{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y7LWKMZWEERERIAUFXBZNBZNKI","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":"f4ea5c152d4144ee5f19fc2f53494e802364ec8d975f43d71692c1dad2f0e846","cross_cats_sorted":["gr-qc","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2013-10-30T16:37:32Z","title_canon_sha256":"28d657db628f220b0c8957df847b320e658be513076c308f3b5ec78b0a8d8929"},"schema_version":"1.0","source":{"id":"1310.8225","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.8225","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"arxiv_version","alias_value":"1310.8225v2","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.8225","created_at":"2026-05-18T03:00:51Z"},{"alias_kind":"pith_short_12","alias_value":"Y7LWKMZWEERE","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y7LWKMZWEERERIAU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y7LWKMZW","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:045674d95b562a69bcc9382df981c7293917b4272fc1ec7d4cde6a82d21d8045","target":"graph","created_at":"2026-05-18T03:00:51Z","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":"We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra $\\mathcal{S}(\\mathbb{R}^{1,1}) \\otimes M_2(\\mathbb{C})$, which has a non-trivial space of internal degrees of freedom. It turns out that the causality condition imposes restrictions on the motion in the internal space. Moreover, we show that the requirement of causality favours a unitary evolution in the internal space.","authors_text":"Micha{\\l} Eckstein, Nicolas Franco","cross_cats":["gr-qc","math.MP","math.OA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2013-10-30T16:37:32Z","title":"Exploring the Causal Structures of Almost Commutative Geometries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8225","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:e822e63c741c7a0410a4e66a167b56a5770d487931ac37a8905e1057cb88ffe1","target":"record","created_at":"2026-05-18T03:00:51Z","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":"f4ea5c152d4144ee5f19fc2f53494e802364ec8d975f43d71692c1dad2f0e846","cross_cats_sorted":["gr-qc","math.MP","math.OA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math-ph","submitted_at":"2013-10-30T16:37:32Z","title_canon_sha256":"28d657db628f220b0c8957df847b320e658be513076c308f3b5ec78b0a8d8929"},"schema_version":"1.0","source":{"id":"1310.8225","kind":"arxiv","version":2}},"canonical_sha256":"c7d7653336212248a0142dc396872d5201c7ff591152e8dca2a4bdff885cf5c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7d7653336212248a0142dc396872d5201c7ff591152e8dca2a4bdff885cf5c9","first_computed_at":"2026-05-18T03:00:51.334093Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:51.334093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f4QQAUBy+9dH4sLNBgTjLPmUiuLkXktpMCS/6xCYTg1nepbh/ZTVFaZNa21bO8yxe29hamUvdp5JY+PAs+lLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:51.334900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.8225","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e822e63c741c7a0410a4e66a167b56a5770d487931ac37a8905e1057cb88ffe1","sha256:045674d95b562a69bcc9382df981c7293917b4272fc1ec7d4cde6a82d21d8045"],"state_sha256":"ba745f590c599b08c7f0a27b988423a8ddf68f78655a0527af6a7f29ceca2b6b"}