{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GHH3FHXBO4M2R2JAW2USTPFOJ7","short_pith_number":"pith:GHH3FHXB","canonical_record":{"source":{"id":"1806.07282","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-19T14:35:26Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"b60c5b645d563c054a0209dc5a223cb18b9d9108e1165a432603cdeaa8788f51","abstract_canon_sha256":"e068cad70ef03ae0f41b829071aad29d9fda3e3ea0966d18ec922bccab7d552c"},"schema_version":"1.0"},"canonical_sha256":"31cfb29ee17719a8e920b6a929bcae4fe2d5b7ff1a85e01a71bdf078014abdd4","source":{"kind":"arxiv","id":"1806.07282","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07282","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07282v2","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07282","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"GHH3FHXBO4M2","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GHH3FHXBO4M2R2JA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GHH3FHXB","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GHH3FHXBO4M2R2JAW2USTPFOJ7","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07282","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-19T14:35:26Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"b60c5b645d563c054a0209dc5a223cb18b9d9108e1165a432603cdeaa8788f51","abstract_canon_sha256":"e068cad70ef03ae0f41b829071aad29d9fda3e3ea0966d18ec922bccab7d552c"},"schema_version":"1.0"},"canonical_sha256":"31cfb29ee17719a8e920b6a929bcae4fe2d5b7ff1a85e01a71bdf078014abdd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:54.479311Z","signature_b64":"a/NYcod6fvx1dS7r6uINRammOun34v0QdHILnzK1Y2Zpob6th8ItjWPSvfUaN/UzKhEUhAGWaSHmkfwfkX+mAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31cfb29ee17719a8e920b6a929bcae4fe2d5b7ff1a85e01a71bdf078014abdd4","last_reissued_at":"2026-05-17T23:51:54.478858Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:54.478858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07282","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":"2026-05-17T23:51:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/wcyUhhqmVM9mmePdkk4np4Yq4l2h5v2Cz1GNPS1FfVvKsdhw1usoVZLcy3XKaP2oN/sKvtOCUXqIBPv1Z5Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:35:40.141477Z"},"content_sha256":"bdff62ddb21e27b8ac0550a7b890f69f0ea425c0129d7eeea169dd3e0dcbdac5","schema_version":"1.0","event_id":"sha256:bdff62ddb21e27b8ac0550a7b890f69f0ea425c0129d7eeea169dd3e0dcbdac5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GHH3FHXBO4M2R2JAW2USTPFOJ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fermion masses, mass-mixing and the almost commutative geometry of 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, Ludwik Dabrowski","submitted_at":"2018-06-19T14:35:26Z","abstract_excerpt":"We investigate whether the Standard Model, within the accuracy of current experimental measurements, satisfies the Hodge duality condition introduced and studied in Dabrowski, D'Andrea, Sitarz, Lett Math Phys (2018) 108:1323. We show that the neutrino and quark mass-mixing and the difference of fermion masses is necessary for this property. We demonstrate that the current data supports the new geometric feature of the Standard Model, Hodge duality, provided that all neutrinos are massive."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07282","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":"2026-05-17T23:51:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0H+3MhFr6wvBZGmVTPv8+pZRV/qZw1QxWEBYAHb8EtJVoBdLVWgmDfcJLzFaLMtQAbcLf2ThJ+idW+wno7zWBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:35:40.142181Z"},"content_sha256":"2933037760a56bd363e6ebb42f8efc05b12407fb8f5d2810acfd6ad5080920a6","schema_version":"1.0","event_id":"sha256:2933037760a56bd363e6ebb42f8efc05b12407fb8f5d2810acfd6ad5080920a6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7/bundle.json","state_url":"https://pith.science/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7/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":"2026-05-20T05:35:40Z","links":{"resolver":"https://pith.science/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7","bundle":"https://pith.science/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7/bundle.json","state":"https://pith.science/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHH3FHXBO4M2R2JAW2USTPFOJ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GHH3FHXBO4M2R2JAW2USTPFOJ7","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":"e068cad70ef03ae0f41b829071aad29d9fda3e3ea0966d18ec922bccab7d552c","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-19T14:35:26Z","title_canon_sha256":"b60c5b645d563c054a0209dc5a223cb18b9d9108e1165a432603cdeaa8788f51"},"schema_version":"1.0","source":{"id":"1806.07282","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07282","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07282v2","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07282","created_at":"2026-05-17T23:51:54Z"},{"alias_kind":"pith_short_12","alias_value":"GHH3FHXBO4M2","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GHH3FHXBO4M2R2JA","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GHH3FHXB","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:2933037760a56bd363e6ebb42f8efc05b12407fb8f5d2810acfd6ad5080920a6","target":"graph","created_at":"2026-05-17T23:51:54Z","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 whether the Standard Model, within the accuracy of current experimental measurements, satisfies the Hodge duality condition introduced and studied in Dabrowski, D'Andrea, Sitarz, Lett Math Phys (2018) 108:1323. We show that the neutrino and quark mass-mixing and the difference of fermion masses is necessary for this property. We demonstrate that the current data supports the new geometric feature of the Standard Model, Hodge duality, provided that all neutrinos are massive.","authors_text":"Andrzej Sitarz, Ludwik Dabrowski","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-19T14:35:26Z","title":"Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07282","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:bdff62ddb21e27b8ac0550a7b890f69f0ea425c0129d7eeea169dd3e0dcbdac5","target":"record","created_at":"2026-05-17T23:51:54Z","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":"e068cad70ef03ae0f41b829071aad29d9fda3e3ea0966d18ec922bccab7d552c","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-06-19T14:35:26Z","title_canon_sha256":"b60c5b645d563c054a0209dc5a223cb18b9d9108e1165a432603cdeaa8788f51"},"schema_version":"1.0","source":{"id":"1806.07282","kind":"arxiv","version":2}},"canonical_sha256":"31cfb29ee17719a8e920b6a929bcae4fe2d5b7ff1a85e01a71bdf078014abdd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31cfb29ee17719a8e920b6a929bcae4fe2d5b7ff1a85e01a71bdf078014abdd4","first_computed_at":"2026-05-17T23:51:54.478858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:54.478858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a/NYcod6fvx1dS7r6uINRammOun34v0QdHILnzK1Y2Zpob6th8ItjWPSvfUaN/UzKhEUhAGWaSHmkfwfkX+mAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:54.479311Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07282","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdff62ddb21e27b8ac0550a7b890f69f0ea425c0129d7eeea169dd3e0dcbdac5","sha256:2933037760a56bd363e6ebb42f8efc05b12407fb8f5d2810acfd6ad5080920a6"],"state_sha256":"25af8194bef0f9ed9cc86d27323d01895d4b04326f87b1483ba117831db845c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uJLv8lWsM6fMLHwkhqQ8kkE4eGJtODEEhI9r6yiucIG0FVhdhiS1gI/VVeag7d/j2rCjGk8cUNYUbOHgMkzwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T05:35:40.146170Z","bundle_sha256":"ad9231633f07e98b9ce6f62bb13993fefe6ebc7903c72c4bfc9fcde50a552339"}}