{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:BIOGV6Z6XVCTQT6JWMETNEX6BI","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":"346c964f80c01e7b300122d06e4b45560ec452749338191ee329c3560f9c96a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-21T02:09:37Z","title_canon_sha256":"416241afc56d77a415e15157120915fa1de1a11c55a91d4a6fc4a965131e0760"},"schema_version":"1.0","source":{"id":"2206.10077","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.10077","created_at":"2026-07-05T11:55:58Z"},{"alias_kind":"arxiv_version","alias_value":"2206.10077v3","created_at":"2026-07-05T11:55:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.10077","created_at":"2026-07-05T11:55:58Z"},{"alias_kind":"pith_short_12","alias_value":"BIOGV6Z6XVCT","created_at":"2026-07-05T11:55:58Z"},{"alias_kind":"pith_short_16","alias_value":"BIOGV6Z6XVCTQT6J","created_at":"2026-07-05T11:55:58Z"},{"alias_kind":"pith_short_8","alias_value":"BIOGV6Z6","created_at":"2026-07-05T11:55:58Z"}],"graph_snapshots":[{"event_id":"sha256:416c92fb4f1477dcb8d2d9df9c094a4d617a53f1ba8f2f9b540dfa9aeb689dab","target":"graph","created_at":"2026-07-05T11:55:58Z","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/2206.10077/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an integral surgery formula for framed instanton homology $I^\\sharp(Y_m(K))$ for any knot $K$ in a $3$-manifold $Y$ with $[K]=0\\in H_1(Y;\\mathbb{Q})$ and $m\\neq 0$. Though the statement is similar to Ozsv\\'ath-Szab\\'o's integral surgery formula for Heegaard Floer homology, the proof is new and based on sutured instanton homology $SHI$ and the octahedral lemma in the derived category. As a corollary, we obtain an exact triangle between $I^\\sharp(Y_m(K))$, $I^\\sharp(Y_{m+k}(K))$ and $k$ copies of $I^\\sharp(Y)$ for any $m\\neq 0$ and large $k$. In the proof of the formula, we discover man","authors_text":"Fan Ye, Zhenkun Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-21T02:09:37Z","title":"Knot surgery formulae for instanton Floer homology I: the main theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.10077","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":"sha256:5da061b4e247ae88cc4548545c6935ce2610282b9c34efd98b6fb0d5eb0534a3","target":"record","created_at":"2026-07-05T11:55:58Z","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":"346c964f80c01e7b300122d06e4b45560ec452749338191ee329c3560f9c96a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2022-06-21T02:09:37Z","title_canon_sha256":"416241afc56d77a415e15157120915fa1de1a11c55a91d4a6fc4a965131e0760"},"schema_version":"1.0","source":{"id":"2206.10077","kind":"arxiv","version":3}},"canonical_sha256":"0a1c6afb3ebd45384fc9b3093692fe0a192c8deb88b8838f3e1a41fc9196008e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a1c6afb3ebd45384fc9b3093692fe0a192c8deb88b8838f3e1a41fc9196008e","first_computed_at":"2026-07-05T11:55:58.371929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:58.371929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SH9UPPULDQDTI6sYqqNK0v5aem+bztid63BTqXxUDAZfvyGQngbzxq1lpom2Gajvir8cY48XFG5EuGV1ypZ0BA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:58.372419Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.10077","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5da061b4e247ae88cc4548545c6935ce2610282b9c34efd98b6fb0d5eb0534a3","sha256:416c92fb4f1477dcb8d2d9df9c094a4d617a53f1ba8f2f9b540dfa9aeb689dab"],"state_sha256":"d0fe95c8e986a60823ea186b82d440d7bd6ea075f7cc4fbe81011fa062812634"}