{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5TGTK7LSK4RYSEOKJI3LMOFPVW","short_pith_number":"pith:5TGTK7LS","schema_version":"1.0","canonical_sha256":"eccd357d7257238911ca4a36b638afada8758775b61dd8760cbee5820c2841f7","source":{"kind":"arxiv","id":"2507.00175","version":1},"attestation_state":"computed","paper":{"title":"Stable deformed $\\mathfrak{gl}_N$ homology of torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eugene Gorsky, Joshua Wang, Matthew Hogancamp, William Ballinger","submitted_at":"2025-06-30T18:32:47Z","abstract_excerpt":"We compute the $E_2$ page in the Rasmussen spectral sequence from triply graded to $\\mathfrak{gl}_N$ Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of the conjecture of the second author, Oblomkov, and Rasmussen. The main tool is the link-splitting deformation, or $y$-ification, of link homology; in the $y$-ified context, the relevant Rasmussen spectral sequence collapses and we explicitly compute the $y$-ified $\\mathfrak{gl}_N$ stable Khovanov--Rozansky homology of torus knots for all $N$."},"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":"2507.00175","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-06-30T18:32:47Z","cross_cats_sorted":[],"title_canon_sha256":"0c2c5f64c5c9d1274e8d4a2b124ff3808390d02ba3782982d40f1092eaf58692","abstract_canon_sha256":"8276bd45c00ec47f5439d0822480760722962f3e38af301d0e09276be272875b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:29:38.553615Z","signature_b64":"9Cr0hRdmrNlPni8sUvBwTblYu9JjpZUfqBAnsXvQzkQur9PY5/xKqgTlOPKsgulrqa5MmvfspnxMyhrb/bwhDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eccd357d7257238911ca4a36b638afada8758775b61dd8760cbee5820c2841f7","last_reissued_at":"2026-07-05T11:29:38.553093Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:29:38.553093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stable deformed $\\mathfrak{gl}_N$ homology of torus knots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Eugene Gorsky, Joshua Wang, Matthew Hogancamp, William Ballinger","submitted_at":"2025-06-30T18:32:47Z","abstract_excerpt":"We compute the $E_2$ page in the Rasmussen spectral sequence from triply graded to $\\mathfrak{gl}_N$ Khovanov--Rozansky stable homology of torus knots. This confirms a weak form of the conjecture of the second author, Oblomkov, and Rasmussen. The main tool is the link-splitting deformation, or $y$-ification, of link homology; in the $y$-ified context, the relevant Rasmussen spectral sequence collapses and we explicitly compute the $y$-ified $\\mathfrak{gl}_N$ stable Khovanov--Rozansky homology of torus knots for all $N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.00175","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/2507.00175/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":"2507.00175","created_at":"2026-07-05T11:29:38.553158+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.00175v1","created_at":"2026-07-05T11:29:38.553158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.00175","created_at":"2026-07-05T11:29:38.553158+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TGTK7LSK4RY","created_at":"2026-07-05T11:29:38.553158+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TGTK7LSK4RYSEOK","created_at":"2026-07-05T11:29:38.553158+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TGTK7LS","created_at":"2026-07-05T11:29:38.553158+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2508.21776","citing_title":"Colored knot Floer homology: structures and examples","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW","json":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW.json","graph_json":"https://pith.science/api/pith-number/5TGTK7LSK4RYSEOKJI3LMOFPVW/graph.json","events_json":"https://pith.science/api/pith-number/5TGTK7LSK4RYSEOKJI3LMOFPVW/events.json","paper":"https://pith.science/paper/5TGTK7LS"},"agent_actions":{"view_html":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW","download_json":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW.json","view_paper":"https://pith.science/paper/5TGTK7LS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.00175&json=true","fetch_graph":"https://pith.science/api/pith-number/5TGTK7LSK4RYSEOKJI3LMOFPVW/graph.json","fetch_events":"https://pith.science/api/pith-number/5TGTK7LSK4RYSEOKJI3LMOFPVW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW/action/storage_attestation","attest_author":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW/action/author_attestation","sign_citation":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW/action/citation_signature","submit_replication":"https://pith.science/pith/5TGTK7LSK4RYSEOKJI3LMOFPVW/action/replication_record"}},"created_at":"2026-07-05T11:29:38.553158+00:00","updated_at":"2026-07-05T11:29:38.553158+00:00"}