{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:S6NNINXQMSV66F24MXFZPCCE2Q","short_pith_number":"pith:S6NNINXQ","canonical_record":{"source":{"id":"1408.6841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-08-28T20:00:07Z","cross_cats_sorted":["hep-ph","math.AG"],"title_canon_sha256":"fc312d5ab8cb6d59b82cd4d088975c51bf8f7816657cc875ebeee33d9f605c79","abstract_canon_sha256":"70806c4a524363810e76ecabc5a271f48c4d3dabb9438c3ef3a5ecb3c3328625"},"schema_version":"1.0"},"canonical_sha256":"979ad436f064abef175c65cb978844d405c2cbdf7d829b1263ec20b2f123a4bf","source":{"kind":"arxiv","id":"1408.6841","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6841","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6841v1","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6841","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"S6NNINXQMSV6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S6NNINXQMSV66F24","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S6NNINXQ","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:S6NNINXQMSV66F24MXFZPCCE2Q","target":"record","payload":{"canonical_record":{"source":{"id":"1408.6841","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-08-28T20:00:07Z","cross_cats_sorted":["hep-ph","math.AG"],"title_canon_sha256":"fc312d5ab8cb6d59b82cd4d088975c51bf8f7816657cc875ebeee33d9f605c79","abstract_canon_sha256":"70806c4a524363810e76ecabc5a271f48c4d3dabb9438c3ef3a5ecb3c3328625"},"schema_version":"1.0"},"canonical_sha256":"979ad436f064abef175c65cb978844d405c2cbdf7d829b1263ec20b2f123a4bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:00.151133Z","signature_b64":"uZNPd+1m6U6L/gpzz0JdSh/qNMGcZMyRRSXZ76dVnH6Eup5wbQMM/iOam3w40LNoTDjOZiddM+IsKU4XipXeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"979ad436f064abef175c65cb978844d405c2cbdf7d829b1263ec20b2f123a4bf","last_reissued_at":"2026-05-18T02:44:00.150594Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:00.150594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.6841","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nZTTB/YAZkSUW6Z5X1i/uXPh0R0yyjamjX44izCMtMgMfNSnUG97HA1cBgex+j7j6Y5QYAHceVTqhjtQ+jt8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:37:46.209961Z"},"content_sha256":"5b146d2d07c637216e07e31613ba6147ea33803d90619e626ed7ff21e0756f01","schema_version":"1.0","event_id":"sha256:5b146d2d07c637216e07e31613ba6147ea33803d90619e626ed7ff21e0756f01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:S6NNINXQMSV66F24MXFZPCCE2Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Generations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math.AG"],"primary_cat":"hep-th","authors_text":"Brent D. Nelson, Cyril Matti, Michael Stillman, Vishnu Jejjala, Yang-Hui He","submitted_at":"2014-08-28T20:00:07Z","abstract_excerpt":"We present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic variety for multiple generations of Standard Model matter and Higgs doublets. The space is shown to have Calabi-Yau, Grassmannian, and toric signatures which sensitively depend on the number of generations of leptons, as well as inclusion of Majorana mass terms for right-handed neutrinos. We speculate as to why three generations is special."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6841","kind":"arxiv","version":1},"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":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+8hvu5r/Xoj8xpmvalpmjsTxHBX0wWcRa1/42qbj8NAO3sg9gRZ7JwBFJyfCdJD6VgA4oTdHYYsWkutpwt8LAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T09:37:46.210680Z"},"content_sha256":"5194c8a31a32552a0bc2196aced058d3d6e0611f8cb198f8977a7527e26b1459","schema_version":"1.0","event_id":"sha256:5194c8a31a32552a0bc2196aced058d3d6e0611f8cb198f8977a7527e26b1459"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S6NNINXQMSV66F24MXFZPCCE2Q/bundle.json","state_url":"https://pith.science/pith/S6NNINXQMSV66F24MXFZPCCE2Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S6NNINXQMSV66F24MXFZPCCE2Q/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":"2026-05-26T09:37:46Z","links":{"resolver":"https://pith.science/pith/S6NNINXQMSV66F24MXFZPCCE2Q","bundle":"https://pith.science/pith/S6NNINXQMSV66F24MXFZPCCE2Q/bundle.json","state":"https://pith.science/pith/S6NNINXQMSV66F24MXFZPCCE2Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S6NNINXQMSV66F24MXFZPCCE2Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:S6NNINXQMSV66F24MXFZPCCE2Q","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":"70806c4a524363810e76ecabc5a271f48c4d3dabb9438c3ef3a5ecb3c3328625","cross_cats_sorted":["hep-ph","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-08-28T20:00:07Z","title_canon_sha256":"fc312d5ab8cb6d59b82cd4d088975c51bf8f7816657cc875ebeee33d9f605c79"},"schema_version":"1.0","source":{"id":"1408.6841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.6841","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.6841v1","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.6841","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"S6NNINXQMSV6","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"S6NNINXQMSV66F24","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"S6NNINXQ","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:5194c8a31a32552a0bc2196aced058d3d6e0611f8cb198f8977a7527e26b1459","target":"graph","created_at":"2026-05-18T02:44:00Z","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 present an intriguing and precise interplay between algebraic geometry and the phenomenology of generations of particles. Using the electroweak sector of the MSSM as a testing ground, we compute the moduli space of vacua as an algebraic variety for multiple generations of Standard Model matter and Higgs doublets. The space is shown to have Calabi-Yau, Grassmannian, and toric signatures which sensitively depend on the number of generations of leptons, as well as inclusion of Majorana mass terms for right-handed neutrinos. We speculate as to why three generations is special.","authors_text":"Brent D. Nelson, Cyril Matti, Michael Stillman, Vishnu Jejjala, Yang-Hui He","cross_cats":["hep-ph","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-08-28T20:00:07Z","title":"The Geometry of Generations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.6841","kind":"arxiv","version":1},"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":"sha256:5b146d2d07c637216e07e31613ba6147ea33803d90619e626ed7ff21e0756f01","target":"record","created_at":"2026-05-18T02:44:00Z","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":"70806c4a524363810e76ecabc5a271f48c4d3dabb9438c3ef3a5ecb3c3328625","cross_cats_sorted":["hep-ph","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-08-28T20:00:07Z","title_canon_sha256":"fc312d5ab8cb6d59b82cd4d088975c51bf8f7816657cc875ebeee33d9f605c79"},"schema_version":"1.0","source":{"id":"1408.6841","kind":"arxiv","version":1}},"canonical_sha256":"979ad436f064abef175c65cb978844d405c2cbdf7d829b1263ec20b2f123a4bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979ad436f064abef175c65cb978844d405c2cbdf7d829b1263ec20b2f123a4bf","first_computed_at":"2026-05-18T02:44:00.150594Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:00.150594Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uZNPd+1m6U6L/gpzz0JdSh/qNMGcZMyRRSXZ76dVnH6Eup5wbQMM/iOam3w40LNoTDjOZiddM+IsKU4XipXeBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:00.151133Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.6841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5b146d2d07c637216e07e31613ba6147ea33803d90619e626ed7ff21e0756f01","sha256:5194c8a31a32552a0bc2196aced058d3d6e0611f8cb198f8977a7527e26b1459"],"state_sha256":"f30715362c38dcf9ad502732f757e9d895036e6f0dd499bfdebb8ea87aae82b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MtSOnae9tzgQAQPa2pjT+nZ8X8QpO7tgGfudSYlp80LQDgz/Es+6xd1aKw6MTzM6o/E6gtOmlATvwLsfRzZmAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T09:37:46.214976Z","bundle_sha256":"28a1a05519f575bb3e6e7725d020b8ed1dc454957e86ddaa152bd432e594fdfd"}}