{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:NXG2FCFXWTSDXLFYO3DSEKZJOH","short_pith_number":"pith:NXG2FCFX","canonical_record":{"source":{"id":"math/0609832","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-09-29T05:41:03Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"26d4fc2a86c20d892a3365a286827c5b940f8e3965988db43b4a79fa3eb892a8","abstract_canon_sha256":"8b665790724bccc0ddaac7d1b29228fcba6d2aba9b667acc736f343932834f0e"},"schema_version":"1.0"},"canonical_sha256":"6dcda288b7b4e43bacb876c7222b2971ee34bab875ccb0bef05457ab69f36686","source":{"kind":"arxiv","id":"math/0609832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609832","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609832v1","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609832","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"NXG2FCFXWTSD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"NXG2FCFXWTSDXLFY","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"NXG2FCFX","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:NXG2FCFXWTSDXLFYO3DSEKZJOH","target":"record","payload":{"canonical_record":{"source":{"id":"math/0609832","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2006-09-29T05:41:03Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"26d4fc2a86c20d892a3365a286827c5b940f8e3965988db43b4a79fa3eb892a8","abstract_canon_sha256":"8b665790724bccc0ddaac7d1b29228fcba6d2aba9b667acc736f343932834f0e"},"schema_version":"1.0"},"canonical_sha256":"6dcda288b7b4e43bacb876c7222b2971ee34bab875ccb0bef05457ab69f36686","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:31.783943Z","signature_b64":"3bnT4QSAEEBtbNDGYeFO3315a5/+iqXLyVWJkOYnQ9JdO8WzQ62sZAjguSI4MtGzIsARs6IwlRqFG6hJDukYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6dcda288b7b4e43bacb876c7222b2971ee34bab875ccb0bef05457ab69f36686","last_reissued_at":"2026-05-18T02:41:31.783590Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:31.783590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0609832","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":"2026-05-18T02:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hR561fS5H/BIWT+jlA07zzV2lfoe88nZattil1/RdK1PE3qNECVOJIysTOshR6hrzIPWigBdzCIoQGbFrz97Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:22:44.564660Z"},"content_sha256":"a18e85693a29bcb00175dfd964f88474324b4cb34a86d58ab4e3c8579783c43b","schema_version":"1.0","event_id":"sha256:a18e85693a29bcb00175dfd964f88474324b4cb34a86d58ab4e3c8579783c43b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:NXG2FCFXWTSDXLFYO3DSEKZJOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Confluence Theory for Graphs","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"math.QA","authors_text":"Adam S. Sikora, Bruce W. Westbury","submitted_at":"2006-09-29T05:41:03Z","abstract_excerpt":"We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg's spiders) in an arbitrary surface. As a further consequence of this result, we find canonical bases of SU_3-skein modules of cylinders over orientable surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609832","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":"2026-05-18T02:41:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GlztdSZoYPio3Pxw9ewXvpmO2EsfHJKFTd1cJ9bBlsyeYDg/y9DZPqL7VAOumlYtdAom2Et0pB0vUExd9nLKBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T00:22:44.565006Z"},"content_sha256":"43d5b038358fe8250d06c7d98d73b3daffa64f03c82894ea183f96038588e35c","schema_version":"1.0","event_id":"sha256:43d5b038358fe8250d06c7d98d73b3daffa64f03c82894ea183f96038588e35c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH/bundle.json","state_url":"https://pith.science/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH/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":"2026-06-05T00:22:44Z","links":{"resolver":"https://pith.science/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH","bundle":"https://pith.science/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH/bundle.json","state":"https://pith.science/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NXG2FCFXWTSDXLFYO3DSEKZJOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:NXG2FCFXWTSDXLFYO3DSEKZJOH","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":"8b665790724bccc0ddaac7d1b29228fcba6d2aba9b667acc736f343932834f0e","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2006-09-29T05:41:03Z","title_canon_sha256":"26d4fc2a86c20d892a3365a286827c5b940f8e3965988db43b4a79fa3eb892a8"},"schema_version":"1.0","source":{"id":"math/0609832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609832","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609832v1","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609832","created_at":"2026-05-18T02:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"NXG2FCFXWTSD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"NXG2FCFXWTSDXLFY","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"NXG2FCFX","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:43d5b038358fe8250d06c7d98d73b3daffa64f03c82894ea183f96038588e35c","target":"graph","created_at":"2026-05-18T02:41:31Z","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 develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg's spiders) in an arbitrary surface. As a further consequence of this result, we find canonical bases of SU_3-skein modules of cylinders over orientable surfaces.","authors_text":"Adam S. Sikora, Bruce W. Westbury","cross_cats":["math.GT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2006-09-29T05:41:03Z","title":"Confluence Theory for Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609832","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:a18e85693a29bcb00175dfd964f88474324b4cb34a86d58ab4e3c8579783c43b","target":"record","created_at":"2026-05-18T02:41:31Z","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":"8b665790724bccc0ddaac7d1b29228fcba6d2aba9b667acc736f343932834f0e","cross_cats_sorted":["math.GT"],"license":"","primary_cat":"math.QA","submitted_at":"2006-09-29T05:41:03Z","title_canon_sha256":"26d4fc2a86c20d892a3365a286827c5b940f8e3965988db43b4a79fa3eb892a8"},"schema_version":"1.0","source":{"id":"math/0609832","kind":"arxiv","version":1}},"canonical_sha256":"6dcda288b7b4e43bacb876c7222b2971ee34bab875ccb0bef05457ab69f36686","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6dcda288b7b4e43bacb876c7222b2971ee34bab875ccb0bef05457ab69f36686","first_computed_at":"2026-05-18T02:41:31.783590Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:31.783590Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3bnT4QSAEEBtbNDGYeFO3315a5/+iqXLyVWJkOYnQ9JdO8WzQ62sZAjguSI4MtGzIsARs6IwlRqFG6hJDukYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:31.783943Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a18e85693a29bcb00175dfd964f88474324b4cb34a86d58ab4e3c8579783c43b","sha256:43d5b038358fe8250d06c7d98d73b3daffa64f03c82894ea183f96038588e35c"],"state_sha256":"ce9354395ed724d5039add090e81dd15b7b3c036869d0849c9b05da4d33bb2f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nmcD+ZUD0EDtL2Oom3TbUW3ctjimYjbKt8cpFDpRbRA1L/Dyti4SOwJUgz6yc/GVJFATR4sqPt7tKPs6pRE2DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T00:22:44.567002Z","bundle_sha256":"b97dbb8190229fb481be7e18c6febeccf4050677ed449a8e5337723a469a85d2"}}