{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:ZXJZ7ZCNYA45XDWBLVS56T26WF","short_pith_number":"pith:ZXJZ7ZCN","canonical_record":{"source":{"id":"gr-qc/9403049","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1994-03-28T07:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"8420463c739e5c39df15f8c3c7af6a212437c3825d862c092bf910039d18238d","abstract_canon_sha256":"9e9a5187ac2f2994ea0204615510ca851ee67c018bd795c63750eed29b9575b3"},"schema_version":"1.0"},"canonical_sha256":"cdd39fe44dc039db8ec15d65df4f5eb14710ae4dda2fb7f128aa1a2dbf9b3c73","source":{"kind":"arxiv","id":"gr-qc/9403049","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9403049","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9403049v1","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9403049","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZXJZ7ZCNYA45","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZXJZ7ZCNYA45XDWB","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZXJZ7ZCN","created_at":"2026-07-04T15:56:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:ZXJZ7ZCNYA45XDWBLVS56T26WF","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/9403049","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"1994-03-28T07:11:00Z","cross_cats_sorted":[],"title_canon_sha256":"8420463c739e5c39df15f8c3c7af6a212437c3825d862c092bf910039d18238d","abstract_canon_sha256":"9e9a5187ac2f2994ea0204615510ca851ee67c018bd795c63750eed29b9575b3"},"schema_version":"1.0"},"canonical_sha256":"cdd39fe44dc039db8ec15d65df4f5eb14710ae4dda2fb7f128aa1a2dbf9b3c73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:56:54.087885Z","signature_b64":"TMyYFAouVWinQXm2EMISrxCYwkI/lyJVoCod2niHs+Zu0CEnx30wMqX+64bshHX9L7+2qwduI+KhluQYfsEOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdd39fe44dc039db8ec15d65df4f5eb14710ae4dda2fb7f128aa1a2dbf9b3c73","last_reissued_at":"2026-07-04T15:56:54.087460Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:56:54.087460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/9403049","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":"2026-07-04T15:56:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FzZWFpzf5+LvJmw1IEshCh9bnp3PzNALcAdaQJ5u6LjAx1YLYEkq0BqHzDJ+K4nbAx4br2tAocJ+INJ4JgwSDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:55:56.340358Z"},"content_sha256":"b2541cc579077b82bdf1cad92b5bd786d4418b0b2a4b1085f1a46dc141a4f6dc","schema_version":"1.0","event_id":"sha256:b2541cc579077b82bdf1cad92b5bd786d4418b0b2a4b1085f1a46dc141a4f6dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:ZXJZ7ZCNYA45XDWBLVS56T26WF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Open and Closed Universes, Initial Singularities and Inflation","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Arvind Borde","submitted_at":"1994-03-28T07:11:00Z","abstract_excerpt":"The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9403049","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/9403049/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":"2026-07-04T15:56:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOitjz19oBfnyc0geet1I6uKi1WU1DIzLyO/Ay/0ACecLa6rM0a73y6DXOA1rE/Y3FzbWIC/TbUp+YGuDTGbCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T04:55:56.341032Z"},"content_sha256":"4b9c65b61d03c673359a7b91bfc3be9484a60467f2df5cef1ea0ef2e35ac6159","schema_version":"1.0","event_id":"sha256:4b9c65b61d03c673359a7b91bfc3be9484a60467f2df5cef1ea0ef2e35ac6159"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF/bundle.json","state_url":"https://pith.science/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF/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":"2026-08-04T04:55:56Z","links":{"resolver":"https://pith.science/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF","bundle":"https://pith.science/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF/bundle.json","state":"https://pith.science/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZXJZ7ZCNYA45XDWBLVS56T26WF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:ZXJZ7ZCNYA45XDWBLVS56T26WF","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":"9e9a5187ac2f2994ea0204615510ca851ee67c018bd795c63750eed29b9575b3","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1994-03-28T07:11:00Z","title_canon_sha256":"8420463c739e5c39df15f8c3c7af6a212437c3825d862c092bf910039d18238d"},"schema_version":"1.0","source":{"id":"gr-qc/9403049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9403049","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9403049v1","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9403049","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"pith_short_12","alias_value":"ZXJZ7ZCNYA45","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZXJZ7ZCNYA45XDWB","created_at":"2026-07-04T15:56:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZXJZ7ZCN","created_at":"2026-07-04T15:56:54Z"}],"graph_snapshots":[{"event_id":"sha256:4b9c65b61d03c673359a7b91bfc3be9484a60467f2df5cef1ea0ef2e35ac6159","target":"graph","created_at":"2026-07-04T15:56:54Z","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/gr-qc/9403049/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known ","authors_text":"Arvind Borde","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1994-03-28T07:11:00Z","title":"Open and Closed Universes, Initial Singularities and Inflation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9403049","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:b2541cc579077b82bdf1cad92b5bd786d4418b0b2a4b1085f1a46dc141a4f6dc","target":"record","created_at":"2026-07-04T15:56:54Z","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":"9e9a5187ac2f2994ea0204615510ca851ee67c018bd795c63750eed29b9575b3","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1994-03-28T07:11:00Z","title_canon_sha256":"8420463c739e5c39df15f8c3c7af6a212437c3825d862c092bf910039d18238d"},"schema_version":"1.0","source":{"id":"gr-qc/9403049","kind":"arxiv","version":1}},"canonical_sha256":"cdd39fe44dc039db8ec15d65df4f5eb14710ae4dda2fb7f128aa1a2dbf9b3c73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdd39fe44dc039db8ec15d65df4f5eb14710ae4dda2fb7f128aa1a2dbf9b3c73","first_computed_at":"2026-07-04T15:56:54.087460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:56:54.087460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMyYFAouVWinQXm2EMISrxCYwkI/lyJVoCod2niHs+Zu0CEnx30wMqX+64bshHX9L7+2qwduI+KhluQYfsEOCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:56:54.087885Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9403049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2541cc579077b82bdf1cad92b5bd786d4418b0b2a4b1085f1a46dc141a4f6dc","sha256:4b9c65b61d03c673359a7b91bfc3be9484a60467f2df5cef1ea0ef2e35ac6159"],"state_sha256":"5d95da5cb6f06e36f7ee6f1d5b995f65aa40ac18e6acb6bced5b966e51ff913b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPwBCY8R5LsxDNT+/RBiE3DS9zYEui3Da/WnkO6Rea18cvdM/I3HAi5pL4xBGOzvqh9p3uSwOM+HWVIpsunwBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T04:55:56.346109Z","bundle_sha256":"a9f22e6e18bbc57c6a92e97d758f933bd1d395ed52d741cfb0266edb399ae122"}}