{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:6F4HVUXFISOU5TF7QF3ZU2DGQQ","short_pith_number":"pith:6F4HVUXF","canonical_record":{"source":{"id":"1007.0598","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2010-07-04T23:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"f8069e49a43599b9388f674f4ccb9a38b13233afb562ef6990b3284fda3cd1e6","abstract_canon_sha256":"80fd3818923bb081f1371ad3bc240185114d884dc29fa8f434a86127a1ba6fbc"},"schema_version":"1.0"},"canonical_sha256":"f1787ad2e5449d4eccbf81779a6866843e58c596c1a28c727cc53aa7fc6a1713","source":{"kind":"arxiv","id":"1007.0598","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0598","created_at":"2026-05-18T04:07:08Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0598v6","created_at":"2026-05-18T04:07:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0598","created_at":"2026-05-18T04:07:08Z"},{"alias_kind":"pith_short_12","alias_value":"6F4HVUXFISOU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6F4HVUXFISOU5TF7","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6F4HVUXF","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:6F4HVUXFISOU5TF7QF3ZU2DGQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1007.0598","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2010-07-04T23:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"f8069e49a43599b9388f674f4ccb9a38b13233afb562ef6990b3284fda3cd1e6","abstract_canon_sha256":"80fd3818923bb081f1371ad3bc240185114d884dc29fa8f434a86127a1ba6fbc"},"schema_version":"1.0"},"canonical_sha256":"f1787ad2e5449d4eccbf81779a6866843e58c596c1a28c727cc53aa7fc6a1713","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:08.071270Z","signature_b64":"2EVsicKm9/mCq8pRtEUO4wF4tQbMDQfgO17b4S0QVNUY+nGhFlhRZbjxqon0ByVZzceNVVXArC22I1IwCC3IDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1787ad2e5449d4eccbf81779a6866843e58c596c1a28c727cc53aa7fc6a1713","last_reissued_at":"2026-05-18T04:07:08.070628Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:08.070628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.0598","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:07:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73+5MlKyNGY8IsGse7U2jgkecJ38lEcqjprkgsV62ko0NNKrlkXgD7CaGhPb9rh7N4PEZMawMpLE4jKIAnPrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:40:48.405030Z"},"content_sha256":"7746f554e71ed6c28439572e6d859d1f3c6dd953a4542c22772a3e42f8acffd4","schema_version":"1.0","event_id":"sha256:7746f554e71ed6c28439572e6d859d1f3c6dd953a4542c22772a3e42f8acffd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:6F4HVUXFISOU5TF7QF3ZU2DGQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on the classical solutions of Friedmann's equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Arthur Viglioni, Domingos Soares","submitted_at":"2010-07-04T23:24:33Z","abstract_excerpt":"Graphical representations of classical Friedmann's models are often misleading when one considers the age of the universe. Most textbooks disregard conceptual differences in the representations, as far as ages are concerned. We discuss the details of the scale-factor versus time function for Friedmann's solutions in the time range that includes the ages of model universes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0598","kind":"arxiv","version":6},"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":"2026-05-18T04:07:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"prgj1aLh0EoOyGxW08Cf0wNmAcxGgeGB+pR6MMhwDjR4rb0EW6PMWA1gZEmBwP0RvUMdeyIQqK6DLCDDLZi7DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:40:48.405382Z"},"content_sha256":"f46c4d11915214162757ca1a35f939932ca7e542243ec268748a25aa50799108","schema_version":"1.0","event_id":"sha256:f46c4d11915214162757ca1a35f939932ca7e542243ec268748a25aa50799108"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ/bundle.json","state_url":"https://pith.science/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ/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":"2026-05-28T05:40:48Z","links":{"resolver":"https://pith.science/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ","bundle":"https://pith.science/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ/bundle.json","state":"https://pith.science/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6F4HVUXFISOU5TF7QF3ZU2DGQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6F4HVUXFISOU5TF7QF3ZU2DGQQ","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":"80fd3818923bb081f1371ad3bc240185114d884dc29fa8f434a86127a1ba6fbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2010-07-04T23:24:33Z","title_canon_sha256":"f8069e49a43599b9388f674f4ccb9a38b13233afb562ef6990b3284fda3cd1e6"},"schema_version":"1.0","source":{"id":"1007.0598","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.0598","created_at":"2026-05-18T04:07:08Z"},{"alias_kind":"arxiv_version","alias_value":"1007.0598v6","created_at":"2026-05-18T04:07:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.0598","created_at":"2026-05-18T04:07:08Z"},{"alias_kind":"pith_short_12","alias_value":"6F4HVUXFISOU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6F4HVUXFISOU5TF7","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6F4HVUXF","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:f46c4d11915214162757ca1a35f939932ca7e542243ec268748a25aa50799108","target":"graph","created_at":"2026-05-18T04:07:08Z","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":"Graphical representations of classical Friedmann's models are often misleading when one considers the age of the universe. Most textbooks disregard conceptual differences in the representations, as far as ages are concerned. We discuss the details of the scale-factor versus time function for Friedmann's solutions in the time range that includes the ages of model universes.","authors_text":"Arthur Viglioni, Domingos Soares","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2010-07-04T23:24:33Z","title":"Note on the classical solutions of Friedmann's equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.0598","kind":"arxiv","version":6},"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":"sha256:7746f554e71ed6c28439572e6d859d1f3c6dd953a4542c22772a3e42f8acffd4","target":"record","created_at":"2026-05-18T04:07:08Z","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":"80fd3818923bb081f1371ad3bc240185114d884dc29fa8f434a86127a1ba6fbc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2010-07-04T23:24:33Z","title_canon_sha256":"f8069e49a43599b9388f674f4ccb9a38b13233afb562ef6990b3284fda3cd1e6"},"schema_version":"1.0","source":{"id":"1007.0598","kind":"arxiv","version":6}},"canonical_sha256":"f1787ad2e5449d4eccbf81779a6866843e58c596c1a28c727cc53aa7fc6a1713","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1787ad2e5449d4eccbf81779a6866843e58c596c1a28c727cc53aa7fc6a1713","first_computed_at":"2026-05-18T04:07:08.070628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:08.070628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2EVsicKm9/mCq8pRtEUO4wF4tQbMDQfgO17b4S0QVNUY+nGhFlhRZbjxqon0ByVZzceNVVXArC22I1IwCC3IDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:08.071270Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.0598","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7746f554e71ed6c28439572e6d859d1f3c6dd953a4542c22772a3e42f8acffd4","sha256:f46c4d11915214162757ca1a35f939932ca7e542243ec268748a25aa50799108"],"state_sha256":"457a524e2a46314764683c13444e5529de8e2c6df8a1139f763b59fb16a7f533"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5s+zsvq7FND85Wua6UOTUyURorI7Z5nxiX3X78ayFqrurMm/fv6iUt4XLJsJ3uInax1EXxQm6Qxf99r7sDQxAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:40:48.407253Z","bundle_sha256":"7f27aa4558c78d03cf0845c11e1a2720b49541c150775725f8ccfb05741d1e78"}}