{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:YHRF6P3XMLU2PRSVMQZK3GB6WU","short_pith_number":"pith:YHRF6P3X","canonical_record":{"source":{"id":"astro-ph/9612218","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1996-12-23T09:17:34Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"cfa5368981157869293e03e20160cf9b2a986eaa49e8c188936e0907aac1bec9","abstract_canon_sha256":"f239477de8b088b15caf82e7178451c2cfa9373cb7f9ad1c58ab2fe0ba551c93"},"schema_version":"1.0"},"canonical_sha256":"c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7","source":{"kind":"arxiv","id":"astro-ph/9612218","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9612218","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9612218v3","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9612218","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"YHRF6P3XMLU2","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"pith_short_16","alias_value":"YHRF6P3XMLU2PRSV","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"pith_short_8","alias_value":"YHRF6P3X","created_at":"2026-07-04T16:00:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:YHRF6P3XMLU2PRSVMQZK3GB6WU","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/9612218","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"1996-12-23T09:17:34Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"cfa5368981157869293e03e20160cf9b2a986eaa49e8c188936e0907aac1bec9","abstract_canon_sha256":"f239477de8b088b15caf82e7178451c2cfa9373cb7f9ad1c58ab2fe0ba551c93"},"schema_version":"1.0"},"canonical_sha256":"c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:00:21.165589Z","signature_b64":"fqpejrFJdmpt6fsZYYulA5V6nx0vkZPkPZbMYoJ/h6DqHQj7apLoCtscCLuJ1un/ZGfD7poriOqvXQv7Me+UBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7","last_reissued_at":"2026-07-04T16:00:21.165202Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:00:21.165202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/9612218","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:00:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7EpI+lcOzBN93s+vlNvjb13JAbgOcNlI8oU/8jxRO1slTadJorV8lHYLjRT2Y78IDUJZfI16OI4qvOfTrV2cCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:51:07.391848Z"},"content_sha256":"d8112f929c70d32825daacecc053433eb636bb2d4cf277f59a0dfc89364922be","schema_version":"1.0","event_id":"sha256:d8112f929c70d32825daacecc053433eb636bb2d4cf277f59a0dfc89364922be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:YHRF6P3XMLU2PRSVMQZK3GB6WU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Age of the Universe: Influence of the Inhomogeneities on the global Expansion-Factor","license":"","headline":"","cross_cats":["gr-qc"],"primary_cat":"astro-ph","authors_text":"G. B\\\"orner, H. Russ, M. H. Soffel, M. Kasai","submitted_at":"1996-12-23T09:17:34Z","abstract_excerpt":"For the first time we calculate quantitatively the influence of inhomogeneities on the global expansion factor by averaging the Friedmann equation. In the framework of the relativistic second-order Zel'dovich-approximation scheme for irrotational dust we use observational results in form of the normalisation constant fixed by the COBE results and we check different power spectra, namely for adiabatic CDM, isocurvature CDM, HDM, WDM, Strings and Textures. We find that the influence of the inhomogeneities on the global expansion factor is very small. So the error in determining the age of the un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9612218","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/9612218/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:00:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7vydg5954YUIXVs+Is7zDiYWhBBWA5YRH/spo47h6ScyAlPrhcYppPZbcVl0PdYlDX+Gq/yxONCniWzOD4KlAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T08:51:07.392258Z"},"content_sha256":"06277bbe2bde7c02b1cad6589d5d1f33d1e7a3db3f7b3258547c6f5752f95d53","schema_version":"1.0","event_id":"sha256:06277bbe2bde7c02b1cad6589d5d1f33d1e7a3db3f7b3258547c6f5752f95d53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU/bundle.json","state_url":"https://pith.science/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU/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":"2026-07-06T08:51:07Z","links":{"resolver":"https://pith.science/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU","bundle":"https://pith.science/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU/bundle.json","state":"https://pith.science/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YHRF6P3XMLU2PRSVMQZK3GB6WU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:YHRF6P3XMLU2PRSVMQZK3GB6WU","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":"f239477de8b088b15caf82e7178451c2cfa9373cb7f9ad1c58ab2fe0ba551c93","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"astro-ph","submitted_at":"1996-12-23T09:17:34Z","title_canon_sha256":"cfa5368981157869293e03e20160cf9b2a986eaa49e8c188936e0907aac1bec9"},"schema_version":"1.0","source":{"id":"astro-ph/9612218","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/9612218","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/9612218v3","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/9612218","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"pith_short_12","alias_value":"YHRF6P3XMLU2","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"pith_short_16","alias_value":"YHRF6P3XMLU2PRSV","created_at":"2026-07-04T16:00:21Z"},{"alias_kind":"pith_short_8","alias_value":"YHRF6P3X","created_at":"2026-07-04T16:00:21Z"}],"graph_snapshots":[{"event_id":"sha256:06277bbe2bde7c02b1cad6589d5d1f33d1e7a3db3f7b3258547c6f5752f95d53","target":"graph","created_at":"2026-07-04T16:00:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/astro-ph/9612218/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For the first time we calculate quantitatively the influence of inhomogeneities on the global expansion factor by averaging the Friedmann equation. In the framework of the relativistic second-order Zel'dovich-approximation scheme for irrotational dust we use observational results in form of the normalisation constant fixed by the COBE results and we check different power spectra, namely for adiabatic CDM, isocurvature CDM, HDM, WDM, Strings and Textures. We find that the influence of the inhomogeneities on the global expansion factor is very small. So the error in determining the age of the un","authors_text":"G. B\\\"orner, H. Russ, M. H. Soffel, M. Kasai","cross_cats":["gr-qc"],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"1996-12-23T09:17:34Z","title":"Age of the Universe: Influence of the Inhomogeneities on the global Expansion-Factor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/9612218","kind":"arxiv","version":3},"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:d8112f929c70d32825daacecc053433eb636bb2d4cf277f59a0dfc89364922be","target":"record","created_at":"2026-07-04T16:00:21Z","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":"f239477de8b088b15caf82e7178451c2cfa9373cb7f9ad1c58ab2fe0ba551c93","cross_cats_sorted":["gr-qc"],"license":"","primary_cat":"astro-ph","submitted_at":"1996-12-23T09:17:34Z","title_canon_sha256":"cfa5368981157869293e03e20160cf9b2a986eaa49e8c188936e0907aac1bec9"},"schema_version":"1.0","source":{"id":"astro-ph/9612218","kind":"arxiv","version":3}},"canonical_sha256":"c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1e25f3f7762e9a7c6556432ad983eb50581f4ae867cd5e1235ca359dd57e2c7","first_computed_at":"2026-07-04T16:00:21.165202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:00:21.165202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fqpejrFJdmpt6fsZYYulA5V6nx0vkZPkPZbMYoJ/h6DqHQj7apLoCtscCLuJ1un/ZGfD7poriOqvXQv7Me+UBA==","signature_status":"signed_v1","signed_at":"2026-07-04T16:00:21.165589Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/9612218","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d8112f929c70d32825daacecc053433eb636bb2d4cf277f59a0dfc89364922be","sha256:06277bbe2bde7c02b1cad6589d5d1f33d1e7a3db3f7b3258547c6f5752f95d53"],"state_sha256":"44c4b168acafacfcc1f3e961180dedb75a9c1448b46cbc97a2eca8180b369723"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EPJL1K1Hgb8blzZqgIu0eumIiPEjzbikdJPSJpcgmrc67vgfTymaP2g8zTJ/S6B5uwdyIzXpoLn80Pz1Y9ljBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T08:51:07.394446Z","bundle_sha256":"438931b249e16bb2ffe7e395600b55abd8fe7097f56319c5f57605e2868dc43c"}}