{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:UOOR6RRB6QT4T7ERBOKKIEI6PZ","short_pith_number":"pith:UOOR6RRB","canonical_record":{"source":{"id":"math/0110241","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2001-10-22T13:41:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9eeb6e92df5997c812d3f53130a203312a2b1401f6a01693d353013ec320bce5","abstract_canon_sha256":"aeebcc040fa3d101e01c7714272ca2763c9f096fc217feaf04653483c314db70"},"schema_version":"1.0"},"canonical_sha256":"a39d1f4621f427c9fc910b94a4111e7e43cde6301c801f3137d17d226062ece9","source":{"kind":"arxiv","id":"math/0110241","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110241","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110241v1","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110241","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"UOOR6RRB6QT4","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"pith_short_16","alias_value":"UOOR6RRB6QT4T7ER","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"pith_short_8","alias_value":"UOOR6RRB","created_at":"2026-07-04T14:35:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:UOOR6RRB6QT4T7ERBOKKIEI6PZ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0110241","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CA","submitted_at":"2001-10-22T13:41:41Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"9eeb6e92df5997c812d3f53130a203312a2b1401f6a01693d353013ec320bce5","abstract_canon_sha256":"aeebcc040fa3d101e01c7714272ca2763c9f096fc217feaf04653483c314db70"},"schema_version":"1.0"},"canonical_sha256":"a39d1f4621f427c9fc910b94a4111e7e43cde6301c801f3137d17d226062ece9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:35.076402Z","signature_b64":"HyZTwgUih1cFTBZOME+loV71/RMsO2E9ts9q0so1iSfxDkKXfYO1736M8O7a3e6elH3s4Q+yCNiYBN/NDVoWBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a39d1f4621f427c9fc910b94a4111e7e43cde6301c801f3137d17d226062ece9","last_reissued_at":"2026-07-04T14:35:35.076032Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:35.076032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0110241","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":"2026-07-04T14:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iX4R7pzet2/SuDa1UuBTYcHD1HiWCe0ezXwl/WI47GRnqYLnuSDnuCERT/B+vF7QnuZZePv3jukFXwQpSGQFCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T05:38:44.734986Z"},"content_sha256":"76aa1777df15df92f9d22e70908da420e61d88dacfd8d2db98c387ea1390b9dc","schema_version":"1.0","event_id":"sha256:76aa1777df15df92f9d22e70908da420e61d88dacfd8d2db98c387ea1390b9dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:UOOR6RRB6QT4T7ERBOKKIEI6PZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Igor Podlubny","submitted_at":"2001-10-22T13:41:41Z","abstract_excerpt":"A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized for giving a new geometric and physical interpretation of more general convolution integrals of the Volterra type.\n  Besides this, a new physical interpretation is suggested for the Stieltjes integral."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110241","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0110241/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:35:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5LE6RcLB6ovyWURUpAxEmQnE/yHELbsOtp16JoCLvgmdHif54wV7YRnxYbHd3J6DHW13HqQarz6CK4GdiJxyDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T05:38:44.735377Z"},"content_sha256":"b78b03b8916da2d07356de033e6a428f3d8c1d3a222052181268ee858611c6c5","schema_version":"1.0","event_id":"sha256:b78b03b8916da2d07356de033e6a428f3d8c1d3a222052181268ee858611c6c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ/bundle.json","state_url":"https://pith.science/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ/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":"2026-08-17T05:38:44Z","links":{"resolver":"https://pith.science/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ","bundle":"https://pith.science/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ/bundle.json","state":"https://pith.science/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOOR6RRB6QT4T7ERBOKKIEI6PZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:UOOR6RRB6QT4T7ERBOKKIEI6PZ","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":"aeebcc040fa3d101e01c7714272ca2763c9f096fc217feaf04653483c314db70","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CA","submitted_at":"2001-10-22T13:41:41Z","title_canon_sha256":"9eeb6e92df5997c812d3f53130a203312a2b1401f6a01693d353013ec320bce5"},"schema_version":"1.0","source":{"id":"math/0110241","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0110241","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"arxiv_version","alias_value":"math/0110241v1","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0110241","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"pith_short_12","alias_value":"UOOR6RRB6QT4","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"pith_short_16","alias_value":"UOOR6RRB6QT4T7ER","created_at":"2026-07-04T14:35:35Z"},{"alias_kind":"pith_short_8","alias_value":"UOOR6RRB","created_at":"2026-07-04T14:35:35Z"}],"graph_snapshots":[{"event_id":"sha256:b78b03b8916da2d07356de033e6a428f3d8c1d3a222052181268ee858611c6c5","target":"graph","created_at":"2026-07-04T14:35:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0110241/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A solution to the more than 300-years old problem of geometric and physical interpretation of fractional integration and differentiation (i.e., integration and differentiation of an arbitrary real order) is suggested for the Riemann-Liouville fractional integration and differentiation, the Caputo fractional differentiation, the Riesz potential, and the Feller potential. It is also generalized for giving a new geometric and physical interpretation of more general convolution integrals of the Volterra type.\n  Besides this, a new physical interpretation is suggested for the Stieltjes integral.","authors_text":"Igor Podlubny","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.CA","submitted_at":"2001-10-22T13:41:41Z","title":"Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0110241","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":"sha256:76aa1777df15df92f9d22e70908da420e61d88dacfd8d2db98c387ea1390b9dc","target":"record","created_at":"2026-07-04T14:35:35Z","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":"aeebcc040fa3d101e01c7714272ca2763c9f096fc217feaf04653483c314db70","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.CA","submitted_at":"2001-10-22T13:41:41Z","title_canon_sha256":"9eeb6e92df5997c812d3f53130a203312a2b1401f6a01693d353013ec320bce5"},"schema_version":"1.0","source":{"id":"math/0110241","kind":"arxiv","version":1}},"canonical_sha256":"a39d1f4621f427c9fc910b94a4111e7e43cde6301c801f3137d17d226062ece9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a39d1f4621f427c9fc910b94a4111e7e43cde6301c801f3137d17d226062ece9","first_computed_at":"2026-07-04T14:35:35.076032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:35.076032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HyZTwgUih1cFTBZOME+loV71/RMsO2E9ts9q0so1iSfxDkKXfYO1736M8O7a3e6elH3s4Q+yCNiYBN/NDVoWBw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:35.076402Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0110241","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:76aa1777df15df92f9d22e70908da420e61d88dacfd8d2db98c387ea1390b9dc","sha256:b78b03b8916da2d07356de033e6a428f3d8c1d3a222052181268ee858611c6c5"],"state_sha256":"099ff5e65b9b059710127034268e366bb2b3e6dfc3ce06a3aea4c91c66c89395"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zP1IPkIEI8FECfGFGiAUWoUCFLIZuPOy1JGiIAdjrvkW9LIMLQdx1j/dfnyRCrlfZvd37hfAas99BcOBDhFYAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T05:38:44.737951Z","bundle_sha256":"229baad308a8b592519d217b10c4214a314f8970d72a6b9278ac48624e5caad0"}}