{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:7A7WM5ANHHK5QIVHG4Y7G6QBSG","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":"d6992c081b984ecb8ecdbf475e2c8f9a86fbcb6384e5b3efda09c3cf438559a0","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-01-15T00:00:00Z","title_canon_sha256":"f63248235ec3f39ed03e83bfe5d7b8782e18d8861d7fe26be53c67b6900c7dc0"},"schema_version":"1.0","source":{"id":"math/9501222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9501222","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9501222v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9501222","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"7A7WM5ANHHK5","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"7A7WM5ANHHK5QIVH","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"7A7WM5AN","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:c4856877880a265abd10478e297dd3bfea2c4a40600f9345dff4eef73b9e0cdd","target":"graph","created_at":"2026-05-18T01:05:50Z","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":"The bounded proper forcing axiom BPFA is the statement that for any family of aleph_1 many maximal antichains of a proper forcing notion, each of size aleph_1, there is a directed set meeting all these antichains.\n  A regular cardinal kappa is called {Sigma}_1-reflecting, if for any regular cardinal chi, for all formulas phi, ``H(chi) models `phi ' '' implies ``exists delta < kappa, H(delta) models `phi ' ''\n  We show that BPFA is equivalent to the statement that two nonisomorphic models of size aleph_1 cannot be made isomorphic by a proper forcing notion, and we show that the consistency stre","authors_text":"Martin Goldstern, Saharon Shelah","cross_cats":[],"headline":"","license":"","primary_cat":"math.LO","submitted_at":"1995-01-15T00:00:00Z","title":"The Bounded Proper Forcing Axiom"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9501222","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":"sha256:2bcdc8e8d77904f6900f562f336b671ca2be31b023593451ee4ebc8ffc10ccfd","target":"record","created_at":"2026-05-18T01:05:50Z","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":"d6992c081b984ecb8ecdbf475e2c8f9a86fbcb6384e5b3efda09c3cf438559a0","cross_cats_sorted":[],"license":"","primary_cat":"math.LO","submitted_at":"1995-01-15T00:00:00Z","title_canon_sha256":"f63248235ec3f39ed03e83bfe5d7b8782e18d8861d7fe26be53c67b6900c7dc0"},"schema_version":"1.0","source":{"id":"math/9501222","kind":"arxiv","version":1}},"canonical_sha256":"f83f66740d39d5d822a73731f37a0191aef049adfec715976781b5551bda97fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f83f66740d39d5d822a73731f37a0191aef049adfec715976781b5551bda97fc","first_computed_at":"2026-05-18T01:05:50.611687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.611687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gABkBeZcFnOIaxLAo5rwdviUniAUr9gcuOePkilTctR52l3xahOqbp1FKAMWdLRQhTQZc5X2kB/D25+DQyu7Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.612441Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9501222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2bcdc8e8d77904f6900f562f336b671ca2be31b023593451ee4ebc8ffc10ccfd","sha256:c4856877880a265abd10478e297dd3bfea2c4a40600f9345dff4eef73b9e0cdd"],"state_sha256":"dc6c0b5a874c1e619dbe945aa512be7a14474fe72ea7cbfb9391271e419129d1"}