{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:UPHUINELI6EPOVVLTDSSY5SUHR","short_pith_number":"pith:UPHUINEL","canonical_record":{"source":{"id":"2607.06985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2026-07-08T04:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"e194a17693338dcf121ca7101b73936ba4293819f9a51553a65b0225e83c92ae","abstract_canon_sha256":"82da583c15106664d4712c063a9e6a3de94305111b9539f0151d85e4f5caa961"},"schema_version":"1.0"},"canonical_sha256":"a3cf44348b4788f756ab98e52c76543c6fae793258d7aa1f37c9c8b53c814447","source":{"kind":"arxiv","id":"2607.06985","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06985","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06985v1","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06985","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"UPHUINELI6EP","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"pith_short_16","alias_value":"UPHUINELI6EPOVVL","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"pith_short_8","alias_value":"UPHUINEL","created_at":"2026-07-09T01:20:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:UPHUINELI6EPOVVLTDSSY5SUHR","target":"record","payload":{"canonical_record":{"source":{"id":"2607.06985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2026-07-08T04:12:10Z","cross_cats_sorted":[],"title_canon_sha256":"e194a17693338dcf121ca7101b73936ba4293819f9a51553a65b0225e83c92ae","abstract_canon_sha256":"82da583c15106664d4712c063a9e6a3de94305111b9539f0151d85e4f5caa961"},"schema_version":"1.0"},"canonical_sha256":"a3cf44348b4788f756ab98e52c76543c6fae793258d7aa1f37c9c8b53c814447","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-09T01:20:11.675160Z","signature_b64":"hG8ranbzA8Id5NzkVHuahqZ1x6on18LovhfLWtmgx+2vl4Yw3YoXp0JNQizzc+3+lOeO6n2wZOTnMW9R3eLvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3cf44348b4788f756ab98e52c76543c6fae793258d7aa1f37c9c8b53c814447","last_reissued_at":"2026-07-09T01:20:11.674793Z","signature_status":"signed_v1","first_computed_at":"2026-07-09T01:20:11.674793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.06985","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":"2026-07-09T01:20:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y4pZ2QmdRIwx/rHwhVjb1FhDwB2vmGi8/QetGxxfIi+F/z+JJeRnlrv2MIZ+fxPeJT6lPvBh1LhBBKj2RhNzAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:32:47.447855Z"},"content_sha256":"3ab689320d8bb6a75556fd1b50da2a304c57d2e6cb34635c49e70dfdc4638cbc","schema_version":"1.0","event_id":"sha256:3ab689320d8bb6a75556fd1b50da2a304c57d2e6cb34635c49e70dfdc4638cbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:UPHUINELI6EPOVVLTDSSY5SUHR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbative determination of CP phase in CKM matrix using rephasing invariants of hierarchical mass matrices and their inverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Masaki J. S. Yang","submitted_at":"2026-07-08T04:12:10Z","abstract_excerpt":"In this paper, we derive approximate expressions for the CP phase $\\delta$ in the CKM matrix by a perturbative singular value decomposition for hierarchical quark mass matrices $m_{q}$. The diagonalization is achieved through a seesaw-like procedure in which the heavier generations are successively integrated out, naturally leading to mixing matrices expressed in terms of the mass matrix and its inverse $m_{q}^{-1}$. As a result, in the basis where the up-type quark mass matrix is diagonal, $\\delta$ is reduced to the fourth-order invariant $\\delta \\simeq \\arg [ - m^{-1}_{d12} m_{d23}^{} / m^{-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06985","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.06985/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-09T01:20:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"imJIuODanGigxp9yGuZLsHRiYx/B1WXEwBhAxgC+mthDQfS4l+cjLZvQ+PZ5m19m/QnYm2nFraooAs8EHUlmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T00:32:47.448333Z"},"content_sha256":"162414aa16b14465bad6dc9ec267acdeb94f2f24e37cb916bdfcafd643b04d0d","schema_version":"1.0","event_id":"sha256:162414aa16b14465bad6dc9ec267acdeb94f2f24e37cb916bdfcafd643b04d0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPHUINELI6EPOVVLTDSSY5SUHR/bundle.json","state_url":"https://pith.science/pith/UPHUINELI6EPOVVLTDSSY5SUHR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPHUINELI6EPOVVLTDSSY5SUHR/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":"2026-08-04T00:32:47Z","links":{"resolver":"https://pith.science/pith/UPHUINELI6EPOVVLTDSSY5SUHR","bundle":"https://pith.science/pith/UPHUINELI6EPOVVLTDSSY5SUHR/bundle.json","state":"https://pith.science/pith/UPHUINELI6EPOVVLTDSSY5SUHR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPHUINELI6EPOVVLTDSSY5SUHR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UPHUINELI6EPOVVLTDSSY5SUHR","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":"82da583c15106664d4712c063a9e6a3de94305111b9539f0151d85e4f5caa961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2026-07-08T04:12:10Z","title_canon_sha256":"e194a17693338dcf121ca7101b73936ba4293819f9a51553a65b0225e83c92ae"},"schema_version":"1.0","source":{"id":"2607.06985","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.06985","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"arxiv_version","alias_value":"2607.06985v1","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.06985","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"pith_short_12","alias_value":"UPHUINELI6EP","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"pith_short_16","alias_value":"UPHUINELI6EPOVVL","created_at":"2026-07-09T01:20:11Z"},{"alias_kind":"pith_short_8","alias_value":"UPHUINEL","created_at":"2026-07-09T01:20:11Z"}],"graph_snapshots":[{"event_id":"sha256:162414aa16b14465bad6dc9ec267acdeb94f2f24e37cb916bdfcafd643b04d0d","target":"graph","created_at":"2026-07-09T01:20:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.06985/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we derive approximate expressions for the CP phase $\\delta$ in the CKM matrix by a perturbative singular value decomposition for hierarchical quark mass matrices $m_{q}$. The diagonalization is achieved through a seesaw-like procedure in which the heavier generations are successively integrated out, naturally leading to mixing matrices expressed in terms of the mass matrix and its inverse $m_{q}^{-1}$. As a result, in the basis where the up-type quark mass matrix is diagonal, $\\delta$ is reduced to the fourth-order invariant $\\delta \\simeq \\arg [ - m^{-1}_{d12} m_{d23}^{} / m^{-","authors_text":"Masaki J. S. Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2026-07-08T04:12:10Z","title":"Perturbative determination of CP phase in CKM matrix using rephasing invariants of hierarchical mass matrices and their inverses"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.06985","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":"sha256:3ab689320d8bb6a75556fd1b50da2a304c57d2e6cb34635c49e70dfdc4638cbc","target":"record","created_at":"2026-07-09T01:20:11Z","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":"82da583c15106664d4712c063a9e6a3de94305111b9539f0151d85e4f5caa961","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2026-07-08T04:12:10Z","title_canon_sha256":"e194a17693338dcf121ca7101b73936ba4293819f9a51553a65b0225e83c92ae"},"schema_version":"1.0","source":{"id":"2607.06985","kind":"arxiv","version":1}},"canonical_sha256":"a3cf44348b4788f756ab98e52c76543c6fae793258d7aa1f37c9c8b53c814447","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3cf44348b4788f756ab98e52c76543c6fae793258d7aa1f37c9c8b53c814447","first_computed_at":"2026-07-09T01:20:11.674793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-09T01:20:11.674793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hG8ranbzA8Id5NzkVHuahqZ1x6on18LovhfLWtmgx+2vl4Yw3YoXp0JNQizzc+3+lOeO6n2wZOTnMW9R3eLvBA==","signature_status":"signed_v1","signed_at":"2026-07-09T01:20:11.675160Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.06985","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ab689320d8bb6a75556fd1b50da2a304c57d2e6cb34635c49e70dfdc4638cbc","sha256:162414aa16b14465bad6dc9ec267acdeb94f2f24e37cb916bdfcafd643b04d0d"],"state_sha256":"66bf69eee0fcf6db84f4775d6dbe6022dab4db0f6ad2e164ec6b0d7a60accaf7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ILsbpYy3KHe+cMQpBdgab7Sbewgifq6uvwfEuzCvTGTwv29VPVgG4TxlPKoIaXhQ+NC/Fr4MHlQ8VpEx+3uwCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T00:32:47.452916Z","bundle_sha256":"45bd7d3a299dc7c76216b40cf3650e422883930d8deda3fed458c55ee6abc73b"}}