{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WFMPUXPW7DI7NWWVTRF6WGRLMV","short_pith_number":"pith:WFMPUXPW","canonical_record":{"source":{"id":"1804.09482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T11:15:12Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"3e3864e5cf801ca8cb0e966184e6a09c786d6b2c30f78a1b29cd6c5c1f9247cf","abstract_canon_sha256":"b7ed31daa63dc3ab315b63fed7a24633b0bcccfe8fb39a2f9093bc7fdab8c8e8"},"schema_version":"1.0"},"canonical_sha256":"b158fa5df6f8d1f6dad59c4beb1a2b6559e5810dc9a1e21219fd2d39a759fdea","source":{"kind":"arxiv","id":"1804.09482","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09482","created_at":"2026-05-18T00:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09482v2","created_at":"2026-05-18T00:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09482","created_at":"2026-05-18T00:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"WFMPUXPW7DI7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WFMPUXPW7DI7NWWV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WFMPUXPW","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WFMPUXPW7DI7NWWVTRF6WGRLMV","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09482","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T11:15:12Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"3e3864e5cf801ca8cb0e966184e6a09c786d6b2c30f78a1b29cd6c5c1f9247cf","abstract_canon_sha256":"b7ed31daa63dc3ab315b63fed7a24633b0bcccfe8fb39a2f9093bc7fdab8c8e8"},"schema_version":"1.0"},"canonical_sha256":"b158fa5df6f8d1f6dad59c4beb1a2b6559e5810dc9a1e21219fd2d39a759fdea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:52.378717Z","signature_b64":"aDvkyltpCvv3ppxPXD5B+attJ7Vl/w74RB+SFfK0KcbdgPtfpu+bvfMm3rw0wAZsytyfJ9HFhVtbs0AA56fJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b158fa5df6f8d1f6dad59c4beb1a2b6559e5810dc9a1e21219fd2d39a759fdea","last_reissued_at":"2026-05-18T00:12:52.378113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:52.378113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09482","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":"2026-05-18T00:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t+dlT5cxiPjNtAR5tSNrc4p57WPTL7W8/s10i9DDorgxnlJ0vpwBMUMjcqz1+MIX/wYGOYavfZ2af1gSwtbwCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T01:28:04.790052Z"},"content_sha256":"31e561982426f4731f867a28fb0d4f43de2e6095492cae85d1126b822e98178f","schema_version":"1.0","event_id":"sha256:31e561982426f4731f867a28fb0d4f43de2e6095492cae85d1126b822e98178f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WFMPUXPW7DI7NWWVTRF6WGRLMV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finite Pseudo-Riemannian Spectral Triples and The Standard Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"Andrzej Sitarz, Arkadiusz Bochniak","submitted_at":"2018-04-25T11:15:12Z","abstract_excerpt":"Starting from the formulation of pseudo-Riemannian generalisation of real spectral triples we develop the data of geometries over finite-dimensional algebras with indefinite metric and their Riemannian parts. We then discuss the Standard Model spectral triple in this formalism and interpret the physical symmetry preserving the lepton number as a shadow of a finite pseudo-Riemannian structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09482","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":"2026-05-18T00:12:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"25MgI05Lm3bG7UyDQ7GWr7tVzIoTqUB9vBxXDsNn+v5PeeUu9eAqxLs0A/QVJFf1wrIV1/FiSCorEjJP6Xk7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T01:28:04.790716Z"},"content_sha256":"50e84c7e0533383eb96f444b3aaeb1b710980004440e123ee8e578b2212cf956","schema_version":"1.0","event_id":"sha256:50e84c7e0533383eb96f444b3aaeb1b710980004440e123ee8e578b2212cf956"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV/bundle.json","state_url":"https://pith.science/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV/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":"2026-05-20T01:28:04Z","links":{"resolver":"https://pith.science/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV","bundle":"https://pith.science/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV/bundle.json","state":"https://pith.science/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WFMPUXPW7DI7NWWVTRF6WGRLMV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WFMPUXPW7DI7NWWVTRF6WGRLMV","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":"b7ed31daa63dc3ab315b63fed7a24633b0bcccfe8fb39a2f9093bc7fdab8c8e8","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T11:15:12Z","title_canon_sha256":"3e3864e5cf801ca8cb0e966184e6a09c786d6b2c30f78a1b29cd6c5c1f9247cf"},"schema_version":"1.0","source":{"id":"1804.09482","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09482","created_at":"2026-05-18T00:12:52Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09482v2","created_at":"2026-05-18T00:12:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09482","created_at":"2026-05-18T00:12:52Z"},{"alias_kind":"pith_short_12","alias_value":"WFMPUXPW7DI7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WFMPUXPW7DI7NWWV","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WFMPUXPW","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:50e84c7e0533383eb96f444b3aaeb1b710980004440e123ee8e578b2212cf956","target":"graph","created_at":"2026-05-18T00:12:52Z","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":"Starting from the formulation of pseudo-Riemannian generalisation of real spectral triples we develop the data of geometries over finite-dimensional algebras with indefinite metric and their Riemannian parts. We then discuss the Standard Model spectral triple in this formalism and interpret the physical symmetry preserving the lepton number as a shadow of a finite pseudo-Riemannian structure.","authors_text":"Andrzej Sitarz, Arkadiusz Bochniak","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T11:15:12Z","title":"Finite Pseudo-Riemannian Spectral Triples and The Standard Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09482","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":"sha256:31e561982426f4731f867a28fb0d4f43de2e6095492cae85d1126b822e98178f","target":"record","created_at":"2026-05-18T00:12:52Z","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":"b7ed31daa63dc3ab315b63fed7a24633b0bcccfe8fb39a2f9093bc7fdab8c8e8","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-04-25T11:15:12Z","title_canon_sha256":"3e3864e5cf801ca8cb0e966184e6a09c786d6b2c30f78a1b29cd6c5c1f9247cf"},"schema_version":"1.0","source":{"id":"1804.09482","kind":"arxiv","version":2}},"canonical_sha256":"b158fa5df6f8d1f6dad59c4beb1a2b6559e5810dc9a1e21219fd2d39a759fdea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b158fa5df6f8d1f6dad59c4beb1a2b6559e5810dc9a1e21219fd2d39a759fdea","first_computed_at":"2026-05-18T00:12:52.378113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:52.378113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aDvkyltpCvv3ppxPXD5B+attJ7Vl/w74RB+SFfK0KcbdgPtfpu+bvfMm3rw0wAZsytyfJ9HFhVtbs0AA56fJBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:52.378717Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09482","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31e561982426f4731f867a28fb0d4f43de2e6095492cae85d1126b822e98178f","sha256:50e84c7e0533383eb96f444b3aaeb1b710980004440e123ee8e578b2212cf956"],"state_sha256":"0b71c198ab757ce20cc31119de5ac369af844ed1334477f4e6d0cb0bd689b951"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qxswI3YK+zr8DRDEZHrZNE0tPLlbMEnC7qdEuJ0iU96QYzYuIpqu467SHWpRW+Cfdaaed4n70uvPB/PQKIlhAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T01:28:04.793807Z","bundle_sha256":"398979072b5a3746e0211bfc05f65967fb26a876fa8214c66cfbe3a6fd8e455f"}}