{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T4DCOPZB5JZUMTEXYOT5BCX5T2","short_pith_number":"pith:T4DCOPZB","canonical_record":{"source":{"id":"1508.00638","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-08-04T01:42:29Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"982411ff247641e44fc978403439889455929b27d86c5c798142f65261969906","abstract_canon_sha256":"4b8cd31a791e48404b27e45938a90e4988c8c098e93dc10461139f7cfdadb813"},"schema_version":"1.0"},"canonical_sha256":"9f06273f21ea73464c97c3a7d08afd9ea1516a896a3929feda41c06465b2e805","source":{"kind":"arxiv","id":"1508.00638","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00638","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00638v5","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00638","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"T4DCOPZB5JZU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T4DCOPZB5JZUMTEX","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T4DCOPZB","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T4DCOPZB5JZUMTEXYOT5BCX5T2","target":"record","payload":{"canonical_record":{"source":{"id":"1508.00638","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-08-04T01:42:29Z","cross_cats_sorted":["physics.class-ph"],"title_canon_sha256":"982411ff247641e44fc978403439889455929b27d86c5c798142f65261969906","abstract_canon_sha256":"4b8cd31a791e48404b27e45938a90e4988c8c098e93dc10461139f7cfdadb813"},"schema_version":"1.0"},"canonical_sha256":"9f06273f21ea73464c97c3a7d08afd9ea1516a896a3929feda41c06465b2e805","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:09.751424Z","signature_b64":"AQA9cMaj7nMspq/9HEI0dzTQeyl/OGTwqtCp7tO9XrgZAPxXv7JCmTJdZ+SLyJMMo7mGO1RQrDDrMMnPE4wzBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f06273f21ea73464c97c3a7d08afd9ea1516a896a3929feda41c06465b2e805","last_reissued_at":"2026-05-18T01:16:09.750948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:09.750948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.00638","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":"2026-05-18T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fpV9V1iFnNyb3RfEcDNIRY1jqPRAIVkiyP/aFzwnjkwmc0tiW1QlDiK39nDpz62X64soGIuIzKIW77w4mFdjCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:46:09.742457Z"},"content_sha256":"2a90856685ada41837e4e8b1353acbaec381c988c063f9cb32aea29ee25a6d3b","schema_version":"1.0","event_id":"sha256:2a90856685ada41837e4e8b1353acbaec381c988c063f9cb32aea29ee25a6d3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T4DCOPZB5JZUMTEXYOT5BCX5T2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.class-ph"],"primary_cat":"cond-mat.mtrl-sci","authors_text":"Sven Peter N\\\"asholm, Sverre Holm, Vikash Pandey","submitted_at":"2015-08-04T01:42:29Z","abstract_excerpt":"We apply the framework of tempered fractional calculus to investigate the spatial dispersion of elastic waves in a one-dimensional elastic bar characterized by range-dependent nonlocal interactions. The measure of the interaction is given by the attenuation kernel present in the constitutive stress-strain relation of the bar, which follows from the Kr\\\"oner-Eringen's model of nonlocal elasticity. We employ a fractional power-law attenuation kernel and spatially temper it, to make the model physically valid and mathematically consistent. The spatial dispersion relation is derived, but it turns "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00638","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":"2026-05-18T01:16:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4U/Ro6Rc6oVOqdQHVNTMNOnrmMcbf0xgWNj5mAddYImVxPw3Xm94TTMsPAqkjyszVRBqcT5du1cfvuJJlhHJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:46:09.743149Z"},"content_sha256":"fd6ceb784cd000f8cec8798ce3022ec7634b78c666acd54b1fd4ef854eca758a","schema_version":"1.0","event_id":"sha256:fd6ceb784cd000f8cec8798ce3022ec7634b78c666acd54b1fd4ef854eca758a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2/bundle.json","state_url":"https://pith.science/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2/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":"2026-06-11T20:46:09Z","links":{"resolver":"https://pith.science/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2","bundle":"https://pith.science/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2/bundle.json","state":"https://pith.science/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4DCOPZB5JZUMTEXYOT5BCX5T2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T4DCOPZB5JZUMTEXYOT5BCX5T2","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":"4b8cd31a791e48404b27e45938a90e4988c8c098e93dc10461139f7cfdadb813","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-08-04T01:42:29Z","title_canon_sha256":"982411ff247641e44fc978403439889455929b27d86c5c798142f65261969906"},"schema_version":"1.0","source":{"id":"1508.00638","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00638","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00638v5","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00638","created_at":"2026-05-18T01:16:09Z"},{"alias_kind":"pith_short_12","alias_value":"T4DCOPZB5JZU","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T4DCOPZB5JZUMTEX","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T4DCOPZB","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:fd6ceb784cd000f8cec8798ce3022ec7634b78c666acd54b1fd4ef854eca758a","target":"graph","created_at":"2026-05-18T01:16:09Z","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 apply the framework of tempered fractional calculus to investigate the spatial dispersion of elastic waves in a one-dimensional elastic bar characterized by range-dependent nonlocal interactions. The measure of the interaction is given by the attenuation kernel present in the constitutive stress-strain relation of the bar, which follows from the Kr\\\"oner-Eringen's model of nonlocal elasticity. We employ a fractional power-law attenuation kernel and spatially temper it, to make the model physically valid and mathematically consistent. The spatial dispersion relation is derived, but it turns ","authors_text":"Sven Peter N\\\"asholm, Sverre Holm, Vikash Pandey","cross_cats":["physics.class-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-08-04T01:42:29Z","title":"Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00638","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":"sha256:2a90856685ada41837e4e8b1353acbaec381c988c063f9cb32aea29ee25a6d3b","target":"record","created_at":"2026-05-18T01:16:09Z","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":"4b8cd31a791e48404b27e45938a90e4988c8c098e93dc10461139f7cfdadb813","cross_cats_sorted":["physics.class-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.mtrl-sci","submitted_at":"2015-08-04T01:42:29Z","title_canon_sha256":"982411ff247641e44fc978403439889455929b27d86c5c798142f65261969906"},"schema_version":"1.0","source":{"id":"1508.00638","kind":"arxiv","version":5}},"canonical_sha256":"9f06273f21ea73464c97c3a7d08afd9ea1516a896a3929feda41c06465b2e805","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f06273f21ea73464c97c3a7d08afd9ea1516a896a3929feda41c06465b2e805","first_computed_at":"2026-05-18T01:16:09.750948Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:09.750948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AQA9cMaj7nMspq/9HEI0dzTQeyl/OGTwqtCp7tO9XrgZAPxXv7JCmTJdZ+SLyJMMo7mGO1RQrDDrMMnPE4wzBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:09.751424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00638","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a90856685ada41837e4e8b1353acbaec381c988c063f9cb32aea29ee25a6d3b","sha256:fd6ceb784cd000f8cec8798ce3022ec7634b78c666acd54b1fd4ef854eca758a"],"state_sha256":"77e3c9f974f933256b29b8fa18107d184dbf381ffafb0f1f339eb1142dc928ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T+1Vc+S/D4cmLquHNlThXmjoh1GZiqrU+P9DY1MlSmbAG66r5F4mAY4OSuYuplbMW+tZ6VKfQh9TPNte5t1aDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:46:09.747105Z","bundle_sha256":"bd8fb89cd10dfaec9813f3c664f0762dde7911559f0d391a9cf88ce40230d7c5"}}