{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IFBGVYFNRD3QEH4TUPG2Q5JB2L","short_pith_number":"pith:IFBGVYFN","canonical_record":{"source":{"id":"1107.0948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-07-05T19:03:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"10ee06a61527b96a9937c27597fcf246eeacc26bf94b779b3faba048813c679f","abstract_canon_sha256":"23acca8a659b0eb352ea5d738cfd85b5e11c4156ad891e807470d6cf93c7d82d"},"schema_version":"1.0"},"canonical_sha256":"41426ae0ad88f7021f93a3cda87521d2c3647b5007828f9e43df2f6f0d4cb3c1","source":{"kind":"arxiv","id":"1107.0948","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0948","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0948v3","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0948","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"IFBGVYFNRD3Q","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IFBGVYFNRD3QEH4T","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IFBGVYFN","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IFBGVYFNRD3QEH4TUPG2Q5JB2L","target":"record","payload":{"canonical_record":{"source":{"id":"1107.0948","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-07-05T19:03:37Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"10ee06a61527b96a9937c27597fcf246eeacc26bf94b779b3faba048813c679f","abstract_canon_sha256":"23acca8a659b0eb352ea5d738cfd85b5e11c4156ad891e807470d6cf93c7d82d"},"schema_version":"1.0"},"canonical_sha256":"41426ae0ad88f7021f93a3cda87521d2c3647b5007828f9e43df2f6f0d4cb3c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:01:24.550545Z","signature_b64":"gnsnuzSeVbqYIbc1fz5VyByvs3fD9QmIrSva2dKdJQfywDn4jSaRoqgC9+LEbsNuv2BVXt1rJainEpjogzUFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41426ae0ad88f7021f93a3cda87521d2c3647b5007828f9e43df2f6f0d4cb3c1","last_reissued_at":"2026-05-18T02:01:24.550018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:01:24.550018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.0948","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":"2026-05-18T02:01:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D5SBNqn5rJYCKQraz1Q5vEZuhXFlP3gK7GfJ3sq+tPBbyJN9ErCNnCEOoEQO4gSsyHc4mPtUd0cvhY4RpQtxAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:52:18.563276Z"},"content_sha256":"fad923bf863e74394e374013686b1bd7fd94858a73eb6d58000ec30dc1954683","schema_version":"1.0","event_id":"sha256:fad923bf863e74394e374013686b1bd7fd94858a73eb6d58000ec30dc1954683"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IFBGVYFNRD3QEH4TUPG2Q5JB2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalar-tensor representation of $f(R)$ gravity and Birkhoff's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Diego S\\'aez-G\\'omez, Salvatore Capozziello","submitted_at":"2011-07-05T19:03:37Z","abstract_excerpt":"Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar-tensor representation. Modified gravity has become very popular at recent times as it is able to reproduce the unification of inflation and late-time acceleration with no need of a dark energy component or an inflaton field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to General Relativity, the well known Brans-Dicke theory. As a novelty, here both theories are studied by using a conformal transformation and w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0948","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":""},"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":"2026-05-18T02:01:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IW0PhXLstztRRJT2t3fRxcAjRvqsnUumg8IzNoD4qzcjgnS2OMRjLeIjJ9uajMN5vfZcX2AbMLohfol7Q8p0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:52:18.563945Z"},"content_sha256":"2bb31384b9f5da68954a58973c65c17a08ba767be80e2b38eee800efe5241640","schema_version":"1.0","event_id":"sha256:2bb31384b9f5da68954a58973c65c17a08ba767be80e2b38eee800efe5241640"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L/bundle.json","state_url":"https://pith.science/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L/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":"2026-05-26T04:52:18Z","links":{"resolver":"https://pith.science/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L","bundle":"https://pith.science/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L/bundle.json","state":"https://pith.science/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IFBGVYFNRD3QEH4TUPG2Q5JB2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IFBGVYFNRD3QEH4TUPG2Q5JB2L","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":"23acca8a659b0eb352ea5d738cfd85b5e11c4156ad891e807470d6cf93c7d82d","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-07-05T19:03:37Z","title_canon_sha256":"10ee06a61527b96a9937c27597fcf246eeacc26bf94b779b3faba048813c679f"},"schema_version":"1.0","source":{"id":"1107.0948","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0948","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0948v3","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0948","created_at":"2026-05-18T02:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"IFBGVYFNRD3Q","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IFBGVYFNRD3QEH4T","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IFBGVYFN","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:2bb31384b9f5da68954a58973c65c17a08ba767be80e2b38eee800efe5241640","target":"graph","created_at":"2026-05-18T02:01:24Z","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":"Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar-tensor representation. Modified gravity has become very popular at recent times as it is able to reproduce the unification of inflation and late-time acceleration with no need of a dark energy component or an inflaton field. Here, another aspect of modified f(R) gravity is studied, specifically the range of validity of Birkhoff's theorem, compared with another alternative to General Relativity, the well known Brans-Dicke theory. As a novelty, here both theories are studied by using a conformal transformation and w","authors_text":"Diego S\\'aez-G\\'omez, Salvatore Capozziello","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-07-05T19:03:37Z","title":"Scalar-tensor representation of $f(R)$ gravity and Birkhoff's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0948","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:fad923bf863e74394e374013686b1bd7fd94858a73eb6d58000ec30dc1954683","target":"record","created_at":"2026-05-18T02:01:24Z","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":"23acca8a659b0eb352ea5d738cfd85b5e11c4156ad891e807470d6cf93c7d82d","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-07-05T19:03:37Z","title_canon_sha256":"10ee06a61527b96a9937c27597fcf246eeacc26bf94b779b3faba048813c679f"},"schema_version":"1.0","source":{"id":"1107.0948","kind":"arxiv","version":3}},"canonical_sha256":"41426ae0ad88f7021f93a3cda87521d2c3647b5007828f9e43df2f6f0d4cb3c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41426ae0ad88f7021f93a3cda87521d2c3647b5007828f9e43df2f6f0d4cb3c1","first_computed_at":"2026-05-18T02:01:24.550018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:01:24.550018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gnsnuzSeVbqYIbc1fz5VyByvs3fD9QmIrSva2dKdJQfywDn4jSaRoqgC9+LEbsNuv2BVXt1rJainEpjogzUFAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:01:24.550545Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0948","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fad923bf863e74394e374013686b1bd7fd94858a73eb6d58000ec30dc1954683","sha256:2bb31384b9f5da68954a58973c65c17a08ba767be80e2b38eee800efe5241640"],"state_sha256":"01f33f29960e6deb126ccb9773ac1e1517448287da833ba144a8efbc40bfdee1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IlH/MIsxCDj4ArKSWt/mybUuRaflL7wccAuCSSQh1IQUvKkBkXBYsaRPac6hHjQ2eV3zbc4TRYAT3I/IBhzbBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:52:18.567724Z","bundle_sha256":"19f8cf87c14ae68e8a114b4baef1a6bc81d6f75f8061d88e6ab3a526cd9b56d2"}}