{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QNCFIAS6MXKVU3NET3TVI6SY7N","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":"628a1b553cbf9bbdfb049a8bc535d1b768e9f253de68dce5871e32d00e0ffca0","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-01-14T09:36:10Z","title_canon_sha256":"d73626116a8cf5993d145b5d8485320705bfef078b0d1bff310c3dd9629e5407"},"schema_version":"1.0","source":{"id":"2501.07966","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.07966","created_at":"2026-07-05T10:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"2501.07966v3","created_at":"2026-07-05T10:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.07966","created_at":"2026-07-05T10:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"QNCFIAS6MXKV","created_at":"2026-07-05T10:30:03Z"},{"alias_kind":"pith_short_16","alias_value":"QNCFIAS6MXKVU3NE","created_at":"2026-07-05T10:30:03Z"},{"alias_kind":"pith_short_8","alias_value":"QNCFIAS6","created_at":"2026-07-05T10:30:03Z"}],"graph_snapshots":[{"event_id":"sha256:7394338ac696fed71d9a0c99199b2142c3e157d6a1ad9697fe5e6b450f3e4e95","target":"graph","created_at":"2026-07-05T10:30:03Z","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/2501.07966/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the horizontal component of the Peano curve has quadratic variation equal the limit of quadratic variations along the Lebesgue partitions for grids of the form $3^{-n}p\\mathbb{Z}+3^{-n}r$, $n=1,2,\\ldots$, where $p$ is a rational number, while $r$ is irrational number, but the value of such quadratic variation depends on $p$.\n  This also yields that the horizontal component of the Peano curve is an example of a deterministic function possessing local time (density of the occupation measure) with respect to the Lebesgue measure, whose local time can be expressed as the limit of norm","authors_text":"Darlington Hove, Farai J. Mhlanga, Phumlani L. Zondi, Rafa{\\l} M. {\\L}ochowski","cross_cats":["math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-01-14T09:36:10Z","title":"Quadratic variation and local times of the horizontal component of the Peano curve (square filling curve)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07966","kind":"arxiv","version":3},"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":"sha256:77b8537b153a12f2eba486464ba6848164d6fc6ec2bd70b9dce13282bff48e80","target":"record","created_at":"2026-07-05T10:30:03Z","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":"628a1b553cbf9bbdfb049a8bc535d1b768e9f253de68dce5871e32d00e0ffca0","cross_cats_sorted":["math.PR"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CA","submitted_at":"2025-01-14T09:36:10Z","title_canon_sha256":"d73626116a8cf5993d145b5d8485320705bfef078b0d1bff310c3dd9629e5407"},"schema_version":"1.0","source":{"id":"2501.07966","kind":"arxiv","version":3}},"canonical_sha256":"834454025e65d55a6da49ee7547a58fb62fc37398e626353c1a63ebe149fc5db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"834454025e65d55a6da49ee7547a58fb62fc37398e626353c1a63ebe149fc5db","first_computed_at":"2026-07-05T10:30:03.567227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:30:03.567227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UW7yqsn72Q3xZBw/nBgZ/8ULjIUrUyhC1BFDmSZFysn6m4b+x3LJC/02pLTRZ9ACXrr9wUt5xUt+MP/0YUnqCw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:30:03.567723Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.07966","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77b8537b153a12f2eba486464ba6848164d6fc6ec2bd70b9dce13282bff48e80","sha256:7394338ac696fed71d9a0c99199b2142c3e157d6a1ad9697fe5e6b450f3e4e95"],"state_sha256":"3bee9ea9c6d9a229cc3a9e9e9924e2f17eef8c3a96902c0a9004ab98f58eecdf"}