{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7UTQTCLDZ4OY3QCT2YE4GP4LV6","short_pith_number":"pith:7UTQTCLD","canonical_record":{"source":{"id":"1309.5695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-09-23T04:59:15Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"1ddf4477a1f731263ea579eb4d3d57d181be488a8fafd27bab8db855193a9fb9","abstract_canon_sha256":"78f981d2caff061d91706113acae7b58b5c27e87ceb4fa01bd0d73e4ed9d1ae7"},"schema_version":"1.0"},"canonical_sha256":"fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc","source":{"kind":"arxiv","id":"1309.5695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5695","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5695v1","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5695","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"7UTQTCLDZ4OY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7UTQTCLDZ4OY3QCT","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7UTQTCLD","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7UTQTCLDZ4OY3QCT2YE4GP4LV6","target":"record","payload":{"canonical_record":{"source":{"id":"1309.5695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-09-23T04:59:15Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"1ddf4477a1f731263ea579eb4d3d57d181be488a8fafd27bab8db855193a9fb9","abstract_canon_sha256":"78f981d2caff061d91706113acae7b58b5c27e87ceb4fa01bd0d73e4ed9d1ae7"},"schema_version":"1.0"},"canonical_sha256":"fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:11.126591Z","signature_b64":"AczLN43OWNg/mTtSzXMACwQqWHJunaDpn3M0pQEI++HFU8e1b83UH/Dvu8o/xQcbVwEDtNwC1JM2LN8qFploDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc","last_reissued_at":"2026-05-18T03:12:11.125775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:11.125775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.5695","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":"2026-05-18T03:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUhkqfFcBca+ThsORMNVzQOKSQZTsKOxWo9g0tWIwvOzR757fMqoOqnQZQA8J7w2ochBRBsm2A8BD/njzI8pDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:20:38.061596Z"},"content_sha256":"722b08752220ea1a1c220293a3a2f85910427676aca68552fe584556393124cd","schema_version":"1.0","event_id":"sha256:722b08752220ea1a1c220293a3a2f85910427676aca68552fe584556393124cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7UTQTCLDZ4OY3QCT2YE4GP4LV6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Intermediate homogenization of the Universe and the problem of gravitational entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph.CO","authors_text":"Krzysztof Bolejko, William R. Stoeger","submitted_at":"2013-09-23T04:59:15Z","abstract_excerpt":"This paper studies intermediate homogenization of inhomogeneous cosmological models. It shows that spherically symmetric models, regardless of the equation of state, can undergo intermediate homogenization, i.e. a model can approach a homogeneous and isotropic state (which acts as a saddle point) from a relatively wide range of initial inhomogeneous conditions. The homogenization is not permanent - just temporary. Eventually the model evolves toward a future inhomogeneous state. We also looked at the problem of the gravitational entropy. All definitions of entropy that we checked give decreasi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5695","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":"2026-05-18T03:12:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HoHcdDgc94Ewws3pLltwSgrQZvpGTZHaO8Cm2N3qo8NtMbuOVmlbiaVwP5G2n4svWRo3UkAZuXFPo5vCxya2Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T00:20:38.062224Z"},"content_sha256":"d3f25b23a2cad0d6e67ca3a90fdf72720b20ccca79c8a576d38d4fbfd1cebb1c","schema_version":"1.0","event_id":"sha256:d3f25b23a2cad0d6e67ca3a90fdf72720b20ccca79c8a576d38d4fbfd1cebb1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6/bundle.json","state_url":"https://pith.science/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6/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":"2026-06-07T00:20:38Z","links":{"resolver":"https://pith.science/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6","bundle":"https://pith.science/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6/bundle.json","state":"https://pith.science/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UTQTCLDZ4OY3QCT2YE4GP4LV6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7UTQTCLDZ4OY3QCT2YE4GP4LV6","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":"78f981d2caff061d91706113acae7b58b5c27e87ceb4fa01bd0d73e4ed9d1ae7","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-09-23T04:59:15Z","title_canon_sha256":"1ddf4477a1f731263ea579eb4d3d57d181be488a8fafd27bab8db855193a9fb9"},"schema_version":"1.0","source":{"id":"1309.5695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.5695","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"arxiv_version","alias_value":"1309.5695v1","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.5695","created_at":"2026-05-18T03:12:11Z"},{"alias_kind":"pith_short_12","alias_value":"7UTQTCLDZ4OY","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"7UTQTCLDZ4OY3QCT","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"7UTQTCLD","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:d3f25b23a2cad0d6e67ca3a90fdf72720b20ccca79c8a576d38d4fbfd1cebb1c","target":"graph","created_at":"2026-05-18T03:12:11Z","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":"This paper studies intermediate homogenization of inhomogeneous cosmological models. It shows that spherically symmetric models, regardless of the equation of state, can undergo intermediate homogenization, i.e. a model can approach a homogeneous and isotropic state (which acts as a saddle point) from a relatively wide range of initial inhomogeneous conditions. The homogenization is not permanent - just temporary. Eventually the model evolves toward a future inhomogeneous state. We also looked at the problem of the gravitational entropy. All definitions of entropy that we checked give decreasi","authors_text":"Krzysztof Bolejko, William R. Stoeger","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-09-23T04:59:15Z","title":"Intermediate homogenization of the Universe and the problem of gravitational entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.5695","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":"sha256:722b08752220ea1a1c220293a3a2f85910427676aca68552fe584556393124cd","target":"record","created_at":"2026-05-18T03:12:11Z","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":"78f981d2caff061d91706113acae7b58b5c27e87ceb4fa01bd0d73e4ed9d1ae7","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2013-09-23T04:59:15Z","title_canon_sha256":"1ddf4477a1f731263ea579eb4d3d57d181be488a8fafd27bab8db855193a9fb9"},"schema_version":"1.0","source":{"id":"1309.5695","kind":"arxiv","version":1}},"canonical_sha256":"fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd27098963cf1d8dc053d609c33f8bafba76d90854a17cee053b103050623cfc","first_computed_at":"2026-05-18T03:12:11.125775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:11.125775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AczLN43OWNg/mTtSzXMACwQqWHJunaDpn3M0pQEI++HFU8e1b83UH/Dvu8o/xQcbVwEDtNwC1JM2LN8qFploDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:11.126591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.5695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:722b08752220ea1a1c220293a3a2f85910427676aca68552fe584556393124cd","sha256:d3f25b23a2cad0d6e67ca3a90fdf72720b20ccca79c8a576d38d4fbfd1cebb1c"],"state_sha256":"0ecec293360748e1791726af42f93e7a3a5fd47278c0844abd7c6933a5d8ea16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6gHcohflEdQdHqZuraKxAse2qUuSJsvOnwgCceEQuI3LFpDRpmKjp2bjzwe1VW8jf7G8oXA/tL8f5dNgy6uWBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T00:20:38.065550Z","bundle_sha256":"eff767ccbfa3a87dcec5184121efd412f5e800897d7765a36b3bee236a017137"}}