{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:OOQICKC65W7JFQBTPOACTKIJKS","short_pith_number":"pith:OOQICKC6","schema_version":"1.0","canonical_sha256":"73a081285eedbe92c0337b8029a909549bfc129cb4689755d93cfe17670938ea","source":{"kind":"arxiv","id":"1705.05430","version":2},"attestation_state":"computed","paper":{"title":"Natural Fermion Hierarchies from Random Yukawa Couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Gero von Gersdorff","submitted_at":"2017-05-15T20:13:04Z","abstract_excerpt":"The Standard Model of particle physics requires Yukawa matrices with eigenval- ues that differ by orders of magnitude. We propose a novel way to explain this fact without any small or large parameters. The mechanism is based on the observation that products of matrices of random order one-numbers have hierarchical spectra. The same mechanism can easily account for the hierarchical structure of the quark mixing matrix."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.05430","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2017-05-15T20:13:04Z","cross_cats_sorted":[],"title_canon_sha256":"5bbf830ddce4ee21b87d89dc0ae9e90e1265361e8c9c3dd4918cba1bf55f545f","abstract_canon_sha256":"5519327a1599d7e53301e14e74750c91b93f9af599bb32721374fff3a5c63cc4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:10.243194Z","signature_b64":"GP3lmv6494I+cqz9zWEWpHCjyxmtQyotsZDD1Rut5xD3ubmMJiNvB4x6CiXVyG3yDW0H2X1y+kphgXGq3RqGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73a081285eedbe92c0337b8029a909549bfc129cb4689755d93cfe17670938ea","last_reissued_at":"2026-05-18T00:32:10.242548Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:10.242548Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Natural Fermion Hierarchies from Random Yukawa Couplings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Gero von Gersdorff","submitted_at":"2017-05-15T20:13:04Z","abstract_excerpt":"The Standard Model of particle physics requires Yukawa matrices with eigenval- ues that differ by orders of magnitude. We propose a novel way to explain this fact without any small or large parameters. The mechanism is based on the observation that products of matrices of random order one-numbers have hierarchical spectra. The same mechanism can easily account for the hierarchical structure of the quark mixing matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05430","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.05430","created_at":"2026-05-18T00:32:10.242650+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.05430v2","created_at":"2026-05-18T00:32:10.242650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05430","created_at":"2026-05-18T00:32:10.242650+00:00"},{"alias_kind":"pith_short_12","alias_value":"OOQICKC65W7J","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_16","alias_value":"OOQICKC65W7JFQBT","created_at":"2026-05-18T12:31:34.259226+00:00"},{"alias_kind":"pith_short_8","alias_value":"OOQICKC6","created_at":"2026-05-18T12:31:34.259226+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS","json":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS.json","graph_json":"https://pith.science/api/pith-number/OOQICKC65W7JFQBTPOACTKIJKS/graph.json","events_json":"https://pith.science/api/pith-number/OOQICKC65W7JFQBTPOACTKIJKS/events.json","paper":"https://pith.science/paper/OOQICKC6"},"agent_actions":{"view_html":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS","download_json":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS.json","view_paper":"https://pith.science/paper/OOQICKC6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.05430&json=true","fetch_graph":"https://pith.science/api/pith-number/OOQICKC65W7JFQBTPOACTKIJKS/graph.json","fetch_events":"https://pith.science/api/pith-number/OOQICKC65W7JFQBTPOACTKIJKS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS/action/storage_attestation","attest_author":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS/action/author_attestation","sign_citation":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS/action/citation_signature","submit_replication":"https://pith.science/pith/OOQICKC65W7JFQBTPOACTKIJKS/action/replication_record"}},"created_at":"2026-05-18T00:32:10.242650+00:00","updated_at":"2026-05-18T00:32:10.242650+00:00"}