{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:YFBLXJ4IQIFE4TM65BRU3SEIZI","short_pith_number":"pith:YFBLXJ4I","canonical_record":{"source":{"id":"1501.05476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-22T12:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"ab106cfed353e87844996069c97cf71d1f9459da9f9ce59a50a9f6b4961f56c2","abstract_canon_sha256":"5af4cbbcb8430f36912834a4e50010dbbcd638e3555ffdc2c2302e930e9fcf68"},"schema_version":"1.0"},"canonical_sha256":"c142bba788820a4e4d9ee8634dc888ca1e9269b8af3aec18ce17f5c6165b8bb6","source":{"kind":"arxiv","id":"1501.05476","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05476","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05476v2","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05476","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"YFBLXJ4IQIFE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YFBLXJ4IQIFE4TM6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YFBLXJ4I","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:YFBLXJ4IQIFE4TM65BRU3SEIZI","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-22T12:31:19Z","cross_cats_sorted":[],"title_canon_sha256":"ab106cfed353e87844996069c97cf71d1f9459da9f9ce59a50a9f6b4961f56c2","abstract_canon_sha256":"5af4cbbcb8430f36912834a4e50010dbbcd638e3555ffdc2c2302e930e9fcf68"},"schema_version":"1.0"},"canonical_sha256":"c142bba788820a4e4d9ee8634dc888ca1e9269b8af3aec18ce17f5c6165b8bb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:30.968833Z","signature_b64":"fVNE09lvIJkO23RQVwx4LT8wq7XCa5ygFpMHdE05Iozo2CSuo7CBY90yi41X01Mhr8aNT6hPGeBuWC0pzq5ACQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c142bba788820a4e4d9ee8634dc888ca1e9269b8af3aec18ce17f5c6165b8bb6","last_reissued_at":"2026-05-18T02:28:30.968139Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:30.968139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05476","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1RXkquBZ+CGSSmNCVRcxaNGQVSUAMNtdRNf2a4ctRlQMYbvJJOtLacWr7kmd9ZtWoIDvDXFozwXQPrVpFjoMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:20:00.341544Z"},"content_sha256":"802f419a50fbc88c7a17ee463c36a2b33bf8d0351fdadd2572a82f0a085f4cc8","schema_version":"1.0","event_id":"sha256:802f419a50fbc88c7a17ee463c36a2b33bf8d0351fdadd2572a82f0a085f4cc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:YFBLXJ4IQIFE4TM65BRU3SEIZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groupoid Fell bundles for product systems over quasi-lattice ordered groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Adam Rennie, Aidan Sims, David Robertson","submitted_at":"2015-01-22T12:31:19Z","abstract_excerpt":"Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica-Toeplitz algebra of the product system. Under the additional hypothesis that the left actions in the product system are implemented by injective homomorphisms, we show that the cross-sectional algebra of the restriction of the bundle to a natural boundary subgroupoid coincides with the Cuntz-Nica-Pimsner algebra of the product system. We apply these results to improve on existing suf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05476","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T02:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uvr/fze7sj6qCErgH7xlHE7cW9yCBDo94qWqVJ5nsMNLBROLHWS/sixdcPzLI0mC6M6cC97q4SfojHkyp8mfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:20:00.342275Z"},"content_sha256":"5636ce464094545e154e2c4eebaaa404db5b6b5644b406287de7cbcb41e41f5a","schema_version":"1.0","event_id":"sha256:5636ce464094545e154e2c4eebaaa404db5b6b5644b406287de7cbcb41e41f5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI/bundle.json","state_url":"https://pith.science/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI/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":"2026-06-11T15:20:00Z","links":{"resolver":"https://pith.science/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI","bundle":"https://pith.science/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI/bundle.json","state":"https://pith.science/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YFBLXJ4IQIFE4TM65BRU3SEIZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YFBLXJ4IQIFE4TM65BRU3SEIZI","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":"5af4cbbcb8430f36912834a4e50010dbbcd638e3555ffdc2c2302e930e9fcf68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-22T12:31:19Z","title_canon_sha256":"ab106cfed353e87844996069c97cf71d1f9459da9f9ce59a50a9f6b4961f56c2"},"schema_version":"1.0","source":{"id":"1501.05476","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05476","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05476v2","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05476","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"YFBLXJ4IQIFE","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"YFBLXJ4IQIFE4TM6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"YFBLXJ4I","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:5636ce464094545e154e2c4eebaaa404db5b6b5644b406287de7cbcb41e41f5a","target":"graph","created_at":"2026-05-18T02:28:30Z","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":"Consider a product system over the positive cone of a quasi-lattice ordered group. We construct a Fell bundle over an associated groupoid so that the cross-sectional algebra of the bundle is isomorphic to the Nica-Toeplitz algebra of the product system. Under the additional hypothesis that the left actions in the product system are implemented by injective homomorphisms, we show that the cross-sectional algebra of the restriction of the bundle to a natural boundary subgroupoid coincides with the Cuntz-Nica-Pimsner algebra of the product system. We apply these results to improve on existing suf","authors_text":"Adam Rennie, Aidan Sims, David Robertson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-22T12:31:19Z","title":"Groupoid Fell bundles for product systems over quasi-lattice ordered groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05476","kind":"arxiv","version":2},"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":"sha256:802f419a50fbc88c7a17ee463c36a2b33bf8d0351fdadd2572a82f0a085f4cc8","target":"record","created_at":"2026-05-18T02:28:30Z","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":"5af4cbbcb8430f36912834a4e50010dbbcd638e3555ffdc2c2302e930e9fcf68","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-22T12:31:19Z","title_canon_sha256":"ab106cfed353e87844996069c97cf71d1f9459da9f9ce59a50a9f6b4961f56c2"},"schema_version":"1.0","source":{"id":"1501.05476","kind":"arxiv","version":2}},"canonical_sha256":"c142bba788820a4e4d9ee8634dc888ca1e9269b8af3aec18ce17f5c6165b8bb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c142bba788820a4e4d9ee8634dc888ca1e9269b8af3aec18ce17f5c6165b8bb6","first_computed_at":"2026-05-18T02:28:30.968139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:30.968139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fVNE09lvIJkO23RQVwx4LT8wq7XCa5ygFpMHdE05Iozo2CSuo7CBY90yi41X01Mhr8aNT6hPGeBuWC0pzq5ACQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:30.968833Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05476","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:802f419a50fbc88c7a17ee463c36a2b33bf8d0351fdadd2572a82f0a085f4cc8","sha256:5636ce464094545e154e2c4eebaaa404db5b6b5644b406287de7cbcb41e41f5a"],"state_sha256":"c5cca045b256448a8aac249d2452610a597abf3a1676dc94807751962c586617"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y2G8Q9+60m+8oj/q/gz0rxPIQfR+xigOl1O5pXbFirWXUzS5pKEIX4Cb1DMb2jowgTJwlf5DrU1s4DZ++j4uBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:20:00.346197Z","bundle_sha256":"7480fc4ce26d7f033f16fa4714aff25c93f0fed9c9fa6263878174d464e1a20a"}}