{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7HF3TRM5ISTMYF6YSY677RLUXE","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":"e33f446787f22812b05af395cd9c2d7d0b92d264086b2d46d617ad954cd0c761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2014-11-12T17:25:56Z","title_canon_sha256":"48aa248ace39389c6d6d5c29298696fa07725e2a9dc98490c12c3eea13539f69"},"schema_version":"1.0","source":{"id":"1411.3648","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.3648","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"arxiv_version","alias_value":"1411.3648v1","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.3648","created_at":"2026-05-18T02:37:43Z"},{"alias_kind":"pith_short_12","alias_value":"7HF3TRM5ISTM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"7HF3TRM5ISTMYF6Y","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"7HF3TRM5","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:e1f592c75801b92d23b631d682540570454e5e65a2a0a4a58824d7a111973d0c","target":"graph","created_at":"2026-05-18T02:37:43Z","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":"A recent paper by Harmut Traunm\\\"uller shows that the most adequate equation to interpret the observations on magnitude and redshift from 892 type 1a supernovae would be mu = 5 log[(1+z) ln(1+z)] + const. We discuss this result which is exacly the one we have obtained few years ago when postulating a relation between the speed of light and the expansion of the universe. We also compare our analytical result to the conclusion of Marosi who studied 280 supernovae and gamma-ray bursts in the range 0.1014 < z < 8.1. The difference between his results and ours is at worst of 0.3 %.","authors_text":"Bernard Vigoureux, Jean-Marie Vigoureux, Michel Langlois","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2014-11-12T17:25:56Z","title":"An Analytical Expression for the Hubble diagram of supernovae and gamma-ray bursts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.3648","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:caf213547df3f5cb324febdb6759aee1d5086c218b3052d5f3c8275d2b9a4ad1","target":"record","created_at":"2026-05-18T02:37:43Z","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":"e33f446787f22812b05af395cd9c2d7d0b92d264086b2d46d617ad954cd0c761","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2014-11-12T17:25:56Z","title_canon_sha256":"48aa248ace39389c6d6d5c29298696fa07725e2a9dc98490c12c3eea13539f69"},"schema_version":"1.0","source":{"id":"1411.3648","kind":"arxiv","version":1}},"canonical_sha256":"f9cbb9c59d44a6cc17d8963dffc574b9084b1a10eb9088f55f8ced2338b8988a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9cbb9c59d44a6cc17d8963dffc574b9084b1a10eb9088f55f8ced2338b8988a","first_computed_at":"2026-05-18T02:37:43.240535Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:43.240535Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XKgx0eBeLdVayhxrFBbCoLjuhXbCOyLChiC/ZbX2Yi41huPvCNe7OZ278Z2F2VfYvKc3eDwyh3zDMTHZlJAkAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:43.240916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.3648","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caf213547df3f5cb324febdb6759aee1d5086c218b3052d5f3c8275d2b9a4ad1","sha256:e1f592c75801b92d23b631d682540570454e5e65a2a0a4a58824d7a111973d0c"],"state_sha256":"126af09e357da973b906b611ca930170eca3f7694b103d389607ceb7f5224e67"}