{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:2VAKB5BKGBSXCKZU5O72D55SA2","short_pith_number":"pith:2VAKB5BK","canonical_record":{"source":{"id":"1708.08167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-28T02:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"6387056866dfd180c351ca4e5152596cee908db7c0af2621fbbe3a2250d5df5e","abstract_canon_sha256":"3cbf6b40d90e1103da0c5bf519f24b15122c675dd70501635425c9a4aacecb41"},"schema_version":"1.0"},"canonical_sha256":"d540a0f42a3065712b34ebbfa1f7b206a30b3c16ccb504e5f50855883f06f9bb","source":{"kind":"arxiv","id":"1708.08167","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08167","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08167v2","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08167","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"2VAKB5BKGBSX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2VAKB5BKGBSXCKZU","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2VAKB5BK","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:2VAKB5BKGBSXCKZU5O72D55SA2","target":"record","payload":{"canonical_record":{"source":{"id":"1708.08167","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-28T02:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"6387056866dfd180c351ca4e5152596cee908db7c0af2621fbbe3a2250d5df5e","abstract_canon_sha256":"3cbf6b40d90e1103da0c5bf519f24b15122c675dd70501635425c9a4aacecb41"},"schema_version":"1.0"},"canonical_sha256":"d540a0f42a3065712b34ebbfa1f7b206a30b3c16ccb504e5f50855883f06f9bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:23.111298Z","signature_b64":"PkQ5IBb0Mv7LfiUouuaPtPCG2ebGH1PGrsggRXEHzrOaAZo7AQVJWThKXzltEEFOcZaMToA1zphKWED4bjrPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d540a0f42a3065712b34ebbfa1f7b206a30b3c16ccb504e5f50855883f06f9bb","last_reissued_at":"2026-05-18T00:23:23.110512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:23.110512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.08167","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z6xHJ7HdeUQd4CgteJhshaw+g6bWNaA+2tH1A64W+kbrnEFpc55i1V7epfpzULtMBRSaNn7+O1DSiXOTGepECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:38:13.288062Z"},"content_sha256":"f42a363538bb7d5f57ece15a0188d99d8036d53e3d44f5e27df67a7d55269055","schema_version":"1.0","event_id":"sha256:f42a363538bb7d5f57ece15a0188d99d8036d53e3d44f5e27df67a7d55269055"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:2VAKB5BKGBSXCKZU5O72D55SA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subcomplete forcing principles and definable well-orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Gunter Fuchs","submitted_at":"2017-08-28T02:42:56Z","abstract_excerpt":"It is shown that the boldface maximality principle for subcomplete forcing, together with the assumption that the universe has only set-many grounds, implies the existence of a (parameter-free) definable well-ordering of $\\mathcal{P}(\\omega_1)$. The same conclusion follows from the boldface maximality for subcomplete forcing, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that $x^\\#$ does not exist, for some $x\\subseteq\\omega_1$, implies the existence of a well-order of $\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08167","kind":"arxiv","version":2},"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":"2026-05-18T00:23:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TCSft3pdjptaCFIrEr4fM6+X1ryBTA06hA150MiYw3sTha+IO/VEudJAizHmc2q8QpWU+NpvpqR0yWSwD3WfDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:38:13.288456Z"},"content_sha256":"b8550a5dfd9f2b52eed0829c65c51c8e4821db3c2bcb7a29b03a21bab9c10948","schema_version":"1.0","event_id":"sha256:b8550a5dfd9f2b52eed0829c65c51c8e4821db3c2bcb7a29b03a21bab9c10948"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2VAKB5BKGBSXCKZU5O72D55SA2/bundle.json","state_url":"https://pith.science/pith/2VAKB5BKGBSXCKZU5O72D55SA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2VAKB5BKGBSXCKZU5O72D55SA2/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":"2026-05-30T12:38:13Z","links":{"resolver":"https://pith.science/pith/2VAKB5BKGBSXCKZU5O72D55SA2","bundle":"https://pith.science/pith/2VAKB5BKGBSXCKZU5O72D55SA2/bundle.json","state":"https://pith.science/pith/2VAKB5BKGBSXCKZU5O72D55SA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2VAKB5BKGBSXCKZU5O72D55SA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:2VAKB5BKGBSXCKZU5O72D55SA2","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":"3cbf6b40d90e1103da0c5bf519f24b15122c675dd70501635425c9a4aacecb41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-28T02:42:56Z","title_canon_sha256":"6387056866dfd180c351ca4e5152596cee908db7c0af2621fbbe3a2250d5df5e"},"schema_version":"1.0","source":{"id":"1708.08167","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.08167","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"arxiv_version","alias_value":"1708.08167v2","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08167","created_at":"2026-05-18T00:23:23Z"},{"alias_kind":"pith_short_12","alias_value":"2VAKB5BKGBSX","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"2VAKB5BKGBSXCKZU","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"2VAKB5BK","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:b8550a5dfd9f2b52eed0829c65c51c8e4821db3c2bcb7a29b03a21bab9c10948","target":"graph","created_at":"2026-05-18T00:23:23Z","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":"It is shown that the boldface maximality principle for subcomplete forcing, together with the assumption that the universe has only set-many grounds, implies the existence of a (parameter-free) definable well-ordering of $\\mathcal{P}(\\omega_1)$. The same conclusion follows from the boldface maximality for subcomplete forcing, assuming there is no inner model with an inaccessible limit of measurable cardinals. Similarly, the bounded subcomplete forcing axiom, together with the assumption that $x^\\#$ does not exist, for some $x\\subseteq\\omega_1$, implies the existence of a well-order of $\\mathca","authors_text":"Gunter Fuchs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-28T02:42:56Z","title":"Subcomplete forcing principles and definable well-orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08167","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:f42a363538bb7d5f57ece15a0188d99d8036d53e3d44f5e27df67a7d55269055","target":"record","created_at":"2026-05-18T00:23:23Z","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":"3cbf6b40d90e1103da0c5bf519f24b15122c675dd70501635425c9a4aacecb41","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-08-28T02:42:56Z","title_canon_sha256":"6387056866dfd180c351ca4e5152596cee908db7c0af2621fbbe3a2250d5df5e"},"schema_version":"1.0","source":{"id":"1708.08167","kind":"arxiv","version":2}},"canonical_sha256":"d540a0f42a3065712b34ebbfa1f7b206a30b3c16ccb504e5f50855883f06f9bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d540a0f42a3065712b34ebbfa1f7b206a30b3c16ccb504e5f50855883f06f9bb","first_computed_at":"2026-05-18T00:23:23.110512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:23.110512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PkQ5IBb0Mv7LfiUouuaPtPCG2ebGH1PGrsggRXEHzrOaAZo7AQVJWThKXzltEEFOcZaMToA1zphKWED4bjrPDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:23.111298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.08167","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f42a363538bb7d5f57ece15a0188d99d8036d53e3d44f5e27df67a7d55269055","sha256:b8550a5dfd9f2b52eed0829c65c51c8e4821db3c2bcb7a29b03a21bab9c10948"],"state_sha256":"d1c9cb5ea3bc293f6d0692ad90cf705bf8adce5ec0f00bb9dce2bc068ae69b40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrPl7I1FSnTiV2c1FFyab/xGjfuvx6JpLe2hasJBLXss9xgQp16xxzCIwawUibsVe/s7G0BHalYNUOW+++02DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:38:13.290992Z","bundle_sha256":"2cc8c4fff80d11e9ecdbb6722b0935000df3678775b523526b676cc34be90d28"}}