{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YNWPVPGF5WSUGHT2T3Z5XDXNUK","short_pith_number":"pith:YNWPVPGF","canonical_record":{"source":{"id":"1310.0705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-02T13:50:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"23a9710ba5137775be0ba733221f870ecbea8204df0dec7b0dbfba861e4694c1","abstract_canon_sha256":"3fdb241dd5feb5887307b7608c66ddf6f1b5a1ed10ce46cfe96cad4acb425eed"},"schema_version":"1.0"},"canonical_sha256":"c36cfabcc5eda5431e7a9ef3db8eeda29aeb40e30e64fdc20f949fd9ed56392d","source":{"kind":"arxiv","id":"1310.0705","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0705","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0705v2","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0705","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"YNWPVPGF5WSU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YNWPVPGF5WSUGHT2","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YNWPVPGF","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YNWPVPGF5WSUGHT2T3Z5XDXNUK","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0705","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-02T13:50:28Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"23a9710ba5137775be0ba733221f870ecbea8204df0dec7b0dbfba861e4694c1","abstract_canon_sha256":"3fdb241dd5feb5887307b7608c66ddf6f1b5a1ed10ce46cfe96cad4acb425eed"},"schema_version":"1.0"},"canonical_sha256":"c36cfabcc5eda5431e7a9ef3db8eeda29aeb40e30e64fdc20f949fd9ed56392d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:04.584345Z","signature_b64":"dd4EfeCfs03t2Caceigg9KI7DbUwUnhrKGvjlLnVmv/O8skjREqZFfF99ta2+n29XzDQu/HN6hmlW2Mf/9BTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c36cfabcc5eda5431e7a9ef3db8eeda29aeb40e30e64fdc20f949fd9ed56392d","last_reissued_at":"2026-05-18T02:46:04.583645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:04.583645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0705","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":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vrAdo33QwXwtP6ifY9E09BhlC+i72NIjaJ0vDpj98xEgBv7Tp7QDHef+jT2jWuUbiZzUMDdNFaWt3cRJsGIHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:59:10.874327Z"},"content_sha256":"2af2b52a2a33ab52197583191fe7b5a7dd662df78c497d8636706658a056d368","schema_version":"1.0","event_id":"sha256:2af2b52a2a33ab52197583191fe7b5a7dd662df78c497d8636706658a056d368"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YNWPVPGF5WSUGHT2T3Z5XDXNUK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gelfand spectra in Grothendieck toposes using geometric mathematics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CT","authors_text":"Bas Spitters (Universit\\'e Paris-Sud/INRIA Saclay), IMAPP), Sander Wolters (Radboud University Nijmegen, Steven Vickers (School of Computer Science, University of Birmingham)","submitted_at":"2013-10-02T13:50:28Z","abstract_excerpt":"In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A)  of sheaves on a locale and a commutative C*-algebra, a,  within that topos.  The Gelfand spectrum of a is a locale S in this topos, which is equivalent to a bundle over the base locale.  We further develop this external presentation of the locale S, by noting that the construction of the Gelfand spectrum in a general topos can be described using geometric logic.  As a consequence, the spectrum, seen as a bundle, is computed fibrewise.\n  As a by-produc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0705","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":"2026-05-18T02:46:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zNxUWyzF5j7yGztfETl5Wx8vnGY0/yrnvvqvaueuk6gImFnzi89H7GEW0A5TQylMYIcT9Hvoh94pJgyi5TE0Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:59:10.874675Z"},"content_sha256":"afbd86a3b547ad0baefdf780a42126a8e4d9b29f6b3564d198ffb28e11dca75e","schema_version":"1.0","event_id":"sha256:afbd86a3b547ad0baefdf780a42126a8e4d9b29f6b3564d198ffb28e11dca75e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK/bundle.json","state_url":"https://pith.science/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK/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":"2026-06-01T22:59:10Z","links":{"resolver":"https://pith.science/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK","bundle":"https://pith.science/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK/bundle.json","state":"https://pith.science/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNWPVPGF5WSUGHT2T3Z5XDXNUK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YNWPVPGF5WSUGHT2T3Z5XDXNUK","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":"3fdb241dd5feb5887307b7608c66ddf6f1b5a1ed10ce46cfe96cad4acb425eed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-02T13:50:28Z","title_canon_sha256":"23a9710ba5137775be0ba733221f870ecbea8204df0dec7b0dbfba861e4694c1"},"schema_version":"1.0","source":{"id":"1310.0705","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0705","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0705v2","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0705","created_at":"2026-05-18T02:46:04Z"},{"alias_kind":"pith_short_12","alias_value":"YNWPVPGF5WSU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YNWPVPGF5WSUGHT2","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YNWPVPGF","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:afbd86a3b547ad0baefdf780a42126a8e4d9b29f6b3564d198ffb28e11dca75e","target":"graph","created_at":"2026-05-18T02:46:04Z","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 the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A)  of sheaves on a locale and a commutative C*-algebra, a,  within that topos.  The Gelfand spectrum of a is a locale S in this topos, which is equivalent to a bundle over the base locale.  We further develop this external presentation of the locale S, by noting that the construction of the Gelfand spectrum in a general topos can be described using geometric logic.  As a consequence, the spectrum, seen as a bundle, is computed fibrewise.\n  As a by-produc","authors_text":"Bas Spitters (Universit\\'e Paris-Sud/INRIA Saclay), IMAPP), Sander Wolters (Radboud University Nijmegen, Steven Vickers (School of Computer Science, University of Birmingham)","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-02T13:50:28Z","title":"Gelfand spectra in Grothendieck toposes using geometric mathematics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0705","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":"sha256:2af2b52a2a33ab52197583191fe7b5a7dd662df78c497d8636706658a056d368","target":"record","created_at":"2026-05-18T02:46:04Z","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":"3fdb241dd5feb5887307b7608c66ddf6f1b5a1ed10ce46cfe96cad4acb425eed","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2013-10-02T13:50:28Z","title_canon_sha256":"23a9710ba5137775be0ba733221f870ecbea8204df0dec7b0dbfba861e4694c1"},"schema_version":"1.0","source":{"id":"1310.0705","kind":"arxiv","version":2}},"canonical_sha256":"c36cfabcc5eda5431e7a9ef3db8eeda29aeb40e30e64fdc20f949fd9ed56392d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c36cfabcc5eda5431e7a9ef3db8eeda29aeb40e30e64fdc20f949fd9ed56392d","first_computed_at":"2026-05-18T02:46:04.583645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:04.583645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dd4EfeCfs03t2Caceigg9KI7DbUwUnhrKGvjlLnVmv/O8skjREqZFfF99ta2+n29XzDQu/HN6hmlW2Mf/9BTAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:04.584345Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0705","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2af2b52a2a33ab52197583191fe7b5a7dd662df78c497d8636706658a056d368","sha256:afbd86a3b547ad0baefdf780a42126a8e4d9b29f6b3564d198ffb28e11dca75e"],"state_sha256":"11bcbc404252a2e0c1bf4cab89c9eaf78ec4ba8d133e8a20c6e414838bd7c85d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PStm7qYjeLHkQLXnx92OG7zkvkqeepmvj/zPIsOoyDqtwAukHFnaoZFM7OfRkxYTqe3Z1/ZQtR4yv7hD3R0cDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:59:10.876575Z","bundle_sha256":"65d7c3aea84a62a09aa8b36106ad4c5b516343f52bd5680ef35827822c3b5c98"}}