{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:2V5DX6C4UFZM5MS5LN33WYFL47","short_pith_number":"pith:2V5DX6C4","canonical_record":{"source":{"id":"math/0510382","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2005-10-18T15:04:59Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"40ea5de66c20c66586a7c6d9b40804e75753f8bed3e2878e62ca3f9057a959c7","abstract_canon_sha256":"1823b264bf1b5ec48cc5c07078b1b56c85336a88292f91b3130418fa84e6f7d7"},"schema_version":"1.0"},"canonical_sha256":"d57a3bf85ca172ceb25d5b77bb60abe7c8b091e6d05c93dc661025d14a8af001","source":{"kind":"arxiv","id":"math/0510382","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510382","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510382v2","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510382","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"2V5DX6C4UFZM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2V5DX6C4UFZM5MS5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2V5DX6C4","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:2V5DX6C4UFZM5MS5LN33WYFL47","target":"record","payload":{"canonical_record":{"source":{"id":"math/0510382","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2005-10-18T15:04:59Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"40ea5de66c20c66586a7c6d9b40804e75753f8bed3e2878e62ca3f9057a959c7","abstract_canon_sha256":"1823b264bf1b5ec48cc5c07078b1b56c85336a88292f91b3130418fa84e6f7d7"},"schema_version":"1.0"},"canonical_sha256":"d57a3bf85ca172ceb25d5b77bb60abe7c8b091e6d05c93dc661025d14a8af001","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:21.983242Z","signature_b64":"DFcYJCFnD9wABvRAFN14/OTBhxlEtpSQKpacftGyzXsoZFd9ox0rPoJG0jFWtEnbSlONq3D3wuNjMfJktA14Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d57a3bf85ca172ceb25d5b77bb60abe7c8b091e6d05c93dc661025d14a8af001","last_reissued_at":"2026-05-18T02:54:21.982874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:21.982874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0510382","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VzcgwJEiD/3SKjk6PdfkBZoEGP3TF4AAu5qiTgZfa59df0+i1H+mAEJdrbWa+16Ovgaz+g4Ius/di3gL7k09Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:20:12.747000Z"},"content_sha256":"72d9fd64d63737ad6543174c3d2b9e6b25309421a96b38ee6d6de38f9a8151a1","schema_version":"1.0","event_id":"sha256:72d9fd64d63737ad6543174c3d2b9e6b25309421a96b38ee6d6de38f9a8151a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:2V5DX6C4UFZM5MS5LN33WYFL47","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorification of the colored Jones polynomial and Rasmussen invariant of links","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Anna Beliakova, Stephan Wehrli","submitted_at":"2005-10-18T15:04:59Z","abstract_excerpt":"We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that, for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510382","kind":"arxiv","version":2},"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":"2026-05-18T02:54:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+zphy1IvJkzLKx2jO/g8cQg617G5k1qewbm/ldXvIQhT9wR4ADHf4bFmpGC0//eGBusKI3uFAWRCWQwTierDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:20:12.747392Z"},"content_sha256":"bc6fc2427fa6c177d13ae797d668fe104a95d09c2f9efc234a9a1558659bad87","schema_version":"1.0","event_id":"sha256:bc6fc2427fa6c177d13ae797d668fe104a95d09c2f9efc234a9a1558659bad87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2V5DX6C4UFZM5MS5LN33WYFL47/bundle.json","state_url":"https://pith.science/pith/2V5DX6C4UFZM5MS5LN33WYFL47/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2V5DX6C4UFZM5MS5LN33WYFL47/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":"2026-05-27T02:20:12Z","links":{"resolver":"https://pith.science/pith/2V5DX6C4UFZM5MS5LN33WYFL47","bundle":"https://pith.science/pith/2V5DX6C4UFZM5MS5LN33WYFL47/bundle.json","state":"https://pith.science/pith/2V5DX6C4UFZM5MS5LN33WYFL47/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2V5DX6C4UFZM5MS5LN33WYFL47/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:2V5DX6C4UFZM5MS5LN33WYFL47","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":"1823b264bf1b5ec48cc5c07078b1b56c85336a88292f91b3130418fa84e6f7d7","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2005-10-18T15:04:59Z","title_canon_sha256":"40ea5de66c20c66586a7c6d9b40804e75753f8bed3e2878e62ca3f9057a959c7"},"schema_version":"1.0","source":{"id":"math/0510382","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510382","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510382v2","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510382","created_at":"2026-05-18T02:54:21Z"},{"alias_kind":"pith_short_12","alias_value":"2V5DX6C4UFZM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"2V5DX6C4UFZM5MS5","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"2V5DX6C4","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:bc6fc2427fa6c177d13ae797d668fe104a95d09c2f9efc234a9a1558659bad87","target":"graph","created_at":"2026-05-18T02:54:21Z","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 define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The Bar-Natan functors applied to these brackets produce Khovanov and Lee homology theories categorifying the colored Jones polynomial. Further, we study conditions under which framed colored link cobordisms induce chain transformations between our formal brackets. We conjecture that, for special choice of parameters, Khovanov and Lee homology theories of colored links are functorial (up to sign). Finally, we extend the ","authors_text":"Anna Beliakova, Stephan Wehrli","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2005-10-18T15:04:59Z","title":"Categorification of the colored Jones polynomial and Rasmussen invariant of links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510382","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":"sha256:72d9fd64d63737ad6543174c3d2b9e6b25309421a96b38ee6d6de38f9a8151a1","target":"record","created_at":"2026-05-18T02:54:21Z","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":"1823b264bf1b5ec48cc5c07078b1b56c85336a88292f91b3130418fa84e6f7d7","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2005-10-18T15:04:59Z","title_canon_sha256":"40ea5de66c20c66586a7c6d9b40804e75753f8bed3e2878e62ca3f9057a959c7"},"schema_version":"1.0","source":{"id":"math/0510382","kind":"arxiv","version":2}},"canonical_sha256":"d57a3bf85ca172ceb25d5b77bb60abe7c8b091e6d05c93dc661025d14a8af001","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d57a3bf85ca172ceb25d5b77bb60abe7c8b091e6d05c93dc661025d14a8af001","first_computed_at":"2026-05-18T02:54:21.982874Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:21.982874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DFcYJCFnD9wABvRAFN14/OTBhxlEtpSQKpacftGyzXsoZFd9ox0rPoJG0jFWtEnbSlONq3D3wuNjMfJktA14Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:21.983242Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510382","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72d9fd64d63737ad6543174c3d2b9e6b25309421a96b38ee6d6de38f9a8151a1","sha256:bc6fc2427fa6c177d13ae797d668fe104a95d09c2f9efc234a9a1558659bad87"],"state_sha256":"b68a7cd741e531b934d570612623e2b22a5bbe35eac6883a0ae8dbaf5cfac0fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PAoco6xSihUTXSy6SQWxn7l6AzlxjLyKM1pT6ZQ5SxGEiMrupnj0uUBin9WbN4jjyM1aJd9wp2RCfTgnUduaAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:20:12.750528Z","bundle_sha256":"39dbb488a0e1c4a9416d8f82af3569b63a942c090d43997488191affc908b106"}}