{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4WGOUKJJH53ZYZFON7GQOF5J33","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":"aee67c29338e8a47cfd54173854ae74c83f5cf1913dcfbed5663ba4050f4df52","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-05-15T17:31:06Z","title_canon_sha256":"4a2f903034ac0805da65ed9fdc2fe6b3abbc6bd5422dac84a653f307caaf59fa"},"schema_version":"1.0","source":{"id":"2605.16220","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.16220","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2605.16220v1","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.16220","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"4WGOUKJJH53Z","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"4WGOUKJJH53ZYZFO","created_at":"2026-05-20T00:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"4WGOUKJJ","created_at":"2026-05-20T00:01:58Z"}],"graph_snapshots":[{"event_id":"sha256:cda9d0bf14a2e97e31a82b2633571b83584ce52a2ede5265ee0978c7e483be25","target":"graph","created_at":"2026-05-20T00:01:58Z","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":[{"findings_count":0,"name":"shingle_duplication","ran_at":"2026-05-19T17:49:44.664597Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"citation_quote_validity","ran_at":"2026-05-19T17:49:44.153453Z","status":"skipped","version":"0.1.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:24.751113Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"external_links","ran_at":"2026-05-19T17:31:32.389126Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"cited_work_retraction","ran_at":"2026-05-19T17:22:05.817419Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T16:41:55.384524Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.16220/integrity.json","findings":[],"snapshot_sha256":"2a0a6b8569f542ce66191bc1d5f5740c0941d0f24faa34372851f7325c6c4316","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Gravitational models with non-minimal couplings involving functions of the matter Lagrangian and curvature have become popular in recent decades. By coupling the matter Lagrangian directly to the gravitational Lagrangian, one hopes to construct theories that can explain dark energy or dark matter without introducing additional sources. When this matter Lagrangian describes a perfect fluid, some technicalities are involved in its variational formulation. We present a careful derivation of the gravitational field equations together with the complete set of fluid equations. The fluid's equations ","authors_text":"Christian G. Boehmer, Eissa Al-Nasrallah, Erik Jensko","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-05-15T17:31:06Z","title":"Non-minimal fluid Lagrangian couplings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.16220","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":"sha256:5154e12df967780f8bf7c2505f8ccc157fa7aad25bdc27e4b7f98e1f97f10437","target":"record","created_at":"2026-05-20T00:01:58Z","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":"aee67c29338e8a47cfd54173854ae74c83f5cf1913dcfbed5663ba4050f4df52","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2026-05-15T17:31:06Z","title_canon_sha256":"4a2f903034ac0805da65ed9fdc2fe6b3abbc6bd5422dac84a653f307caaf59fa"},"schema_version":"1.0","source":{"id":"2605.16220","kind":"arxiv","version":1}},"canonical_sha256":"e58cea29293f779c64ae6fcd0717a9decf7981467ade05d37de1628b7681ae36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e58cea29293f779c64ae6fcd0717a9decf7981467ade05d37de1628b7681ae36","first_computed_at":"2026-05-20T00:01:58.677851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:58.677851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NGcDuJxuOA2V8oPKJFbqDHQq3Pd0TidWOl1NelbPdYHcir5GDLzVW43afb1puar/zdUwzSGHSWFc5khspDz6DA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:58.678543Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16220","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5154e12df967780f8bf7c2505f8ccc157fa7aad25bdc27e4b7f98e1f97f10437","sha256:cda9d0bf14a2e97e31a82b2633571b83584ce52a2ede5265ee0978c7e483be25"],"state_sha256":"ba33d0b3419f34db0b05f802b5eecc9eb6cd440c7e908364d77a5dc27b4539a3"}