{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FQTWKPF5K267OOS5QQVK4IBHHS","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":"1a7b8592ddfa0a5efde98e4bf9e532fb5bddbba16c8c1a804b159dde46d3a4e3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-31T15:45:02Z","title_canon_sha256":"1b1d7b8c084ec0d31d54d0b92bd5f4d123d90a4e32f4afa9081bb402c81ea341"},"schema_version":"1.0","source":{"id":"1501.00156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.00156","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1501.00156v2","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00156","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"FQTWKPF5K267","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FQTWKPF5K267OOS5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FQTWKPF5","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:ce6835f2b54499473da8ddf8c3463e1f7405025c87abd1d59d32ef39f18c1ae5","target":"graph","created_at":"2026-05-18T00:58:55Z","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 discuss some properties of the spectral triple $(A_F,H_F,D_F,J_F,\\gamma_F)$ describing the internal space in the noncommutative geometry approach to the Standard Model, with $A_F=\\mathbb{C}\\oplus\\mathbb{H}\\oplus M_3(\\mathbb{C})$. We show that, if we want $H_F$ to be a Morita equivalence bimodule between $A_F$ and the associated Clifford algebra, two terms must be added to the Dirac operator; we then study its relation with the orientability condition for a spectral triple. We also illustrate what changes if one considers a spectral triple with a degenerate representation, based on the compl","authors_text":"Francesco D'Andrea, Ludwik Dabrowski","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-31T15:45:02Z","title":"The Standard Model in Noncommutative Geometry and Morita equivalence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00156","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":"sha256:18a7a10ef9e7d9cc6af8791e33ea72ceacc4bf625aedbcd23ab708e1f25eb3c9","target":"record","created_at":"2026-05-18T00:58:55Z","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":"1a7b8592ddfa0a5efde98e4bf9e532fb5bddbba16c8c1a804b159dde46d3a4e3","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-12-31T15:45:02Z","title_canon_sha256":"1b1d7b8c084ec0d31d54d0b92bd5f4d123d90a4e32f4afa9081bb402c81ea341"},"schema_version":"1.0","source":{"id":"1501.00156","kind":"arxiv","version":2}},"canonical_sha256":"2c27653cbd56bdf73a5d842aae20273cbdffd843237f08487a4ce796888fde5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c27653cbd56bdf73a5d842aae20273cbdffd843237f08487a4ce796888fde5e","first_computed_at":"2026-05-18T00:58:55.657129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.657129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eeMJ3lc3KHy7bgYbTUpPVYmm8l4KHLvyIBTwxa0Yr1yynoLZ4yeaHpJLTMGeArNhPB1pzO/dFABuHyJuACApAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.657883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.00156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18a7a10ef9e7d9cc6af8791e33ea72ceacc4bf625aedbcd23ab708e1f25eb3c9","sha256:ce6835f2b54499473da8ddf8c3463e1f7405025c87abd1d59d32ef39f18c1ae5"],"state_sha256":"d7e58db1facbb4b48ee41997407986f7d43bb785a0c18f7076cadc9af01582e7"}