{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FNB5FBRT4AZ2V55SGZ5WG726K3","short_pith_number":"pith:FNB5FBRT","canonical_record":{"source":{"id":"1212.2298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-12-11T04:41:31Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"95d2e415c9a6db0191d7f6cb727500fb63372687d9ba0a10cc22315c65a8739a","abstract_canon_sha256":"b20a368b328def5909cd8263c17f379cb4878f290eafb005d15e80e63eb5de94"},"schema_version":"1.0"},"canonical_sha256":"2b43d28633e033aaf7b2367b637f5e56c95037b890cfcad3942d9915287b1d63","source":{"kind":"arxiv","id":"1212.2298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2298","created_at":"2026-05-18T01:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2298v1","created_at":"2026-05-18T01:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2298","created_at":"2026-05-18T01:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"FNB5FBRT4AZ2","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FNB5FBRT4AZ2V55S","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FNB5FBRT","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FNB5FBRT4AZ2V55SGZ5WG726K3","target":"record","payload":{"canonical_record":{"source":{"id":"1212.2298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-12-11T04:41:31Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"95d2e415c9a6db0191d7f6cb727500fb63372687d9ba0a10cc22315c65a8739a","abstract_canon_sha256":"b20a368b328def5909cd8263c17f379cb4878f290eafb005d15e80e63eb5de94"},"schema_version":"1.0"},"canonical_sha256":"2b43d28633e033aaf7b2367b637f5e56c95037b890cfcad3942d9915287b1d63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:52:40.239080Z","signature_b64":"8sc/jWwcjQSzWS2KLTwbxqCAE47Q9o5fbzXIWT6X9CqKYqiGSWMr5MEmTlmytVmY3kY8rwYA77tfWioulfnsCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b43d28633e033aaf7b2367b637f5e56c95037b890cfcad3942d9915287b1d63","last_reissued_at":"2026-05-18T01:52:40.238368Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:52:40.238368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.2298","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":"2026-05-18T01:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BhMFnArP+dAFIqh7z7no7bwIQDi7VejgQ719TVwuIutFbxjdu0MkRjq04i8rBjTvlw6FWukj8FVL0doIraFaAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:20:27.926168Z"},"content_sha256":"fba391d8f0f3cfdc26879fad95f05cddde3d316e3011b52b6e99adb9093ae944","schema_version":"1.0","event_id":"sha256:fba391d8f0f3cfdc26879fad95f05cddde3d316e3011b52b6e99adb9093ae944"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FNB5FBRT4AZ2V55SGZ5WG726K3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"Austin Peel, M. A. Troxel (The University of Texas at Dallas), Mustapha Ishak","submitted_at":"2012-12-11T04:41:31Z","abstract_excerpt":"We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including Lambda, the time evolution of the density contrast as well as kinematic quantities can be tracked through the mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2298","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":"2026-05-18T01:52:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nioCojsS/AjgNPVs0i88G3FjZTf7uPtJGsvq/8PeqVJMaoeEQTYmty+D+UkoM4vmfWOxz1WlM/mSL45YHhE2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T18:20:27.926541Z"},"content_sha256":"d1657679461ad1d7c41971258ed00e99f7442967170a5bd750fa08c969e79721","schema_version":"1.0","event_id":"sha256:d1657679461ad1d7c41971258ed00e99f7442967170a5bd750fa08c969e79721"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FNB5FBRT4AZ2V55SGZ5WG726K3/bundle.json","state_url":"https://pith.science/pith/FNB5FBRT4AZ2V55SGZ5WG726K3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FNB5FBRT4AZ2V55SGZ5WG726K3/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":"2026-06-01T18:20:27Z","links":{"resolver":"https://pith.science/pith/FNB5FBRT4AZ2V55SGZ5WG726K3","bundle":"https://pith.science/pith/FNB5FBRT4AZ2V55SGZ5WG726K3/bundle.json","state":"https://pith.science/pith/FNB5FBRT4AZ2V55SGZ5WG726K3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FNB5FBRT4AZ2V55SGZ5WG726K3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FNB5FBRT4AZ2V55SGZ5WG726K3","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":"b20a368b328def5909cd8263c17f379cb4878f290eafb005d15e80e63eb5de94","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-12-11T04:41:31Z","title_canon_sha256":"95d2e415c9a6db0191d7f6cb727500fb63372687d9ba0a10cc22315c65a8739a"},"schema_version":"1.0","source":{"id":"1212.2298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.2298","created_at":"2026-05-18T01:52:40Z"},{"alias_kind":"arxiv_version","alias_value":"1212.2298v1","created_at":"2026-05-18T01:52:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2298","created_at":"2026-05-18T01:52:40Z"},{"alias_kind":"pith_short_12","alias_value":"FNB5FBRT4AZ2","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FNB5FBRT4AZ2V55S","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FNB5FBRT","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:d1657679461ad1d7c41971258ed00e99f7442967170a5bd750fa08c969e79721","target":"graph","created_at":"2026-05-18T01:52:40Z","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 use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including Lambda, the time evolution of the density contrast as well as kinematic quantities can be tracked through the mat","authors_text":"Austin Peel, M. A. Troxel (The University of Texas at Dallas), Mustapha Ishak","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-12-11T04:41:31Z","title":"Large-scale growth evolution in the Szekeres inhomogeneous cosmological models with comparison to growth data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2298","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:fba391d8f0f3cfdc26879fad95f05cddde3d316e3011b52b6e99adb9093ae944","target":"record","created_at":"2026-05-18T01:52:40Z","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":"b20a368b328def5909cd8263c17f379cb4878f290eafb005d15e80e63eb5de94","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2012-12-11T04:41:31Z","title_canon_sha256":"95d2e415c9a6db0191d7f6cb727500fb63372687d9ba0a10cc22315c65a8739a"},"schema_version":"1.0","source":{"id":"1212.2298","kind":"arxiv","version":1}},"canonical_sha256":"2b43d28633e033aaf7b2367b637f5e56c95037b890cfcad3942d9915287b1d63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b43d28633e033aaf7b2367b637f5e56c95037b890cfcad3942d9915287b1d63","first_computed_at":"2026-05-18T01:52:40.238368Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:40.238368Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8sc/jWwcjQSzWS2KLTwbxqCAE47Q9o5fbzXIWT6X9CqKYqiGSWMr5MEmTlmytVmY3kY8rwYA77tfWioulfnsCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:40.239080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.2298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fba391d8f0f3cfdc26879fad95f05cddde3d316e3011b52b6e99adb9093ae944","sha256:d1657679461ad1d7c41971258ed00e99f7442967170a5bd750fa08c969e79721"],"state_sha256":"d33c7d9d86652d387ec7d0073d1c121acac03ed7e5db5a3451f4be9dbe4d1dbc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mNzdzIZamVaRM70wnbEVbSlV9z2stK+kvCy/lK4fu2a31jaQL1djHY11i6avUAJ2a/UIIulVpq39ivXmBvW9Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T18:20:27.928513Z","bundle_sha256":"a06e31597b71b221e980bb73da12aea427efc6596a93a21866580d1d998a664e"}}