{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:YNAWZDWFUJ3Q4LY6NNPR3LRXK2","short_pith_number":"pith:YNAWZDWF","canonical_record":{"source":{"id":"2110.04501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-09T08:15:14Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"296f718e2828d60b60ba053dedea9e51d14b9d4e82dee602c8898a0793987b8e","abstract_canon_sha256":"826d52f712744c64026592427fdbc35ac12734ce35f4553cf2863df312531408"},"schema_version":"1.0"},"canonical_sha256":"c3416c8ec5a2770e2f1e6b5f1dae37568d7d6ad1a2fba89f4e4ec44f3df02678","source":{"kind":"arxiv","id":"2110.04501","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.04501","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"2110.04501v3","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.04501","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"YNAWZDWFUJ3Q","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"pith_short_16","alias_value":"YNAWZDWFUJ3Q4LY6","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"pith_short_8","alias_value":"YNAWZDWF","created_at":"2026-07-05T04:19:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:YNAWZDWFUJ3Q4LY6NNPR3LRXK2","target":"record","payload":{"canonical_record":{"source":{"id":"2110.04501","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-09T08:15:14Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"296f718e2828d60b60ba053dedea9e51d14b9d4e82dee602c8898a0793987b8e","abstract_canon_sha256":"826d52f712744c64026592427fdbc35ac12734ce35f4553cf2863df312531408"},"schema_version":"1.0"},"canonical_sha256":"c3416c8ec5a2770e2f1e6b5f1dae37568d7d6ad1a2fba89f4e4ec44f3df02678","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:19:22.527151Z","signature_b64":"kIV6zUMxLYlwKaHHKHz+jxEyBS+/WlW6zMiyYUvO3u5bconGFIKjSPuN23gR4zX/dBl/e98IDyZKf317DXH+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3416c8ec5a2770e2f1e6b5f1dae37568d7d6ad1a2fba89f4e4ec44f3df02678","last_reissued_at":"2026-07-05T04:19:22.526702Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:19:22.526702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.04501","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6aJZNnnqRdc4qpX5RdZ1YozlHOXvZ/26PVy20rugG0raeDKDGZaVnXwliBhJwRy3/XseYIHiTN/zr+suqOCKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:20:41.260355Z"},"content_sha256":"21c840f2dacbcc0568cc45c6e8537d6f55e18a01b9312b2952f5a697dc695a66","schema_version":"1.0","event_id":"sha256:21c840f2dacbcc0568cc45c6e8537d6f55e18a01b9312b2952f5a697dc695a66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:YNAWZDWFUJ3Q4LY6NNPR3LRXK2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Left regular representations of Garside categories I. C*-algebras and groupoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Xin Li","submitted_at":"2021-10-09T08:15:14Z","abstract_excerpt":"We initiate the study of C*-algebras and groupoids arising from left regular representations of Garside categories, a notion which originated from the study of Braid groups. Every higher rank graph is a Garside category in a natural way. We develop a general classification result for closed invariant subspaces of our groupoids as well as criteria for topological freeness and local contractiveness, properties which are relevant for the structure of the corresponding C*-algebras. Our results provide a conceptual explanation for previous results on gauge-invariant ideals of higher rank graph C*-a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.04501","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.04501/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:19:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PYrlItvn/XxlrLhhSjF2sRHrlQEtq3eO8kdEIJpbWZToOwcDFbgUImrClscPPmCZHm7zisHzI7p+AvJkqUytAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T17:20:41.261306Z"},"content_sha256":"6ee082d702f0dd3ce8e27334e3b0a0482650a98a90da4e543cadcf973c6959f8","schema_version":"1.0","event_id":"sha256:6ee082d702f0dd3ce8e27334e3b0a0482650a98a90da4e543cadcf973c6959f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2/bundle.json","state_url":"https://pith.science/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2/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":"2026-08-09T17:20:41Z","links":{"resolver":"https://pith.science/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2","bundle":"https://pith.science/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2/bundle.json","state":"https://pith.science/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNAWZDWFUJ3Q4LY6NNPR3LRXK2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:YNAWZDWFUJ3Q4LY6NNPR3LRXK2","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":"826d52f712744c64026592427fdbc35ac12734ce35f4553cf2863df312531408","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-09T08:15:14Z","title_canon_sha256":"296f718e2828d60b60ba053dedea9e51d14b9d4e82dee602c8898a0793987b8e"},"schema_version":"1.0","source":{"id":"2110.04501","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.04501","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"arxiv_version","alias_value":"2110.04501v3","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.04501","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"pith_short_12","alias_value":"YNAWZDWFUJ3Q","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"pith_short_16","alias_value":"YNAWZDWFUJ3Q4LY6","created_at":"2026-07-05T04:19:22Z"},{"alias_kind":"pith_short_8","alias_value":"YNAWZDWF","created_at":"2026-07-05T04:19:22Z"}],"graph_snapshots":[{"event_id":"sha256:6ee082d702f0dd3ce8e27334e3b0a0482650a98a90da4e543cadcf973c6959f8","target":"graph","created_at":"2026-07-05T04:19:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.04501/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We initiate the study of C*-algebras and groupoids arising from left regular representations of Garside categories, a notion which originated from the study of Braid groups. Every higher rank graph is a Garside category in a natural way. We develop a general classification result for closed invariant subspaces of our groupoids as well as criteria for topological freeness and local contractiveness, properties which are relevant for the structure of the corresponding C*-algebras. Our results provide a conceptual explanation for previous results on gauge-invariant ideals of higher rank graph C*-a","authors_text":"Xin Li","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-09T08:15:14Z","title":"Left regular representations of Garside categories I. C*-algebras and groupoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.04501","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":"sha256:21c840f2dacbcc0568cc45c6e8537d6f55e18a01b9312b2952f5a697dc695a66","target":"record","created_at":"2026-07-05T04:19:22Z","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":"826d52f712744c64026592427fdbc35ac12734ce35f4553cf2863df312531408","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2021-10-09T08:15:14Z","title_canon_sha256":"296f718e2828d60b60ba053dedea9e51d14b9d4e82dee602c8898a0793987b8e"},"schema_version":"1.0","source":{"id":"2110.04501","kind":"arxiv","version":3}},"canonical_sha256":"c3416c8ec5a2770e2f1e6b5f1dae37568d7d6ad1a2fba89f4e4ec44f3df02678","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c3416c8ec5a2770e2f1e6b5f1dae37568d7d6ad1a2fba89f4e4ec44f3df02678","first_computed_at":"2026-07-05T04:19:22.526702Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:19:22.526702Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kIV6zUMxLYlwKaHHKHz+jxEyBS+/WlW6zMiyYUvO3u5bconGFIKjSPuN23gR4zX/dBl/e98IDyZKf317DXH+DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:19:22.527151Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.04501","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21c840f2dacbcc0568cc45c6e8537d6f55e18a01b9312b2952f5a697dc695a66","sha256:6ee082d702f0dd3ce8e27334e3b0a0482650a98a90da4e543cadcf973c6959f8"],"state_sha256":"8f31922a391445e3aa3d2428aa3fe77379804ad822445f73d722865aae16c535"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LBb7TOTVc1on2jRYTLZ4tChcDgZfCIr/B0/7QxuYujS72WIPY7eLFT/UQaDefl+WKjRjUeVPnhtdWg4aBSopDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T17:20:41.266646Z","bundle_sha256":"aa7d49fe9045ce42f35ec5d41def41d8514f4efa3133a1f13eb51efa43b8cc0a"}}