{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B5WRQCUW6TRTLBMWOC55J5EELF","short_pith_number":"pith:B5WRQCUW","canonical_record":{"source":{"id":"1412.8151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T11:26:31Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"3422c0eb9e80d78bb50b68017cd18393c385762da163aa1ea5e62e496c25318e","abstract_canon_sha256":"d5adb0ef3832073077f3847451a4a8b80bf0eeb8bfd0d4de95d8173f247994b9"},"schema_version":"1.0"},"canonical_sha256":"0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c","source":{"kind":"arxiv","id":"1412.8151","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8151","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8151v1","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8151","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"B5WRQCUW6TRT","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B5WRQCUW6TRTLBMW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B5WRQCUW","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B5WRQCUW6TRTLBMWOC55J5EELF","target":"record","payload":{"canonical_record":{"source":{"id":"1412.8151","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T11:26:31Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"3422c0eb9e80d78bb50b68017cd18393c385762da163aa1ea5e62e496c25318e","abstract_canon_sha256":"d5adb0ef3832073077f3847451a4a8b80bf0eeb8bfd0d4de95d8173f247994b9"},"schema_version":"1.0"},"canonical_sha256":"0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:23.955648Z","signature_b64":"SNYGr6i6ItXo+Q0KGRRvLXyoF0q8P5etHpE5L+NAikaDO3S0n5Jj/nsqyAvxqM22S5/lwKaLGwvsQBTt2xMLBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c","last_reissued_at":"2026-05-18T02:30:23.954935Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:23.954935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.8151","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":"2026-05-18T02:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SDAXb1Q7OjIDvzwKmrHy6UEw7Zn9NY9dLWt5Kf4U06ytJjq4h/JEuXQCiW5+RTjQ10y3C3vlBOIq8T+P8Ir8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:10:48.382558Z"},"content_sha256":"fdde9ae23b5a8ce1cd2ba513fc0e6cae915b5336eb9edbca605642ab9c11edee","schema_version":"1.0","event_id":"sha256:fdde9ae23b5a8ce1cd2ba513fc0e6cae915b5336eb9edbca605642ab9c11edee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B5WRQCUW6TRTLBMWOC55J5EELF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mathematical Validity of the f(R) Theory of Modified Gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.AP","authors_text":"Philippe G. LeFloch, Yue Ma","submitted_at":"2014-12-28T11:26:31Z","abstract_excerpt":"We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert functional, is replaced by a function f=f(R). The field equations involve up to fourth-order derivatives of the spacetime metric, and the challenge is to understand the structure of these high-order terms. We propose a formulation of the initial value problem in modified gravity when the initial data are prescribed on a hypersurface. In addition to the induced m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8151","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":""},"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":"2026-05-18T02:30:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XSvigeoHNmimtEf+JDAciREpFVGI9YYVPLftk4kuN2rBd9+htJApQ0yH+OVRGKoaY85ICIKss5UGe/HiDUVwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T13:10:48.382912Z"},"content_sha256":"e14ff09e3f9fccaddcb396a7e2bf5312b6c0ab5bbad45bb946f2fe456dde855d","schema_version":"1.0","event_id":"sha256:e14ff09e3f9fccaddcb396a7e2bf5312b6c0ab5bbad45bb946f2fe456dde855d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B5WRQCUW6TRTLBMWOC55J5EELF/bundle.json","state_url":"https://pith.science/pith/B5WRQCUW6TRTLBMWOC55J5EELF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B5WRQCUW6TRTLBMWOC55J5EELF/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":"2026-06-11T13:10:48Z","links":{"resolver":"https://pith.science/pith/B5WRQCUW6TRTLBMWOC55J5EELF","bundle":"https://pith.science/pith/B5WRQCUW6TRTLBMWOC55J5EELF/bundle.json","state":"https://pith.science/pith/B5WRQCUW6TRTLBMWOC55J5EELF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B5WRQCUW6TRTLBMWOC55J5EELF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B5WRQCUW6TRTLBMWOC55J5EELF","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":"d5adb0ef3832073077f3847451a4a8b80bf0eeb8bfd0d4de95d8173f247994b9","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T11:26:31Z","title_canon_sha256":"3422c0eb9e80d78bb50b68017cd18393c385762da163aa1ea5e62e496c25318e"},"schema_version":"1.0","source":{"id":"1412.8151","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.8151","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"arxiv_version","alias_value":"1412.8151v1","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.8151","created_at":"2026-05-18T02:30:23Z"},{"alias_kind":"pith_short_12","alias_value":"B5WRQCUW6TRT","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B5WRQCUW6TRTLBMW","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B5WRQCUW","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:e14ff09e3f9fccaddcb396a7e2bf5312b6c0ab5bbad45bb946f2fe456dde855d","target":"graph","created_at":"2026-05-18T02:30:23Z","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"},"paper":{"abstract_excerpt":"We establish a well-posedness theory for the f(R) theory of modified gravity, which is a generalization of Einstein's theory of gravitation. The scalar curvature R of the spacetime, which arises in the integrand of the Einstein-Hilbert functional, is replaced by a function f=f(R). The field equations involve up to fourth-order derivatives of the spacetime metric, and the challenge is to understand the structure of these high-order terms. We propose a formulation of the initial value problem in modified gravity when the initial data are prescribed on a hypersurface. In addition to the induced m","authors_text":"Philippe G. LeFloch, Yue Ma","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T11:26:31Z","title":"Mathematical Validity of the f(R) Theory of Modified Gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.8151","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:fdde9ae23b5a8ce1cd2ba513fc0e6cae915b5336eb9edbca605642ab9c11edee","target":"record","created_at":"2026-05-18T02:30:23Z","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":"d5adb0ef3832073077f3847451a4a8b80bf0eeb8bfd0d4de95d8173f247994b9","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-28T11:26:31Z","title_canon_sha256":"3422c0eb9e80d78bb50b68017cd18393c385762da163aa1ea5e62e496c25318e"},"schema_version":"1.0","source":{"id":"1412.8151","kind":"arxiv","version":1}},"canonical_sha256":"0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f6d180a96f4e335859670bbd4f4845968739a4ed13db307e93bf0b0cdb4e04c","first_computed_at":"2026-05-18T02:30:23.954935Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:23.954935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SNYGr6i6ItXo+Q0KGRRvLXyoF0q8P5etHpE5L+NAikaDO3S0n5Jj/nsqyAvxqM22S5/lwKaLGwvsQBTt2xMLBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:23.955648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.8151","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdde9ae23b5a8ce1cd2ba513fc0e6cae915b5336eb9edbca605642ab9c11edee","sha256:e14ff09e3f9fccaddcb396a7e2bf5312b6c0ab5bbad45bb946f2fe456dde855d"],"state_sha256":"9fe046db536a6819b5e75ef763308134eabe789a355135370c871da0afbe16dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kShdF3RjuUroJGGvnnnnLww94r/VP3Z4yUN+ic0tEiga0a3J20A23a2Hz1R1BjS9lBMr+NHAe/XuIUC/E9moBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T13:10:48.384941Z","bundle_sha256":"79aae8e14174af73834d164cfc1cbc1d35675b7dd2b53778546b1b572e241e83"}}