{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:6XT7X5AXHPN3IP6REO5PZ3QE4P","short_pith_number":"pith:6XT7X5AX","canonical_record":{"source":{"id":"0908.0367","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-04T00:10:04Z","cross_cats_sorted":["math-ph","math.LO","math.MP"],"title_canon_sha256":"3e48a9050f8217dcbcaacb3863af9a9916a341adc0481473a9c107c614fdce4b","abstract_canon_sha256":"367ae2d578d60cf9c60c09168dc8daac928bc589d5965db66abca778252c1541"},"schema_version":"1.0"},"canonical_sha256":"f5e7fbf4173bdbb43fd123bafcee04e3c23761930d56296db33e5ece6f521663","source":{"kind":"arxiv","id":"0908.0367","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0367","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0367v3","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0367","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"6XT7X5AXHPN3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6XT7X5AXHPN3IP6R","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6XT7X5AX","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:6XT7X5AXHPN3IP6REO5PZ3QE4P","target":"record","payload":{"canonical_record":{"source":{"id":"0908.0367","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-04T00:10:04Z","cross_cats_sorted":["math-ph","math.LO","math.MP"],"title_canon_sha256":"3e48a9050f8217dcbcaacb3863af9a9916a341adc0481473a9c107c614fdce4b","abstract_canon_sha256":"367ae2d578d60cf9c60c09168dc8daac928bc589d5965db66abca778252c1541"},"schema_version":"1.0"},"canonical_sha256":"f5e7fbf4173bdbb43fd123bafcee04e3c23761930d56296db33e5ece6f521663","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.390351Z","signature_b64":"ah2GvYZRdS5lQT/Knk09yPyq+doMBo5xKqqxqbI/VNW179BWC90Zn6TnXHe5yLDLsEQgEovxmpi6IcQ5Ln9WBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5e7fbf4173bdbb43fd123bafcee04e3c23761930d56296db33e5ece6f521663","last_reissued_at":"2026-05-18T00:06:44.389999Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.389999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0908.0367","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EhfA3l+xdax6jQGrK5kf4cAZRwBCS43k/QyjYiPBSRKQn6K/pCgHoynlZ3+L2SQ9zpx9Bm2kj4h2CeOuYJJNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:46:37.879161Z"},"content_sha256":"14aa46267afd2d974c46054a4cb4cc568d9dcb4a1ac56a421ba91c3d66fe1bc9","schema_version":"1.0","event_id":"sha256:14aa46267afd2d974c46054a4cb4cc568d9dcb4a1ac56a421ba91c3d66fe1bc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:6XT7X5AXHPN3IP6REO5PZ3QE4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orthomodular-Valued Models for Quantum Set Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.LO","math.MP"],"primary_cat":"quant-ph","authors_text":"Masanao Ozawa","submitted_at":"2009-08-04T00:10:04Z","abstract_excerpt":"In 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo-Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti's model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0367","kind":"arxiv","version":3},"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":"2026-05-18T00:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLOLq8q6uWYNVv6w5uzn5dZRoQJOgxoWCClJKVi6qQud3TscYGHJePqYCJFwlJZ8nkgMYKXNMBxSnRXiwsZZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T19:46:37.880048Z"},"content_sha256":"ee406d9935b2bbdc5289d02156ab1988092ae7878f1d3a8e2fbb29384bb70b52","schema_version":"1.0","event_id":"sha256:ee406d9935b2bbdc5289d02156ab1988092ae7878f1d3a8e2fbb29384bb70b52"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P/bundle.json","state_url":"https://pith.science/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P/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":"2026-05-31T19:46:37Z","links":{"resolver":"https://pith.science/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P","bundle":"https://pith.science/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P/bundle.json","state":"https://pith.science/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6XT7X5AXHPN3IP6REO5PZ3QE4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:6XT7X5AXHPN3IP6REO5PZ3QE4P","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":"367ae2d578d60cf9c60c09168dc8daac928bc589d5965db66abca778252c1541","cross_cats_sorted":["math-ph","math.LO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-04T00:10:04Z","title_canon_sha256":"3e48a9050f8217dcbcaacb3863af9a9916a341adc0481473a9c107c614fdce4b"},"schema_version":"1.0","source":{"id":"0908.0367","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.0367","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"0908.0367v3","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.0367","created_at":"2026-05-18T00:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"6XT7X5AXHPN3","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"6XT7X5AXHPN3IP6R","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"6XT7X5AX","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:ee406d9935b2bbdc5289d02156ab1988092ae7878f1d3a8e2fbb29384bb70b52","target":"graph","created_at":"2026-05-18T00:06:44Z","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 1981, Takeuti introduced quantum set theory by constructing a model of set theory based on quantum logic represented by the lattice of closed linear subspaces of a Hilbert space in a manner analogous to Boolean-valued models of set theory, and showed that appropriate counterparts of the axioms of Zermelo-Fraenkel set theory with the axiom of choice (ZFC) hold in the model. In this paper, we aim at unifying Takeuti's model with Boolean-valued models by constructing models based on general complete orthomodular lattices, and generalizing the transfer principle in Boolean-valued models, which ","authors_text":"Masanao Ozawa","cross_cats":["math-ph","math.LO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-04T00:10:04Z","title":"Orthomodular-Valued Models for Quantum Set Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.0367","kind":"arxiv","version":3},"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":"sha256:14aa46267afd2d974c46054a4cb4cc568d9dcb4a1ac56a421ba91c3d66fe1bc9","target":"record","created_at":"2026-05-18T00:06:44Z","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":"367ae2d578d60cf9c60c09168dc8daac928bc589d5965db66abca778252c1541","cross_cats_sorted":["math-ph","math.LO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2009-08-04T00:10:04Z","title_canon_sha256":"3e48a9050f8217dcbcaacb3863af9a9916a341adc0481473a9c107c614fdce4b"},"schema_version":"1.0","source":{"id":"0908.0367","kind":"arxiv","version":3}},"canonical_sha256":"f5e7fbf4173bdbb43fd123bafcee04e3c23761930d56296db33e5ece6f521663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f5e7fbf4173bdbb43fd123bafcee04e3c23761930d56296db33e5ece6f521663","first_computed_at":"2026-05-18T00:06:44.389999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:44.389999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ah2GvYZRdS5lQT/Knk09yPyq+doMBo5xKqqxqbI/VNW179BWC90Zn6TnXHe5yLDLsEQgEovxmpi6IcQ5Ln9WBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:44.390351Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.0367","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14aa46267afd2d974c46054a4cb4cc568d9dcb4a1ac56a421ba91c3d66fe1bc9","sha256:ee406d9935b2bbdc5289d02156ab1988092ae7878f1d3a8e2fbb29384bb70b52"],"state_sha256":"419f711fbb8421d90752cb99a4e8b85ee784a362d8cee44d5a155f8de2e09e17"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F8RK2MqTEMEzPHDshK1KrMHSpYtR8SdBZu8ho12FZ8QMQ65894OYK+QmNCsf47gprQ3qPkiKJW4ISUy4E4kWDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T19:46:37.884724Z","bundle_sha256":"94c728130b83479bf10de0cb2e36ee4f66f0dd7e2d90f21721e816e34f09d1a9"}}