{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:Y3NASFZJYHFCZ2BXWDUFWSR5ZV","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":"244096f716b70f4622baa2e98c3e5235e8475e1daef3ce184b446ea47fbb957e","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2022-02-02T18:45:12Z","title_canon_sha256":"669c1a82fe3082bc45f660358c1dd1d430e6a352c8fb7cfb9ed00b485468c288"},"schema_version":"1.0","source":{"id":"2202.01202","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.01202","created_at":"2026-07-05T04:48:41Z"},{"alias_kind":"arxiv_version","alias_value":"2202.01202v1","created_at":"2026-07-05T04:48:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.01202","created_at":"2026-07-05T04:48:41Z"},{"alias_kind":"pith_short_12","alias_value":"Y3NASFZJYHFC","created_at":"2026-07-05T04:48:41Z"},{"alias_kind":"pith_short_16","alias_value":"Y3NASFZJYHFCZ2BX","created_at":"2026-07-05T04:48:41Z"},{"alias_kind":"pith_short_8","alias_value":"Y3NASFZJ","created_at":"2026-07-05T04:48:41Z"}],"graph_snapshots":[{"event_id":"sha256:cbd86a6e62aa5ff99c8cc3c6a14f40d1a7d6ce9785a6d947dbe7c7643a1cb175","target":"graph","created_at":"2026-07-05T04:48:41Z","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/2202.01202/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze the properties that any late-time modification of the $\\Lambda$CDM expansion history must have in order to consistently solve both the $H_0$ and the $\\sigma_8$ tensions. Taking a model-independent approach, we obtain a set of necessary conditions that can be applied to generic late-time extensions. Our results are fully analytical and merely based on the assumptions that the deviations from the $\\Lambda$CDM background remain small. For the concrete case of a dark energy fluid with equation of state $w(z)$, we derive the following general requirements: (i) Solving the $H_0$ tension d","authors_text":"Hector Villarrubia-Rojo, Jann Zosso, Lavinia Heisenberg","cross_cats":["gr-qc","hep-th"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2022-02-02T18:45:12Z","title":"Can late-time extensions solve the $H_0$ and $\\sigma_8$ tensions?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.01202","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:bb786479b303b67cbe2619ab8d8f7cf22c9fa58f30e8e5723a159c12bc133709","target":"record","created_at":"2026-07-05T04:48:41Z","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":"244096f716b70f4622baa2e98c3e5235e8475e1daef3ce184b446ea47fbb957e","cross_cats_sorted":["gr-qc","hep-th"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"astro-ph.CO","submitted_at":"2022-02-02T18:45:12Z","title_canon_sha256":"669c1a82fe3082bc45f660358c1dd1d430e6a352c8fb7cfb9ed00b485468c288"},"schema_version":"1.0","source":{"id":"2202.01202","kind":"arxiv","version":1}},"canonical_sha256":"c6da091729c1ca2ce837b0e85b4a3dcd7e42cea37a795a202c57c1f98a28e3f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6da091729c1ca2ce837b0e85b4a3dcd7e42cea37a795a202c57c1f98a28e3f2","first_computed_at":"2026-07-05T04:48:41.946883Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:48:41.946883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Uem42c1WpUYVMjYpbigUrQJdZIiZUW+dOTpKYmc38+l2LhRabUepRTnu57+G3bZy9d9hq96wJEIw49wpeP+xAA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:48:41.947295Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.01202","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb786479b303b67cbe2619ab8d8f7cf22c9fa58f30e8e5723a159c12bc133709","sha256:cbd86a6e62aa5ff99c8cc3c6a14f40d1a7d6ce9785a6d947dbe7c7643a1cb175"],"state_sha256":"19c33d11553ac20bf89ebf72bf5876225e046c585ee436127764684affe6975c"}