{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:FYEEVAKNQ4EWT5CGURGPQWFSBK","short_pith_number":"pith:FYEEVAKN","canonical_record":{"source":{"id":"2211.07380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-11-09T15:12:57Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d3a3739c28e3ed446857d753b34289aa06785b324dbf8d4507662b235d91483f","abstract_canon_sha256":"2cb24ae913beed179757c8c4b86c9be8f6c162e9d7a3bdd209021215af7ab4b7"},"schema_version":"1.0"},"canonical_sha256":"2e084a814d870969f446a44cf858b20a958a8c4a3bbdfb3fff2394f8ea85dc7d","source":{"kind":"arxiv","id":"2211.07380","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07380","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07380v3","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07380","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"FYEEVAKNQ4EW","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"pith_short_16","alias_value":"FYEEVAKNQ4EWT5CG","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"pith_short_8","alias_value":"FYEEVAKN","created_at":"2026-07-05T06:06:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:FYEEVAKNQ4EWT5CGURGPQWFSBK","target":"record","payload":{"canonical_record":{"source":{"id":"2211.07380","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-11-09T15:12:57Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"d3a3739c28e3ed446857d753b34289aa06785b324dbf8d4507662b235d91483f","abstract_canon_sha256":"2cb24ae913beed179757c8c4b86c9be8f6c162e9d7a3bdd209021215af7ab4b7"},"schema_version":"1.0"},"canonical_sha256":"2e084a814d870969f446a44cf858b20a958a8c4a3bbdfb3fff2394f8ea85dc7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:06:55.059524Z","signature_b64":"/aMzqkalRn0kneGtf1rRQuzvupNnVx04oFJjurf6vBPUHTB1UImtWnBbZ9qkChH7pyA/WVtmVX+EZysJf33tCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e084a814d870969f446a44cf858b20a958a8c4a3bbdfb3fff2394f8ea85dc7d","last_reissued_at":"2026-07-05T06:06:55.059128Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:06:55.059128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.07380","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jNddASWgNsSaNGeF/BxR3ZuSDgj1DYKSpCHeFokwCPXpiBgv968ktpo0xQVyD/Rj3OBrE4rD4kRlZw7HCnyVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:58:31.919361Z"},"content_sha256":"5a9271477567c232c286b9b88832b78bcfcd702f2922da0bec9b573219f89c65","schema_version":"1.0","event_id":"sha256:5a9271477567c232c286b9b88832b78bcfcd702f2922da0bec9b573219f89c65"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:FYEEVAKNQ4EWT5CGURGPQWFSBK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Hoang Ky Nguyen","submitted_at":"2022-11-09T15:12:57Z","abstract_excerpt":"In violation of the generalized Lichnerowicz theorem advocated by Nelson and others, quadratic gravity admits vacua with non-constant scalar curvature. In a recent publication [Phys. Rev. D 106, 104004 (2022)], we revitalized a program that Buchdahl originated but prematurely abandoned circa 1962 [Nuovo Cimento 23, 141 (1962)], and uncovered a novel exhaustive class of static spherically symmetric vacua for pure $R^2$ gravity. The Buchdahl-inspired metrics we obtained therein are exact solutions which exhibit non-constant scalar curvature. A product of fourth-order gravity, the metrics entail "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07380","kind":"arxiv","version":3},"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/2211.07380/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":"2026-07-05T06:06:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXUfHQ8vsIQLzA6bs6LnZO7NV5Vk9W7lh40A63Jkyy5SvnEwRdF/TrEyhFWB3GgxQZi9Z+Nimy2T6CIIBfK1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:58:31.920316Z"},"content_sha256":"5e9fb0fc21ff67575b87ead94aab27b2017d71372d09b2fbb0689e0e8f162177","schema_version":"1.0","event_id":"sha256:5e9fb0fc21ff67575b87ead94aab27b2017d71372d09b2fbb0689e0e8f162177"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK/bundle.json","state_url":"https://pith.science/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK/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":"2026-08-09T01:58:31Z","links":{"resolver":"https://pith.science/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK","bundle":"https://pith.science/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK/bundle.json","state":"https://pith.science/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FYEEVAKNQ4EWT5CGURGPQWFSBK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:FYEEVAKNQ4EWT5CGURGPQWFSBK","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":"2cb24ae913beed179757c8c4b86c9be8f6c162e9d7a3bdd209021215af7ab4b7","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-11-09T15:12:57Z","title_canon_sha256":"d3a3739c28e3ed446857d753b34289aa06785b324dbf8d4507662b235d91483f"},"schema_version":"1.0","source":{"id":"2211.07380","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.07380","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"2211.07380v3","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.07380","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"FYEEVAKNQ4EW","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"pith_short_16","alias_value":"FYEEVAKNQ4EWT5CG","created_at":"2026-07-05T06:06:55Z"},{"alias_kind":"pith_short_8","alias_value":"FYEEVAKN","created_at":"2026-07-05T06:06:55Z"}],"graph_snapshots":[{"event_id":"sha256:5e9fb0fc21ff67575b87ead94aab27b2017d71372d09b2fbb0689e0e8f162177","target":"graph","created_at":"2026-07-05T06:06:55Z","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/2211.07380/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In violation of the generalized Lichnerowicz theorem advocated by Nelson and others, quadratic gravity admits vacua with non-constant scalar curvature. In a recent publication [Phys. Rev. D 106, 104004 (2022)], we revitalized a program that Buchdahl originated but prematurely abandoned circa 1962 [Nuovo Cimento 23, 141 (1962)], and uncovered a novel exhaustive class of static spherically symmetric vacua for pure $R^2$ gravity. The Buchdahl-inspired metrics we obtained therein are exact solutions which exhibit non-constant scalar curvature. A product of fourth-order gravity, the metrics entail ","authors_text":"Hoang Ky Nguyen","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-11-09T15:12:57Z","title":"Beyond Schwarzschild-de Sitter spacetimes: III. A perturbative vacuum with non-constant scalar curvature in $R+R^2$ gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.07380","kind":"arxiv","version":3},"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":"sha256:5a9271477567c232c286b9b88832b78bcfcd702f2922da0bec9b573219f89c65","target":"record","created_at":"2026-07-05T06:06:55Z","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":"2cb24ae913beed179757c8c4b86c9be8f6c162e9d7a3bdd209021215af7ab4b7","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2022-11-09T15:12:57Z","title_canon_sha256":"d3a3739c28e3ed446857d753b34289aa06785b324dbf8d4507662b235d91483f"},"schema_version":"1.0","source":{"id":"2211.07380","kind":"arxiv","version":3}},"canonical_sha256":"2e084a814d870969f446a44cf858b20a958a8c4a3bbdfb3fff2394f8ea85dc7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e084a814d870969f446a44cf858b20a958a8c4a3bbdfb3fff2394f8ea85dc7d","first_computed_at":"2026-07-05T06:06:55.059128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:06:55.059128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/aMzqkalRn0kneGtf1rRQuzvupNnVx04oFJjurf6vBPUHTB1UImtWnBbZ9qkChH7pyA/WVtmVX+EZysJf33tCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:06:55.059524Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.07380","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a9271477567c232c286b9b88832b78bcfcd702f2922da0bec9b573219f89c65","sha256:5e9fb0fc21ff67575b87ead94aab27b2017d71372d09b2fbb0689e0e8f162177"],"state_sha256":"32e740888c10b92982dccc3e726b98dd6cea2a24e6e6bde414c4cabccac84ff8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RuYNqts6VQpy0xRVJ6vQMNi42M7/NjaQn+Yr0CoEbOB+bQ2yi3LpPltZTmj2ESz0kX98i5RHFSU3AQ/PAdu5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T01:58:31.926475Z","bundle_sha256":"39d4fb36912c532d34c84475bdf85d33b20ef7949cce9493f215a7a8951a6992"}}