{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:EP7U4UB5ZXENNLVNRO7HLLYLCQ","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":"523d2d7598c94beba86a61b8b19076524a502f5e60e4141ddd42f0188f428e20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-01-05T13:05:41Z","title_canon_sha256":"c2e895e0af5904038dcfcc97b347e3a11de5cdd0fa98a20c4dc1249d11ea4559"},"schema_version":"1.0","source":{"id":"1201.1161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1161","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1161v1","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1161","created_at":"2026-05-18T04:05:05Z"},{"alias_kind":"pith_short_12","alias_value":"EP7U4UB5ZXEN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"EP7U4UB5ZXENNLVN","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"EP7U4UB5","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:3187a2fb69646d5144044c4183f0ba13f814f647554dcf80676b7295b8c1ab10","target":"graph","created_at":"2026-05-18T04:05:05Z","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":"In this paper we investigate Cauchy completeness and exponentiablity for quantale enriched categories, paying particular attention to probabilistic metric spaces.","authors_text":"Carla David Reis, Dirk Hofmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-01-05T13:05:41Z","title":"Probabilistic Metric Spaces as enriched categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1161","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":"sha256:50d9ddd909ebc723e96ea8223a10622262bebde519bbe84158d856869aa55ad1","target":"record","created_at":"2026-05-18T04:05:05Z","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":"523d2d7598c94beba86a61b8b19076524a502f5e60e4141ddd42f0188f428e20","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2012-01-05T13:05:41Z","title_canon_sha256":"c2e895e0af5904038dcfcc97b347e3a11de5cdd0fa98a20c4dc1249d11ea4559"},"schema_version":"1.0","source":{"id":"1201.1161","kind":"arxiv","version":1}},"canonical_sha256":"23ff4e503dcdc8d6aead8bbe75af0b1423c9c5705b1ab63001aad7c9df8eb935","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23ff4e503dcdc8d6aead8bbe75af0b1423c9c5705b1ab63001aad7c9df8eb935","first_computed_at":"2026-05-18T04:05:05.918533Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:05.918533Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rW2loZSvSMC16k/YYvJfjhrFmLI5f63J0tR6MTNpKLIypatVTknwkm1GdatFKOQmpFxiJYip5wcIBgy4ObSgCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:05.919217Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50d9ddd909ebc723e96ea8223a10622262bebde519bbe84158d856869aa55ad1","sha256:3187a2fb69646d5144044c4183f0ba13f814f647554dcf80676b7295b8c1ab10"],"state_sha256":"2c640103d3f9b2511fa8fec2c5659e1fdcdc72261f6d494c181fe6460212c45c"}