{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TXI3JENPHJYC4QZ4PREY34NTXN","short_pith_number":"pith:TXI3JENP","canonical_record":{"source":{"id":"1005.4547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-25T11:58:11Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"6e21735ace82991832b1d489286fdfda4a301b24284aa7a529e737b6d39271f9","abstract_canon_sha256":"e7b0a880f1ed0793e2f16950b69b33433c01312f3942c465c6eb34ab6820ff2f"},"schema_version":"1.0"},"canonical_sha256":"9dd1b491af3a702e433c7c498df1b3bb42f7c3e8ded1da369b4231e921b9bd7a","source":{"kind":"arxiv","id":"1005.4547","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4547","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4547v2","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4547","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"TXI3JENPHJYC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TXI3JENPHJYC4QZ4","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TXI3JENP","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TXI3JENPHJYC4QZ4PREY34NTXN","target":"record","payload":{"canonical_record":{"source":{"id":"1005.4547","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-25T11:58:11Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"6e21735ace82991832b1d489286fdfda4a301b24284aa7a529e737b6d39271f9","abstract_canon_sha256":"e7b0a880f1ed0793e2f16950b69b33433c01312f3942c465c6eb34ab6820ff2f"},"schema_version":"1.0"},"canonical_sha256":"9dd1b491af3a702e433c7c498df1b3bb42f7c3e8ded1da369b4231e921b9bd7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:24.003320Z","signature_b64":"KHTmDCNBYtTpJURLSU4UtN0vY7X6IrrEOkWELJcBSoY4maQI9xFvS2WdHdPw9aienTL1XGxkd5gIkz9ppOlrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dd1b491af3a702e433c7c498df1b3bb42f7c3e8ded1da369b4231e921b9bd7a","last_reissued_at":"2026-05-18T02:33:24.002861Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:24.002861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.4547","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":"2026-05-18T02:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7sjg99Bfm9DlFpsWeZFKogJDhO8gy+YqGSJAevZp+Miee/7c0+x+NwW+3IWAZ6CTYI1VsGt/adNlty4Uo1c7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:53:20.811380Z"},"content_sha256":"4596dad66b0a92cf118869c7208e536ff5bee78749e93d582aaeef68abac7685","schema_version":"1.0","event_id":"sha256:4596dad66b0a92cf118869c7208e536ff5bee78749e93d582aaeef68abac7685"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TXI3JENPHJYC4QZ4PREY34NTXN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-linear static solutions in massive gravity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"gr-qc","authors_text":"Michael V. Bebronne","submitted_at":"2010-05-25T11:58:11Z","abstract_excerpt":"The static vacuum spherically symmetric solutions of massive gravity theories possess two integration constant: the mass M and a scalar charge S. The presence of this scalar charge reflects the modification of the gravitational interaction as compared to General Relativity. Surprisingly, these solutions are non-linear even at large distances from the sources, implying that their asymptotic behavior is different from that obtained in the linear perturbation theory. The aim of this paper is to understand how these modified spherically symmetric solutions emerge from a quasi-linear approximation "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4547","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":"2026-05-18T02:33:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3umT+Fx972cc3W6FuOZ2hxGmPAMFVKOQmHcxVozn85i8258qwGMcuwpr6AC4gZLAAzXq5Xoye17OtReLL9rbAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:53:20.811720Z"},"content_sha256":"91f9b4387705e0f15f9a0b8ed3277373739a1e91771caf5ccb4223c585ec8710","schema_version":"1.0","event_id":"sha256:91f9b4387705e0f15f9a0b8ed3277373739a1e91771caf5ccb4223c585ec8710"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TXI3JENPHJYC4QZ4PREY34NTXN/bundle.json","state_url":"https://pith.science/pith/TXI3JENPHJYC4QZ4PREY34NTXN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TXI3JENPHJYC4QZ4PREY34NTXN/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":"2026-06-01T21:53:20Z","links":{"resolver":"https://pith.science/pith/TXI3JENPHJYC4QZ4PREY34NTXN","bundle":"https://pith.science/pith/TXI3JENPHJYC4QZ4PREY34NTXN/bundle.json","state":"https://pith.science/pith/TXI3JENPHJYC4QZ4PREY34NTXN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TXI3JENPHJYC4QZ4PREY34NTXN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TXI3JENPHJYC4QZ4PREY34NTXN","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":"e7b0a880f1ed0793e2f16950b69b33433c01312f3942c465c6eb34ab6820ff2f","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-25T11:58:11Z","title_canon_sha256":"6e21735ace82991832b1d489286fdfda4a301b24284aa7a529e737b6d39271f9"},"schema_version":"1.0","source":{"id":"1005.4547","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.4547","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1005.4547v2","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.4547","created_at":"2026-05-18T02:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"TXI3JENPHJYC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TXI3JENPHJYC4QZ4","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TXI3JENP","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:91f9b4387705e0f15f9a0b8ed3277373739a1e91771caf5ccb4223c585ec8710","target":"graph","created_at":"2026-05-18T02:33:24Z","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":"The static vacuum spherically symmetric solutions of massive gravity theories possess two integration constant: the mass M and a scalar charge S. The presence of this scalar charge reflects the modification of the gravitational interaction as compared to General Relativity. Surprisingly, these solutions are non-linear even at large distances from the sources, implying that their asymptotic behavior is different from that obtained in the linear perturbation theory. The aim of this paper is to understand how these modified spherically symmetric solutions emerge from a quasi-linear approximation ","authors_text":"Michael V. Bebronne","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-25T11:58:11Z","title":"Quasi-linear static solutions in massive gravity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.4547","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":"sha256:4596dad66b0a92cf118869c7208e536ff5bee78749e93d582aaeef68abac7685","target":"record","created_at":"2026-05-18T02:33:24Z","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":"e7b0a880f1ed0793e2f16950b69b33433c01312f3942c465c6eb34ab6820ff2f","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2010-05-25T11:58:11Z","title_canon_sha256":"6e21735ace82991832b1d489286fdfda4a301b24284aa7a529e737b6d39271f9"},"schema_version":"1.0","source":{"id":"1005.4547","kind":"arxiv","version":2}},"canonical_sha256":"9dd1b491af3a702e433c7c498df1b3bb42f7c3e8ded1da369b4231e921b9bd7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9dd1b491af3a702e433c7c498df1b3bb42f7c3e8ded1da369b4231e921b9bd7a","first_computed_at":"2026-05-18T02:33:24.002861Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:24.002861Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KHTmDCNBYtTpJURLSU4UtN0vY7X6IrrEOkWELJcBSoY4maQI9xFvS2WdHdPw9aienTL1XGxkd5gIkz9ppOlrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:24.003320Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.4547","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4596dad66b0a92cf118869c7208e536ff5bee78749e93d582aaeef68abac7685","sha256:91f9b4387705e0f15f9a0b8ed3277373739a1e91771caf5ccb4223c585ec8710"],"state_sha256":"70ba331e97403f5d4f3f31d1fe950254dd67107f3df50dd4a391d9b863999f85"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mcq349V9uSQDwJInZ3VIxe2XWFLvNm4Nu4ZE1CqBegYknhANMt3FnR0RYg9GtdIWc0sMi+EeykEjtbqhHYS6Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:53:20.813559Z","bundle_sha256":"0d2aab20d885cb6fe473682b31277c865643b4a5adf8c65a5898ef6d1fea4399"}}