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This zigzag Morse filtration generalizes the filtered Morse complex of Mischaikow and Nanda, defined for standard persistence.\n  The maps in the zigzag Morse filtration are forward and backward inclusions, as is"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1807.05172","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2018-07-13T16:43:28Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"ab44e0bcd67ed54a52b3908399ea989efb775ed36cd31a1a05a27737915b051a","abstract_canon_sha256":"8c47b04dab8a1baab1295b0bfc247be41df86f0f419db2ff0dfed8b71c8241a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:55.981186Z","signature_b64":"ZPMdcag6+OvHatuTjdhGpLuStYYdYzi65VK04ZAmxziLOT3G10V042Eb4TYDwgG5ot/YQIlBS72YDSBQ4leZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"45cae9359914762253408877ab0ce99cf45c850dbe271d79950c29bb3ca8ba52","last_reissued_at":"2026-05-17T23:40:55.980280Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:55.980280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Discrete Morse Theory for Computing Zigzag Persistence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"cs.CG","authors_text":"Cl\\'ement Maria, Hannah Schreiber","submitted_at":"2018-07-13T16:43:28Z","abstract_excerpt":"We introduce a theoretical and computational framework to use discrete Morse theory as an efficient preprocessing in order to compute zigzag persistent homology.\n  From a zigzag filtration of complexes $(K_i)$, we introduce a zigzag Morse filtration whose complexes $(A_i)$ are Morse reductions of the original complexes $(K_i)$, and we prove that they both have same persistent homology. 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