{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:OYWOIPJBLFEFKPJJF22S5LNKY4","short_pith_number":"pith:OYWOIPJB","canonical_record":{"source":{"id":"math-ph/0405012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T18:33:33Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"4f0a43f3db8ecd279253e77bec66ed4b106030069b18eb466dfa4163d3ce78ab","abstract_canon_sha256":"c51130256ad18465c7f57cb442eaabd90dfbebf625d53d828dddbcf92c986212"},"schema_version":"1.0"},"canonical_sha256":"762ce43d215948553d292eb52eadaac720f1d5842ee1089c9a3e755cc7cd3621","source":{"kind":"arxiv","id":"math-ph/0405012","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0405012","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0405012v1","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0405012","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"OYWOIPJBLFEF","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OYWOIPJBLFEFKPJJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OYWOIPJB","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:OYWOIPJBLFEFKPJJF22S5LNKY4","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0405012","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T18:33:33Z","cross_cats_sorted":["hep-th","math.MP"],"title_canon_sha256":"4f0a43f3db8ecd279253e77bec66ed4b106030069b18eb466dfa4163d3ce78ab","abstract_canon_sha256":"c51130256ad18465c7f57cb442eaabd90dfbebf625d53d828dddbcf92c986212"},"schema_version":"1.0"},"canonical_sha256":"762ce43d215948553d292eb52eadaac720f1d5842ee1089c9a3e755cc7cd3621","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:18.975619Z","signature_b64":"HaF6ajUOVuUJa1h5Wl0NWghWqRjn5kWZQK/ou+/Wfg3sf/HEC8RmDCpH0SbfKtJB51QbBNsDZ+4VsXAqTWnVBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"762ce43d215948553d292eb52eadaac720f1d5842ee1089c9a3e755cc7cd3621","last_reissued_at":"2026-05-18T04:36:18.974977Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:18.974977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0405012","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":"2026-05-18T04:36:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUiI5wBYt1n8/+0Fe0qXr89RNApSOyvyyUJlB3DBV92F6CAF3gJQspXgQOab2QLjjqs7haVl6qEiOcOXXUhRBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:14:17.078568Z"},"content_sha256":"7cb09b043428b3e9e2286f6b730ecb7e0ba211cb4c68bfbceb24088daf7e8fb1","schema_version":"1.0","event_id":"sha256:7cb09b043428b3e9e2286f6b730ecb7e0ba211cb4c68bfbceb24088daf7e8fb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:OYWOIPJBLFEFKPJJF22S5LNKY4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangians with linear velocities within Riemann-Liouville fractional derivatives","license":"","headline":"","cross_cats":["hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"D.Baleanu, T. Avkar","submitted_at":"2004-05-04T18:33:33Z","abstract_excerpt":"Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the recovery of the classical results was discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0405012","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":"2026-05-18T04:36:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1kqxhFalsV/j8BkcezCNKhmqvQJAQ6VRUPFvvUQts62+LgHrjzAh66wTj3iNKPWPJg1LnM/6okVyBgdPmtbDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T23:14:17.079036Z"},"content_sha256":"d6beeb4dc934b1825003d575f9a5b96896b51d23c7d71b575bdbdf544e869136","schema_version":"1.0","event_id":"sha256:d6beeb4dc934b1825003d575f9a5b96896b51d23c7d71b575bdbdf544e869136"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OYWOIPJBLFEFKPJJF22S5LNKY4/bundle.json","state_url":"https://pith.science/pith/OYWOIPJBLFEFKPJJF22S5LNKY4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OYWOIPJBLFEFKPJJF22S5LNKY4/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":"2026-06-24T23:14:17Z","links":{"resolver":"https://pith.science/pith/OYWOIPJBLFEFKPJJF22S5LNKY4","bundle":"https://pith.science/pith/OYWOIPJBLFEFKPJJF22S5LNKY4/bundle.json","state":"https://pith.science/pith/OYWOIPJBLFEFKPJJF22S5LNKY4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OYWOIPJBLFEFKPJJF22S5LNKY4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:OYWOIPJBLFEFKPJJF22S5LNKY4","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":"c51130256ad18465c7f57cb442eaabd90dfbebf625d53d828dddbcf92c986212","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T18:33:33Z","title_canon_sha256":"4f0a43f3db8ecd279253e77bec66ed4b106030069b18eb466dfa4163d3ce78ab"},"schema_version":"1.0","source":{"id":"math-ph/0405012","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0405012","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0405012v1","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0405012","created_at":"2026-05-18T04:36:18Z"},{"alias_kind":"pith_short_12","alias_value":"OYWOIPJBLFEF","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"OYWOIPJBLFEFKPJJ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"OYWOIPJB","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d6beeb4dc934b1825003d575f9a5b96896b51d23c7d71b575bdbdf544e869136","target":"graph","created_at":"2026-05-18T04:36:18Z","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":"Lagrangians linear in velocities were analyzed using the fractional calculus and the Euler-Lagrange equations were derived. Two examples were investigated in details, the explicit solutions of Euler-Lagrange equations were obtained and the recovery of the classical results was discussed.","authors_text":"D.Baleanu, T. Avkar","cross_cats":["hep-th","math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T18:33:33Z","title":"Lagrangians with linear velocities within Riemann-Liouville fractional derivatives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0405012","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":"sha256:7cb09b043428b3e9e2286f6b730ecb7e0ba211cb4c68bfbceb24088daf7e8fb1","target":"record","created_at":"2026-05-18T04:36:18Z","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":"c51130256ad18465c7f57cb442eaabd90dfbebf625d53d828dddbcf92c986212","cross_cats_sorted":["hep-th","math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2004-05-04T18:33:33Z","title_canon_sha256":"4f0a43f3db8ecd279253e77bec66ed4b106030069b18eb466dfa4163d3ce78ab"},"schema_version":"1.0","source":{"id":"math-ph/0405012","kind":"arxiv","version":1}},"canonical_sha256":"762ce43d215948553d292eb52eadaac720f1d5842ee1089c9a3e755cc7cd3621","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"762ce43d215948553d292eb52eadaac720f1d5842ee1089c9a3e755cc7cd3621","first_computed_at":"2026-05-18T04:36:18.974977Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:18.974977Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HaF6ajUOVuUJa1h5Wl0NWghWqRjn5kWZQK/ou+/Wfg3sf/HEC8RmDCpH0SbfKtJB51QbBNsDZ+4VsXAqTWnVBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:18.975619Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0405012","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cb09b043428b3e9e2286f6b730ecb7e0ba211cb4c68bfbceb24088daf7e8fb1","sha256:d6beeb4dc934b1825003d575f9a5b96896b51d23c7d71b575bdbdf544e869136"],"state_sha256":"79148af355f622685a115d45f6a0af3ffde3f0364c331787d51fd69141c8e799"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p/dL0BG4nsTrsrt7wwtVBtldAUYV9n/syuKEDl7wpybbC9N7m9HE3eDHyfatIlrW7x5KteSL1+9zJqZGk3DJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T23:14:17.081594Z","bundle_sha256":"ee0971c189f01aba98f6d4f43c84e94d4e6a81c7fe011ec2131bdd692ef6069f"}}