{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5JEZ3FA75CDH3ESOXWYKJED7VQ","short_pith_number":"pith:5JEZ3FA7","canonical_record":{"source":{"id":"1805.01536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-25T06:55:03Z","cross_cats_sorted":["math.DS","nlin.CD"],"title_canon_sha256":"669f91009826396ad139300d897a23c660fcec6d7874730708abbaf3355dd481","abstract_canon_sha256":"c04974dd91a69e9de754fb6986b6ae76f61d0f6c50c3ce9af1330cfd3fc3a877"},"schema_version":"1.0"},"canonical_sha256":"ea499d941fe8867d924ebdb0a4907fac3ebbbc39b7032f2bdbcc5e818e2f673d","source":{"kind":"arxiv","id":"1805.01536","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01536","created_at":"2026-05-18T00:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01536v2","created_at":"2026-05-18T00:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01536","created_at":"2026-05-18T00:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"5JEZ3FA75CDH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JEZ3FA75CDH3ESO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JEZ3FA7","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5JEZ3FA75CDH3ESOXWYKJED7VQ","target":"record","payload":{"canonical_record":{"source":{"id":"1805.01536","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-25T06:55:03Z","cross_cats_sorted":["math.DS","nlin.CD"],"title_canon_sha256":"669f91009826396ad139300d897a23c660fcec6d7874730708abbaf3355dd481","abstract_canon_sha256":"c04974dd91a69e9de754fb6986b6ae76f61d0f6c50c3ce9af1330cfd3fc3a877"},"schema_version":"1.0"},"canonical_sha256":"ea499d941fe8867d924ebdb0a4907fac3ebbbc39b7032f2bdbcc5e818e2f673d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:14.191498Z","signature_b64":"XDK3f+u9M5EKWdYi11mbs0Dnd25uwWU+l4PoxHJZ8i6zBkEkjzoi9XyQX16WqSmZTO2/V9Mcz06I/RVdRcagBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ea499d941fe8867d924ebdb0a4907fac3ebbbc39b7032f2bdbcc5e818e2f673d","last_reissued_at":"2026-05-18T00:09:14.190804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:14.190804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.01536","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oBeCH/I5WTsRCeYou3t7hhu1slCKOcqKaJEr1io52hVhB/IZS2VFPHdkF40ijLK5kGZIYIugxBZfNUv4yiZkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:41:00.098591Z"},"content_sha256":"832bfcfd6756cd53754b62057cd7215ccc4927646582f21a50fd2d3e4204a751","schema_version":"1.0","event_id":"sha256:832bfcfd6756cd53754b62057cd7215ccc4927646582f21a50fd2d3e4204a751"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5JEZ3FA75CDH3ESOXWYKJED7VQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Diffusion on middle-$\\xi$ Cantor sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.CD"],"primary_cat":"math.CA","authors_text":"Ali Khalili Golmankhaneh, Alireza Khalili Golmankhaneh, Arran Fernandez, Dumitru Baleanu","submitted_at":"2018-04-25T06:55:03Z","abstract_excerpt":"In this paper, we study $C^{\\zeta}$-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the $C^{\\zeta}$-calculus on the generalized Cantor sets known as middle-$\\xi$ Cantor sets. We have suggested a calculus on the middle-$\\xi$ Cantor sets for different values of $\\xi$ with $0<\\xi<1$. Differential equations on the middle-$\\xi$ Cantor sets hav"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01536","kind":"arxiv","version":2},"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":"2026-05-18T00:09:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLzu1T/qfO9YXiFx3ZkBafHPFyN8kwtkUiuIUo12ApRaRJV/HlH5L9LmZSMM6wOb/YB1KvXy4xIfOIKHUoZkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T15:41:00.099268Z"},"content_sha256":"5f16b0b5922095f3dfe4f19d8900d3078bd86315e345305e298e4fa8fdaab316","schema_version":"1.0","event_id":"sha256:5f16b0b5922095f3dfe4f19d8900d3078bd86315e345305e298e4fa8fdaab316"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ/bundle.json","state_url":"https://pith.science/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ/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":"2026-06-07T15:41:00Z","links":{"resolver":"https://pith.science/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ","bundle":"https://pith.science/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ/bundle.json","state":"https://pith.science/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5JEZ3FA75CDH3ESOXWYKJED7VQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5JEZ3FA75CDH3ESOXWYKJED7VQ","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":"c04974dd91a69e9de754fb6986b6ae76f61d0f6c50c3ce9af1330cfd3fc3a877","cross_cats_sorted":["math.DS","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-25T06:55:03Z","title_canon_sha256":"669f91009826396ad139300d897a23c660fcec6d7874730708abbaf3355dd481"},"schema_version":"1.0","source":{"id":"1805.01536","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.01536","created_at":"2026-05-18T00:09:14Z"},{"alias_kind":"arxiv_version","alias_value":"1805.01536v2","created_at":"2026-05-18T00:09:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.01536","created_at":"2026-05-18T00:09:14Z"},{"alias_kind":"pith_short_12","alias_value":"5JEZ3FA75CDH","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5JEZ3FA75CDH3ESO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5JEZ3FA7","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:5f16b0b5922095f3dfe4f19d8900d3078bd86315e345305e298e4fa8fdaab316","target":"graph","created_at":"2026-05-18T00:09:14Z","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 paper, we study $C^{\\zeta}$-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the $C^{\\zeta}$-calculus on the generalized Cantor sets known as middle-$\\xi$ Cantor sets. We have suggested a calculus on the middle-$\\xi$ Cantor sets for different values of $\\xi$ with $0<\\xi<1$. Differential equations on the middle-$\\xi$ Cantor sets hav","authors_text":"Ali Khalili Golmankhaneh, Alireza Khalili Golmankhaneh, Arran Fernandez, Dumitru Baleanu","cross_cats":["math.DS","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-25T06:55:03Z","title":"Diffusion on middle-$\\xi$ Cantor sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.01536","kind":"arxiv","version":2},"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":"sha256:832bfcfd6756cd53754b62057cd7215ccc4927646582f21a50fd2d3e4204a751","target":"record","created_at":"2026-05-18T00:09:14Z","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":"c04974dd91a69e9de754fb6986b6ae76f61d0f6c50c3ce9af1330cfd3fc3a877","cross_cats_sorted":["math.DS","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2018-04-25T06:55:03Z","title_canon_sha256":"669f91009826396ad139300d897a23c660fcec6d7874730708abbaf3355dd481"},"schema_version":"1.0","source":{"id":"1805.01536","kind":"arxiv","version":2}},"canonical_sha256":"ea499d941fe8867d924ebdb0a4907fac3ebbbc39b7032f2bdbcc5e818e2f673d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ea499d941fe8867d924ebdb0a4907fac3ebbbc39b7032f2bdbcc5e818e2f673d","first_computed_at":"2026-05-18T00:09:14.190804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:14.190804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XDK3f+u9M5EKWdYi11mbs0Dnd25uwWU+l4PoxHJZ8i6zBkEkjzoi9XyQX16WqSmZTO2/V9Mcz06I/RVdRcagBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:14.191498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.01536","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:832bfcfd6756cd53754b62057cd7215ccc4927646582f21a50fd2d3e4204a751","sha256:5f16b0b5922095f3dfe4f19d8900d3078bd86315e345305e298e4fa8fdaab316"],"state_sha256":"6c6ae89231fdbd49500600e8dded059ffc9900a658bf57eeae1e494fdd924473"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OQfWAHqn9npTZugqSWNAieSs96hARbwMPk4adw9WwI2Ei5NJbV0EV2+DPQTsaNSSq3UZUNMoMyYEmRcAjoQwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T15:41:00.103125Z","bundle_sha256":"b87b21f110a99415cc5f71bd6ae08cd07e52601d7c1707ea360c3da295d9c232"}}