{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IHOHAXK2YABDRMFEF7VIEBOBXN","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":"25393fa7c076a68cea65ba3eaf4b2e9abc9d06737b4d63612d4765e49b0fe2ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-05T17:26:58Z","title_canon_sha256":"365c5acd5fe86bc6adab6c06fd18c43fab74b0ad872d6661dd21571caa65879b"},"schema_version":"1.0","source":{"id":"1809.01637","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01637","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01637v1","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01637","created_at":"2026-05-18T00:06:26Z"},{"alias_kind":"pith_short_12","alias_value":"IHOHAXK2YABD","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_16","alias_value":"IHOHAXK2YABDRMFE","created_at":"2026-05-18T12:32:31Z"},{"alias_kind":"pith_short_8","alias_value":"IHOHAXK2","created_at":"2026-05-18T12:32:31Z"}],"graph_snapshots":[{"event_id":"sha256:d71e497775b5aaac3c1b75e31b05e738fe7f0df6326a0acfa3873ece18180275","target":"graph","created_at":"2026-05-18T00:06:26Z","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":"In previous work, we introduced a natural $\\mathcal{A}_{\\infty}$-structure on the $\\mathrm{Pin}(2)$-monopole Floer chain complex of a closed, oriented three-manifold $Y$, and showed that it is non-formal in the simplest case in which $Y$ is the three-sphere $S^3$. In this paper, we provide explicit descriptions of several Massey products induced on homology, and discuss how they can be used to compute the $\\mathrm{Pin}(2)$-monopole Floer homology of connected sums in many concrete examples.","authors_text":"Francesco Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-05T17:26:58Z","title":"Non-formality in $\\mathrm{Pin}(2)$-monopole Floer homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01637","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":"sha256:948ac0b6362a7699c6e60856fffb0476806f16ccd2e10f8ff8f694c21f0a5f91","target":"record","created_at":"2026-05-18T00:06:26Z","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":"25393fa7c076a68cea65ba3eaf4b2e9abc9d06737b4d63612d4765e49b0fe2ee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-09-05T17:26:58Z","title_canon_sha256":"365c5acd5fe86bc6adab6c06fd18c43fab74b0ad872d6661dd21571caa65879b"},"schema_version":"1.0","source":{"id":"1809.01637","kind":"arxiv","version":1}},"canonical_sha256":"41dc705d5ac00238b0a42fea8205c1bb6b45638e7ac8b898f64366e9f75cd82c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41dc705d5ac00238b0a42fea8205c1bb6b45638e7ac8b898f64366e9f75cd82c","first_computed_at":"2026-05-18T00:06:26.996929Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:26.996929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0jeHRmcZlnwbTlEMcPIZ0Qox7YoAN7Y8Q7g8N4tgr3P0vXj48L3At4D98lDzKTfrV5ZIFK45pPYFkgjJLg0BDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:26.997572Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01637","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:948ac0b6362a7699c6e60856fffb0476806f16ccd2e10f8ff8f694c21f0a5f91","sha256:d71e497775b5aaac3c1b75e31b05e738fe7f0df6326a0acfa3873ece18180275"],"state_sha256":"267d6a6bac4d78a80d10acd00fcb022ceaf0fbbcbf8e46a385ce68521d9c10d5"}