{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SJOMW4MT7JWSZW6YPYDP2X3IF5","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":"f883f28cccf43b6ea2f09aa435242fb854c3b7c3d41aeb3a17cfb8372ad34216","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-23T15:52:35Z","title_canon_sha256":"3cbc410bfa9b8fe3179d7524a26f6e55031067d3076df146fde22a35464b4530"},"schema_version":"1.0","source":{"id":"2606.24728","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24728","created_at":"2026-06-24T01:15:40Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24728v1","created_at":"2026-06-24T01:15:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24728","created_at":"2026-06-24T01:15:40Z"},{"alias_kind":"pith_short_12","alias_value":"SJOMW4MT7JWS","created_at":"2026-06-24T01:15:40Z"},{"alias_kind":"pith_short_16","alias_value":"SJOMW4MT7JWSZW6Y","created_at":"2026-06-24T01:15:40Z"},{"alias_kind":"pith_short_8","alias_value":"SJOMW4MT","created_at":"2026-06-24T01:15:40Z"}],"graph_snapshots":[{"event_id":"sha256:d087a6104272ef8980df7bbf981e75f0fa2c87f4089df8cd5b059823efa0da00","target":"graph","created_at":"2026-06-24T01:15:40Z","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/2606.24728/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a natural CQMS structure on a twisted transformation groupoid $C^{\\ast}$-algebra coming from stratified $_{\\text {c}}$Lip-norm introduced by Austad. We obtain upper bounds of metric dimension of reduced $C^{\\ast}$-algebra of a transformation groupoid $\\Gamma\\rtimes X$ and its cocycle twist for a suitably chosen CQMS structure, provided $(X,d)$ is a compact metric space of finite Kolmogorov dimension and $\\Gamma$ is a discrete group of polynomial growth. When $\\Gamma$ has exponential growth, we prove that the dimension is generically $+\\infty$ proving that the dichotomy between poly","authors_text":"Arnab Chattopadhyay, Soumalya Joardar","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-23T15:52:35Z","title":"Metric dimension of $C^{\\ast}$-algebras of cocycle twisted transformation groupoids: Growth and dynamical complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24728","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":"sha256:8b922d83bd2751100acbd1a2e89cf129ab4e6dced9cdd9c93d68c922fd04bfe1","target":"record","created_at":"2026-06-24T01:15:40Z","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":"f883f28cccf43b6ea2f09aa435242fb854c3b7c3d41aeb3a17cfb8372ad34216","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-06-23T15:52:35Z","title_canon_sha256":"3cbc410bfa9b8fe3179d7524a26f6e55031067d3076df146fde22a35464b4530"},"schema_version":"1.0","source":{"id":"2606.24728","kind":"arxiv","version":1}},"canonical_sha256":"925ccb7193fa6d2cdbd87e06fd5f682f5e7e0e098812a7e5e30e88d7d9b07777","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"925ccb7193fa6d2cdbd87e06fd5f682f5e7e0e098812a7e5e30e88d7d9b07777","first_computed_at":"2026-06-24T01:15:40.242482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:15:40.242482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"So2K8QZ8Y+OAbdDdQSgFEBa65z/BFzKbkrfmlNzz77exGtmX+4Nw+EpInn91kEWGO4hFlV6OxtlvNC5TyRRVCw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:15:40.242879Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24728","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b922d83bd2751100acbd1a2e89cf129ab4e6dced9cdd9c93d68c922fd04bfe1","sha256:d087a6104272ef8980df7bbf981e75f0fa2c87f4089df8cd5b059823efa0da00"],"state_sha256":"ce585c119ca5b0cd145720e8716a299a91e5695d7b0563d92e9858538c79110f"}