{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WT2CG2JMZJMK3YDTOAFPWV2Y4E","short_pith_number":"pith:WT2CG2JM","canonical_record":{"source":{"id":"1804.03549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-09T17:52:05Z","cross_cats_sorted":[],"title_canon_sha256":"3d46a6abce59091db7f00e36920c17e90a1984acc6b5c0349618111ecf3acf95","abstract_canon_sha256":"19557f15bec578f252884a8ca80b62b4be8699038796a6c9443ad862e62c7c02"},"schema_version":"1.0"},"canonical_sha256":"b4f423692cca58ade073700afb5758e10c22fee77453375d5d7c905656cf63fe","source":{"kind":"arxiv","id":"1804.03549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03549","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03549v1","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03549","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"WT2CG2JMZJMK","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WT2CG2JMZJMK3YDT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WT2CG2JM","created_at":"2026-05-18T12:33:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WT2CG2JMZJMK3YDTOAFPWV2Y4E","target":"record","payload":{"canonical_record":{"source":{"id":"1804.03549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-09T17:52:05Z","cross_cats_sorted":[],"title_canon_sha256":"3d46a6abce59091db7f00e36920c17e90a1984acc6b5c0349618111ecf3acf95","abstract_canon_sha256":"19557f15bec578f252884a8ca80b62b4be8699038796a6c9443ad862e62c7c02"},"schema_version":"1.0"},"canonical_sha256":"b4f423692cca58ade073700afb5758e10c22fee77453375d5d7c905656cf63fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:47.767235Z","signature_b64":"YOhsx48eISxOcyq6TzKpCq/gr3XjXHdBLV1n1yklWJSS9fV2GkTfV8W1+Z6mSQ9vA0E+AZvw9X/z60lBA21oBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4f423692cca58ade073700afb5758e10c22fee77453375d5d7c905656cf63fe","last_reissued_at":"2026-05-18T00:18:47.766561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:47.766561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.03549","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":"2026-05-18T00:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/BUd9zLUc5a6khQk6NfOueVa3DcvcM49LelSzLQxg877q/RXR17Me0rH8cDDbilDYtNoR9z82ftPL9adAk+nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:36:32.687954Z"},"content_sha256":"b775b4d3366dfc04fd2358a19fad73be13449d3979455b00e60ab51f17e3ebf5","schema_version":"1.0","event_id":"sha256:b775b4d3366dfc04fd2358a19fad73be13449d3979455b00e60ab51f17e3ebf5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WT2CG2JMZJMK3YDTOAFPWV2Y4E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One-cocycle invariants for closed braids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Thomas Fiedler","submitted_at":"2018-04-09T17:52:05Z","abstract_excerpt":"We introduce new polynomial isotopy invariants for closed braids. They are constructed as polynomial valued {\\em Gauss diagram 1-cocycles} evaluated on the full rotation of the closed braid $\\hat \\beta$ around the core of the corresponding solid torus. They can be calculated with polynomial complexity with respect to the braid length and their derivatives evaluated at $x=1$ are finite type invariants of closed braids. Let the solid torus V be standardly embedded in the 3-sphere and let L be the core of the complementary solid torus $S^3\\setminus V$. We give examples which show that a natural r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03549","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":"2026-05-18T00:18:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1tPxYTvTQ2P6B9e5ExPq8EIqsdtHJDmNEPPw/KbLDbcfdB8SYTHDCUw+epbCCyDX0Zmd2Vops/vKA6r/9NvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:36:32.688285Z"},"content_sha256":"64ab9400d20c5cd2bc878259e05fb20001d256792ad0d2956bd5042fd0bd0c71","schema_version":"1.0","event_id":"sha256:64ab9400d20c5cd2bc878259e05fb20001d256792ad0d2956bd5042fd0bd0c71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E/bundle.json","state_url":"https://pith.science/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E/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":"2026-06-27T02:36:32Z","links":{"resolver":"https://pith.science/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E","bundle":"https://pith.science/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E/bundle.json","state":"https://pith.science/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WT2CG2JMZJMK3YDTOAFPWV2Y4E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WT2CG2JMZJMK3YDTOAFPWV2Y4E","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":"19557f15bec578f252884a8ca80b62b4be8699038796a6c9443ad862e62c7c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-09T17:52:05Z","title_canon_sha256":"3d46a6abce59091db7f00e36920c17e90a1984acc6b5c0349618111ecf3acf95"},"schema_version":"1.0","source":{"id":"1804.03549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03549","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03549v1","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03549","created_at":"2026-05-18T00:18:47Z"},{"alias_kind":"pith_short_12","alias_value":"WT2CG2JMZJMK","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WT2CG2JMZJMK3YDT","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WT2CG2JM","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:64ab9400d20c5cd2bc878259e05fb20001d256792ad0d2956bd5042fd0bd0c71","target":"graph","created_at":"2026-05-18T00:18:47Z","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 introduce new polynomial isotopy invariants for closed braids. They are constructed as polynomial valued {\\em Gauss diagram 1-cocycles} evaluated on the full rotation of the closed braid $\\hat \\beta$ around the core of the corresponding solid torus. They can be calculated with polynomial complexity with respect to the braid length and their derivatives evaluated at $x=1$ are finite type invariants of closed braids. Let the solid torus V be standardly embedded in the 3-sphere and let L be the core of the complementary solid torus $S^3\\setminus V$. We give examples which show that a natural r","authors_text":"Thomas Fiedler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-09T17:52:05Z","title":"One-cocycle invariants for closed braids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03549","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:b775b4d3366dfc04fd2358a19fad73be13449d3979455b00e60ab51f17e3ebf5","target":"record","created_at":"2026-05-18T00:18:47Z","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":"19557f15bec578f252884a8ca80b62b4be8699038796a6c9443ad862e62c7c02","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-04-09T17:52:05Z","title_canon_sha256":"3d46a6abce59091db7f00e36920c17e90a1984acc6b5c0349618111ecf3acf95"},"schema_version":"1.0","source":{"id":"1804.03549","kind":"arxiv","version":1}},"canonical_sha256":"b4f423692cca58ade073700afb5758e10c22fee77453375d5d7c905656cf63fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4f423692cca58ade073700afb5758e10c22fee77453375d5d7c905656cf63fe","first_computed_at":"2026-05-18T00:18:47.766561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:47.766561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YOhsx48eISxOcyq6TzKpCq/gr3XjXHdBLV1n1yklWJSS9fV2GkTfV8W1+Z6mSQ9vA0E+AZvw9X/z60lBA21oBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:47.767235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b775b4d3366dfc04fd2358a19fad73be13449d3979455b00e60ab51f17e3ebf5","sha256:64ab9400d20c5cd2bc878259e05fb20001d256792ad0d2956bd5042fd0bd0c71"],"state_sha256":"8bf7f8ba79cb7df990b9da75611e932daa9cc8a9deec52d7d3f49e5d42c76ebd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lbykKaXChdgRE06Due+CkNra/htv2U8eokrOzQXXz6+4NhYixiG32T6cbuzaDTgtI7ONQ/1PPXpOOkSFJ5KtAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:36:32.690087Z","bundle_sha256":"4e07b36083cb7b1502ef8e59af30e33638c5030d460ab7df318fece930bae2f7"}}