{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:J4QVYAOOAEV7VTK4Y2CGOIUZXC","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":"e03fec714e88bf1c1da8d8f63424b90421a0dbec41249eef4a49d9975058abbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-03-02T22:36:55Z","title_canon_sha256":"fe790383ab887401478e43fe5e697b709d677ac6e947ae142b875877bf22fbd6"},"schema_version":"1.0","source":{"id":"1903.00783","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.00783","created_at":"2026-07-05T01:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1903.00783v2","created_at":"2026-07-05T01:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.00783","created_at":"2026-07-05T01:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"J4QVYAOOAEV7","created_at":"2026-07-05T01:39:40Z"},{"alias_kind":"pith_short_16","alias_value":"J4QVYAOOAEV7VTK4","created_at":"2026-07-05T01:39:40Z"},{"alias_kind":"pith_short_8","alias_value":"J4QVYAOO","created_at":"2026-07-05T01:39:40Z"}],"graph_snapshots":[{"event_id":"sha256:ca0bdc7fea11b478e7ca2dac8141ee4ae87dc1c93b725fe6e8a0418a1607829a","target":"graph","created_at":"2026-07-05T01:39:40Z","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/1903.00783/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Reducing a chain complex (whilst preserving its homotopy-type) using algebraic Morse theory gives the same end-result as Gaussian elimination, but AMT does it only on certain rows/columns and with several pivots (in all matrices simultaneously). Crucially, instead of doing costly row/column operations on a sparse matrix, it computes traversals of a bipartite digraph. This significantly reduces the running time and memory load (smaller fill-in and coefficient growth of the matrices). However, computing with AMT requires the construction of a valid set of pivots (called a Morse matching).\n  We d","authors_text":"Leon Lampret","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-03-02T22:36:55Z","title":"Chain complex reduction via fast digraph traversal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00783","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:b0ef3bf07030256357ca1d267cd64b0a74770266cde16ab555e0bd8ee3509564","target":"record","created_at":"2026-07-05T01:39:40Z","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":"e03fec714e88bf1c1da8d8f63424b90421a0dbec41249eef4a49d9975058abbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2019-03-02T22:36:55Z","title_canon_sha256":"fe790383ab887401478e43fe5e697b709d677ac6e947ae142b875877bf22fbd6"},"schema_version":"1.0","source":{"id":"1903.00783","kind":"arxiv","version":2}},"canonical_sha256":"4f215c01ce012bfacd5cc684672299b88f6dd0e90debf0b6e7bedcf4afe26747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f215c01ce012bfacd5cc684672299b88f6dd0e90debf0b6e7bedcf4afe26747","first_computed_at":"2026-07-05T01:39:40.629859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:39:40.629859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9WYiROLkhmaMojAKPgJC3QQPoG+7js8n+5hngm+a5BydwpWlEKQLxBHmhTdAXwSyA4/mStVrGDA5HrLEl5YMBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:39:40.630261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.00783","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0ef3bf07030256357ca1d267cd64b0a74770266cde16ab555e0bd8ee3509564","sha256:ca0bdc7fea11b478e7ca2dac8141ee4ae87dc1c93b725fe6e8a0418a1607829a"],"state_sha256":"f884e32a192b35bd003bafc68a025112b65dd385f53cffa0c5d95ae041586f49"}