{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6RLTUR2EZWZAOJGBDNN545JBR5","short_pith_number":"pith:6RLTUR2E","canonical_record":{"source":{"id":"1405.4581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T02:18:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c89b3258729edd25a9c6ffc029bbb03715fcc5328ed76c0cf584d0928da7d940","abstract_canon_sha256":"a2c3503f6e5d0f1838803a07ee9cfe24ac76c478a058c4b966c0ef4ac34083c9"},"schema_version":"1.0"},"canonical_sha256":"f4573a4744cdb20724c11b5bde75218f41bf323ab9af276027f9e2799598152a","source":{"kind":"arxiv","id":"1405.4581","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4581","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4581v1","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4581","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"6RLTUR2EZWZA","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6RLTUR2EZWZAOJGB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6RLTUR2E","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6RLTUR2EZWZAOJGBDNN545JBR5","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T02:18:12Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c89b3258729edd25a9c6ffc029bbb03715fcc5328ed76c0cf584d0928da7d940","abstract_canon_sha256":"a2c3503f6e5d0f1838803a07ee9cfe24ac76c478a058c4b966c0ef4ac34083c9"},"schema_version":"1.0"},"canonical_sha256":"f4573a4744cdb20724c11b5bde75218f41bf323ab9af276027f9e2799598152a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:12.654170Z","signature_b64":"2UyRQq1+BZe8sFS0zpoHiJtefSEOhDEaoyygg9t0qXDUDwYiOwQvwkwMHol/1p3EGH1/fH+iQyh260gCBVjQBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4573a4744cdb20724c11b5bde75218f41bf323ab9af276027f9e2799598152a","last_reissued_at":"2026-05-18T01:23:12.653589Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:12.653589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4581","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":"2026-05-18T01:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bxbOBGw4uR2SDIgJe75QoZOOIArXKjFd5hsmKr4pnQ+JF5bsgABMuJEkgrFQJVBcFQXgLfm23m9e+O3QveNcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:46:51.992899Z"},"content_sha256":"41bd00dfadc8d3e9048c30bfaa23817db91163de95384b1c9fa174df6eee8720","schema_version":"1.0","event_id":"sha256:41bd00dfadc8d3e9048c30bfaa23817db91163de95384b1c9fa174df6eee8720"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6RLTUR2EZWZAOJGBDNN545JBR5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Validity of the fractional Leibniz rule on a coarse-grained medium yields a modified fractional chain rule","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Jos\\'e Weberszpil","submitted_at":"2014-05-19T02:18:12Z","abstract_excerpt":"In this short communication, we show that the validity of the Leibniz rule for a fractional derivative on a coarse-grained medium brings about a modified chain rule, in agreement with alternative versions of fractional calculus. We compare our results to those of a recent article on this matter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4581","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":"2026-05-18T01:23:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DZAkmvKxGN54qR8mBE820sKrD1s7rAKNApcPwb2saZ/vbwQg9+vtsgzPGVzqNpXL4byQz6xjETkpvbQRtE6eDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T07:46:51.993245Z"},"content_sha256":"cca83feb769723495d02ca2d4a6a98b14df36e4369a1c759721a8271f04940cc","schema_version":"1.0","event_id":"sha256:cca83feb769723495d02ca2d4a6a98b14df36e4369a1c759721a8271f04940cc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6RLTUR2EZWZAOJGBDNN545JBR5/bundle.json","state_url":"https://pith.science/pith/6RLTUR2EZWZAOJGBDNN545JBR5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6RLTUR2EZWZAOJGBDNN545JBR5/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":"2026-06-26T07:46:51Z","links":{"resolver":"https://pith.science/pith/6RLTUR2EZWZAOJGBDNN545JBR5","bundle":"https://pith.science/pith/6RLTUR2EZWZAOJGBDNN545JBR5/bundle.json","state":"https://pith.science/pith/6RLTUR2EZWZAOJGBDNN545JBR5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6RLTUR2EZWZAOJGBDNN545JBR5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6RLTUR2EZWZAOJGBDNN545JBR5","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":"a2c3503f6e5d0f1838803a07ee9cfe24ac76c478a058c4b966c0ef4ac34083c9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T02:18:12Z","title_canon_sha256":"c89b3258729edd25a9c6ffc029bbb03715fcc5328ed76c0cf584d0928da7d940"},"schema_version":"1.0","source":{"id":"1405.4581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4581","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4581v1","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4581","created_at":"2026-05-18T01:23:12Z"},{"alias_kind":"pith_short_12","alias_value":"6RLTUR2EZWZA","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6RLTUR2EZWZAOJGB","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6RLTUR2E","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:cca83feb769723495d02ca2d4a6a98b14df36e4369a1c759721a8271f04940cc","target":"graph","created_at":"2026-05-18T01:23:12Z","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":"In this short communication, we show that the validity of the Leibniz rule for a fractional derivative on a coarse-grained medium brings about a modified chain rule, in agreement with alternative versions of fractional calculus. We compare our results to those of a recent article on this matter.","authors_text":"Jos\\'e Weberszpil","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T02:18:12Z","title":"Validity of the fractional Leibniz rule on a coarse-grained medium yields a modified fractional chain rule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4581","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":"sha256:41bd00dfadc8d3e9048c30bfaa23817db91163de95384b1c9fa174df6eee8720","target":"record","created_at":"2026-05-18T01:23:12Z","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":"a2c3503f6e5d0f1838803a07ee9cfe24ac76c478a058c4b966c0ef4ac34083c9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2014-05-19T02:18:12Z","title_canon_sha256":"c89b3258729edd25a9c6ffc029bbb03715fcc5328ed76c0cf584d0928da7d940"},"schema_version":"1.0","source":{"id":"1405.4581","kind":"arxiv","version":1}},"canonical_sha256":"f4573a4744cdb20724c11b5bde75218f41bf323ab9af276027f9e2799598152a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4573a4744cdb20724c11b5bde75218f41bf323ab9af276027f9e2799598152a","first_computed_at":"2026-05-18T01:23:12.653589Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:12.653589Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2UyRQq1+BZe8sFS0zpoHiJtefSEOhDEaoyygg9t0qXDUDwYiOwQvwkwMHol/1p3EGH1/fH+iQyh260gCBVjQBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:12.654170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41bd00dfadc8d3e9048c30bfaa23817db91163de95384b1c9fa174df6eee8720","sha256:cca83feb769723495d02ca2d4a6a98b14df36e4369a1c759721a8271f04940cc"],"state_sha256":"4b06b03a0e0c5e30a0b71d9f54f06b875b9e6460f5847fc962bcdd284314da1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j7uNAVGUNg3tIDEWDRhGOgwHA5qOH0QftaN0aEMoNIWtyI1qsnkLv4Se5Afs1xU9S5sTVKoGVPXIN/ySUS4UBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T07:46:51.995199Z","bundle_sha256":"07adc1e0eb29aeaeae731e65cc98fc64b0d1e256f3d261353f725a9175abd7ed"}}