{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:W6F53XG4IIECTVYBQGELBEO7V3","short_pith_number":"pith:W6F53XG4","canonical_record":{"source":{"id":"0810.1785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-10T00:08:39Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"384808be0e60c77e21faec72abbb72042f1ac6997ff155b5869da36b39da83be","abstract_canon_sha256":"9b8e2ba85a24085514bf10768bbdf151f0daabc6d41f7d3ec1451c86cef9120e"},"schema_version":"1.0"},"canonical_sha256":"b78bdddcdc420829d7018188b091dfaedccea488cb18a9b5b3bf78abff028c72","source":{"kind":"arxiv","id":"0810.1785","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1785","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1785v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1785","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"W6F53XG4IIEC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"W6F53XG4IIECTVYB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"W6F53XG4","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:W6F53XG4IIECTVYBQGELBEO7V3","target":"record","payload":{"canonical_record":{"source":{"id":"0810.1785","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-10T00:08:39Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"384808be0e60c77e21faec72abbb72042f1ac6997ff155b5869da36b39da83be","abstract_canon_sha256":"9b8e2ba85a24085514bf10768bbdf151f0daabc6d41f7d3ec1451c86cef9120e"},"schema_version":"1.0"},"canonical_sha256":"b78bdddcdc420829d7018188b091dfaedccea488cb18a9b5b3bf78abff028c72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:51.463722Z","signature_b64":"KpiZiDfztgr9JPITnthkix/MMME4uAoexlnc8C6QZ2nIdxstyDO0pRSmdI+dC/m+iQ9t208uWezT4ATXU2GQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b78bdddcdc420829d7018188b091dfaedccea488cb18a9b5b3bf78abff028c72","last_reissued_at":"2026-05-18T02:41:51.463295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:51.463295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0810.1785","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XP7CzkIdHb0x+wPBO3gXtH8uqCuLEaZwNv7joOwaGjlMRJLpgwgZ3ULoU8f0zrgw77u40brx2fmO/VPFDKzoBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:14:43.903063Z"},"content_sha256":"0c6124fa6647cf61669121a3b5277c452a2acf8808e264d76a6acfeec1226e47","schema_version":"1.0","event_id":"sha256:0c6124fa6647cf61669121a3b5277c452a2acf8808e264d76a6acfeec1226e47"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:W6F53XG4IIECTVYBQGELBEO7V3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A homotopy-theoretic view of Bott-Taubes integrals and knot spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Robin Koytcheff","submitted_at":"2008-10-10T00:08:39Z","abstract_excerpt":"We construct cohomology classes in the space of knots by considering a bundle over this space and \"integrating along the fiber\" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated differential forms along the fiber to get knot invariants. By doing this \"integration\" homotopy-theoretically, we are able to produce integral cohomology classes. We then show how this integration is compatible with the homology operations on the space of long knots, as studied by B"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1785","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:41:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2uqdLo5GTp8W2LHNhSaD3ifMwe268F6mLs0D1/IJvC5nJl9jjE76uchsC/FCw9ApWhoU9EIB6b2E4UBLf1TDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T00:14:43.903795Z"},"content_sha256":"704f39607c93f94a25f7f09a52590f488e621949aa3d45fc81aef1832968215a","schema_version":"1.0","event_id":"sha256:704f39607c93f94a25f7f09a52590f488e621949aa3d45fc81aef1832968215a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W6F53XG4IIECTVYBQGELBEO7V3/bundle.json","state_url":"https://pith.science/pith/W6F53XG4IIECTVYBQGELBEO7V3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W6F53XG4IIECTVYBQGELBEO7V3/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-08T00:14:43Z","links":{"resolver":"https://pith.science/pith/W6F53XG4IIECTVYBQGELBEO7V3","bundle":"https://pith.science/pith/W6F53XG4IIECTVYBQGELBEO7V3/bundle.json","state":"https://pith.science/pith/W6F53XG4IIECTVYBQGELBEO7V3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W6F53XG4IIECTVYBQGELBEO7V3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:W6F53XG4IIECTVYBQGELBEO7V3","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":"9b8e2ba85a24085514bf10768bbdf151f0daabc6d41f7d3ec1451c86cef9120e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-10T00:08:39Z","title_canon_sha256":"384808be0e60c77e21faec72abbb72042f1ac6997ff155b5869da36b39da83be"},"schema_version":"1.0","source":{"id":"0810.1785","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0810.1785","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"arxiv_version","alias_value":"0810.1785v1","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0810.1785","created_at":"2026-05-18T02:41:51Z"},{"alias_kind":"pith_short_12","alias_value":"W6F53XG4IIEC","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"W6F53XG4IIECTVYB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"W6F53XG4","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:704f39607c93f94a25f7f09a52590f488e621949aa3d45fc81aef1832968215a","target":"graph","created_at":"2026-05-18T02:41:51Z","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":"We construct cohomology classes in the space of knots by considering a bundle over this space and \"integrating along the fiber\" classes coming from the cohomology of configuration spaces using a Pontrjagin-Thom construction. The bundle we consider is essentially the one considered by Bott and Taubes, who integrated differential forms along the fiber to get knot invariants. By doing this \"integration\" homotopy-theoretically, we are able to produce integral cohomology classes. We then show how this integration is compatible with the homology operations on the space of long knots, as studied by B","authors_text":"Robin Koytcheff","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-10T00:08:39Z","title":"A homotopy-theoretic view of Bott-Taubes integrals and knot spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0810.1785","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":"sha256:0c6124fa6647cf61669121a3b5277c452a2acf8808e264d76a6acfeec1226e47","target":"record","created_at":"2026-05-18T02:41:51Z","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":"9b8e2ba85a24085514bf10768bbdf151f0daabc6d41f7d3ec1451c86cef9120e","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-10-10T00:08:39Z","title_canon_sha256":"384808be0e60c77e21faec72abbb72042f1ac6997ff155b5869da36b39da83be"},"schema_version":"1.0","source":{"id":"0810.1785","kind":"arxiv","version":1}},"canonical_sha256":"b78bdddcdc420829d7018188b091dfaedccea488cb18a9b5b3bf78abff028c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b78bdddcdc420829d7018188b091dfaedccea488cb18a9b5b3bf78abff028c72","first_computed_at":"2026-05-18T02:41:51.463295Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:51.463295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KpiZiDfztgr9JPITnthkix/MMME4uAoexlnc8C6QZ2nIdxstyDO0pRSmdI+dC/m+iQ9t208uWezT4ATXU2GQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:51.463722Z","signed_message":"canonical_sha256_bytes"},"source_id":"0810.1785","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c6124fa6647cf61669121a3b5277c452a2acf8808e264d76a6acfeec1226e47","sha256:704f39607c93f94a25f7f09a52590f488e621949aa3d45fc81aef1832968215a"],"state_sha256":"e05ff106f661c6c36559646be3088a6ae5497c4d97a4f377bd65caf4aae87ee8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2yMAq0x2bdX7rtm4onMfhPbOclgRw2Q5Ch+SqN7FEl8ApTGJ9eTrFcSnc2XByNl0Ee8BPJhKQ+NsBdwZBfASDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T00:14:43.907624Z","bundle_sha256":"13ea3d3ba6429d97219943f93d55568128e08179c4d9260eb112d9c711f56bc5"}}