{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:MEFVSH6X4NMHMW3DEDA5S3YLNW","short_pith_number":"pith:MEFVSH6X","canonical_record":{"source":{"id":"1404.5241","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-04-21T16:48:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f0201f8f2dabcb1c6f08be626ba848d15bcc108313877693e7f56dbbf5285d96","abstract_canon_sha256":"81cb70ecae39a22cf22f5b5b8f280cfacbf74d4265f6ca63b569e5b659297991"},"schema_version":"1.0"},"canonical_sha256":"610b591fd7e358765b6320c1d96f0b6da98bb98cb4ca455664b76aa2cbf37200","source":{"kind":"arxiv","id":"1404.5241","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5241","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5241v3","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5241","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"MEFVSH6X4NMH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MEFVSH6X4NMHMW3D","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MEFVSH6X","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:MEFVSH6X4NMHMW3DEDA5S3YLNW","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5241","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-04-21T16:48:53Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f0201f8f2dabcb1c6f08be626ba848d15bcc108313877693e7f56dbbf5285d96","abstract_canon_sha256":"81cb70ecae39a22cf22f5b5b8f280cfacbf74d4265f6ca63b569e5b659297991"},"schema_version":"1.0"},"canonical_sha256":"610b591fd7e358765b6320c1d96f0b6da98bb98cb4ca455664b76aa2cbf37200","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:57.167285Z","signature_b64":"owDZqJegRl0KVjqHmBDWwhfDGwNqbtciltB7lWx9Vp1F+ZqErdDU+5Rzuid6ieHZuXlxok0MhlteQtdQFoSkCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"610b591fd7e358765b6320c1d96f0b6da98bb98cb4ca455664b76aa2cbf37200","last_reissued_at":"2026-05-18T02:27:57.166778Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:57.166778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5241","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":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vWRNm1igSw30ybXE6+ZQh63Jg3pJcuKOsTOWl1QMxWp9Q0FHiVUH4OobhyY5W1yWgIbNR4J5jaSeDhUIR/t/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:10:36.137207Z"},"content_sha256":"de66aa2be297e29f6582f81cb1515598353f4f652be63c791dfb87bdcd5ed4cc","schema_version":"1.0","event_id":"sha256:de66aa2be297e29f6582f81cb1515598353f4f652be63c791dfb87bdcd5ed4cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:MEFVSH6X4NMHMW3DEDA5S3YLNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Standard Extensions of Gradient Elasticity: Fractional Non-Locality, Memory and Fractality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Elias C. Aifantis, Vasily E. Tarasov","submitted_at":"2014-04-21T16:48:53Z","abstract_excerpt":"Derivatives and integrals of non-integer order may have a wide application in describing complex properties of materials including long-term memory, non-locality of power-law type and fractality. In this paper we consider extensions of elasticity theory that allow us to describe elasticity of materials with fractional non-locality, memory and fractality. The basis of our consideration is an extension of the usual variational principle for fractional non-locality and fractality. For materials with power-law non-locality described by Riesz derivatives of non-integer order, we suggest a fractiona"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5241","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":"2026-05-18T02:27:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FFFugpMUOdroDlaLOj26H4Kbl11O7WPniOUC3hzDlK2s4ffHz7u4Rjy8+/fB0HX6gVqAT7YsiCAmWZVobzb3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:10:36.137559Z"},"content_sha256":"af3a4f1dd478a3b81cdd541628d3903fd4e687628b3d1eaf47f6a2b656625a93","schema_version":"1.0","event_id":"sha256:af3a4f1dd478a3b81cdd541628d3903fd4e687628b3d1eaf47f6a2b656625a93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW/bundle.json","state_url":"https://pith.science/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW/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":"2026-06-02T05:10:36Z","links":{"resolver":"https://pith.science/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW","bundle":"https://pith.science/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW/bundle.json","state":"https://pith.science/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEFVSH6X4NMHMW3DEDA5S3YLNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MEFVSH6X4NMHMW3DEDA5S3YLNW","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":"81cb70ecae39a22cf22f5b5b8f280cfacbf74d4265f6ca63b569e5b659297991","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-04-21T16:48:53Z","title_canon_sha256":"f0201f8f2dabcb1c6f08be626ba848d15bcc108313877693e7f56dbbf5285d96"},"schema_version":"1.0","source":{"id":"1404.5241","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5241","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5241v3","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5241","created_at":"2026-05-18T02:27:57Z"},{"alias_kind":"pith_short_12","alias_value":"MEFVSH6X4NMH","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MEFVSH6X4NMHMW3D","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MEFVSH6X","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:af3a4f1dd478a3b81cdd541628d3903fd4e687628b3d1eaf47f6a2b656625a93","target":"graph","created_at":"2026-05-18T02:27:57Z","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":"Derivatives and integrals of non-integer order may have a wide application in describing complex properties of materials including long-term memory, non-locality of power-law type and fractality. In this paper we consider extensions of elasticity theory that allow us to describe elasticity of materials with fractional non-locality, memory and fractality. The basis of our consideration is an extension of the usual variational principle for fractional non-locality and fractality. For materials with power-law non-locality described by Riesz derivatives of non-integer order, we suggest a fractiona","authors_text":"Elias C. Aifantis, Vasily E. Tarasov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-04-21T16:48:53Z","title":"Non-Standard Extensions of Gradient Elasticity: Fractional Non-Locality, Memory and Fractality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5241","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:de66aa2be297e29f6582f81cb1515598353f4f652be63c791dfb87bdcd5ed4cc","target":"record","created_at":"2026-05-18T02:27:57Z","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":"81cb70ecae39a22cf22f5b5b8f280cfacbf74d4265f6ca63b569e5b659297991","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2014-04-21T16:48:53Z","title_canon_sha256":"f0201f8f2dabcb1c6f08be626ba848d15bcc108313877693e7f56dbbf5285d96"},"schema_version":"1.0","source":{"id":"1404.5241","kind":"arxiv","version":3}},"canonical_sha256":"610b591fd7e358765b6320c1d96f0b6da98bb98cb4ca455664b76aa2cbf37200","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"610b591fd7e358765b6320c1d96f0b6da98bb98cb4ca455664b76aa2cbf37200","first_computed_at":"2026-05-18T02:27:57.166778Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:57.166778Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"owDZqJegRl0KVjqHmBDWwhfDGwNqbtciltB7lWx9Vp1F+ZqErdDU+5Rzuid6ieHZuXlxok0MhlteQtdQFoSkCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:57.167285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5241","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de66aa2be297e29f6582f81cb1515598353f4f652be63c791dfb87bdcd5ed4cc","sha256:af3a4f1dd478a3b81cdd541628d3903fd4e687628b3d1eaf47f6a2b656625a93"],"state_sha256":"bcbf858ac3392d8d8ad2bff9b48dd15d4003566bbcc221b5f1d5fd8c1b5cd573"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R47a0wrbdZNvQ4FO2JWbY5TyvFSOXiJKXAGwf2n7jlhW354qaPRD0TKV2IfP/UzRyPZfU8zY7QAzuUrGKiWVAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:10:36.139406Z","bundle_sha256":"3f8672cf64e71ebfe2052de6c435956fe9c09e621e9f9be6d19dd79e8cf340ba"}}