{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4SXYX2JCIIBNLVBNZA4E7PTCDD","short_pith_number":"pith:4SXYX2JC","canonical_record":{"source":{"id":"1106.3010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T15:55:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"58cbef3fe7f54d0bb965330d3b23f70a8426b8ef80defd5375465abb634ee004","abstract_canon_sha256":"bc59b6fb404a06561d81382424477f5d4f13d2df2837fbe9303579fd75cb9617"},"schema_version":"1.0"},"canonical_sha256":"e4af8be9224202d5d42dc8384fbe6218c388027193036e595f24735c0d0460f3","source":{"kind":"arxiv","id":"1106.3010","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3010","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3010v1","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3010","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"4SXYX2JCIIBN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4SXYX2JCIIBNLVBN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4SXYX2JC","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4SXYX2JCIIBNLVBNZA4E7PTCDD","target":"record","payload":{"canonical_record":{"source":{"id":"1106.3010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T15:55:50Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"58cbef3fe7f54d0bb965330d3b23f70a8426b8ef80defd5375465abb634ee004","abstract_canon_sha256":"bc59b6fb404a06561d81382424477f5d4f13d2df2837fbe9303579fd75cb9617"},"schema_version":"1.0"},"canonical_sha256":"e4af8be9224202d5d42dc8384fbe6218c388027193036e595f24735c0d0460f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:08.652263Z","signature_b64":"IEzKSKxUnMAFNeasx/LQ4YjDUGu2zNntjVha8e4NBCh4EyKhdnba3ivyof9UyuPmgokUp5mT9TKggKcFrIWcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4af8be9224202d5d42dc8384fbe6218c388027193036e595f24735c0d0460f3","last_reissued_at":"2026-05-18T04:10:08.651057Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:08.651057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1106.3010","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":"2026-05-18T04:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uT+gyGEnEkmwdf9Rm2PdoSKtpB//kvBuGelgbS+atganGlnwDLadxNXYnlK5EgfHpJPoAlUyfftjRiheUC02AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:51:56.204928Z"},"content_sha256":"97cb89d52129bb0fd0a55b2916696ee6d260e74c4974325acd7c8b406bae31ba","schema_version":"1.0","event_id":"sha256:97cb89d52129bb0fd0a55b2916696ee6d260e74c4974325acd7c8b406bae31ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4SXYX2JCIIBNLVBNZA4E7PTCDD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Xiao-Jun Yang","submitted_at":"2011-06-15T15:55:50Z","abstract_excerpt":"This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3010","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":"2026-05-18T04:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mvveHvSH4egQZSNlvBdfNK9eRPZrixrMX+n8BKUybe616PLN3wPcAck0USvXjjf/S3FS1uNsAzB5Rwl27dNmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:51:56.205275Z"},"content_sha256":"e221731904adb4e859bbd74fd501aae951af86841de01dce258c126692186806","schema_version":"1.0","event_id":"sha256:e221731904adb4e859bbd74fd501aae951af86841de01dce258c126692186806"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD/bundle.json","state_url":"https://pith.science/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD/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":"2026-06-20T06:51:56Z","links":{"resolver":"https://pith.science/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD","bundle":"https://pith.science/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD/bundle.json","state":"https://pith.science/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4SXYX2JCIIBNLVBNZA4E7PTCDD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4SXYX2JCIIBNLVBNZA4E7PTCDD","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":"bc59b6fb404a06561d81382424477f5d4f13d2df2837fbe9303579fd75cb9617","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T15:55:50Z","title_canon_sha256":"58cbef3fe7f54d0bb965330d3b23f70a8426b8ef80defd5375465abb634ee004"},"schema_version":"1.0","source":{"id":"1106.3010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3010","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3010v1","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3010","created_at":"2026-05-18T04:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"4SXYX2JCIIBN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4SXYX2JCIIBNLVBN","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4SXYX2JC","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:e221731904adb4e859bbd74fd501aae951af86841de01dce258c126692186806","target":"graph","created_at":"2026-05-18T04:10:08Z","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":"This paper presents a better approach to model an engineering problem in fractal-time space based on local fractional calculus. Some examples are given to elucidate to establish governing equations with local fractional derivative.","authors_text":"Xiao-Jun Yang","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T15:55:50Z","title":"Applications of local fractional calculus to engineering in fractal time-space: Local fractional differential equations with local fractional derivative"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3010","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":"sha256:97cb89d52129bb0fd0a55b2916696ee6d260e74c4974325acd7c8b406bae31ba","target":"record","created_at":"2026-05-18T04:10:08Z","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":"bc59b6fb404a06561d81382424477f5d4f13d2df2837fbe9303579fd75cb9617","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-15T15:55:50Z","title_canon_sha256":"58cbef3fe7f54d0bb965330d3b23f70a8426b8ef80defd5375465abb634ee004"},"schema_version":"1.0","source":{"id":"1106.3010","kind":"arxiv","version":1}},"canonical_sha256":"e4af8be9224202d5d42dc8384fbe6218c388027193036e595f24735c0d0460f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4af8be9224202d5d42dc8384fbe6218c388027193036e595f24735c0d0460f3","first_computed_at":"2026-05-18T04:10:08.651057Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:08.651057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IEzKSKxUnMAFNeasx/LQ4YjDUGu2zNntjVha8e4NBCh4EyKhdnba3ivyof9UyuPmgokUp5mT9TKggKcFrIWcBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:08.652263Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97cb89d52129bb0fd0a55b2916696ee6d260e74c4974325acd7c8b406bae31ba","sha256:e221731904adb4e859bbd74fd501aae951af86841de01dce258c126692186806"],"state_sha256":"481ca9345aa8eaea9f8be0c370a6ed5b9722dfa52b4b732047e7e60fb63a5e6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VYI5gW/9Vt5yGHDDX7YmxF1W1jzzDfbHHxFEWZ2VDuydB7jwnjvvumiMBwtEvHHccguvo4U8edX8SpeHbCHQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:51:56.207598Z","bundle_sha256":"a24a85b67b4aa56e4fc860dd65fcc6f6bd0055d760deed5770d18dcd7e2d5937"}}