{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:AXAS25SHVJZUEIIHMRCY4QBCR5","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":"981172f1c33e6ce5aeb93a86a2c655b75c209fcbc9437d76a90d45467e924d6d","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"2004-06-29T22:48:33Z","title_canon_sha256":"9535c7c36b4d303f00ad4553348cf929d66228574044dfce1ece7d88c225959f"},"schema_version":"1.0","source":{"id":"math/0406612","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0406612","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"arxiv_version","alias_value":"math/0406612v2","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0406612","created_at":"2026-05-18T03:37:19Z"},{"alias_kind":"pith_short_12","alias_value":"AXAS25SHVJZU","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"AXAS25SHVJZUEIIH","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"AXAS25SH","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:d6d5bf672c391b7144e63a8520af080c5fef6f456d7d7b56bb8c47a389b7dfba","target":"graph","created_at":"2026-05-18T03:37:19Z","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":"We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such.","authors_text":"Andrzej Roslanowski, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"2004-06-29T22:48:33Z","title":"How much sweetness is there in the universe?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0406612","kind":"arxiv","version":2},"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:bbf1ef63c0176392b8a82c27d1a941042270a0f3fe9407df0dc66cd1b6dc6d84","target":"record","created_at":"2026-05-18T03:37:19Z","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":"981172f1c33e6ce5aeb93a86a2c655b75c209fcbc9437d76a90d45467e924d6d","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"2004-06-29T22:48:33Z","title_canon_sha256":"9535c7c36b4d303f00ad4553348cf929d66228574044dfce1ece7d88c225959f"},"schema_version":"1.0","source":{"id":"math/0406612","kind":"arxiv","version":2}},"canonical_sha256":"05c12d7647aa7342210764458e40228f44b4ad03325c9f73cbe307f7bb4ff05d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05c12d7647aa7342210764458e40228f44b4ad03325c9f73cbe307f7bb4ff05d","first_computed_at":"2026-05-18T03:37:19.401829Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:19.401829Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X+tC+4vZmqWaeEnCcM9eCMyod9ySfYUAgWfmJPekdH+pdY4yEMtnaf0iquY0PGH13XcG9VDmQOezYH10TGZqBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:19.402343Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0406612","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bbf1ef63c0176392b8a82c27d1a941042270a0f3fe9407df0dc66cd1b6dc6d84","sha256:d6d5bf672c391b7144e63a8520af080c5fef6f456d7d7b56bb8c47a389b7dfba"],"state_sha256":"d8b9ff7de69ffc33b7bfa2c7513451a10756015c119e8cdbed3b1d95ad601c5a"}