{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:2MQMBDLSLRTA4FUDQ53MGBOBXG","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":"52e901a5b0ab3134ff4cf79a1e7afb68b8a422e04b6a0e1a8449680b7b7cbb09","cross_cats_sorted":["gr-qc","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-23T15:25:31Z","title_canon_sha256":"8181a5e713eb4e14ae6f2cc801eccefdc5ab115f8fbbf507897eb8d76a5c74dd"},"schema_version":"1.0","source":{"id":"astro-ph/0002434","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0002434","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0002434v3","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0002434","created_at":"2026-05-18T04:25:12Z"},{"alias_kind":"pith_short_12","alias_value":"2MQMBDLSLRTA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"2MQMBDLSLRTA4FUD","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"2MQMBDLS","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:5d1a74fe605bf276d57eaf50561b2ad7df6a35ce87ad9bf006f994e7814744ed","target":"graph","created_at":"2026-05-18T04:25:12Z","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":"On the largest scales there is evidence of discrete structure, examples of this are superclusters and voids and also by redshift taking discrete values. In this paper it is proposed that discrete redshift can be explained by using the spherical harmonic integer l; this occurs both in the metric or density perturbations and also in the solution of wave equations in Robertson-Walker spacetime. It is argued that the near conservation of energy implies that l varies regularly for wave equations in Robertson-Walker spacetime, whereas for density perturbations l cannot vary regularly. Once this is a","authors_text":"Mark D. Roberts","cross_cats":["gr-qc","hep-th"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2000-02-23T15:25:31Z","title":"Quantum Perturbative Approach to Discrete Redshift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0002434","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":"sha256:7c0c4b790ec7ed4a22f60cc59609ff573d5c7e08092eea9e0db483cc2e1be5e1","target":"record","created_at":"2026-05-18T04:25:12Z","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":"52e901a5b0ab3134ff4cf79a1e7afb68b8a422e04b6a0e1a8449680b7b7cbb09","cross_cats_sorted":["gr-qc","hep-th"],"license":"","primary_cat":"astro-ph","submitted_at":"2000-02-23T15:25:31Z","title_canon_sha256":"8181a5e713eb4e14ae6f2cc801eccefdc5ab115f8fbbf507897eb8d76a5c74dd"},"schema_version":"1.0","source":{"id":"astro-ph/0002434","kind":"arxiv","version":3}},"canonical_sha256":"d320c08d725c660e16838776c305c1b9aa51b45b7e0c7298c346787537bc027f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d320c08d725c660e16838776c305c1b9aa51b45b7e0c7298c346787537bc027f","first_computed_at":"2026-05-18T04:25:12.088163Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:25:12.088163Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMhcYyzvmFlLPF4Q1RjFzuYmr58tGc/4Tu7Svl5APnG4N5vw3dcxWjrRsTpOTkMvEybGtbZPr9MYSgmidrG0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:25:12.088910Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0002434","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7c0c4b790ec7ed4a22f60cc59609ff573d5c7e08092eea9e0db483cc2e1be5e1","sha256:5d1a74fe605bf276d57eaf50561b2ad7df6a35ce87ad9bf006f994e7814744ed"],"state_sha256":"8ce127048cce9fc0b5a863db3a55ede7b6921e42e942f53c7f5740c71790c194"}