{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:SL3Q3JXCDV6ID6V72PI67PANBD","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":"c025f04eba81f38ce1c0f3e53bf6811ef4e8769beb8dbc37cf9ff7951ade7899","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-10-27T17:16:06Z","title_canon_sha256":"117088a72333c32790b6fa4a1e435b0e1e9ecea034941ccd7dd4f4be6fba2cc2"},"schema_version":"1.0","source":{"id":"2410.20523","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.20523","created_at":"2026-07-05T11:03:53Z"},{"alias_kind":"arxiv_version","alias_value":"2410.20523v2","created_at":"2026-07-05T11:03:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.20523","created_at":"2026-07-05T11:03:53Z"},{"alias_kind":"pith_short_12","alias_value":"SL3Q3JXCDV6I","created_at":"2026-07-05T11:03:53Z"},{"alias_kind":"pith_short_16","alias_value":"SL3Q3JXCDV6ID6V7","created_at":"2026-07-05T11:03:53Z"},{"alias_kind":"pith_short_8","alias_value":"SL3Q3JXC","created_at":"2026-07-05T11:03:53Z"}],"graph_snapshots":[{"event_id":"sha256:660b4ffe27988e3955e87327459aca0bb94c7dfc83672c99b3ecf4816c6d08a4","target":"graph","created_at":"2026-07-05T11:03:53Z","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/2410.20523/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use Ng's LSFT algebra to upgrade Sabloff duality of Legendrian knots to a quasi-isomorphism of $A_\\infty$ bimodules over the positive augmentation category $\\mathcal{A}ug_+$. We also extend the Ekholm-Etnyre-Sabloff exact sequence to an exact sequence of $\\mathcal{A}ug_+$-bimodules, using a quotient category $\\mathcal{C}$ of short Reeb chords. In addition, we define curved augmentations of the LSFT algebra and show that they can be used to construct a homotopy inverse of the $A_\\infty$ Sabloff map, together with all higher homotopies. The above results suggest a conjectural recipe for an ex","authors_text":"Zhenyi Chen","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-10-27T17:16:06Z","title":"$A_\\infty$ Sabloff Duality via the LSFT Algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20523","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:c9c9aedb310f108c85ed17faeb6635c6e36ad160c2dd1d55580bdfd9e1464492","target":"record","created_at":"2026-07-05T11:03:53Z","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":"c025f04eba81f38ce1c0f3e53bf6811ef4e8769beb8dbc37cf9ff7951ade7899","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2024-10-27T17:16:06Z","title_canon_sha256":"117088a72333c32790b6fa4a1e435b0e1e9ecea034941ccd7dd4f4be6fba2cc2"},"schema_version":"1.0","source":{"id":"2410.20523","kind":"arxiv","version":2}},"canonical_sha256":"92f70da6e21d7c81fabfd3d1efbc0d08f8b745d4922022d8c6c468f1e1bde935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92f70da6e21d7c81fabfd3d1efbc0d08f8b745d4922022d8c6c468f1e1bde935","first_computed_at":"2026-07-05T11:03:53.210499Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:03:53.210499Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiSUzEB2m9I5/2hYvLLxCp5aoE1m5itU3MgI/MjWGue1xDaqtE+49qgJnulrh4XczM0zipnBneTBKHqaq8YRCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:03:53.210911Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.20523","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9c9aedb310f108c85ed17faeb6635c6e36ad160c2dd1d55580bdfd9e1464492","sha256:660b4ffe27988e3955e87327459aca0bb94c7dfc83672c99b3ecf4816c6d08a4"],"state_sha256":"17b3f0145daa794e77273ecc50c90263ce84c9f1840d96b91db6885ca6a73836"}