{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1998:72KK75DML4QLSBA22YZPCJKNBD","short_pith_number":"pith:72KK75DM","canonical_record":{"source":{"id":"chao-dyn/9810030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-23T08:37:12Z","cross_cats_sorted":["cond-mat","nlin.CD"],"title_canon_sha256":"bc96afa7fe635f81d6eba9c27b34043300c29ec2f8722778c6ab95fbbcbc047a","abstract_canon_sha256":"d2cd475d478100d5259b4b453ce35b8fb5a9da5bb98ac5e6a0ffcc444c0c5a95"},"schema_version":"1.0"},"canonical_sha256":"fe94aff46c5f20b9041ad632f1254d08c5ebfa2e8f0558e5c3545f27fb2c4436","source":{"kind":"arxiv","id":"chao-dyn/9810030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9810030","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9810030v1","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9810030","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"72KK75DML4QL","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"72KK75DML4QLSBA2","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"72KK75DM","created_at":"2026-05-18T12:25:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1998:72KK75DML4QLSBA22YZPCJKNBD","target":"record","payload":{"canonical_record":{"source":{"id":"chao-dyn/9810030","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-23T08:37:12Z","cross_cats_sorted":["cond-mat","nlin.CD"],"title_canon_sha256":"bc96afa7fe635f81d6eba9c27b34043300c29ec2f8722778c6ab95fbbcbc047a","abstract_canon_sha256":"d2cd475d478100d5259b4b453ce35b8fb5a9da5bb98ac5e6a0ffcc444c0c5a95"},"schema_version":"1.0"},"canonical_sha256":"fe94aff46c5f20b9041ad632f1254d08c5ebfa2e8f0558e5c3545f27fb2c4436","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:40:11.544329Z","signature_b64":"NZnutrCf8BKQQSrD+8qlQ1wASe9w3hqilhN5VSsqUVZ5pBczdNXxZ/h/7Mp/LirNWdpeNORUnrt+83NVh8RfCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe94aff46c5f20b9041ad632f1254d08c5ebfa2e8f0558e5c3545f27fb2c4436","last_reissued_at":"2026-05-18T01:40:11.543644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:40:11.543644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"chao-dyn/9810030","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":"2026-05-18T01:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k4AP2BkuvoyxWDYF17mPZVMRByvk/E76x7skvBQeg2fQRRpfhEn4eWdODL/+KFsvz6qRXYeXsKd0mVeL6vn3BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:29:16.295916Z"},"content_sha256":"ac6aed11201eb631df80f3b37e168ee91be65cc10a25f847056e6918bffb28fc","schema_version":"1.0","event_id":"sha256:ac6aed11201eb631df80f3b37e168ee91be65cc10a25f847056e6918bffb28fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1998:72KK75DML4QLSBA22YZPCJKNBD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fractional Calculus and the Evolution of Fractal Phenomena","license":"","headline":"","cross_cats":["cond-mat","nlin.CD"],"primary_cat":"chao-dyn","authors_text":"Andrea Rocco, Bruce J. West","submitted_at":"1998-10-23T08:37:12Z","abstract_excerpt":"It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal function with a greater (lesser) fractal dimension. We also determine that the GWF is a solution to such a fractional differential stochastic equation of motion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9810030","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":"2026-05-18T01:40:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"42tcztN9mPEmji2uknr8aNqNbhj4h1pUo22SkrauFTLsmdxz1EoaG2RaXBg3anusPdsnFjGZMOb9LcJ1UlA/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T12:29:16.296274Z"},"content_sha256":"e0d2f2570d269c76a73b3778d7d95349b19e6e2ce79df363ef7cc8cc0b747cd1","schema_version":"1.0","event_id":"sha256:e0d2f2570d269c76a73b3778d7d95349b19e6e2ce79df363ef7cc8cc0b747cd1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/72KK75DML4QLSBA22YZPCJKNBD/bundle.json","state_url":"https://pith.science/pith/72KK75DML4QLSBA22YZPCJKNBD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/72KK75DML4QLSBA22YZPCJKNBD/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":"2026-06-03T12:29:16Z","links":{"resolver":"https://pith.science/pith/72KK75DML4QLSBA22YZPCJKNBD","bundle":"https://pith.science/pith/72KK75DML4QLSBA22YZPCJKNBD/bundle.json","state":"https://pith.science/pith/72KK75DML4QLSBA22YZPCJKNBD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/72KK75DML4QLSBA22YZPCJKNBD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:72KK75DML4QLSBA22YZPCJKNBD","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":"d2cd475d478100d5259b4b453ce35b8fb5a9da5bb98ac5e6a0ffcc444c0c5a95","cross_cats_sorted":["cond-mat","nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-23T08:37:12Z","title_canon_sha256":"bc96afa7fe635f81d6eba9c27b34043300c29ec2f8722778c6ab95fbbcbc047a"},"schema_version":"1.0","source":{"id":"chao-dyn/9810030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9810030","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9810030v1","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9810030","created_at":"2026-05-18T01:40:11Z"},{"alias_kind":"pith_short_12","alias_value":"72KK75DML4QL","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"72KK75DML4QLSBA2","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"72KK75DM","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:e0d2f2570d269c76a73b3778d7d95349b19e6e2ce79df363ef7cc8cc0b747cd1","target":"graph","created_at":"2026-05-18T01:40:11Z","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":"It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal function with a greater (lesser) fractal dimension. We also determine that the GWF is a solution to such a fractional differential stochastic equation of motion.","authors_text":"Andrea Rocco, Bruce J. West","cross_cats":["cond-mat","nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-23T08:37:12Z","title":"Fractional Calculus and the Evolution of Fractal Phenomena"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9810030","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:ac6aed11201eb631df80f3b37e168ee91be65cc10a25f847056e6918bffb28fc","target":"record","created_at":"2026-05-18T01:40:11Z","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":"d2cd475d478100d5259b4b453ce35b8fb5a9da5bb98ac5e6a0ffcc444c0c5a95","cross_cats_sorted":["cond-mat","nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1998-10-23T08:37:12Z","title_canon_sha256":"bc96afa7fe635f81d6eba9c27b34043300c29ec2f8722778c6ab95fbbcbc047a"},"schema_version":"1.0","source":{"id":"chao-dyn/9810030","kind":"arxiv","version":1}},"canonical_sha256":"fe94aff46c5f20b9041ad632f1254d08c5ebfa2e8f0558e5c3545f27fb2c4436","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe94aff46c5f20b9041ad632f1254d08c5ebfa2e8f0558e5c3545f27fb2c4436","first_computed_at":"2026-05-18T01:40:11.543644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:40:11.543644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NZnutrCf8BKQQSrD+8qlQ1wASe9w3hqilhN5VSsqUVZ5pBczdNXxZ/h/7Mp/LirNWdpeNORUnrt+83NVh8RfCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:40:11.544329Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9810030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac6aed11201eb631df80f3b37e168ee91be65cc10a25f847056e6918bffb28fc","sha256:e0d2f2570d269c76a73b3778d7d95349b19e6e2ce79df363ef7cc8cc0b747cd1"],"state_sha256":"f8e02d5de1f7775be48d473230ec313dc9fa2b55af08c84ba0217ad74d61a0d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PzQJ4oejXbkgj1n8Sic38yUGEjz6frsfOcQgSiyOalbG1R91MeQhxIfsxHrIiVcnOtvk5hkPNJNl5+u2PHBEDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T12:29:16.298241Z","bundle_sha256":"c22828bc068dd50c1a4a28323f582684815b535a471b59f86ca691c0500eb986"}}