{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:PVIJFVOZ7B33TZJAM6GPMEWIJY","short_pith_number":"pith:PVIJFVOZ","canonical_record":{"source":{"id":"2202.11881","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-24T03:25:20Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"994fc6f1a8a22158f25afb3353988e665f23455bc859d3e562620a54bf379840","abstract_canon_sha256":"6ca90898605a05fb1329dc4ec7b4dc1ac9078ab12769e1cd948064ab73ea6c4e"},"schema_version":"1.0"},"canonical_sha256":"7d5092d5d9f877b9e520678cf612c84e346762e2ae978a5c6eab2bd6d160754e","source":{"kind":"arxiv","id":"2202.11881","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.11881","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"2202.11881v1","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.11881","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"PVIJFVOZ7B33","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"PVIJFVOZ7B33TZJA","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"PVIJFVOZ","created_at":"2026-07-05T04:54:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:PVIJFVOZ7B33TZJAM6GPMEWIJY","target":"record","payload":{"canonical_record":{"source":{"id":"2202.11881","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-24T03:25:20Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"994fc6f1a8a22158f25afb3353988e665f23455bc859d3e562620a54bf379840","abstract_canon_sha256":"6ca90898605a05fb1329dc4ec7b4dc1ac9078ab12769e1cd948064ab73ea6c4e"},"schema_version":"1.0"},"canonical_sha256":"7d5092d5d9f877b9e520678cf612c84e346762e2ae978a5c6eab2bd6d160754e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:54:53.208226Z","signature_b64":"WYPHPGh4+s0TUyymfB8cWNzI9bL5LM87lpEBbyHMcUVfqrC58yMJZXIfO9Y4GsdSyylAZTJk6GEKxZAwMqZBCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d5092d5d9f877b9e520678cf612c84e346762e2ae978a5c6eab2bd6d160754e","last_reissued_at":"2026-07-05T04:54:53.207738Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:54:53.207738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.11881","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bz7xtoz/4Wj7cGd8FpQde4jGJkRfkb9RnmFD4dISwSW/OKtAjVLGv8G3YRyHXeJhxvKU/7zfLwoE620/Jm7vBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:28:15.647202Z"},"content_sha256":"0057d012d429bc255bb06da4926aa5f18e971bb1b856cf0e299fef919a966bc8","schema_version":"1.0","event_id":"sha256:0057d012d429bc255bb06da4926aa5f18e971bb1b856cf0e299fef919a966bc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:PVIJFVOZ7B33TZJAM6GPMEWIJY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Modified-gravity theories with nondynamical background fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Carlos M. Reyes, Marco Schreck","submitted_at":"2022-02-24T03:25:20Z","abstract_excerpt":"We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\\mu\\nu}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.11881","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2202.11881/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:54:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u2vy90cJUE4V4Vi67KgEAxdmeE0nBQrlhmXnN+aGU5b0ng6b5OVnOEdnmhx+BGuLgFINv3pZgW+deSAlxxDzAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T10:28:15.648208Z"},"content_sha256":"127e7f59ca1cd4f8ab8f510cf8cefe3223b9db2641df70d9d9129ac4408d3eeb","schema_version":"1.0","event_id":"sha256:127e7f59ca1cd4f8ab8f510cf8cefe3223b9db2641df70d9d9129ac4408d3eeb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY/bundle.json","state_url":"https://pith.science/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T10:28:15Z","links":{"resolver":"https://pith.science/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY","bundle":"https://pith.science/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY/bundle.json","state":"https://pith.science/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PVIJFVOZ7B33TZJAM6GPMEWIJY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:PVIJFVOZ7B33TZJAM6GPMEWIJY","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":"6ca90898605a05fb1329dc4ec7b4dc1ac9078ab12769e1cd948064ab73ea6c4e","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-24T03:25:20Z","title_canon_sha256":"994fc6f1a8a22158f25afb3353988e665f23455bc859d3e562620a54bf379840"},"schema_version":"1.0","source":{"id":"2202.11881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.11881","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"arxiv_version","alias_value":"2202.11881v1","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.11881","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"pith_short_12","alias_value":"PVIJFVOZ7B33","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"pith_short_16","alias_value":"PVIJFVOZ7B33TZJA","created_at":"2026-07-05T04:54:53Z"},{"alias_kind":"pith_short_8","alias_value":"PVIJFVOZ","created_at":"2026-07-05T04:54:53Z"}],"graph_snapshots":[{"event_id":"sha256:127e7f59ca1cd4f8ab8f510cf8cefe3223b9db2641df70d9d9129ac4408d3eeb","target":"graph","created_at":"2026-07-05T04:54:53Z","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/2202.11881/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the dynamics of a modified-gravity theory, which is supplemented by an extended Gibbons-Hawking-York boundary term and incorporates diffeomorphism violation through nondynamical background fields denoted as $u$ and $s^{\\mu\\nu}$ in the literature. An ADM decomposition allows us to project the modified Einstein equations into purely spacelike hypersurfaces, which implies the field equations for the induced dynamical three-metric. We also obtain the Hamilton-Jacobi equations of motion for the canonical variables of the theory based on its Hamiltonian, which was derived in a previous work","authors_text":"Carlos M. Reyes, Marco Schreck","cross_cats":["gr-qc"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-24T03:25:20Z","title":"Modified-gravity theories with nondynamical background fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.11881","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":"sha256:0057d012d429bc255bb06da4926aa5f18e971bb1b856cf0e299fef919a966bc8","target":"record","created_at":"2026-07-05T04:54:53Z","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":"6ca90898605a05fb1329dc4ec7b4dc1ac9078ab12769e1cd948064ab73ea6c4e","cross_cats_sorted":["gr-qc"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2022-02-24T03:25:20Z","title_canon_sha256":"994fc6f1a8a22158f25afb3353988e665f23455bc859d3e562620a54bf379840"},"schema_version":"1.0","source":{"id":"2202.11881","kind":"arxiv","version":1}},"canonical_sha256":"7d5092d5d9f877b9e520678cf612c84e346762e2ae978a5c6eab2bd6d160754e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7d5092d5d9f877b9e520678cf612c84e346762e2ae978a5c6eab2bd6d160754e","first_computed_at":"2026-07-05T04:54:53.207738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:54:53.207738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYPHPGh4+s0TUyymfB8cWNzI9bL5LM87lpEBbyHMcUVfqrC58yMJZXIfO9Y4GsdSyylAZTJk6GEKxZAwMqZBCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:54:53.208226Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.11881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0057d012d429bc255bb06da4926aa5f18e971bb1b856cf0e299fef919a966bc8","sha256:127e7f59ca1cd4f8ab8f510cf8cefe3223b9db2641df70d9d9129ac4408d3eeb"],"state_sha256":"47f049261b004fe344ecb8d7f1f854af4040502842cda2c3831d6b4862483e3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EMUEWJJPUnTGrrnzAtI0RE5jn5U+Ms0du91h4Y1UdluAOsSwzQQugodKoaeiIKMo9DiVGQCB+U0pzxtIfGisDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T10:28:15.654753Z","bundle_sha256":"7711f520aa1fdbf7da77cb0ce2d0169e59cbf0292e6d760647d93b136c318c14"}}