{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:N4RDEDD5OTUAVY7ROGUDYKGRLY","short_pith_number":"pith:N4RDEDD5","schema_version":"1.0","canonical_sha256":"6f22320c7d74e80ae3f171a83c28d15e14f6918580f311142ee598e223b0dc09","source":{"kind":"arxiv","id":"2404.06618","version":1},"attestation_state":"computed","paper":{"title":"Invariant splitting principles for the Lipshitz--Ozsv\\'ath--Thurston correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gary Guth, Sungkyung Kang","submitted_at":"2024-04-09T21:08:16Z","abstract_excerpt":"We prove that the Lipshitz-Ozsv\\'ath-Thurston correspondence between extended type D structures of knot complements and $\\mathbb{F}[U, V]/(UV)$ knot Floer complexes can be arranged so that $\\iota_K$-invariant splittings of knot Floer chain complexes correspond to $\\iota_{S^3 \\setminus K}$-invariant splittings of bordered Floer homology of knot complements. For patterns satisfying the satellite extension property, which include cabling patterns, this provides a novel way to compute the involutive knot Floer homology of satellites from that of their companions. As a topological application, we s"},"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":"2404.06618","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2024-04-09T21:08:16Z","cross_cats_sorted":[],"title_canon_sha256":"ac53ea41f4305ae89eb662cce1a73b27a1d5c4e47e6b4edbeb67e86214a4f255","abstract_canon_sha256":"123c03f4c140e6947d8d7eab7dff86f8b67622e404565d2ad8e7202cb3fcc61e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:06:14.812756Z","signature_b64":"9dzxQD8/PeU8naBdB0KUMpvC3z1SVQk49xYgZiUiJiJcxSytdl8FKq3sk6raJLOmnszXGNB5+1a+9bWtrYubAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f22320c7d74e80ae3f171a83c28d15e14f6918580f311142ee598e223b0dc09","last_reissued_at":"2026-07-05T08:06:14.812409Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:06:14.812409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant splitting principles for the Lipshitz--Ozsv\\'ath--Thurston correspondence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Gary Guth, Sungkyung Kang","submitted_at":"2024-04-09T21:08:16Z","abstract_excerpt":"We prove that the Lipshitz-Ozsv\\'ath-Thurston correspondence between extended type D structures of knot complements and $\\mathbb{F}[U, V]/(UV)$ knot Floer complexes can be arranged so that $\\iota_K$-invariant splittings of knot Floer chain complexes correspond to $\\iota_{S^3 \\setminus K}$-invariant splittings of bordered Floer homology of knot complements. For patterns satisfying the satellite extension property, which include cabling patterns, this provides a novel way to compute the involutive knot Floer homology of satellites from that of their companions. As a topological application, we s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2404.06618","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2404.06618/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2404.06618","created_at":"2026-07-05T08:06:14.812466+00:00"},{"alias_kind":"arxiv_version","alias_value":"2404.06618v1","created_at":"2026-07-05T08:06:14.812466+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2404.06618","created_at":"2026-07-05T08:06:14.812466+00:00"},{"alias_kind":"pith_short_12","alias_value":"N4RDEDD5OTUA","created_at":"2026-07-05T08:06:14.812466+00:00"},{"alias_kind":"pith_short_16","alias_value":"N4RDEDD5OTUAVY7R","created_at":"2026-07-05T08:06:14.812466+00:00"},{"alias_kind":"pith_short_8","alias_value":"N4RDEDD5","created_at":"2026-07-05T08:06:14.812466+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.12809","citing_title":"The link surgery formula and equivariant surgeries","ref_index":44,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY","json":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY.json","graph_json":"https://pith.science/api/pith-number/N4RDEDD5OTUAVY7ROGUDYKGRLY/graph.json","events_json":"https://pith.science/api/pith-number/N4RDEDD5OTUAVY7ROGUDYKGRLY/events.json","paper":"https://pith.science/paper/N4RDEDD5"},"agent_actions":{"view_html":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY","download_json":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY.json","view_paper":"https://pith.science/paper/N4RDEDD5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2404.06618&json=true","fetch_graph":"https://pith.science/api/pith-number/N4RDEDD5OTUAVY7ROGUDYKGRLY/graph.json","fetch_events":"https://pith.science/api/pith-number/N4RDEDD5OTUAVY7ROGUDYKGRLY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY/action/storage_attestation","attest_author":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY/action/author_attestation","sign_citation":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY/action/citation_signature","submit_replication":"https://pith.science/pith/N4RDEDD5OTUAVY7ROGUDYKGRLY/action/replication_record"}},"created_at":"2026-07-05T08:06:14.812466+00:00","updated_at":"2026-07-05T08:06:14.812466+00:00"}