{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:XRVCCQWBXF47GCTCTM6AUKZVF6","short_pith_number":"pith:XRVCCQWB","canonical_record":{"source":{"id":"1408.2851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-12T20:58:53Z","cross_cats_sorted":[],"title_canon_sha256":"9f792d162146491ceb431abf8d8aa327108b643cda8794526310a075440b0265","abstract_canon_sha256":"9f21ebf2c30e90b1d172c4ab68acd1a71e844c31d10bc59c2535911806c5cb96"},"schema_version":"1.0"},"canonical_sha256":"bc6a2142c1b979f30a629b3c0a2b352fad8f42a5bfa83694a1a874018dcdd219","source":{"kind":"arxiv","id":"1408.2851","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2851","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2851v1","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2851","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"XRVCCQWBXF47","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XRVCCQWBXF47GCTC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XRVCCQWB","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:XRVCCQWBXF47GCTCTM6AUKZVF6","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2851","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-12T20:58:53Z","cross_cats_sorted":[],"title_canon_sha256":"9f792d162146491ceb431abf8d8aa327108b643cda8794526310a075440b0265","abstract_canon_sha256":"9f21ebf2c30e90b1d172c4ab68acd1a71e844c31d10bc59c2535911806c5cb96"},"schema_version":"1.0"},"canonical_sha256":"bc6a2142c1b979f30a629b3c0a2b352fad8f42a5bfa83694a1a874018dcdd219","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:21.139078Z","signature_b64":"x1uLreNahImTYrKgzN3gyePQSfzeWOs2ud0OJptxB2Xs7RwUegXBvAI6CrFR5vpAIAnYO9k/MndYkf3AOZc1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc6a2142c1b979f30a629b3c0a2b352fad8f42a5bfa83694a1a874018dcdd219","last_reissued_at":"2026-05-18T02:45:21.138665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:21.138665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2851","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":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qv8eajiTo2tcUH04rT+U+/ZFOzTcoZRLXoX6uFXi7OHS2qP/sXecXHAHwjs9HIpJcJ9aS8YDMIcuyFz6L0DIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:11:49.074567Z"},"content_sha256":"9e1478df8a24234b39c3476bfc75b867af9d191b185fb08182ee5f3e58425817","schema_version":"1.0","event_id":"sha256:9e1478df8a24234b39c3476bfc75b867af9d191b185fb08182ee5f3e58425817"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:XRVCCQWBXF47GCTCTM6AUKZVF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The onto mapping property of Sierpinski","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Arnold W. Miller","submitted_at":"2014-08-12T20:58:53Z","abstract_excerpt":"Define\n  (*) There exists $(\\phi_n:\\omega_1\\to \\omega_1:n<\\omega)$ such that for every uncountable $I$ which is a subset of $\\omega_1$ there exists $n$ such that $\\phi_n$ maps $I$ onto $\\omega_1$.\n  This is roughly what Sierpinski in his book on the continuum hypothesis refers to as $P_3$ but I think he brings reals number line into it. I don't know French so I cannot say for sure what he says but I think he proves that (*) follows from the continuum hypothesis. We show that the existence of a Luzin set implies (*); and (*) implies that there exists a nonmeager set of reals of size $\\omega_1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2851","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":""},"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":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flpiXMsbLt3H4a70qpnU/ORMU57FAFtdCOj389tioGuM8CVKWaj260o3IGsQ7xiodXapDTiLVNUpOhwww4CRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T08:11:49.074916Z"},"content_sha256":"777ff2a8d199d25dd476bbd7a6022bdf67d989a65a16414c6d485b92b03d452e","schema_version":"1.0","event_id":"sha256:777ff2a8d199d25dd476bbd7a6022bdf67d989a65a16414c6d485b92b03d452e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XRVCCQWBXF47GCTCTM6AUKZVF6/bundle.json","state_url":"https://pith.science/pith/XRVCCQWBXF47GCTCTM6AUKZVF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XRVCCQWBXF47GCTCTM6AUKZVF6/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":"2026-06-20T08:11:49Z","links":{"resolver":"https://pith.science/pith/XRVCCQWBXF47GCTCTM6AUKZVF6","bundle":"https://pith.science/pith/XRVCCQWBXF47GCTCTM6AUKZVF6/bundle.json","state":"https://pith.science/pith/XRVCCQWBXF47GCTCTM6AUKZVF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XRVCCQWBXF47GCTCTM6AUKZVF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XRVCCQWBXF47GCTCTM6AUKZVF6","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":"9f21ebf2c30e90b1d172c4ab68acd1a71e844c31d10bc59c2535911806c5cb96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-12T20:58:53Z","title_canon_sha256":"9f792d162146491ceb431abf8d8aa327108b643cda8794526310a075440b0265"},"schema_version":"1.0","source":{"id":"1408.2851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2851","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2851v1","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2851","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"XRVCCQWBXF47","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XRVCCQWBXF47GCTC","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XRVCCQWB","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:777ff2a8d199d25dd476bbd7a6022bdf67d989a65a16414c6d485b92b03d452e","target":"graph","created_at":"2026-05-18T02:45:21Z","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":"Define\n  (*) There exists $(\\phi_n:\\omega_1\\to \\omega_1:n<\\omega)$ such that for every uncountable $I$ which is a subset of $\\omega_1$ there exists $n$ such that $\\phi_n$ maps $I$ onto $\\omega_1$.\n  This is roughly what Sierpinski in his book on the continuum hypothesis refers to as $P_3$ but I think he brings reals number line into it. I don't know French so I cannot say for sure what he says but I think he proves that (*) follows from the continuum hypothesis. We show that the existence of a Luzin set implies (*); and (*) implies that there exists a nonmeager set of reals of size $\\omega_1$.","authors_text":"Arnold W. Miller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-12T20:58:53Z","title":"The onto mapping property of Sierpinski"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2851","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":"sha256:9e1478df8a24234b39c3476bfc75b867af9d191b185fb08182ee5f3e58425817","target":"record","created_at":"2026-05-18T02:45:21Z","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":"9f21ebf2c30e90b1d172c4ab68acd1a71e844c31d10bc59c2535911806c5cb96","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-12T20:58:53Z","title_canon_sha256":"9f792d162146491ceb431abf8d8aa327108b643cda8794526310a075440b0265"},"schema_version":"1.0","source":{"id":"1408.2851","kind":"arxiv","version":1}},"canonical_sha256":"bc6a2142c1b979f30a629b3c0a2b352fad8f42a5bfa83694a1a874018dcdd219","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc6a2142c1b979f30a629b3c0a2b352fad8f42a5bfa83694a1a874018dcdd219","first_computed_at":"2026-05-18T02:45:21.138665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:21.138665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x1uLreNahImTYrKgzN3gyePQSfzeWOs2ud0OJptxB2Xs7RwUegXBvAI6CrFR5vpAIAnYO9k/MndYkf3AOZc1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:21.139078Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e1478df8a24234b39c3476bfc75b867af9d191b185fb08182ee5f3e58425817","sha256:777ff2a8d199d25dd476bbd7a6022bdf67d989a65a16414c6d485b92b03d452e"],"state_sha256":"68110f11156298a297d6f5afcf0e5facc8f481ba03415f58dd620509458c88cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2snQygsAqvmjJaprhVmlI/6m26GQbdMZjUsEeLu5n4RJ2uWcelrHSytjWGTX8Dmw8zAk1zcZ2Gb9el4h7lszCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T08:11:49.076919Z","bundle_sha256":"8258a2f5664be0d6191eb26869cd58c914075fdc7ab725f70b14f47e44f98c98"}}