{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:2G7QOUQD4TZAY4KC5DZKYQQTZI","short_pith_number":"pith:2G7QOUQD","canonical_record":{"source":{"id":"math/0611717","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-11-23T12:01:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e64a89c135afc860c3fcdd2eba2a6d9fb40c9bf09a62b02b7f7d3b7f6dbbe830","abstract_canon_sha256":"0938f2551aecdb9ee0e289b118bf945ff0b7a1fbb9032255601c2bb20371d0d8"},"schema_version":"1.0"},"canonical_sha256":"d1bf075203e4f20c7142e8f2ac4213ca28a43cc8c134b9ee1ff249bdd2123720","source":{"kind":"arxiv","id":"math/0611717","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611717","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611717v3","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611717","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"2G7QOUQD4TZA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"2G7QOUQD4TZAY4KC","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"2G7QOUQD","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:2G7QOUQD4TZAY4KC5DZKYQQTZI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0611717","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2006-11-23T12:01:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e64a89c135afc860c3fcdd2eba2a6d9fb40c9bf09a62b02b7f7d3b7f6dbbe830","abstract_canon_sha256":"0938f2551aecdb9ee0e289b118bf945ff0b7a1fbb9032255601c2bb20371d0d8"},"schema_version":"1.0"},"canonical_sha256":"d1bf075203e4f20c7142e8f2ac4213ca28a43cc8c134b9ee1ff249bdd2123720","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:02.106514Z","signature_b64":"Ks+ZL/FEn+OdHs/Y4Yf4A1PBLKhpXcIjEHQ7s3TVCiUvAoz79i+wMQJciAmNqofJORvne6/mlQDrRu/UmEC4DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1bf075203e4f20c7142e8f2ac4213ca28a43cc8c134b9ee1ff249bdd2123720","last_reissued_at":"2026-05-18T04:02:02.105618Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:02.105618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0611717","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":"2026-05-18T04:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+KufavcvkXYHVEY6/PNKktl1y6NWe2tuI8huZnYYQDtN0NlLVXJwJhv9HAg+LkKct0vy81UYJnvFUvLZtenlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:30:39.453815Z"},"content_sha256":"6b6560ac876a063569f59350dad7bb9aedd5b38c69294c71fbce34aa5321d57d","schema_version":"1.0","event_id":"sha256:6b6560ac876a063569f59350dad7bb9aedd5b38c69294c71fbce34aa5321d57d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:2G7QOUQD4TZAY4KC5DZKYQQTZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Yamada Polynomial and Khovanov Cohomology","license":"","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"A. Vesnin, V. Vershinin","submitted_at":"2006-11-23T12:01:06Z","abstract_excerpt":"For any graph G we define bigraded cohomology groups whose graded Euler characteristic is a multiple of the Yamada polynomial of G."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611717","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":"2026-05-18T04:02:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EM60Lz/pCaSxcqNLozLuaGSTrQTv+3h28Jm9CgaWIuN0QCg8EOlBZL5bH/M8qF1TrWnLfRa9F3PxHIHRDNzIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T21:30:39.454456Z"},"content_sha256":"7c78f6f295ee7b05c3a1cdc51672c683d473de20f458b406da19a470a9a925b6","schema_version":"1.0","event_id":"sha256:7c78f6f295ee7b05c3a1cdc51672c683d473de20f458b406da19a470a9a925b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI/bundle.json","state_url":"https://pith.science/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI/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":"2026-06-05T21:30:39Z","links":{"resolver":"https://pith.science/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI","bundle":"https://pith.science/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI/bundle.json","state":"https://pith.science/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2G7QOUQD4TZAY4KC5DZKYQQTZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:2G7QOUQD4TZAY4KC5DZKYQQTZI","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":"0938f2551aecdb9ee0e289b118bf945ff0b7a1fbb9032255601c2bb20371d0d8","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.GT","submitted_at":"2006-11-23T12:01:06Z","title_canon_sha256":"e64a89c135afc860c3fcdd2eba2a6d9fb40c9bf09a62b02b7f7d3b7f6dbbe830"},"schema_version":"1.0","source":{"id":"math/0611717","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0611717","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"arxiv_version","alias_value":"math/0611717v3","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0611717","created_at":"2026-05-18T04:02:02Z"},{"alias_kind":"pith_short_12","alias_value":"2G7QOUQD4TZA","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"2G7QOUQD4TZAY4KC","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"2G7QOUQD","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:7c78f6f295ee7b05c3a1cdc51672c683d473de20f458b406da19a470a9a925b6","target":"graph","created_at":"2026-05-18T04:02:02Z","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":"For any graph G we define bigraded cohomology groups whose graded Euler characteristic is a multiple of the Yamada polynomial of G.","authors_text":"A. Vesnin, V. Vershinin","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2006-11-23T12:01:06Z","title":"Yamada Polynomial and Khovanov Cohomology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0611717","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":"sha256:6b6560ac876a063569f59350dad7bb9aedd5b38c69294c71fbce34aa5321d57d","target":"record","created_at":"2026-05-18T04:02:02Z","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":"0938f2551aecdb9ee0e289b118bf945ff0b7a1fbb9032255601c2bb20371d0d8","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.GT","submitted_at":"2006-11-23T12:01:06Z","title_canon_sha256":"e64a89c135afc860c3fcdd2eba2a6d9fb40c9bf09a62b02b7f7d3b7f6dbbe830"},"schema_version":"1.0","source":{"id":"math/0611717","kind":"arxiv","version":3}},"canonical_sha256":"d1bf075203e4f20c7142e8f2ac4213ca28a43cc8c134b9ee1ff249bdd2123720","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1bf075203e4f20c7142e8f2ac4213ca28a43cc8c134b9ee1ff249bdd2123720","first_computed_at":"2026-05-18T04:02:02.105618Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:02.105618Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ks+ZL/FEn+OdHs/Y4Yf4A1PBLKhpXcIjEHQ7s3TVCiUvAoz79i+wMQJciAmNqofJORvne6/mlQDrRu/UmEC4DA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:02.106514Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0611717","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b6560ac876a063569f59350dad7bb9aedd5b38c69294c71fbce34aa5321d57d","sha256:7c78f6f295ee7b05c3a1cdc51672c683d473de20f458b406da19a470a9a925b6"],"state_sha256":"d8bba44d84351382d0727f6dd0200305abbb5883fd88aa4152c7fbcba2255ed8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F85EpiKJVPZ5cRqFGYvoTrRt68ugXrx/A3SWNkKxhkClE7xQzTch+vlmMzKHfNV02xNjiODsICrOXCwf3GeWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T21:30:39.457090Z","bundle_sha256":"86d5edf8b5aafd9b026928eca5260ec9d9c686d188c242ccd63061f68804c41b"}}