{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WXB7DJKDWRJ7YVFCDIOEND6WVZ","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":"48ecebe2929352689a331461309b4ab1a53937cef207a570939ec2e2639b28e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-31T22:05:28Z","title_canon_sha256":"d2d365e104a4509225fd2d60f505366e95dac70c20435e210172129bfe71d64f"},"schema_version":"1.0","source":{"id":"1109.0043","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.0043","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"arxiv_version","alias_value":"1109.0043v2","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.0043","created_at":"2026-05-18T03:42:21Z"},{"alias_kind":"pith_short_12","alias_value":"WXB7DJKDWRJ7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WXB7DJKDWRJ7YVFC","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WXB7DJKD","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c208569411149de1a1e9b1c61106941df91d0e6cbd216dd352b9fede9aa38c3c","target":"graph","created_at":"2026-05-18T03:42:21Z","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":"The truncated variation, $TV^c$, is a fairly new concept introduced in [5]. Roughly speaking, given a c\\`adl\\`ag function $f$, its truncated variation is \"the total variation which does not pay attention to small changes of $f$, below some threshold $c>0$\". The very basic consequence of such approach is that contrary to the total variation, $TV^c$ is always finite. This is appealing to the stochastic analysis where so-far large classes of processes, like semimartingales or diffusions, could not be studied with the total variation. Recently in [6], another characterization of $TV^c$ was found. ","authors_text":"Piotr Mi{\\l}o\\'s, Rafa{\\l} M. {\\L}ochowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-31T22:05:28Z","title":"On truncated variation, upward truncated variation and downward truncated variation for diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.0043","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":"sha256:6fe2ab76b1567984ed4dd8da0276c3062e6e2ea4fbdd802d7cab9435efd1c22e","target":"record","created_at":"2026-05-18T03:42:21Z","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":"48ecebe2929352689a331461309b4ab1a53937cef207a570939ec2e2639b28e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-31T22:05:28Z","title_canon_sha256":"d2d365e104a4509225fd2d60f505366e95dac70c20435e210172129bfe71d64f"},"schema_version":"1.0","source":{"id":"1109.0043","kind":"arxiv","version":2}},"canonical_sha256":"b5c3f1a543b453fc54a21a1c468fd6ae429b13fd18bbd17d51fec422d4d282fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5c3f1a543b453fc54a21a1c468fd6ae429b13fd18bbd17d51fec422d4d282fe","first_computed_at":"2026-05-18T03:42:21.548532Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:21.548532Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7LZrDRAtv5mh+tIaLjwtQp2DUkHSJDTgargGG2tTGELAdegO3SHByZ8GTPBdffT5zgblG96hbikxkx1UVgw5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:21.549240Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.0043","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fe2ab76b1567984ed4dd8da0276c3062e6e2ea4fbdd802d7cab9435efd1c22e","sha256:c208569411149de1a1e9b1c61106941df91d0e6cbd216dd352b9fede9aa38c3c"],"state_sha256":"85b37ee5b3836f20ae7fa2193166a10b0dc0600355414948591782fe1c6a4b58"}