{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:JU6F7QLWZMNSYCMTYB4ICAWCVF","short_pith_number":"pith:JU6F7QLW","canonical_record":{"source":{"id":"0912.1445","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-12-08T09:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"b6a154137c3b2832e6480e0106b92030eeb0fb91026aad9f27edbd585ad0a499","abstract_canon_sha256":"4b46c8f7726db98559706305e58ef399dfcad7b9616b48460345c50c547dbbf5"},"schema_version":"1.0"},"canonical_sha256":"4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3","source":{"kind":"arxiv","id":"0912.1445","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1445","created_at":"2026-05-18T02:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1445v4","created_at":"2026-05-18T02:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1445","created_at":"2026-05-18T02:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"JU6F7QLWZMNS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JU6F7QLWZMNSYCMT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JU6F7QLW","created_at":"2026-05-18T12:26:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:JU6F7QLWZMNSYCMTYB4ICAWCVF","target":"record","payload":{"canonical_record":{"source":{"id":"0912.1445","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-12-08T09:31:53Z","cross_cats_sorted":[],"title_canon_sha256":"b6a154137c3b2832e6480e0106b92030eeb0fb91026aad9f27edbd585ad0a499","abstract_canon_sha256":"4b46c8f7726db98559706305e58ef399dfcad7b9616b48460345c50c547dbbf5"},"schema_version":"1.0"},"canonical_sha256":"4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:33:57.238882Z","signature_b64":"quwghYyxsLDD4Mz/CAPwK/rhyBkdEc2+ZO/VS81+4kmsZbtHE+HTBPjZSjNQpyNOlcsCiFfVGIb4usBW9MVvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3","last_reissued_at":"2026-05-18T02:33:57.238427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:33:57.238427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.1445","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jK86GmlXO9w27s/5zIkQ98HkjzKEx4OWdn3/lJK9+dp7kmdap4gsB2/py24GYsLxcnOxDNVzxSVXzzkNVOtiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:20:16.976790Z"},"content_sha256":"6557c335e72a4533ac652e83251574ac60de862f1a0cf42a6846a20c74255daa","schema_version":"1.0","event_id":"sha256:6557c335e72a4533ac652e83251574ac60de862f1a0cf42a6846a20c74255daa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:JU6F7QLWZMNSYCMTYB4ICAWCVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing the linear growth rate of cosmological density perturbations in an f(R) model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Kazuhiro Yamamoto, Tatsuya Narikawa","submitted_at":"2009-12-08T09:31:53Z","abstract_excerpt":"We investigate the linear growth rate of cosmological matter density perturbations of a viable f(R) model both numerically and analytically. We find that the growth rate in the scalar-tensor regime can be characterized by a simple analytic formula. We also investigate a prospect of constraining the Compton wavelength scale of the f(R) model with a future weak lensing survey."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1445","kind":"arxiv","version":4},"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":"2026-05-18T02:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aQIiZEjLBaFdarrOsPN3lcOhJqjo4Vm8VjM0qK6Q4xlrO1t4elG7+HfhgfVpW6tcJ/PTpGb+h9T/5hQ0PeXfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T14:20:16.977449Z"},"content_sha256":"ab4031a8bf94c3a83c19b861818c4ae1aeca78d3ba920f1759b5adde55d1e927","schema_version":"1.0","event_id":"sha256:ab4031a8bf94c3a83c19b861818c4ae1aeca78d3ba920f1759b5adde55d1e927"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF/bundle.json","state_url":"https://pith.science/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF/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":"2026-05-25T14:20:16Z","links":{"resolver":"https://pith.science/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF","bundle":"https://pith.science/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF/bundle.json","state":"https://pith.science/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JU6F7QLWZMNSYCMTYB4ICAWCVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JU6F7QLWZMNSYCMTYB4ICAWCVF","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":"4b46c8f7726db98559706305e58ef399dfcad7b9616b48460345c50c547dbbf5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-12-08T09:31:53Z","title_canon_sha256":"b6a154137c3b2832e6480e0106b92030eeb0fb91026aad9f27edbd585ad0a499"},"schema_version":"1.0","source":{"id":"0912.1445","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.1445","created_at":"2026-05-18T02:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"0912.1445v4","created_at":"2026-05-18T02:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.1445","created_at":"2026-05-18T02:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"JU6F7QLWZMNS","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JU6F7QLWZMNSYCMT","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JU6F7QLW","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:ab4031a8bf94c3a83c19b861818c4ae1aeca78d3ba920f1759b5adde55d1e927","target":"graph","created_at":"2026-05-18T02:33:57Z","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 investigate the linear growth rate of cosmological matter density perturbations of a viable f(R) model both numerically and analytically. We find that the growth rate in the scalar-tensor regime can be characterized by a simple analytic formula. We also investigate a prospect of constraining the Compton wavelength scale of the f(R) model with a future weak lensing survey.","authors_text":"Kazuhiro Yamamoto, Tatsuya Narikawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-12-08T09:31:53Z","title":"Characterizing the linear growth rate of cosmological density perturbations in an f(R) model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.1445","kind":"arxiv","version":4},"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":"sha256:6557c335e72a4533ac652e83251574ac60de862f1a0cf42a6846a20c74255daa","target":"record","created_at":"2026-05-18T02:33:57Z","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":"4b46c8f7726db98559706305e58ef399dfcad7b9616b48460345c50c547dbbf5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2009-12-08T09:31:53Z","title_canon_sha256":"b6a154137c3b2832e6480e0106b92030eeb0fb91026aad9f27edbd585ad0a499"},"schema_version":"1.0","source":{"id":"0912.1445","kind":"arxiv","version":4}},"canonical_sha256":"4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3","first_computed_at":"2026-05-18T02:33:57.238427Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:33:57.238427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"quwghYyxsLDD4Mz/CAPwK/rhyBkdEc2+ZO/VS81+4kmsZbtHE+HTBPjZSjNQpyNOlcsCiFfVGIb4usBW9MVvBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:33:57.238882Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.1445","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6557c335e72a4533ac652e83251574ac60de862f1a0cf42a6846a20c74255daa","sha256:ab4031a8bf94c3a83c19b861818c4ae1aeca78d3ba920f1759b5adde55d1e927"],"state_sha256":"4a94dd86ea795b4f2519fd15c8cebe9af0df6773e4c4411d73d5c59de3f73802"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6EFOqJC5SYzyY7j7d1BOG1VYuneOz8E9aSp+ycWdTzk2Rf4c8qgl9usUYtqG+JcIglnvCQrbZc4tgLA+dPzCDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T14:20:16.981222Z","bundle_sha256":"8f664b346f2ae230cc843e26635cac22906115b2b3f456883c2b2b9e313e957c"}}