{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ILFARHVCCSGA2N4LRGYO7LWMM6","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":"28821d5b4ddca564d809f0f99319bf36d63a45c22cbf5ee66eec6d602c3983cc","cross_cats_sorted":["math.AG","math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-03-20T08:17:34Z","title_canon_sha256":"b85e62b59fe670f0c1585829a722d9d2c95718d5b672f6c4e30d3be83108e607"},"schema_version":"1.0","source":{"id":"2503.15933","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.15933","created_at":"2026-06-25T01:17:44Z"},{"alias_kind":"arxiv_version","alias_value":"2503.15933v3","created_at":"2026-06-25T01:17:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.15933","created_at":"2026-06-25T01:17:44Z"},{"alias_kind":"pith_short_12","alias_value":"ILFARHVCCSGA","created_at":"2026-06-25T01:17:44Z"},{"alias_kind":"pith_short_16","alias_value":"ILFARHVCCSGA2N4L","created_at":"2026-06-25T01:17:44Z"},{"alias_kind":"pith_short_8","alias_value":"ILFARHVC","created_at":"2026-06-25T01:17:44Z"}],"graph_snapshots":[{"event_id":"sha256:bc271468665bbe895a79d7efee95195c3f54878777dfdb39147b3b077c778053","target":"graph","created_at":"2026-06-25T01:17:44Z","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/2503.15933/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a precise unification of three theories that are widely used by symplectic geometers: (Almost) modules over the Novikov ring, Persistence modules, and the Tamarkin category. Our method provides new input in this direction, especially in relation to Vaintrob's Novikov/log-perfectoid mirror symmetry for Novikov toric schemes. The results of this paper can also be treated as a study of persistent homology from a higher algebra point of view.\n  As applications, we establish a version of homological mirror symmetry over the Novikov ring for toric varieties and propose a conjecture for homol","authors_text":"Bingyu Zhang, Tatsuki Kuwagaki","cross_cats":["math.AG","math.AT","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-03-20T08:17:34Z","title":"Almost mathematics, Persistence module, and Tamarkin category"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.15933","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":"sha256:52a6d777ef8fe02fcd67c4442dcd9edc129ebe4f28eb31f27734d2a119be7f04","target":"record","created_at":"2026-06-25T01:17:44Z","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":"28821d5b4ddca564d809f0f99319bf36d63a45c22cbf5ee66eec6d602c3983cc","cross_cats_sorted":["math.AG","math.AT","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2025-03-20T08:17:34Z","title_canon_sha256":"b85e62b59fe670f0c1585829a722d9d2c95718d5b672f6c4e30d3be83108e607"},"schema_version":"1.0","source":{"id":"2503.15933","kind":"arxiv","version":3}},"canonical_sha256":"42ca089ea2148c0d378b89b0efaecc6794914c2631d091cfe7a8c4889b6f1fb2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"42ca089ea2148c0d378b89b0efaecc6794914c2631d091cfe7a8c4889b6f1fb2","first_computed_at":"2026-06-25T01:17:44.103246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-25T01:17:44.103246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jn08x2mGaVzNI/lRUv2go3K6QI4ifv7tAA5fFbO4R9BaQPa78eA3dIFxmiN+6Eqc4VzSXButGVh7db8jB+EIBg==","signature_status":"signed_v1","signed_at":"2026-06-25T01:17:44.103688Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.15933","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52a6d777ef8fe02fcd67c4442dcd9edc129ebe4f28eb31f27734d2a119be7f04","sha256:bc271468665bbe895a79d7efee95195c3f54878777dfdb39147b3b077c778053"],"state_sha256":"87683b02dddcbac6097cb8228e30786be07cc2202c4cad7cd1f9709132a41bf3"}