{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:37LXDZNWH6YJVGPBNELSBS6I2R","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":"ceb7a1295180c275e832282a65643776a5e584419bf4666470c486d9c57fb4d7","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-28T20:02:25Z","title_canon_sha256":"bb0cea19dfd214d27bcbbeb59070d1659c199ee69a37d2c810415364a20e3958"},"schema_version":"1.0","source":{"id":"2607.26226","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.26226","created_at":"2026-07-30T01:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"2607.26226v1","created_at":"2026-07-30T01:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.26226","created_at":"2026-07-30T01:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"37LXDZNWH6YJ","created_at":"2026-07-30T01:17:45Z"},{"alias_kind":"pith_short_16","alias_value":"37LXDZNWH6YJVGPB","created_at":"2026-07-30T01:17:45Z"},{"alias_kind":"pith_short_8","alias_value":"37LXDZNW","created_at":"2026-07-30T01:17:45Z"}],"graph_snapshots":[{"event_id":"sha256:bcbc88480a8a2d76e59cd65f06b565f56d0a5a6667970696f9e7dbdc0a8f34ec","target":"graph","created_at":"2026-07-30T01:17:45Z","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/2607.26226/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show stability of persistent path homology of path complexes. As a consequence, we deduce the stability of persistent path homology of hypergraphs and of sequence hypergraphs, and recover the known stability result for digraphs, originally due to Chowdhury and M\\'emoli.","authors_text":"Chris Kapulkin, Kyle Koyanagi","cross_cats":["cs.CG","math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-28T20:02:25Z","title":"Stability of persistent path homology of path complexes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.26226","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":"sha256:5b9198ce4be8ca28d85815e7f94686630c9feabc00e0ce525832b76211082667","target":"record","created_at":"2026-07-30T01:17:45Z","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":"ceb7a1295180c275e832282a65643776a5e584419bf4666470c486d9c57fb4d7","cross_cats_sorted":["cs.CG","math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2026-07-28T20:02:25Z","title_canon_sha256":"bb0cea19dfd214d27bcbbeb59070d1659c199ee69a37d2c810415364a20e3958"},"schema_version":"1.0","source":{"id":"2607.26226","kind":"arxiv","version":1}},"canonical_sha256":"dfd771e5b63fb09a99e1691720cbc8d4735659fce0f789dd4e35a9f53cb53f6f","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfd771e5b63fb09a99e1691720cbc8d4735659fce0f789dd4e35a9f53cb53f6f","first_computed_at":"2026-07-30T01:17:45.453442Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:17:45.453442Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.26226","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b9198ce4be8ca28d85815e7f94686630c9feabc00e0ce525832b76211082667","sha256:bcbc88480a8a2d76e59cd65f06b565f56d0a5a6667970696f9e7dbdc0a8f34ec"],"state_sha256":"c8514c7699986b4843d403cde2d59c7901717a6967b9065a90dcdf8a3e87f1ff"}