{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:LRKPPGZ7WIL7FHRPS4O4NSJEI5","short_pith_number":"pith:LRKPPGZ7","canonical_record":{"source":{"id":"0910.2762","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-10-15T18:10:43Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"f051262dc0e12f2f0cbda8632b81fa9ff405513bb1848fdfd2a4381100205abd","abstract_canon_sha256":"c9e2df2b5c1da1712c7585ceb8d74c2279f359bd67601f165409caf570af5c72"},"schema_version":"1.0"},"canonical_sha256":"5c54f79b3fb217f29e2f971dc6c9244745167cbcc2dfb92a0022040ea2010b53","source":{"kind":"arxiv","id":"0910.2762","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2762","created_at":"2026-05-18T02:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2762v3","created_at":"2026-05-18T02:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2762","created_at":"2026-05-18T02:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"LRKPPGZ7WIL7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LRKPPGZ7WIL7FHRP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LRKPPGZ7","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:LRKPPGZ7WIL7FHRPS4O4NSJEI5","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2762","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-10-15T18:10:43Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"f051262dc0e12f2f0cbda8632b81fa9ff405513bb1848fdfd2a4381100205abd","abstract_canon_sha256":"c9e2df2b5c1da1712c7585ceb8d74c2279f359bd67601f165409caf570af5c72"},"schema_version":"1.0"},"canonical_sha256":"5c54f79b3fb217f29e2f971dc6c9244745167cbcc2dfb92a0022040ea2010b53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:18.743059Z","signature_b64":"j1kRxUNwGtsGQP6I/2/twhuhmv80uy/PboaZvK2hDSPDkuRh/mSd67s1VCLr+Se4h063y+Rqe2mCCBvwnBhRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c54f79b3fb217f29e2f971dc6c9244745167cbcc2dfb92a0022040ea2010b53","last_reissued_at":"2026-05-18T02:34:18.742428Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:18.742428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2762","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LytPtcKafUq26rgCSBEQ+j/rdHp9pBll//YYdFEVTwlzDY56b8LDz/ZIsCGFAH9DsxK66ccKGKrU8fMx7hbnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:53:14.136813Z"},"content_sha256":"828c17ceb6270f63ce84046ba4ecb9aeabc3e7b75bf5171d88e3125b348d216a","schema_version":"1.0","event_id":"sha256:828c17ceb6270f63ce84046ba4ecb9aeabc3e7b75bf5171d88e3125b348d216a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:LRKPPGZ7WIL7FHRPS4O4NSJEI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Flavor Structure in F-theory Compactifications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph"],"primary_cat":"hep-th","authors_text":"Hirotaka Hayashi, Taizan Watari, Teruhiko Kawano, Yoichi Tsuchiya","submitted_at":"2009-10-15T18:10:43Z","abstract_excerpt":"F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of right-handed neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N_gen = 3 or the number of singularity points of certain types. If there i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2762","kind":"arxiv","version":3},"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":"2026-05-18T02:34:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qoCHB+xqJ8HWSnJSZt0TGKvlYdKM3BIfnp8OADL7O2e4Zkee1UQrCIaapPJchoXIHcMRL21LFzOvAWooG9h1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T02:53:14.137191Z"},"content_sha256":"9960c4bd173c77fd8c65bc854fd7647c1ab81870006ea93a54b96696fd867007","schema_version":"1.0","event_id":"sha256:9960c4bd173c77fd8c65bc854fd7647c1ab81870006ea93a54b96696fd867007"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5/bundle.json","state_url":"https://pith.science/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5/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":"2026-05-26T02:53:14Z","links":{"resolver":"https://pith.science/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5","bundle":"https://pith.science/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5/bundle.json","state":"https://pith.science/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LRKPPGZ7WIL7FHRPS4O4NSJEI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:LRKPPGZ7WIL7FHRPS4O4NSJEI5","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":"c9e2df2b5c1da1712c7585ceb8d74c2279f359bd67601f165409caf570af5c72","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-10-15T18:10:43Z","title_canon_sha256":"f051262dc0e12f2f0cbda8632b81fa9ff405513bb1848fdfd2a4381100205abd"},"schema_version":"1.0","source":{"id":"0910.2762","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2762","created_at":"2026-05-18T02:34:18Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2762v3","created_at":"2026-05-18T02:34:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2762","created_at":"2026-05-18T02:34:18Z"},{"alias_kind":"pith_short_12","alias_value":"LRKPPGZ7WIL7","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"LRKPPGZ7WIL7FHRP","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"LRKPPGZ7","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:9960c4bd173c77fd8c65bc854fd7647c1ab81870006ea93a54b96696fd867007","target":"graph","created_at":"2026-05-18T02:34:18Z","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":"F-theory is one of frameworks in string theory where supersymmetric grand unification is accommodated, and all the Yukawa couplings and Majorana masses of right-handed neutrinos are generated. Yukawa couplings of charged fermions are generated at codimension-3 singularities, and a contribution from a given singularity point is known to be approximately rank 1. Thus, the approximate rank of Yukawa matrices in low-energy effective theory of generic F-theory compactifications are minimum of either the number of generations N_gen = 3 or the number of singularity points of certain types. If there i","authors_text":"Hirotaka Hayashi, Taizan Watari, Teruhiko Kawano, Yoichi Tsuchiya","cross_cats":["hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-10-15T18:10:43Z","title":"Flavor Structure in F-theory Compactifications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2762","kind":"arxiv","version":3},"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":"sha256:828c17ceb6270f63ce84046ba4ecb9aeabc3e7b75bf5171d88e3125b348d216a","target":"record","created_at":"2026-05-18T02:34:18Z","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":"c9e2df2b5c1da1712c7585ceb8d74c2279f359bd67601f165409caf570af5c72","cross_cats_sorted":["hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2009-10-15T18:10:43Z","title_canon_sha256":"f051262dc0e12f2f0cbda8632b81fa9ff405513bb1848fdfd2a4381100205abd"},"schema_version":"1.0","source":{"id":"0910.2762","kind":"arxiv","version":3}},"canonical_sha256":"5c54f79b3fb217f29e2f971dc6c9244745167cbcc2dfb92a0022040ea2010b53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c54f79b3fb217f29e2f971dc6c9244745167cbcc2dfb92a0022040ea2010b53","first_computed_at":"2026-05-18T02:34:18.742428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:18.742428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1kRxUNwGtsGQP6I/2/twhuhmv80uy/PboaZvK2hDSPDkuRh/mSd67s1VCLr+Se4h063y+Rqe2mCCBvwnBhRCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:18.743059Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2762","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:828c17ceb6270f63ce84046ba4ecb9aeabc3e7b75bf5171d88e3125b348d216a","sha256:9960c4bd173c77fd8c65bc854fd7647c1ab81870006ea93a54b96696fd867007"],"state_sha256":"ee2d07a58d05d659ee8310e2bf624e49cb076245a884c0417111321c497f354e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hYRmYsAvzaZOwYqUVZwkgb1wR+JxrXHfdNntsiXjrH4UkgsHL6+IMy82IPSkBIFhRx2qYVt5M9WAjhdrnGI4Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T02:53:14.140397Z","bundle_sha256":"db40b391408a0e7be4f627906b77f813e08de59b61110d1dc62b467375f104a6"}}