{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FZUIUEFSGHDVMUGNPH7AICDW6Q","short_pith_number":"pith:FZUIUEFS","schema_version":"1.0","canonical_sha256":"2e688a10b231c75650cd79fe040876f430c885c871833d78f80043de2e1b5bfd","source":{"kind":"arxiv","id":"2504.16785","version":1},"attestation_state":"computed","paper":{"title":"Non collapse of the Sinha spectral sequence for knots in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Andrea Marino, Paolo Salvatore","submitted_at":"2025-04-23T15:02:19Z","abstract_excerpt":"We give an explicit description up to the third page of the Sinha homology mod 2 spectral sequence for the space of long knots in $\\mathbb{R}^3$, that is conjecturally equivalent to the Vassiliev spectral sequence. The description arises from a multicomplex structure on the Fox Neuwirth chain complexes for euclidean configuration spaces. A computer assisted calculation reveals a non trivial third page differential from a 2-dimensional class, in contrast to the rational case."},"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":"2504.16785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2025-04-23T15:02:19Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"760761a94c83fa1d372a4dd93342bf1ef75c74f6ffc9e9978fe1db280e8ee543","abstract_canon_sha256":"dd61d746dc7253d954f00d71bb4fc1cecdb335a5947edd21fa5a92b5a71d3e92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:08:19.812926Z","signature_b64":"00KYjoO4QSp96PJgaYvt+UmlS0P4pKuoXr4zgjP7T6HT9EBfOw2Gmf+HYaRDL/PpJKvZODHZkL8Uv81k0WmVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e688a10b231c75650cd79fe040876f430c885c871833d78f80043de2e1b5bfd","last_reissued_at":"2026-07-05T11:08:19.812440Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:08:19.812440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non collapse of the Sinha spectral sequence for knots in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Andrea Marino, Paolo Salvatore","submitted_at":"2025-04-23T15:02:19Z","abstract_excerpt":"We give an explicit description up to the third page of the Sinha homology mod 2 spectral sequence for the space of long knots in $\\mathbb{R}^3$, that is conjecturally equivalent to the Vassiliev spectral sequence. The description arises from a multicomplex structure on the Fox Neuwirth chain complexes for euclidean configuration spaces. A computer assisted calculation reveals a non trivial third page differential from a 2-dimensional class, in contrast to the rational case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.16785","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/2504.16785/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":"2504.16785","created_at":"2026-07-05T11:08:19.812493+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.16785v1","created_at":"2026-07-05T11:08:19.812493+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.16785","created_at":"2026-07-05T11:08:19.812493+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZUIUEFSGHDV","created_at":"2026-07-05T11:08:19.812493+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZUIUEFSGHDVMUGN","created_at":"2026-07-05T11:08:19.812493+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZUIUEFS","created_at":"2026-07-05T11:08:19.812493+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.22958","citing_title":"A Fox-Neuwirth Basis for the Sinha Spectral Sequence","ref_index":22,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q","json":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q.json","graph_json":"https://pith.science/api/pith-number/FZUIUEFSGHDVMUGNPH7AICDW6Q/graph.json","events_json":"https://pith.science/api/pith-number/FZUIUEFSGHDVMUGNPH7AICDW6Q/events.json","paper":"https://pith.science/paper/FZUIUEFS"},"agent_actions":{"view_html":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q","download_json":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q.json","view_paper":"https://pith.science/paper/FZUIUEFS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.16785&json=true","fetch_graph":"https://pith.science/api/pith-number/FZUIUEFSGHDVMUGNPH7AICDW6Q/graph.json","fetch_events":"https://pith.science/api/pith-number/FZUIUEFSGHDVMUGNPH7AICDW6Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q/action/storage_attestation","attest_author":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q/action/author_attestation","sign_citation":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q/action/citation_signature","submit_replication":"https://pith.science/pith/FZUIUEFSGHDVMUGNPH7AICDW6Q/action/replication_record"}},"created_at":"2026-07-05T11:08:19.812493+00:00","updated_at":"2026-07-05T11:08:19.812493+00:00"}