{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AWBCGQLX566ZEOUQMSHHK3FFDX","short_pith_number":"pith:AWBCGQLX","canonical_record":{"source":{"id":"1406.4642","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-18T08:51:18Z","cross_cats_sorted":[],"title_canon_sha256":"594db1b07b0ad2793e15dff3cbecf00ab85c523f751b73667c5a53b2ee92d574","abstract_canon_sha256":"067292b09aa042162baa91b74b003a4a8a35cbf7506aa2f3ebebbe4615f01868"},"schema_version":"1.0"},"canonical_sha256":"0582234177efbd923a90648e756ca51dfce26e832b8476a3c08fb6a0e9ec70f7","source":{"kind":"arxiv","id":"1406.4642","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4642","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4642v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4642","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"AWBCGQLX566Z","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AWBCGQLX566ZEOUQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AWBCGQLX","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AWBCGQLX566ZEOUQMSHHK3FFDX","target":"record","payload":{"canonical_record":{"source":{"id":"1406.4642","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-18T08:51:18Z","cross_cats_sorted":[],"title_canon_sha256":"594db1b07b0ad2793e15dff3cbecf00ab85c523f751b73667c5a53b2ee92d574","abstract_canon_sha256":"067292b09aa042162baa91b74b003a4a8a35cbf7506aa2f3ebebbe4615f01868"},"schema_version":"1.0"},"canonical_sha256":"0582234177efbd923a90648e756ca51dfce26e832b8476a3c08fb6a0e9ec70f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.083148Z","signature_b64":"swuAWWR2QlZXu+Jwb/xV+6gpRV8Gx5/kaBZ4y6c5PeZOcsbdA6udRYY8EyFzWavOC29CMC36Pv9FnMMOWLoHDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0582234177efbd923a90648e756ca51dfce26e832b8476a3c08fb6a0e9ec70f7","last_reissued_at":"2026-05-18T01:26:03.082631Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.082631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.4642","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":"2026-05-18T01:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O4NLYVLLxzXXh9XQ4A44kM1BHKHQiM0UG9jV0XhT+Wj2e/rVOncoj5gjtH2QQT0DiAvyXIrEnjqEyEUj4dXDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:23:33.235568Z"},"content_sha256":"842c6ef018d0247687d946b7a892e10461a800a2b21fb0c69c4816ee8eb4a017","schema_version":"1.0","event_id":"sha256:842c6ef018d0247687d946b7a892e10461a800a2b21fb0c69c4816ee8eb4a017"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AWBCGQLX566ZEOUQMSHHK3FFDX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Crossed product extensions of spectral triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Bruno Iochum, Thierry Masson","submitted_at":"2014-06-18T08:51:18Z","abstract_excerpt":"Given a spectral triple $(A,H,D)$ and a $C^*$-dynamical system $(\\mathbf{A}, G, \\alpha)$ where $A$ is dense in $\\mathbf{A}$ and $G$ is a locally compact group, we extend the triple to a triplet $(\\mathcal{B},\\mathcal{H},\\mathcal{D})$ on the crossed product $G \\ltimes_{\\alpha, \\text{red}} \\mathbf{A}$ which can be promoted to a modular-type twisted spectral triple within a general procedure exemplified by two cases: the $C^*$-algebra of the affine group and the conformal group acting on a complete Riemannian spin manifold."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4642","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":""},"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":"2026-05-18T01:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M9gtZR/5kxUusIeJOVT7pKAW34Zw7vxKr6J4nG+HKsc+z2VprTGIoSrlG9vPuEM0R1JRgs1fYzpLuIpKItjFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T01:23:33.236284Z"},"content_sha256":"121b6c3a38fda71bb7f48e42f61ceaaf9de5cfde5506134ea0a19cde4689657d","schema_version":"1.0","event_id":"sha256:121b6c3a38fda71bb7f48e42f61ceaaf9de5cfde5506134ea0a19cde4689657d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWBCGQLX566ZEOUQMSHHK3FFDX/bundle.json","state_url":"https://pith.science/pith/AWBCGQLX566ZEOUQMSHHK3FFDX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWBCGQLX566ZEOUQMSHHK3FFDX/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":"2026-06-10T01:23:33Z","links":{"resolver":"https://pith.science/pith/AWBCGQLX566ZEOUQMSHHK3FFDX","bundle":"https://pith.science/pith/AWBCGQLX566ZEOUQMSHHK3FFDX/bundle.json","state":"https://pith.science/pith/AWBCGQLX566ZEOUQMSHHK3FFDX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWBCGQLX566ZEOUQMSHHK3FFDX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AWBCGQLX566ZEOUQMSHHK3FFDX","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":"067292b09aa042162baa91b74b003a4a8a35cbf7506aa2f3ebebbe4615f01868","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-18T08:51:18Z","title_canon_sha256":"594db1b07b0ad2793e15dff3cbecf00ab85c523f751b73667c5a53b2ee92d574"},"schema_version":"1.0","source":{"id":"1406.4642","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.4642","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1406.4642v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.4642","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"AWBCGQLX566Z","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AWBCGQLX566ZEOUQ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AWBCGQLX","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:121b6c3a38fda71bb7f48e42f61ceaaf9de5cfde5506134ea0a19cde4689657d","target":"graph","created_at":"2026-05-18T01:26:03Z","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"},"paper":{"abstract_excerpt":"Given a spectral triple $(A,H,D)$ and a $C^*$-dynamical system $(\\mathbf{A}, G, \\alpha)$ where $A$ is dense in $\\mathbf{A}$ and $G$ is a locally compact group, we extend the triple to a triplet $(\\mathcal{B},\\mathcal{H},\\mathcal{D})$ on the crossed product $G \\ltimes_{\\alpha, \\text{red}} \\mathbf{A}$ which can be promoted to a modular-type twisted spectral triple within a general procedure exemplified by two cases: the $C^*$-algebra of the affine group and the conformal group acting on a complete Riemannian spin manifold.","authors_text":"Bruno Iochum, Thierry Masson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-18T08:51:18Z","title":"Crossed product extensions of spectral triples"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.4642","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":"sha256:842c6ef018d0247687d946b7a892e10461a800a2b21fb0c69c4816ee8eb4a017","target":"record","created_at":"2026-05-18T01:26:03Z","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":"067292b09aa042162baa91b74b003a4a8a35cbf7506aa2f3ebebbe4615f01868","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-18T08:51:18Z","title_canon_sha256":"594db1b07b0ad2793e15dff3cbecf00ab85c523f751b73667c5a53b2ee92d574"},"schema_version":"1.0","source":{"id":"1406.4642","kind":"arxiv","version":3}},"canonical_sha256":"0582234177efbd923a90648e756ca51dfce26e832b8476a3c08fb6a0e9ec70f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0582234177efbd923a90648e756ca51dfce26e832b8476a3c08fb6a0e9ec70f7","first_computed_at":"2026-05-18T01:26:03.082631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:03.082631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"swuAWWR2QlZXu+Jwb/xV+6gpRV8Gx5/kaBZ4y6c5PeZOcsbdA6udRYY8EyFzWavOC29CMC36Pv9FnMMOWLoHDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:03.083148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.4642","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:842c6ef018d0247687d946b7a892e10461a800a2b21fb0c69c4816ee8eb4a017","sha256:121b6c3a38fda71bb7f48e42f61ceaaf9de5cfde5506134ea0a19cde4689657d"],"state_sha256":"43c9242c5bcef2d1fe4148023da0b320f9e797b55e81dd1e2cadc88a31d614c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+B126506iIYt4A9MPcg7kzyysFCF5aKwxTbvY6y+2y3iDgMIKuqCPelcnKfeAFqFTQDmxcjC8t4wPTgAtx/pAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T01:23:33.240766Z","bundle_sha256":"c7b2ea4eae09dc4eea88d94ccb4304857eecfc461dca35c7909a356403ce77e2"}}