{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BTSCHJ4IACVWSQVHM4VNY5PBS4","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":"b2a27419d21b23bc572dcd24e04f2e25a0785b3fb26cbc7d84a2e57bbe971592","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.pop-ph","submitted_at":"2025-03-28T19:21:05Z","title_canon_sha256":"1271326e16ad985462e8d6f8340506ccb66793b27e9fe1cb2010be627881f77b"},"schema_version":"1.0","source":{"id":"2503.22839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.22839","created_at":"2026-07-05T10:41:26Z"},{"alias_kind":"arxiv_version","alias_value":"2503.22839v1","created_at":"2026-07-05T10:41:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.22839","created_at":"2026-07-05T10:41:26Z"},{"alias_kind":"pith_short_12","alias_value":"BTSCHJ4IACVW","created_at":"2026-07-05T10:41:26Z"},{"alias_kind":"pith_short_16","alias_value":"BTSCHJ4IACVWSQVH","created_at":"2026-07-05T10:41:26Z"},{"alias_kind":"pith_short_8","alias_value":"BTSCHJ4I","created_at":"2026-07-05T10:41:26Z"}],"graph_snapshots":[{"event_id":"sha256:a167eaae46c7aac8f6b3188606c4baa05d5dfc07a3a2c0acaddd99bef0919695","target":"graph","created_at":"2026-07-05T10:41:26Z","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/2503.22839/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The cosmological principle posits that the universe does not exhibit any specific preference for position or direction. However, it remains unclear whether the universe has a distinct preference for parity: whether certain properties are more likely to be classified as even or odd. In this study, we analyze the largest available galaxy group catalogs to explore this hypothesis: specifically, whether the number of galaxies within a galaxy group or cluster is more likely to be odd or even. Our findings convincingly indicate that the universe indeed favors odd numbers, with results achieving a si","authors_text":"Nan Li, Shiyin Shen","cross_cats":["astro-ph.CO","astro-ph.GA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.pop-ph","submitted_at":"2025-03-28T19:21:05Z","title":"The Universe is Odd"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.22839","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:ca45c11df5a8f104261dadc845c08468404d0569448782aa5378060159555553","target":"record","created_at":"2026-07-05T10:41:26Z","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":"b2a27419d21b23bc572dcd24e04f2e25a0785b3fb26cbc7d84a2e57bbe971592","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"physics.pop-ph","submitted_at":"2025-03-28T19:21:05Z","title_canon_sha256":"1271326e16ad985462e8d6f8340506ccb66793b27e9fe1cb2010be627881f77b"},"schema_version":"1.0","source":{"id":"2503.22839","kind":"arxiv","version":1}},"canonical_sha256":"0ce423a78800ab6942a7672adc75e1973574cf71d55bc560092303a5be5a9d98","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ce423a78800ab6942a7672adc75e1973574cf71d55bc560092303a5be5a9d98","first_computed_at":"2026-07-05T10:41:26.464261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:26.464261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8oQwFlSQa49GcI63A83UrsCF7ccEEEZ+JXQKqTNa3o0H9jJJxkpPeiUbUVoNEQGf+n+mj+r0ZMzAtFA9NBf2Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:26.464745Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.22839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca45c11df5a8f104261dadc845c08468404d0569448782aa5378060159555553","sha256:a167eaae46c7aac8f6b3188606c4baa05d5dfc07a3a2c0acaddd99bef0919695"],"state_sha256":"d4a36bdf60f72ed354555385384272f157e943da9bd2b909ff1ae18bbd61acbf"}