{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AFP37YLU5L4DSJHJTI5ZGYKHT7","short_pith_number":"pith:AFP37YLU","canonical_record":{"source":{"id":"1209.1308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-06T15:01:40Z","cross_cats_sorted":[],"title_canon_sha256":"576611378909531e76bf4418653997cb28a4a3c1192948a51a0f6e3862e146a6","abstract_canon_sha256":"a66948b4c9f641cb07449170bb0ebcdc6be689add04d07a1ba2ae3a1a35040a3"},"schema_version":"1.0"},"canonical_sha256":"015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2","source":{"kind":"arxiv","id":"1209.1308","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1308","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1308v3","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1308","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"AFP37YLU5L4D","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AFP37YLU5L4DSJHJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AFP37YLU","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AFP37YLU5L4DSJHJTI5ZGYKHT7","target":"record","payload":{"canonical_record":{"source":{"id":"1209.1308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-06T15:01:40Z","cross_cats_sorted":[],"title_canon_sha256":"576611378909531e76bf4418653997cb28a4a3c1192948a51a0f6e3862e146a6","abstract_canon_sha256":"a66948b4c9f641cb07449170bb0ebcdc6be689add04d07a1ba2ae3a1a35040a3"},"schema_version":"1.0"},"canonical_sha256":"015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:20:50.442749Z","signature_b64":"pYmTskSbZCHd+fTK5J2RE9BUJNNoHDQhZ4IY7XjoPhUeYy+2vUE87c30Hx91cNSeqEeYhFHYyr69sSp+0mrgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2","last_reissued_at":"2026-05-18T02:20:50.441968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:20:50.441968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.1308","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3HKnbFY+AMrqTyRcA04lEaRB/5Ri5JnBNfQdDlH0ogoOWTC9ZoVdycUHDn5FhMXcEHPdAjYMZsbnC+ZlyzBQCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:46:53.980532Z"},"content_sha256":"60f18ce8601b776e32af96a1e23a08579ed18c17226439e0738a183ba51ba8d6","schema_version":"1.0","event_id":"sha256:60f18ce8601b776e32af96a1e23a08579ed18c17226439e0738a183ba51ba8d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AFP37YLU5L4DSJHJTI5ZGYKHT7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariants of closed braids via counting surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Michael Brandenbursky","submitted_at":"2012-09-06T15:01:40Z","abstract_excerpt":"A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we present simple formulas for an infinite family of invariants in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram associated with a closed braid. We then identify the resulting invariants with partial derivatives of the HOMFLY-PT polynomial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1308","kind":"arxiv","version":3},"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":"2026-05-18T02:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fpOB+SUeKiuyytwTZ10VJRmzPO08sXv4O5wQ0l7tBfb1ITBLxtftV5jyxRsFBrB/kmijxmjx4SB+yUM6vuTSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T14:46:53.981198Z"},"content_sha256":"23aadd9c847bce2c7812c669b3b3264aceba6801058cd898ff9a6f717bcb49b0","schema_version":"1.0","event_id":"sha256:23aadd9c847bce2c7812c669b3b3264aceba6801058cd898ff9a6f717bcb49b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7/bundle.json","state_url":"https://pith.science/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7/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":"2026-05-29T14:46:53Z","links":{"resolver":"https://pith.science/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7","bundle":"https://pith.science/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7/bundle.json","state":"https://pith.science/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AFP37YLU5L4DSJHJTI5ZGYKHT7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AFP37YLU5L4DSJHJTI5ZGYKHT7","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":"a66948b4c9f641cb07449170bb0ebcdc6be689add04d07a1ba2ae3a1a35040a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-06T15:01:40Z","title_canon_sha256":"576611378909531e76bf4418653997cb28a4a3c1192948a51a0f6e3862e146a6"},"schema_version":"1.0","source":{"id":"1209.1308","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.1308","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1209.1308v3","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1308","created_at":"2026-05-18T02:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"AFP37YLU5L4D","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AFP37YLU5L4DSJHJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AFP37YLU","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:23aadd9c847bce2c7812c669b3b3264aceba6801058cd898ff9a6f717bcb49b0","target":"graph","created_at":"2026-05-18T02:20:50Z","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":"A Gauss diagram is a simple, combinatorial way to present a link. It is known that any Vassiliev invariant may be obtained from a Gauss diagram formula that involves counting subdiagrams of certain combinatorial types. In this paper we present simple formulas for an infinite family of invariants in terms of counting surfaces of a certain genus and number of boundary components in a Gauss diagram associated with a closed braid. We then identify the resulting invariants with partial derivatives of the HOMFLY-PT polynomial.","authors_text":"Michael Brandenbursky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-06T15:01:40Z","title":"Invariants of closed braids via counting surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1308","kind":"arxiv","version":3},"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":"sha256:60f18ce8601b776e32af96a1e23a08579ed18c17226439e0738a183ba51ba8d6","target":"record","created_at":"2026-05-18T02:20:50Z","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":"a66948b4c9f641cb07449170bb0ebcdc6be689add04d07a1ba2ae3a1a35040a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-09-06T15:01:40Z","title_canon_sha256":"576611378909531e76bf4418653997cb28a4a3c1192948a51a0f6e3862e146a6"},"schema_version":"1.0","source":{"id":"1209.1308","kind":"arxiv","version":3}},"canonical_sha256":"015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"015fbfe174eaf83924e99a3b9361479fd3003703186a42dfb9bc59c5216afde2","first_computed_at":"2026-05-18T02:20:50.441968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:50.441968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pYmTskSbZCHd+fTK5J2RE9BUJNNoHDQhZ4IY7XjoPhUeYy+2vUE87c30Hx91cNSeqEeYhFHYyr69sSp+0mrgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:50.442749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.1308","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60f18ce8601b776e32af96a1e23a08579ed18c17226439e0738a183ba51ba8d6","sha256:23aadd9c847bce2c7812c669b3b3264aceba6801058cd898ff9a6f717bcb49b0"],"state_sha256":"8a594502d629f48d5df5b83b9abe31a653e01dbd82e2fab684a98d4b6dfd2833"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+YrBkP+CJuAUUr1gOV1kt1CvQOnU2X8GCBS2M+yAZfDfH02yo7Pa4hbypaJyKBYM7F6BeaMjanlkzQIaO3sCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T14:46:53.984402Z","bundle_sha256":"7b6b19bc744a04ed3254b509110982353e3c68e56db7d986b3857071b283a22e"}}