{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:ITNT3QVWHWH5UEEDKNSBZYHY6X","short_pith_number":"pith:ITNT3QVW","canonical_record":{"source":{"id":"1107.5682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-07-28T11:33:11Z","cross_cats_sorted":[],"title_canon_sha256":"1ba2c1584cf64a3391fa5044b93100cfb70accc3c5b87a4e6ca1570981a8a815","abstract_canon_sha256":"42bc1f7aac38f0d4c805feea0fa48fd543984c898fc3e9f33ed37f7e8222bea4"},"schema_version":"1.0"},"canonical_sha256":"44db3dc2b63d8fda108353641ce0f8f5dd51c4ec82b706a60e2bd85cca59343c","source":{"kind":"arxiv","id":"1107.5682","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5682","created_at":"2026-05-18T04:16:41Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5682v1","created_at":"2026-05-18T04:16:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5682","created_at":"2026-05-18T04:16:41Z"},{"alias_kind":"pith_short_12","alias_value":"ITNT3QVWHWH5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"ITNT3QVWHWH5UEED","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"ITNT3QVW","created_at":"2026-05-18T12:26:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:ITNT3QVWHWH5UEEDKNSBZYHY6X","target":"record","payload":{"canonical_record":{"source":{"id":"1107.5682","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-07-28T11:33:11Z","cross_cats_sorted":[],"title_canon_sha256":"1ba2c1584cf64a3391fa5044b93100cfb70accc3c5b87a4e6ca1570981a8a815","abstract_canon_sha256":"42bc1f7aac38f0d4c805feea0fa48fd543984c898fc3e9f33ed37f7e8222bea4"},"schema_version":"1.0"},"canonical_sha256":"44db3dc2b63d8fda108353641ce0f8f5dd51c4ec82b706a60e2bd85cca59343c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:16:41.550311Z","signature_b64":"nI8GSeYAiCEEeeO2ws5CN8RZjFMFTGbrrGRrUabLnGm7E4iDnjSmIWE77UMEpbw3oDfPuGSrPild9irAiwL/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44db3dc2b63d8fda108353641ce0f8f5dd51c4ec82b706a60e2bd85cca59343c","last_reissued_at":"2026-05-18T04:16:41.549669Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:16:41.549669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.5682","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":"2026-05-18T04:16:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tjnjSB6Ym051L+Epr/5hf31j8edJ7r0srxwtQkyyXa0XvCowo4f9mpkfqf+MUUV86+IkPE5rCKTlfxDDQhefAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:47:03.847501Z"},"content_sha256":"66695d9e5e3cb965ebf82497b38615e1b13518dbb290a724254605e3b8d8d66c","schema_version":"1.0","event_id":"sha256:66695d9e5e3cb965ebf82497b38615e1b13518dbb290a724254605e3b8d8d66c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:ITNT3QVWHWH5UEEDKNSBZYHY6X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Powers of Derivatives in Classical Mechanics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Vasily E. Tarasov","submitted_at":"2011-07-28T11:33:11Z","abstract_excerpt":"Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \\partial_q+F(q,p) \\partial_p, which are used in equations of motion, are derivative operators. We consider fractional derivatives on a set of classical observables as fractional powers of derivative operators. As a result, we obtain a fractional generalization of the equation of motion. This fractional equation is exactly solved for the simple classical systems. The suggested fractional equations gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5682","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":"2026-05-18T04:16:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLLRIrxL6i01Og97q4GxgT/XiAduGjqDPhbhW6TpUP/j7agXz8QpVY3B/zLp3mPsF0GArSfpBhpuh8bQ/d+5Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:47:03.847843Z"},"content_sha256":"4ab033a115aecb10a617e0d6f392c2291784a7d07a86c43b30613f4260978f12","schema_version":"1.0","event_id":"sha256:4ab033a115aecb10a617e0d6f392c2291784a7d07a86c43b30613f4260978f12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X/bundle.json","state_url":"https://pith.science/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X/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":"2026-06-01T20:47:03Z","links":{"resolver":"https://pith.science/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X","bundle":"https://pith.science/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X/bundle.json","state":"https://pith.science/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ITNT3QVWHWH5UEEDKNSBZYHY6X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ITNT3QVWHWH5UEEDKNSBZYHY6X","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":"42bc1f7aac38f0d4c805feea0fa48fd543984c898fc3e9f33ed37f7e8222bea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-07-28T11:33:11Z","title_canon_sha256":"1ba2c1584cf64a3391fa5044b93100cfb70accc3c5b87a4e6ca1570981a8a815"},"schema_version":"1.0","source":{"id":"1107.5682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.5682","created_at":"2026-05-18T04:16:41Z"},{"alias_kind":"arxiv_version","alias_value":"1107.5682v1","created_at":"2026-05-18T04:16:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.5682","created_at":"2026-05-18T04:16:41Z"},{"alias_kind":"pith_short_12","alias_value":"ITNT3QVWHWH5","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"ITNT3QVWHWH5UEED","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"ITNT3QVW","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:4ab033a115aecb10a617e0d6f392c2291784a7d07a86c43b30613f4260978f12","target":"graph","created_at":"2026-05-18T04:16:41Z","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":"Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \\partial_q+F(q,p) \\partial_p, which are used in equations of motion, are derivative operators. We consider fractional derivatives on a set of classical observables as fractional powers of derivative operators. As a result, we obtain a fractional generalization of the equation of motion. This fractional equation is exactly solved for the simple classical systems. The suggested fractional equations gener","authors_text":"Vasily E. Tarasov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-07-28T11:33:11Z","title":"Fractional Powers of Derivatives in Classical Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.5682","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":"sha256:66695d9e5e3cb965ebf82497b38615e1b13518dbb290a724254605e3b8d8d66c","target":"record","created_at":"2026-05-18T04:16:41Z","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":"42bc1f7aac38f0d4c805feea0fa48fd543984c898fc3e9f33ed37f7e8222bea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-07-28T11:33:11Z","title_canon_sha256":"1ba2c1584cf64a3391fa5044b93100cfb70accc3c5b87a4e6ca1570981a8a815"},"schema_version":"1.0","source":{"id":"1107.5682","kind":"arxiv","version":1}},"canonical_sha256":"44db3dc2b63d8fda108353641ce0f8f5dd51c4ec82b706a60e2bd85cca59343c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44db3dc2b63d8fda108353641ce0f8f5dd51c4ec82b706a60e2bd85cca59343c","first_computed_at":"2026-05-18T04:16:41.549669Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:41.549669Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nI8GSeYAiCEEeeO2ws5CN8RZjFMFTGbrrGRrUabLnGm7E4iDnjSmIWE77UMEpbw3oDfPuGSrPild9irAiwL/Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:41.550311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.5682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66695d9e5e3cb965ebf82497b38615e1b13518dbb290a724254605e3b8d8d66c","sha256:4ab033a115aecb10a617e0d6f392c2291784a7d07a86c43b30613f4260978f12"],"state_sha256":"0c059745261d5ed028fa894359806f1ce2c3503c0248f34a527bbf87394694d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"grs3ZKt811pDNE8NByjFmM5lBykWJp1NS2SUxkGUX6RmMtJxeAPs7a8rvg9of+hLNvkOSCfveXmtaNDTYGtPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:47:03.849822Z","bundle_sha256":"07661caafe5af8dbc4d1752c5b97392f5cce9cbbedadd98bd143d749d6095e35"}}