{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:CTTTU7OFZAE4TSFRHXFC7YRXZQ","short_pith_number":"pith:CTTTU7OF","canonical_record":{"source":{"id":"0904.0409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-04-02T15:46:51Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c4b172cf02dff9253989f544dc47d802940eb8408ed1fca31acd9b0cd5d31f64","abstract_canon_sha256":"e4b42db1c91451ac4fea7700e412d1680ef254485a7e7256659c9a5b080e6f67"},"schema_version":"1.0"},"canonical_sha256":"14e73a7dc5c809c9c8b13dca2fe237cc2531820dade6c1cb88791d0e559f2563","source":{"kind":"arxiv","id":"0904.0409","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0409","created_at":"2026-05-18T02:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0409v1","created_at":"2026-05-18T02:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0409","created_at":"2026-05-18T02:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"CTTTU7OFZAE4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CTTTU7OFZAE4TSFR","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CTTTU7OF","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:CTTTU7OFZAE4TSFRHXFC7YRXZQ","target":"record","payload":{"canonical_record":{"source":{"id":"0904.0409","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-04-02T15:46:51Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"c4b172cf02dff9253989f544dc47d802940eb8408ed1fca31acd9b0cd5d31f64","abstract_canon_sha256":"e4b42db1c91451ac4fea7700e412d1680ef254485a7e7256659c9a5b080e6f67"},"schema_version":"1.0"},"canonical_sha256":"14e73a7dc5c809c9c8b13dca2fe237cc2531820dade6c1cb88791d0e559f2563","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:07.944262Z","signature_b64":"2AP9MzTnzLb6pKszE6rB9SAYAyP5eWqAQKSVCbikwY4UE1BXxK8F/C7EUpLWhnC1JbRjM4oki7+dqQmZ2JJtAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14e73a7dc5c809c9c8b13dca2fe237cc2531820dade6c1cb88791d0e559f2563","last_reissued_at":"2026-05-18T02:14:07.943787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:07.943787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0904.0409","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":"2026-05-18T02:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eqUVcXctlpYGwJmO9WO/qkLKLhTtkYPowoCcnM9JLWVd4ZTXNjQsrkcp0gbMGm5e0yQPFGbjtKPuqCW2SielDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:16:30.688580Z"},"content_sha256":"99944461bd944c3283d64fabd0ff51462c3ddbc764bbc072a56eacf66ea86799","schema_version":"1.0","event_id":"sha256:99944461bd944c3283d64fabd0ff51462c3ddbc764bbc072a56eacf66ea86799"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:CTTTU7OFZAE4TSFRHXFC7YRXZQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On invariants of graphs related to quantum $\\mathfrak{sl}(2)$ at roots of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Nathan Geer, Nicolai Reshetikhin","submitted_at":"2009-04-02T15:46:51Z","abstract_excerpt":"We show how to define invariants of graphs related to quantum $\\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0409","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":"2026-05-18T02:14:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F3eo+XhwnrkABxLFoV8mmfrASure6WpZ2kF7+qfaD4DAp0/J3Zpk1+Pi7i2IXLhqc9M+n30aKt72LAdJk8G5BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T14:16:30.689143Z"},"content_sha256":"c484503e1a09edad0f11a068750f40bbab16762695780a2f2da8659399e9360a","schema_version":"1.0","event_id":"sha256:c484503e1a09edad0f11a068750f40bbab16762695780a2f2da8659399e9360a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ/bundle.json","state_url":"https://pith.science/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ/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":"2026-05-22T14:16:30Z","links":{"resolver":"https://pith.science/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ","bundle":"https://pith.science/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ/bundle.json","state":"https://pith.science/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CTTTU7OFZAE4TSFRHXFC7YRXZQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:CTTTU7OFZAE4TSFRHXFC7YRXZQ","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":"e4b42db1c91451ac4fea7700e412d1680ef254485a7e7256659c9a5b080e6f67","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-04-02T15:46:51Z","title_canon_sha256":"c4b172cf02dff9253989f544dc47d802940eb8408ed1fca31acd9b0cd5d31f64"},"schema_version":"1.0","source":{"id":"0904.0409","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.0409","created_at":"2026-05-18T02:14:07Z"},{"alias_kind":"arxiv_version","alias_value":"0904.0409v1","created_at":"2026-05-18T02:14:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0409","created_at":"2026-05-18T02:14:07Z"},{"alias_kind":"pith_short_12","alias_value":"CTTTU7OFZAE4","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"CTTTU7OFZAE4TSFR","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"CTTTU7OF","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:c484503e1a09edad0f11a068750f40bbab16762695780a2f2da8659399e9360a","target":"graph","created_at":"2026-05-18T02:14:07Z","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 show how to define invariants of graphs related to quantum $\\mathfrak{sl}(2)$ when the graph has more then one connected component and components are colored by blocks of representations with zero quantum dimensions.","authors_text":"Nathan Geer, Nicolai Reshetikhin","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-04-02T15:46:51Z","title":"On invariants of graphs related to quantum $\\mathfrak{sl}(2)$ at roots of unity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0409","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":"sha256:99944461bd944c3283d64fabd0ff51462c3ddbc764bbc072a56eacf66ea86799","target":"record","created_at":"2026-05-18T02:14:07Z","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":"e4b42db1c91451ac4fea7700e412d1680ef254485a7e7256659c9a5b080e6f67","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2009-04-02T15:46:51Z","title_canon_sha256":"c4b172cf02dff9253989f544dc47d802940eb8408ed1fca31acd9b0cd5d31f64"},"schema_version":"1.0","source":{"id":"0904.0409","kind":"arxiv","version":1}},"canonical_sha256":"14e73a7dc5c809c9c8b13dca2fe237cc2531820dade6c1cb88791d0e559f2563","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14e73a7dc5c809c9c8b13dca2fe237cc2531820dade6c1cb88791d0e559f2563","first_computed_at":"2026-05-18T02:14:07.943787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:07.943787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2AP9MzTnzLb6pKszE6rB9SAYAyP5eWqAQKSVCbikwY4UE1BXxK8F/C7EUpLWhnC1JbRjM4oki7+dqQmZ2JJtAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:07.944262Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.0409","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99944461bd944c3283d64fabd0ff51462c3ddbc764bbc072a56eacf66ea86799","sha256:c484503e1a09edad0f11a068750f40bbab16762695780a2f2da8659399e9360a"],"state_sha256":"f610eef4098a3bf20e685b9c27d5ae3ab1b0afa9ff736382fadd1ab73ae02e46"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDJyKIExZmZuJrMCfvoZR8ydRJCiyjhRdourUp83UuhqAaWruFUOFZqLkCwLmHzIZlqwEM4svGbBHIeiu2ofAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T14:16:30.691306Z","bundle_sha256":"e1c2bedd6265696a3fd88960a7dc7ce7ac23a7641f98c68e54ef42bfe7054a73"}}