{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:GN6DUEYWSSW4AHM47E2I3FUWEP","short_pith_number":"pith:GN6DUEYW","canonical_record":{"source":{"id":"1004.1973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-12T14:34:20Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"1661c976b82abd5a14b258e4ed01fd0eb3c025c2a6824a2bec48b577cf56ce30","abstract_canon_sha256":"cf4b8ec1df00c009a19053e5a78c9558b45c1fe9e6e2d15a8b2c7fd5db3fbd0f"},"schema_version":"1.0"},"canonical_sha256":"337c3a131694adc01d9cf9348d969623c1c07daeb3164c7c3b382720021f272f","source":{"kind":"arxiv","id":"1004.1973","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1973","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1973v2","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1973","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"GN6DUEYWSSW4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GN6DUEYWSSW4AHM4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GN6DUEYW","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:GN6DUEYWSSW4AHM47E2I3FUWEP","target":"record","payload":{"canonical_record":{"source":{"id":"1004.1973","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-12T14:34:20Z","cross_cats_sorted":["astro-ph.EP"],"title_canon_sha256":"1661c976b82abd5a14b258e4ed01fd0eb3c025c2a6824a2bec48b577cf56ce30","abstract_canon_sha256":"cf4b8ec1df00c009a19053e5a78c9558b45c1fe9e6e2d15a8b2c7fd5db3fbd0f"},"schema_version":"1.0"},"canonical_sha256":"337c3a131694adc01d9cf9348d969623c1c07daeb3164c7c3b382720021f272f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:34.480352Z","signature_b64":"3iFK3CK9zHbY1TD+F99cPq7tWO/NSvWmHUNy4motttNklo52UjjUBk90gzqsIlSNxKZrc7yUttDqSTdXubtQAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"337c3a131694adc01d9cf9348d969623c1c07daeb3164c7c3b382720021f272f","last_reissued_at":"2026-05-18T02:33:34.479925Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:34.479925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.1973","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fpw2A7vz7uUwwxxthQgT4TycESm0iew4S/R5gDLQVYKW6z94iU3kZqmsPA0nbTRy/nmmErnYFYcXS88vu9HPAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:57:07.126469Z"},"content_sha256":"89c8946d0c4c667954c08188ebc9b35f97af9de666ab52069af2aa97b7ba318c","schema_version":"1.0","event_id":"sha256:89c8946d0c4c667954c08188ebc9b35f97af9de666ab52069af2aa97b7ba318c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:GN6DUEYWSSW4AHM47E2I3FUWEP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.EP"],"primary_cat":"gr-qc","authors_text":"A. Stabile","submitted_at":"2010-04-12T14:34:20Z","abstract_excerpt":"A general analytic procedure is developed for the post-Newtonian limit of $f(R)$-gravity with metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method a general scheme of solutions up to $(v/c)^4$ order is shown. Considering the Taylor expansion of a generic function $f$ it is possible to parameterize the solutions by derivatives of $f$. At Newtonian order, $(v/c)^2$, all more important topics about the Gauss and Birkhoff theorem are discussed. The corrections to \"standard\" gravitational potential ($tt$-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1973","kind":"arxiv","version":2},"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":"2026-05-18T02:33:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X27hg6gW29ynM4T3bsx7gWwPL5T8LUVa9X4h0MyYzQ8qvj6c8e8w3X41I98vH7Web12uJJVuP9W3Dho7wPmUAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:57:07.126933Z"},"content_sha256":"0c7bb63a59229d1310b265e0ba72615a977c118d631af2f0616d9f592c0f2e41","schema_version":"1.0","event_id":"sha256:0c7bb63a59229d1310b265e0ba72615a977c118d631af2f0616d9f592c0f2e41"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GN6DUEYWSSW4AHM47E2I3FUWEP/bundle.json","state_url":"https://pith.science/pith/GN6DUEYWSSW4AHM47E2I3FUWEP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GN6DUEYWSSW4AHM47E2I3FUWEP/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":"2026-08-09T13:57:07Z","links":{"resolver":"https://pith.science/pith/GN6DUEYWSSW4AHM47E2I3FUWEP","bundle":"https://pith.science/pith/GN6DUEYWSSW4AHM47E2I3FUWEP/bundle.json","state":"https://pith.science/pith/GN6DUEYWSSW4AHM47E2I3FUWEP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GN6DUEYWSSW4AHM47E2I3FUWEP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:GN6DUEYWSSW4AHM47E2I3FUWEP","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":"cf4b8ec1df00c009a19053e5a78c9558b45c1fe9e6e2d15a8b2c7fd5db3fbd0f","cross_cats_sorted":["astro-ph.EP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-12T14:34:20Z","title_canon_sha256":"1661c976b82abd5a14b258e4ed01fd0eb3c025c2a6824a2bec48b577cf56ce30"},"schema_version":"1.0","source":{"id":"1004.1973","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1973","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1973v2","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1973","created_at":"2026-05-18T02:33:34Z"},{"alias_kind":"pith_short_12","alias_value":"GN6DUEYWSSW4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"GN6DUEYWSSW4AHM4","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"GN6DUEYW","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:0c7bb63a59229d1310b265e0ba72615a977c118d631af2f0616d9f592c0f2e41","target":"graph","created_at":"2026-05-18T02:33:34Z","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":"A general analytic procedure is developed for the post-Newtonian limit of $f(R)$-gravity with metric approach in the Jordan frame by using the harmonic gauge condition. In a pure perturbative framework and by using the Green function method a general scheme of solutions up to $(v/c)^4$ order is shown. Considering the Taylor expansion of a generic function $f$ it is possible to parameterize the solutions by derivatives of $f$. At Newtonian order, $(v/c)^2$, all more important topics about the Gauss and Birkhoff theorem are discussed. The corrections to \"standard\" gravitational potential ($tt$-c","authors_text":"A. Stabile","cross_cats":["astro-ph.EP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-12T14:34:20Z","title":"The Post-Newtonian Limit of f(R)-gravity in the Harmonic Gauge"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1973","kind":"arxiv","version":2},"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":"sha256:89c8946d0c4c667954c08188ebc9b35f97af9de666ab52069af2aa97b7ba318c","target":"record","created_at":"2026-05-18T02:33:34Z","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":"cf4b8ec1df00c009a19053e5a78c9558b45c1fe9e6e2d15a8b2c7fd5db3fbd0f","cross_cats_sorted":["astro-ph.EP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-04-12T14:34:20Z","title_canon_sha256":"1661c976b82abd5a14b258e4ed01fd0eb3c025c2a6824a2bec48b577cf56ce30"},"schema_version":"1.0","source":{"id":"1004.1973","kind":"arxiv","version":2}},"canonical_sha256":"337c3a131694adc01d9cf9348d969623c1c07daeb3164c7c3b382720021f272f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"337c3a131694adc01d9cf9348d969623c1c07daeb3164c7c3b382720021f272f","first_computed_at":"2026-05-18T02:33:34.479925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:34.479925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3iFK3CK9zHbY1TD+F99cPq7tWO/NSvWmHUNy4motttNklo52UjjUBk90gzqsIlSNxKZrc7yUttDqSTdXubtQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:34.480352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1973","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:89c8946d0c4c667954c08188ebc9b35f97af9de666ab52069af2aa97b7ba318c","sha256:0c7bb63a59229d1310b265e0ba72615a977c118d631af2f0616d9f592c0f2e41"],"state_sha256":"28dc7f96e6170de648a343ce0249580062ab4400d0e85e1b5d035f826fc5fa7d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aA25ASwNg9EmORPVu6E2R7S8QGemmTc33px9Dl1+JYr2Azaxo0lrQZtvZH3BGJWJEYnwfrEQG9ySineuhzxgAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:57:07.130801Z","bundle_sha256":"80dc98911d7aa3a2be3ebbb7410323a25de7943b2cecf4066710cc70103a650d"}}