{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:IH3OF2X3JDJ6QQNFESGSRFMSKC","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":"662bcc2c683e43373040453bb11003bd4dcbff1643de1251f87f14ec64abad4d","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-15T10:23:56Z","title_canon_sha256":"e38e140813ae60c196089cbd00edadc1e6fecaed9f0f32ff401ce2f556cf3cd4"},"schema_version":"1.0","source":{"id":"2606.16521","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.16521","created_at":"2026-06-19T16:10:01Z"},{"alias_kind":"arxiv_version","alias_value":"2606.16521v1","created_at":"2026-06-19T16:10:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.16521","created_at":"2026-06-19T16:10:01Z"},{"alias_kind":"pith_short_12","alias_value":"IH3OF2X3JDJ6","created_at":"2026-06-19T16:10:01Z"},{"alias_kind":"pith_short_16","alias_value":"IH3OF2X3JDJ6QQNF","created_at":"2026-06-19T16:10:01Z"},{"alias_kind":"pith_short_8","alias_value":"IH3OF2X3","created_at":"2026-06-19T16:10:01Z"}],"graph_snapshots":[{"event_id":"sha256:76d390d27c562baf81b09d973526ea835e83942147706e351d08aab1e7d6d5df","target":"graph","created_at":"2026-06-19T16:10:01Z","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/2606.16521/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend the Schr\\\"odinger approach to large-scale structure formation beyond the Newtonian regime by working at first post-Friedmann (1PF) order. The standard Schr\\\"odinger--Poisson system gives a useful reformulation of the dynamics of a self-gravitating pressureless fluid, but it corresponds to the leading post-Friedmann, or Newtonian, limit. It therefore misses the relativistic corrections that enter at next-to-leading order and become relevant on horizon scales and for high-precision cosmological surveys. Starting from the 1PF continuity and Euler equations in a flat $\\Lambda$CDM backgro","authors_text":"Daniele Bertacca, Sabino Matarrese, Yiwen Deng-Huang","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-15T10:23:56Z","title":"A First Post-Friedmann Extension of the Schr\\\"odinger Approach to Cosmic Structure Formation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.16521","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:a20e2349d6d4592e6a8ba3ee7befcf610d3f64223adad2ea4bb4bb3ef5dcecda","target":"record","created_at":"2026-06-19T16:10:01Z","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":"662bcc2c683e43373040453bb11003bd4dcbff1643de1251f87f14ec64abad4d","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2026-06-15T10:23:56Z","title_canon_sha256":"e38e140813ae60c196089cbd00edadc1e6fecaed9f0f32ff401ce2f556cf3cd4"},"schema_version":"1.0","source":{"id":"2606.16521","kind":"arxiv","version":1}},"canonical_sha256":"41f6e2eafb48d3e841a5248d28959250864da7107d0139d13b3d85da01225292","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41f6e2eafb48d3e841a5248d28959250864da7107d0139d13b3d85da01225292","first_computed_at":"2026-06-19T16:10:01.948894Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:01.948894Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n+1eD4PmaOsi4T9Qn7hAL2efEUTrErjsw2WdpBEgwxO2bMLLqw1SGiWXXQmrzDjBrCoceTf730kmgLz5AKcjDQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:01.949247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.16521","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a20e2349d6d4592e6a8ba3ee7befcf610d3f64223adad2ea4bb4bb3ef5dcecda","sha256:76d390d27c562baf81b09d973526ea835e83942147706e351d08aab1e7d6d5df"],"state_sha256":"786593541add3292cf51fe942bd07844cdfb7972502d8fbc2580a863b0f2e42a"}