{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SJAYHASNIZH33ZDRI6XN57STRX","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":"eaabb14f41c3af0509013dd28314845a7a32a01739a593b51adbd993af7d653c","cross_cats_sorted":["cs.CG","cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2018-01-30T18:06:06Z","title_canon_sha256":"4d463a044fd06df095acd7f791ba2541a2a22e228d16c5365a267f459955ca1c"},"schema_version":"1.0","source":{"id":"1801.10118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.10118","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1801.10118v1","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.10118","created_at":"2026-05-18T00:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"SJAYHASNIZH3","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SJAYHASNIZH33ZDR","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SJAYHASN","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:e60f8d2ed665a4d20ee7df860f6040e7e11b0c6f92f042385ce947ca419f557f","target":"graph","created_at":"2026-05-18T00:24:45Z","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"},"paper":{"abstract_excerpt":"Discrete Morse theory emerged as an essential tool for computational geometry and topology. Its core structures are discrete gradient fields, defined as acyclic matchings on a complex $C$, from which topological and geometrical informations of $C$ can be efficiently computed, in particular its homology or Morse-Smale decomposition.\n  Given a function $f$ sampled on $C$, it is possible to derive a discrete gradient that mimics the dynamics of $f$. Many such constructions are based on some variant of a greedy pairing of adjacent cells, given an appropriate weighting. However, proving that the dy","authors_text":"Joao Lagoas, Joao Paixao, Thomas Lewiner, Tiago Novello","cross_cats":["cs.CG","cs.DM","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2018-01-30T18:06:06Z","title":"Greedy Morse matchings and discrete smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10118","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":"sha256:19c0127c3038af573edbcbe29139abc31305b8d0bcaa051b34369613d61a0a02","target":"record","created_at":"2026-05-18T00:24:45Z","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":"eaabb14f41c3af0509013dd28314845a7a32a01739a593b51adbd993af7d653c","cross_cats_sorted":["cs.CG","cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GT","submitted_at":"2018-01-30T18:06:06Z","title_canon_sha256":"4d463a044fd06df095acd7f791ba2541a2a22e228d16c5365a267f459955ca1c"},"schema_version":"1.0","source":{"id":"1801.10118","kind":"arxiv","version":1}},"canonical_sha256":"924183824d464fbde47147aedefe538ddd38289a2a9d8daa51fd62579feefe93","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"924183824d464fbde47147aedefe538ddd38289a2a9d8daa51fd62579feefe93","first_computed_at":"2026-05-18T00:24:45.852086Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:24:45.852086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UGAF7jmp5+j+QVpwq+Z8eqobFC71UdbU+uX1K9CM5E1MJk1Zo+jFGzVvWod1Do/s89MsQDQJmetVawhmck2PDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:24:45.852758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.10118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19c0127c3038af573edbcbe29139abc31305b8d0bcaa051b34369613d61a0a02","sha256:e60f8d2ed665a4d20ee7df860f6040e7e11b0c6f92f042385ce947ca419f557f"],"state_sha256":"719ae6628100037ebf417afff7a1c52d88c1ef939ca1bb282ae91a6d3f210a6c"}