{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WSXUQCZSBDL5NYSLJU3ZIAOGNS","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":"d35fe6d50a057f251960b370dfc0014d991c0c3d071939bb08bee57a942a3481","cross_cats_sorted":["math.CO","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2015-01-27T18:51:28Z","title_canon_sha256":"bb201c048cbfec40b8b70daef2abcf154a9300c3c9378e9368aab1c9102d7c6b"},"schema_version":"1.0","source":{"id":"1501.06869","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06869","created_at":"2026-05-18T01:10:46Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06869v3","created_at":"2026-05-18T01:10:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06869","created_at":"2026-05-18T01:10:46Z"},{"alias_kind":"pith_short_12","alias_value":"WSXUQCZSBDL5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WSXUQCZSBDL5NYSL","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WSXUQCZS","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:99259ce8153f8ebf6115e4d573b1b2506b79c3b3aab5a87896c18738f44a86a4","target":"graph","created_at":"2026-05-18T01:10:46Z","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":"This is the first paper in a general program to automate skein theoretic arguments. In this paper, we study skein theoretic invariants of planar trivalent graphs. Equivalently, we classify trivalent categories, which are nondegenerate pivotal tensor categories over $\\mathbb C$ generated by a symmetric self-dual simple object $X$ and a rotationally invariant morphism $1 \\rightarrow X \\otimes X \\otimes X$. Our main result is that the only trivalent categories with $\\dim \\operatorname{Hom}(1, X^{\\otimes n})$ bounded by $1,0,1,1,4,11,40$ for $0 \\leq n \\leq 6$ are quantum $SO(3)$, quantum $G_2$, a ","authors_text":"Emily Peters, Noah Snyder, Scott Morrison","cross_cats":["math.CO","math.CT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2015-01-27T18:51:28Z","title":"Categories generated by a trivalent vertex"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06869","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:cdae3bfb466f6a2a7d8cda8651c065951ee4c304b6149c8f02116c8a6895445e","target":"record","created_at":"2026-05-18T01:10:46Z","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":"d35fe6d50a057f251960b370dfc0014d991c0c3d071939bb08bee57a942a3481","cross_cats_sorted":["math.CO","math.CT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.QA","submitted_at":"2015-01-27T18:51:28Z","title_canon_sha256":"bb201c048cbfec40b8b70daef2abcf154a9300c3c9378e9368aab1c9102d7c6b"},"schema_version":"1.0","source":{"id":"1501.06869","kind":"arxiv","version":3}},"canonical_sha256":"b4af480b3208d7d6e24b4d379401c66c9356cac12948fac162e4f8b4bd032270","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4af480b3208d7d6e24b4d379401c66c9356cac12948fac162e4f8b4bd032270","first_computed_at":"2026-05-18T01:10:46.023699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:46.023699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yhi0mqgLt1fQdQQQF5VbRYTfzzH3z+b8kM8mYBI6OH/kSXE3TJD+VgEKMh6OD+bIW9T2m5mOvE2bsFqX2FVMCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:46.024195Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06869","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cdae3bfb466f6a2a7d8cda8651c065951ee4c304b6149c8f02116c8a6895445e","sha256:99259ce8153f8ebf6115e4d573b1b2506b79c3b3aab5a87896c18738f44a86a4"],"state_sha256":"7c3630287374847a5826d21b195e77971ca9899365aff54848d557a93012ca42"}