{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:P64JVH64V2DW6EU75NYD4GHV7K","short_pith_number":"pith:P64JVH64","canonical_record":{"source":{"id":"1301.5042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-01-21T23:59:36Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"b05f8145047bd8dc4ccd21bf3831661b4000161a9e2f40fc6b17e53ebcfacc46","abstract_canon_sha256":"cdcd8ab689d0fcc5d3cf6f2a6d9f582062dffa2e2ff7c8467b24a7b90d98a110"},"schema_version":"1.0"},"canonical_sha256":"7fb89a9fdcae876f129feb703e18f5fa851bf602590d101503cc186c9bf9e1ad","source":{"kind":"arxiv","id":"1301.5042","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5042","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5042v1","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5042","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"P64JVH64V2DW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P64JVH64V2DW6EU7","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P64JVH64","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:P64JVH64V2DW6EU75NYD4GHV7K","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5042","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-01-21T23:59:36Z","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"title_canon_sha256":"b05f8145047bd8dc4ccd21bf3831661b4000161a9e2f40fc6b17e53ebcfacc46","abstract_canon_sha256":"cdcd8ab689d0fcc5d3cf6f2a6d9f582062dffa2e2ff7c8467b24a7b90d98a110"},"schema_version":"1.0"},"canonical_sha256":"7fb89a9fdcae876f129feb703e18f5fa851bf602590d101503cc186c9bf9e1ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:38.099149Z","signature_b64":"yPTbNBMCJtYgOycPPdWTDl+YllGFu+zTPRSVLwtY1MCKQX9n4EBVJ+pR2LAoo/5PIeRJsuS/dYrtsVJAZcJkDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7fb89a9fdcae876f129feb703e18f5fa851bf602590d101503cc186c9bf9e1ad","last_reissued_at":"2026-05-18T03:08:38.098265Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:38.098265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5042","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":"2026-05-18T03:08:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lzP3OVH+Bgl1MTANUj5GnLMezY1lAgE4wFgkh+K/85nH1VpHzHYpNcKEC/9aGg5JlgyGVBFx8PEwC5F8MffqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:18:57.640895Z"},"content_sha256":"d6bf45cc4c1a5ae05379fd6fe71db663f7ed8681ce51816ee354c82542e08eac","schema_version":"1.0","event_id":"sha256:d6bf45cc4c1a5ae05379fd6fe71db663f7ed8681ce51816ee354c82542e08eac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:P64JVH64V2DW6EU75NYD4GHV7K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Massive gravity, the elasticity of space-time and perturbations in the dark sector","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph","hep-th"],"primary_cat":"astro-ph.CO","authors_text":"Jonathan A. Pearson, Richard A. Battye","submitted_at":"2013-01-21T23:59:36Z","abstract_excerpt":"We consider a class of modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is entirely specified by a rank 4 tensor that encodes possibly time-dependent masses for the gravitons. This tensor has the same symmetries as an elasticity tensor, suggesting an interpretation of massive gravity as an effective rigidity of space-time. If we choose a form for this tensor which is compatible with the symmetries of FRW and enforce full reparameteri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5042","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":"2026-05-18T03:08:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2RJE3+Orlx/Bj5dJRzvOQy/TzeborMzG7Q4ewM/vpbK2kF9XafLdpxmnzIHJpkXOFMA5xOujqz6d4nuQxv/rBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T03:18:57.641601Z"},"content_sha256":"6595cb9ee02dc9324d7cdf7058d7c9c373a4f58bcc72e23f9dce54e42f76880e","schema_version":"1.0","event_id":"sha256:6595cb9ee02dc9324d7cdf7058d7c9c373a4f58bcc72e23f9dce54e42f76880e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P64JVH64V2DW6EU75NYD4GHV7K/bundle.json","state_url":"https://pith.science/pith/P64JVH64V2DW6EU75NYD4GHV7K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P64JVH64V2DW6EU75NYD4GHV7K/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":"2026-06-09T03:18:57Z","links":{"resolver":"https://pith.science/pith/P64JVH64V2DW6EU75NYD4GHV7K","bundle":"https://pith.science/pith/P64JVH64V2DW6EU75NYD4GHV7K/bundle.json","state":"https://pith.science/pith/P64JVH64V2DW6EU75NYD4GHV7K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P64JVH64V2DW6EU75NYD4GHV7K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:P64JVH64V2DW6EU75NYD4GHV7K","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":"cdcd8ab689d0fcc5d3cf6f2a6d9f582062dffa2e2ff7c8467b24a7b90d98a110","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-01-21T23:59:36Z","title_canon_sha256":"b05f8145047bd8dc4ccd21bf3831661b4000161a9e2f40fc6b17e53ebcfacc46"},"schema_version":"1.0","source":{"id":"1301.5042","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5042","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5042v1","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5042","created_at":"2026-05-18T03:08:38Z"},{"alias_kind":"pith_short_12","alias_value":"P64JVH64V2DW","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"P64JVH64V2DW6EU7","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"P64JVH64","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:6595cb9ee02dc9324d7cdf7058d7c9c373a4f58bcc72e23f9dce54e42f76880e","target":"graph","created_at":"2026-05-18T03:08:38Z","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 consider a class of modified gravity models where the terms added to the standard Einstein-Hilbert Lagrangian are just a function of the metric only. For linearized perturbations around an isotropic space-time, this class of models is entirely specified by a rank 4 tensor that encodes possibly time-dependent masses for the gravitons. This tensor has the same symmetries as an elasticity tensor, suggesting an interpretation of massive gravity as an effective rigidity of space-time. If we choose a form for this tensor which is compatible with the symmetries of FRW and enforce full reparameteri","authors_text":"Jonathan A. Pearson, Richard A. Battye","cross_cats":["gr-qc","hep-ph","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-01-21T23:59:36Z","title":"Massive gravity, the elasticity of space-time and perturbations in the dark sector"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5042","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:d6bf45cc4c1a5ae05379fd6fe71db663f7ed8681ce51816ee354c82542e08eac","target":"record","created_at":"2026-05-18T03:08:38Z","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":"cdcd8ab689d0fcc5d3cf6f2a6d9f582062dffa2e2ff7c8467b24a7b90d98a110","cross_cats_sorted":["gr-qc","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-01-21T23:59:36Z","title_canon_sha256":"b05f8145047bd8dc4ccd21bf3831661b4000161a9e2f40fc6b17e53ebcfacc46"},"schema_version":"1.0","source":{"id":"1301.5042","kind":"arxiv","version":1}},"canonical_sha256":"7fb89a9fdcae876f129feb703e18f5fa851bf602590d101503cc186c9bf9e1ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb89a9fdcae876f129feb703e18f5fa851bf602590d101503cc186c9bf9e1ad","first_computed_at":"2026-05-18T03:08:38.098265Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:38.098265Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yPTbNBMCJtYgOycPPdWTDl+YllGFu+zTPRSVLwtY1MCKQX9n4EBVJ+pR2LAoo/5PIeRJsuS/dYrtsVJAZcJkDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:38.099149Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5042","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d6bf45cc4c1a5ae05379fd6fe71db663f7ed8681ce51816ee354c82542e08eac","sha256:6595cb9ee02dc9324d7cdf7058d7c9c373a4f58bcc72e23f9dce54e42f76880e"],"state_sha256":"2c1ee2265929098d99b8db10183aa03c66fe7920fb8bd4303a1ffa1d32d36dd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NUOE0aDJ125k6RV59ilhAr0VpQP54sQ4WIy5ZTDJDkm93WjgkZV++MvewcuMyuAtBZ6y1HqNWZaNHmTziMswCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T03:18:57.645597Z","bundle_sha256":"beea747a42d6a2c53a920b40f6b2f0896c65993481f06f21de15eace99dc11a4"}}