{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:QSLWX6DUT5Q6MBH5V36QO3LUF3","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":"5a1ea48d3af7e4b9f2a9d031f8f69a215f994b5bf10c95023fa05541f42a1fd4","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-09-27T09:33:26Z","title_canon_sha256":"b2883884f745a7a68c82c0816a19dc4dc90f844049b74c6b393c73694f780225"},"schema_version":"1.0","source":{"id":"math/0609742","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609742","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609742v2","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609742","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"pith_short_12","alias_value":"QSLWX6DUT5Q6","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"pith_short_16","alias_value":"QSLWX6DUT5Q6MBH5","created_at":"2026-07-04T14:56:36Z"},{"alias_kind":"pith_short_8","alias_value":"QSLWX6DU","created_at":"2026-07-04T14:56:36Z"}],"graph_snapshots":[{"event_id":"sha256:2fc91d9cee51e115aaabe534bef51f54bf296f9fff2e7dfb76ad3853e88c700d","target":"graph","created_at":"2026-07-04T14:56:36Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0609742/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"There is a higher dimensional analogue of the perturbative Chern-Simons theory in the sense that a similar perturbative series as in 3-dimension, which is computed via configuration space integral, yields an invariant of higher dimensional knots (Bott-Cattaneo-Rossi invariant), which is constructed by Bott for degree 2 and by Cattaneo-Rossi for higher degrees. However, its feature is yet unknown. In this paper we restrict the study to long ribbon n-knots and characterize the Bott-Cattaneo-Rossi invariant as a finite type invariant of long ribbon n-knots in [HKS]. As a consequence, we obtain a ","authors_text":"Tadayuki Watanabe","cross_cats":[],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2006-09-27T09:33:26Z","title":"Configuration space integral for long n-knots, the Alexander polynomial and knot space cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609742","kind":"arxiv","version":2},"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":"sha256:7b6cced1213ba83855e00aca1ee840755fa639dd36646501d5cbb51487e2b701","target":"record","created_at":"2026-07-04T14:56:36Z","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":"5a1ea48d3af7e4b9f2a9d031f8f69a215f994b5bf10c95023fa05541f42a1fd4","cross_cats_sorted":[],"license":"","primary_cat":"math.GT","submitted_at":"2006-09-27T09:33:26Z","title_canon_sha256":"b2883884f745a7a68c82c0816a19dc4dc90f844049b74c6b393c73694f780225"},"schema_version":"1.0","source":{"id":"math/0609742","kind":"arxiv","version":2}},"canonical_sha256":"84976bf8749f61e604fdaefd076d742efb54d5208b061bf0138143375636cc6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84976bf8749f61e604fdaefd076d742efb54d5208b061bf0138143375636cc6c","first_computed_at":"2026-07-04T14:56:36.503232Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:56:36.503232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXbus7IHaQ6Mj+R7nJUHlkRjU0idAJhTwi00fippu20/kL1QLCajrMea1Tuf9Tu9hXVnQvqYs01WX++jT7YpBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:56:36.503692Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609742","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b6cced1213ba83855e00aca1ee840755fa639dd36646501d5cbb51487e2b701","sha256:2fc91d9cee51e115aaabe534bef51f54bf296f9fff2e7dfb76ad3853e88c700d"],"state_sha256":"2d5763d0afb5850f10882291775442e8951a0bb464f9eaf5b56b08cfd2142890"}