{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:K4IRB6YPKCCNC7OS36GVSYPRBC","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":"b1e51189eab857dcc81bc52ebec746e8fb7a5d4bbab7a1f76bd8d5628bedbfa5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-30T02:58:03Z","title_canon_sha256":"fd2af2ec758d90eced76ce0412611ba50ad2b487ad1851dd4494bc3c7a765d7c"},"schema_version":"1.0","source":{"id":"2606.31070","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.31070","created_at":"2026-07-01T01:17:28Z"},{"alias_kind":"arxiv_version","alias_value":"2606.31070v1","created_at":"2026-07-01T01:17:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31070","created_at":"2026-07-01T01:17:28Z"},{"alias_kind":"pith_short_12","alias_value":"K4IRB6YPKCCN","created_at":"2026-07-01T01:17:28Z"},{"alias_kind":"pith_short_16","alias_value":"K4IRB6YPKCCNC7OS","created_at":"2026-07-01T01:17:28Z"},{"alias_kind":"pith_short_8","alias_value":"K4IRB6YP","created_at":"2026-07-01T01:17:28Z"}],"graph_snapshots":[{"event_id":"sha256:df4be64edc67f108594c5711a25569c6ab5235a0c7766c3fd5ebd2603f42fa2a","target":"graph","created_at":"2026-07-01T01:17:28Z","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/2606.31070/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Motivated by the increasing efforts to understand the covariant structure of physical models associated with General Relativity using different kinds of geometric frameworks, in this article we analyze the four-dimensional Palatini-Cartan model for gravity, which is a well-known generalization of General Relativity, from the perspective of various geometric-covariant formalisms for classical field theory. At the Lagrangian level, we do not only recover the correct field equations of the theory, which are equivalent to the torsion-free condition and the Einstein equations, but we also study the","authors_text":"Alberto Molgado, Iv\\'an Cortes-Cruz, Jasel Berra-Montiel","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-30T02:58:03Z","title":"Geometric formulation for Palatini-Cartan gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31070","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":"sha256:42a1a4ef522cb3cb2cf5d63cc746e877b8647b5c5d48ade6b3d188180ff02a67","target":"record","created_at":"2026-07-01T01:17:28Z","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":"b1e51189eab857dcc81bc52ebec746e8fb7a5d4bbab7a1f76bd8d5628bedbfa5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-30T02:58:03Z","title_canon_sha256":"fd2af2ec758d90eced76ce0412611ba50ad2b487ad1851dd4494bc3c7a765d7c"},"schema_version":"1.0","source":{"id":"2606.31070","kind":"arxiv","version":1}},"canonical_sha256":"571110fb0f5084d17dd2df8d5961f1089ca56fe39598d2ccb86ef7f44fd3a210","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"571110fb0f5084d17dd2df8d5961f1089ca56fe39598d2ccb86ef7f44fd3a210","first_computed_at":"2026-07-01T01:17:28.243640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-01T01:17:28.243640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AA4/IKosIAZ3exZ7EACsfiE0kmsIYq8H/zTO7rGgQAh46f8Q333LLra2YvkJYIctD8xGJJ1+N8mkOpr/QDHUDw==","signature_status":"signed_v1","signed_at":"2026-07-01T01:17:28.244083Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.31070","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42a1a4ef522cb3cb2cf5d63cc746e877b8647b5c5d48ade6b3d188180ff02a67","sha256:df4be64edc67f108594c5711a25569c6ab5235a0c7766c3fd5ebd2603f42fa2a"],"state_sha256":"02616fff00ca07fb535883088b69573a07d1a460009b004657f2ece3616e49e0"}