1b409b87a4ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:42.600765Z","signature_b64":"kZTBWVfIRZvrfgNYzXtpsnE4lk/Igj/lTwXx/j3LdTYi2lMEWer3A0il9S3u/P6ya9j5VqIivHstrsCr3jGbBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe398fc8c66eb64767f049f03f9511743950404b8c5e475b463d1b409b87a4ac","last_reissued_at":"2026-05-18T02:18:42.600063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:42.600063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.05492","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sb1Ymc/DqH+kGx4fAdedwyjK0//yLyZEuqnIcrxiSN/C3qG60XEgk2s8xQ8rEFhxxTasnw+zS/H2xB6CO8ElCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:10:25.791948Z"},"content_sha256":"8795ab3f7035aa46f3d638f209bf246e7cf4e5de06bf585a14aae9cefffe625c","schema_version":"1.0","event_id":"sha256:8795ab3f7035aa46f3d638f209bf246e7cf4e5de06bf585a14aae9cefffe625c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7Y4Y7SGGN23EOZ7QJHYD7FIROQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Vasily E. Tarasov","submitted_at":"2015-02-19T08:14:50Z","abstract_excerpt":"Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with Riesz derivatives of non-integer orders. The continuum equations that are obtained from the lattice model describe fractional generalization of non-local elasticity models. Particular solutions and correspondent asymptotic of the fractional differential equations for displacement fields are suggested for the static case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05492","kind":"arxiv","version":2},"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":"2026-05-18T02:18:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"INgkdERzr/Z6cioAkvNOhmQFSZukmpX6bfC7bQrV6ZTgEe2dPYJ1hG1s7Wx65dnfCkRKsc2u23dqsMtJLSdjDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:10:25.792288Z"},"content_sha256":"12296ce69cc0eb8498c536b61d367999ef07f910acdcf227edf2b0ef93249c49","schema_version":"1.0","event_id":"sha256:12296ce69cc0eb8498c536b61d367999ef07f910acdcf227edf2b0ef93249c49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ/bundle.json","state_url":"https://pith.science/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ/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":"2026-06-01T19:10:25Z","links":{"resolver":"https://pith.science/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ","bundle":"https://pith.science/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ/bundle.json","state":"https://pith.science/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Y4Y7SGGN23EOZ7QJHYD7FIROQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7Y4Y7SGGN23EOZ7QJHYD7FIROQ","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":"ee97fce67cff97dd02aa872441e4aeb39c1ec6a9fb39616e0b3fb84c4d700e68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-19T08:14:50Z","title_canon_sha256":"de9712dee5ec5cbc13812f654e9a0c8e1af158984114708fb1d4217d0847a91e"},"schema_version":"1.0","source":{"id":"1502.05492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05492","created_at":"2026-05-18T02:18:42Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05492v2","created_at":"2026-05-18T02:18:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05492","created_at":"2026-05-18T02:18:42Z"},{"alias_kind":"pith_short_12","alias_value":"7Y4Y7SGGN23E","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7Y4Y7SGGN23EOZ7Q","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7Y4Y7SGG","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:12296ce69cc0eb8498c536b61d367999ef07f910acdcf227edf2b0ef93249c49","target":"graph","created_at":"2026-05-18T02:18:42Z","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":"Lattice models with long-range interactions of power-law type are suggested as a new type of microscopic model for fractional non-local elasticity. Using the transform operation, we map the lattice equations into continuum equation with Riesz derivatives of non-integer orders. The continuum equations that are obtained from the lattice model describe fractional generalization of non-local elasticity models. Particular solutions and correspondent asymptotic of the fractional differential equations for displacement fields are suggested for the static case.","authors_text":"Vasily E. Tarasov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-19T08:14:50Z","title":"Lattice with Long-Range Interaction of Power-Law Type for Fractional Non-Local Elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05492","kind":"arxiv","version":2},"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":"sha256:8795ab3f7035aa46f3d638f209bf246e7cf4e5de06bf585a14aae9cefffe625c","target":"record","created_at":"2026-05-18T02:18:42Z","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":"ee97fce67cff97dd02aa872441e4aeb39c1ec6a9fb39616e0b3fb84c4d700e68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-02-19T08:14:50Z","title_canon_sha256":"de9712dee5ec5cbc13812f654e9a0c8e1af158984114708fb1d4217d0847a91e"},"schema_version":"1.0","source":{"id":"1502.05492","kind":"arxiv","version":2}},"canonical_sha256":"fe398fc8c66eb64767f049f03f9511743950404b8c5e475b463d1b409b87a4ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe398fc8c66eb64767f049f03f9511743950404b8c5e475b463d1b409b87a4ac","first_computed_at":"2026-05-18T02:18:42.600063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:42.600063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kZTBWVfIRZvrfgNYzXtpsnE4lk/Igj/lTwXx/j3LdTYi2lMEWer3A0il9S3u/P6ya9j5VqIivHstrsCr3jGbBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:42.600765Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8795ab3f7035aa46f3d638f209bf246e7cf4e5de06bf585a14aae9cefffe625c","sha256:12296ce69cc0eb8498c536b61d367999ef07f910acdcf227edf2b0ef93249c49"],"state_sha256":"354412212a04a4f2753f5f748fe285656b5bac960dde1fc5faae0d0bd6361675"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XtTIjbyu2AiItUw+ccRGGOd4LVkjbFriIrkc6ao2HlRF7o+UrsJARO05r9ayVuVj7qeywzv8HulLBfx/HQzfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:10:25.794225Z","bundle_sha256":"a308ecbe9d9f0983ff535ea93e59fe8e9445cb1232ca5136af6ad09d18df4492"}}