{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GGBXYL6WMQZBLG675JJU7C2L4I","short_pith_number":"pith:GGBXYL6W","canonical_record":{"source":{"id":"2607.28597","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-07-30T17:47:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ec4a1fe852f2e725c24ea440162ac55a14179a136900958337d2313e8bf47679","abstract_canon_sha256":"dc64f9f468a9a9aec1bd329cbbe14e7366c4ee90baa16ef3310bcdf18e019ced"},"schema_version":"1.0"},"canonical_sha256":"31837c2fd66432159bdfea534f8b4be211332f5aa757ad50cba5aa388a8c2f26","source":{"kind":"arxiv","id":"2607.28597","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28597","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28597v1","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28597","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"GGBXYL6WMQZB","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"pith_short_16","alias_value":"GGBXYL6WMQZBLG67","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"pith_short_8","alias_value":"GGBXYL6W","created_at":"2026-07-31T01:39:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GGBXYL6WMQZBLG675JJU7C2L4I","target":"record","payload":{"canonical_record":{"source":{"id":"2607.28597","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-07-30T17:47:54Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ec4a1fe852f2e725c24ea440162ac55a14179a136900958337d2313e8bf47679","abstract_canon_sha256":"dc64f9f468a9a9aec1bd329cbbe14e7366c4ee90baa16ef3310bcdf18e019ced"},"schema_version":"1.0"},"canonical_sha256":"31837c2fd66432159bdfea534f8b4be211332f5aa757ad50cba5aa388a8c2f26","receipt":{"kind":"pith_receipt","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31837c2fd66432159bdfea534f8b4be211332f5aa757ad50cba5aa388a8c2f26","last_reissued_at":"2026-07-31T01:39:03.698884Z","signature_status":"unsigned_v0","first_computed_at":"2026-07-31T01:39:03.698884Z"},"source_kind":"arxiv","source_id":"2607.28597","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":"2026-07-31T01:39:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NlsQkpotpbboW+twVRrQD2xpJ7tLdsKiby18yKKkPE1Ac1aS1pR9ps2sIYTCau6IgpjmG2iRC03qHrU5EC1MAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:16:05.782395Z"},"content_sha256":"5be36cbd05987089767efbf104beb05c2cd757c9831690c319bc9fcedd269d7d","schema_version":"1.0","event_id":"sha256:5be36cbd05987089767efbf104beb05c2cd757c9831690c319bc9fcedd269d7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GGBXYL6WMQZBLG675JJU7C2L4I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonnuclear Bunce-Deddens algebras","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Jamie Bell","submitted_at":"2026-07-30T17:47:54Z","abstract_excerpt":"We introduce nonnuclear Bunce-Deddens algebras, defined as reduced crossed product C*-algebras associated with free odometer actions of nonamenable countable discrete residually finite groups on a Cantor space. These are nonnuclear counterparts to the generalised Bunce-Deddens algebras introduced by Orfanos. For large classes of groups, we show that they share many regularity properties, including real rank zero, stable rank one, strict comparison of positive elements, and admitting a unique tracial state. In many cases, we deduce that they are even selfless and hence pure. Finally, we compute"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28597","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.28597/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":"2026-07-31T01:39:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBYM7HsOEPMVokqJ+gsDBjuBCcafbQqT8JMsN64j4xmMSROr1cWS0oh+ZrG4dy08VEs0UPdv+KSWq49ASjkGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T16:16:05.832012Z"},"content_sha256":"7e4d5540f9a4618f1f9bb8ff5aa94fb6090f71b9ac188429e1b356f46266763a","schema_version":"1.0","event_id":"sha256:7e4d5540f9a4618f1f9bb8ff5aa94fb6090f71b9ac188429e1b356f46266763a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGBXYL6WMQZBLG675JJU7C2L4I/bundle.json","state_url":"https://pith.science/pith/GGBXYL6WMQZBLG675JJU7C2L4I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGBXYL6WMQZBLG675JJU7C2L4I/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":"2026-08-17T16:16:05Z","links":{"resolver":"https://pith.science/pith/GGBXYL6WMQZBLG675JJU7C2L4I","bundle":"https://pith.science/pith/GGBXYL6WMQZBLG675JJU7C2L4I/bundle.json","state":"https://pith.science/pith/GGBXYL6WMQZBLG675JJU7C2L4I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGBXYL6WMQZBLG675JJU7C2L4I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GGBXYL6WMQZBLG675JJU7C2L4I","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":"dc64f9f468a9a9aec1bd329cbbe14e7366c4ee90baa16ef3310bcdf18e019ced","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-07-30T17:47:54Z","title_canon_sha256":"ec4a1fe852f2e725c24ea440162ac55a14179a136900958337d2313e8bf47679"},"schema_version":"1.0","source":{"id":"2607.28597","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28597","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28597v1","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28597","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"pith_short_12","alias_value":"GGBXYL6WMQZB","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"pith_short_16","alias_value":"GGBXYL6WMQZBLG67","created_at":"2026-07-31T01:39:03Z"},{"alias_kind":"pith_short_8","alias_value":"GGBXYL6W","created_at":"2026-07-31T01:39:03Z"}],"graph_snapshots":[{"event_id":"sha256:7e4d5540f9a4618f1f9bb8ff5aa94fb6090f71b9ac188429e1b356f46266763a","target":"graph","created_at":"2026-07-31T01:39:03Z","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/2607.28597/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce nonnuclear Bunce-Deddens algebras, defined as reduced crossed product C*-algebras associated with free odometer actions of nonamenable countable discrete residually finite groups on a Cantor space. These are nonnuclear counterparts to the generalised Bunce-Deddens algebras introduced by Orfanos. For large classes of groups, we show that they share many regularity properties, including real rank zero, stable rank one, strict comparison of positive elements, and admitting a unique tracial state. In many cases, we deduce that they are even selfless and hence pure. Finally, we compute","authors_text":"Jamie Bell","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-07-30T17:47:54Z","title":"Nonnuclear Bunce-Deddens algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28597","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":"sha256:5be36cbd05987089767efbf104beb05c2cd757c9831690c319bc9fcedd269d7d","target":"record","created_at":"2026-07-31T01:39:03Z","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":"dc64f9f468a9a9aec1bd329cbbe14e7366c4ee90baa16ef3310bcdf18e019ced","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-07-30T17:47:54Z","title_canon_sha256":"ec4a1fe852f2e725c24ea440162ac55a14179a136900958337d2313e8bf47679"},"schema_version":"1.0","source":{"id":"2607.28597","kind":"arxiv","version":1}},"canonical_sha256":"31837c2fd66432159bdfea534f8b4be211332f5aa757ad50cba5aa388a8c2f26","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31837c2fd66432159bdfea534f8b4be211332f5aa757ad50cba5aa388a8c2f26","first_computed_at":"2026-07-31T01:39:03.698884Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:39:03.698884Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.28597","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5be36cbd05987089767efbf104beb05c2cd757c9831690c319bc9fcedd269d7d","sha256:7e4d5540f9a4618f1f9bb8ff5aa94fb6090f71b9ac188429e1b356f46266763a"],"state_sha256":"243d1ec3d81256830a4a71bba2c6749992da016e5dfb71cb220042aba58cac48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kTdCP4oIztjM8WGDTwuuJDGnqtEkOU99SRuXFPH+rMwvcGc5xBlL7RhE9x89/PAA/eLkGEicmpU1/pe3NGUVCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T16:16:05.851231Z","bundle_sha256":"b639d72f5b39ecf622452dcd6f53b06e8af4a162c199d376bebdb92e13e4f905"}}