{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QW7RT4SSF6C6TWJ35SJYAGFPMV","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":"6a4c1b48d4dd27d123117fcb5f5551f1a65e705177d408d2cf22a283a592efed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-12T17:06:48Z","title_canon_sha256":"21654a852d90915ebfe354081c32663a721500fd3eab1581f09cfc59767ef907"},"schema_version":"1.0","source":{"id":"1812.05031","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.05031","created_at":"2026-07-05T04:10:49Z"},{"alias_kind":"arxiv_version","alias_value":"1812.05031v3","created_at":"2026-07-05T04:10:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.05031","created_at":"2026-07-05T04:10:49Z"},{"alias_kind":"pith_short_12","alias_value":"QW7RT4SSF6C6","created_at":"2026-07-05T04:10:49Z"},{"alias_kind":"pith_short_16","alias_value":"QW7RT4SSF6C6TWJ3","created_at":"2026-07-05T04:10:49Z"},{"alias_kind":"pith_short_8","alias_value":"QW7RT4SS","created_at":"2026-07-05T04:10:49Z"}],"graph_snapshots":[{"event_id":"sha256:8c19bb432e0ef3d3421c6ebf516f4f2496ef0676dcae8cc64aeaa52744aaa66a","target":"graph","created_at":"2026-07-05T04:10:49Z","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/1812.05031/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations. Leveraging recent advances in the computation of Steenrod squares, we introduce a new family of computable invariants on mod 2 persistent cohomology termed $Sq^k$-barcodes. We present a complete algorithmic pipeline for their computation and illustrate their real-world applicability using the space of conformations of the cyclo-octane molecule.","authors_text":"Anibal M. Medina-Mardones, Guillaume Tauzin, Umberto Lupo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-12T17:06:48Z","title":"Persistence Steenrod modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05031","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":"sha256:13b228371d48562d3e486d2fa2509b4e6fb865dc0f02bfd469f26fa1d78397e0","target":"record","created_at":"2026-07-05T04:10:49Z","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":"6a4c1b48d4dd27d123117fcb5f5551f1a65e705177d408d2cf22a283a592efed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-12T17:06:48Z","title_canon_sha256":"21654a852d90915ebfe354081c32663a721500fd3eab1581f09cfc59767ef907"},"schema_version":"1.0","source":{"id":"1812.05031","kind":"arxiv","version":3}},"canonical_sha256":"85bf19f2522f85e9d93bec938018af657c71f0bd3995357241f8c5cc29d6a1a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85bf19f2522f85e9d93bec938018af657c71f0bd3995357241f8c5cc29d6a1a2","first_computed_at":"2026-07-05T04:10:49.399831Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:10:49.399831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cIhV+TyjzuiNwt4BWo/whQp1NJjebDFxaB2iMkKEU9eUz0VMV8Wb2r/PY+vq/5XHvU6bMCj75ihJhWjfgWrwDg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:10:49.400289Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.05031","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13b228371d48562d3e486d2fa2509b4e6fb865dc0f02bfd469f26fa1d78397e0","sha256:8c19bb432e0ef3d3421c6ebf516f4f2496ef0676dcae8cc64aeaa52744aaa66a"],"state_sha256":"2a8cbb8cf84ddc84750f554ffe32614214b374d5756cc1f4d1fa10dcd1370a16"}