{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:5MDGX2B64APNXQVVMKVR6TB24W","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":"c253622ce4eb45a7500c841c1af3a25c1480bb117ad58ca6119d5987d1271345","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-10-03T14:13:59Z","title_canon_sha256":"ab58ae24232ddeddebc61a31bf649f25198a323c4eb9b06cb8fc5e15f0774bb3"},"schema_version":"1.0","source":{"id":"1410.0856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.0856","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"arxiv_version","alias_value":"1410.0856v1","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.0856","created_at":"2026-05-18T02:41:09Z"},{"alias_kind":"pith_short_12","alias_value":"5MDGX2B64APN","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"5MDGX2B64APNXQVV","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"5MDGX2B6","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:2db154dda49328cf26b0717a632d2555b06a548f6049ec86cb8ac2205dfe8128","target":"graph","created_at":"2026-05-18T02:41:09Z","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":"Given a II$_1$-subfactor $A\\subset B$ of arbitrary index, we show that the rectangular GICAR category, also called the rectangular planar rook category, faithfully embeds as $A-A$ bimodule maps among the bimodules $\\bigotimes_A^n L^2(B)$. As a corollary, we get a lower bound on the dimension of the centralizer algebras $A_0'\\cap A_{2n}$ for infinite index subfactors, and we also get that $A_0'\\cap A_{2n}$ is nonabelian for $n\\geq 2$, where $(A_n)_{n\\geq 0}$ is the Jones tower for $A_0=A\\subset B=A_1$. We also show that the annular GICAR/planar rook category acts as maps amongst the $A$-central","authors_text":"David Penneys, Vaughan F. R. Jones","cross_cats":["math.CT","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-10-03T14:13:59Z","title":"Infinite index subfactors and the GICAR categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.0856","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":"sha256:95c1858677e3c36e3096530ac4b1c5729085684c90a701f8b5ee2f5310d56a8e","target":"record","created_at":"2026-05-18T02:41:09Z","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":"c253622ce4eb45a7500c841c1af3a25c1480bb117ad58ca6119d5987d1271345","cross_cats_sorted":["math.CT","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-10-03T14:13:59Z","title_canon_sha256":"ab58ae24232ddeddebc61a31bf649f25198a323c4eb9b06cb8fc5e15f0774bb3"},"schema_version":"1.0","source":{"id":"1410.0856","kind":"arxiv","version":1}},"canonical_sha256":"eb066be83ee01edbc2b562ab1f4c3ae594c6beeb2d525846aa1d0ca311ff57d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb066be83ee01edbc2b562ab1f4c3ae594c6beeb2d525846aa1d0ca311ff57d4","first_computed_at":"2026-05-18T02:41:09.590943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:09.590943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWViD8DJoOWsxMh4CwtrE8GByimYFY2AUcjeT4LDQbAezXYFhm7z5a+xbvZokF+4JoM1DZrhtx3gSvbPgg9FBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:09.591286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.0856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95c1858677e3c36e3096530ac4b1c5729085684c90a701f8b5ee2f5310d56a8e","sha256:2db154dda49328cf26b0717a632d2555b06a548f6049ec86cb8ac2205dfe8128"],"state_sha256":"09ad44e54cce99af4221e48fff1a5fbd6ee562a42caae091f2967e88b25820d4"}