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We find that the relative change of the fine-structure constant between its present value and $\\alpha$ of \\sim 4.6 Gyr ago is consistent with zero, Delta alpha/alpha = [-8\\pm 8 (1\\sigma)] x 10^{-7}.\n  We also rederive this bound in models where all gauge and Yukawa couplings vary in an interdependent manner, as would be expected in un"},"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":"astro-ph/0309252","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2003-09-08T20:17:09Z","cross_cats_sorted":["hep-ph"],"title_canon_sha256":"567fa785ef9a5d1f04c86f54c8cd8cbb0fa93d20ca622edfb189e1ccbacb208e","abstract_canon_sha256":"f45b95673a51d1008bb56028aaba8819a4ee5977da91bc2a0a7fa5f8f5a566a1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:49:35.165048Z","signature_b64":"5GX4Erurzz+GOeGzV11mKMBQTQXYgduoey2+yOrZ4VH3++iYOSmhJ0KuXbz1/ZFbjSoSp7kWRRseNrxhtl5mAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a9c4862b331fe2124fb3ff1d1f7c56884c710484960c2c2bd285331f918c64e","last_reissued_at":"2026-07-04T15:49:35.164675Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:49:35.164675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Re-examination of the $^{187}$Re Bound on the Variation of Fundamental Couplings","license":"","headline":"","cross_cats":["hep-ph"],"primary_cat":"astro-ph","authors_text":"Alain Coc, Elisabeth Vangioni-Flam, Gerard Manhes, Keith A. 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