{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:74OMSSO5Y4GDIMENK3ERECHEWM","short_pith_number":"pith:74OMSSO5","canonical_record":{"source":{"id":"2307.00073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-30T18:23:04Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"0d2124331e8342f822f181574d11db49aa5382ca9c4ead455879bbb6f5bfbb1e","abstract_canon_sha256":"d7ae1c54e318b244d55aa5ed803c53b988299f0bcb24fe3959936303ed240c09"},"schema_version":"1.0"},"canonical_sha256":"ff1cc949ddc70c34308d56c91208e4b33d3ecfc99015697d97c7e39f927cdb25","source":{"kind":"arxiv","id":"2307.00073","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.00073","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"2307.00073v2","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.00073","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"74OMSSO5Y4GD","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"pith_short_16","alias_value":"74OMSSO5Y4GDIMEN","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"pith_short_8","alias_value":"74OMSSO5","created_at":"2026-07-05T10:16:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:74OMSSO5Y4GDIMENK3ERECHEWM","target":"record","payload":{"canonical_record":{"source":{"id":"2307.00073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-30T18:23:04Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"0d2124331e8342f822f181574d11db49aa5382ca9c4ead455879bbb6f5bfbb1e","abstract_canon_sha256":"d7ae1c54e318b244d55aa5ed803c53b988299f0bcb24fe3959936303ed240c09"},"schema_version":"1.0"},"canonical_sha256":"ff1cc949ddc70c34308d56c91208e4b33d3ecfc99015697d97c7e39f927cdb25","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:06.154435Z","signature_b64":"iebNuZw+naRRV3NJC8rWItr3Ug5s2egKb74nTNkWgsRjKKY//1BzYSRM33Y6z1aAI7Y6qGyvjxo00NyYouG2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff1cc949ddc70c34308d56c91208e4b33d3ecfc99015697d97c7e39f927cdb25","last_reissued_at":"2026-07-05T10:16:06.153984Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:06.153984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.00073","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":"2026-07-05T10:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YflNi9WjK1KFRjoOaWALWuTsf6VaY4AynHVng2j4bICNOiIPUB6KilrlmzWsFey8lyzzFJyQoQuLbfoiqUAADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:00:13.714525Z"},"content_sha256":"aa8f2ec7d60b135137ac98f0eaf08c2256a4e463278d5814d8491d4d667b843a","schema_version":"1.0","event_id":"sha256:aa8f2ec7d60b135137ac98f0eaf08c2256a4e463278d5814d8491d4d667b843a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:74OMSSO5Y4GDIMENK3ERECHEWM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Foundation for Synthetic Algebraic Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.AG","authors_text":"Felix Cherubini, Matthias Hutzler, Thierry Coquand","submitted_at":"2023-06-30T18:23:04Z","abstract_excerpt":"This is a foundation for algebraic geometry, developed internal to the Zariski topos, building on the work of Kock and Blechschmidt. The Zariski topos consists of sheaves on the site opposite to the category of finitely presented algebras over a fixed ring, with the Zariski topology, i.e. generating covers are given by localization maps $A\\to A_{f_1}$ for finitely many elements $f_1,\\dots,f_n$ that generate the ideal $(1)=A\\subseteq A$. We use homotopy type theory together with three axioms as the internal language of a (higher) Zariski topos. One of our main contributions is the use of higher"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.00073","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2307.00073/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:16:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LP2OKBjSse8sqN7psuryJYo2VtMrbUAm3QnwUOOcLqX3m6HH48LGrajC10n15xu1Vx1yPu6i3XRPF2gky4n2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T17:00:13.715528Z"},"content_sha256":"71595391c54d4bd4f6cc2d2c0c9f1de998f9095a6bb2ee550121d4ed8054deba","schema_version":"1.0","event_id":"sha256:71595391c54d4bd4f6cc2d2c0c9f1de998f9095a6bb2ee550121d4ed8054deba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/74OMSSO5Y4GDIMENK3ERECHEWM/bundle.json","state_url":"https://pith.science/pith/74OMSSO5Y4GDIMENK3ERECHEWM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/74OMSSO5Y4GDIMENK3ERECHEWM/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":"2026-08-13T17:00:13Z","links":{"resolver":"https://pith.science/pith/74OMSSO5Y4GDIMENK3ERECHEWM","bundle":"https://pith.science/pith/74OMSSO5Y4GDIMENK3ERECHEWM/bundle.json","state":"https://pith.science/pith/74OMSSO5Y4GDIMENK3ERECHEWM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/74OMSSO5Y4GDIMENK3ERECHEWM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:74OMSSO5Y4GDIMENK3ERECHEWM","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":"d7ae1c54e318b244d55aa5ed803c53b988299f0bcb24fe3959936303ed240c09","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-30T18:23:04Z","title_canon_sha256":"0d2124331e8342f822f181574d11db49aa5382ca9c4ead455879bbb6f5bfbb1e"},"schema_version":"1.0","source":{"id":"2307.00073","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.00073","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"arxiv_version","alias_value":"2307.00073v2","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.00073","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"pith_short_12","alias_value":"74OMSSO5Y4GD","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"pith_short_16","alias_value":"74OMSSO5Y4GDIMEN","created_at":"2026-07-05T10:16:06Z"},{"alias_kind":"pith_short_8","alias_value":"74OMSSO5","created_at":"2026-07-05T10:16:06Z"}],"graph_snapshots":[{"event_id":"sha256:71595391c54d4bd4f6cc2d2c0c9f1de998f9095a6bb2ee550121d4ed8054deba","target":"graph","created_at":"2026-07-05T10:16:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2307.00073/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This is a foundation for algebraic geometry, developed internal to the Zariski topos, building on the work of Kock and Blechschmidt. The Zariski topos consists of sheaves on the site opposite to the category of finitely presented algebras over a fixed ring, with the Zariski topology, i.e. generating covers are given by localization maps $A\\to A_{f_1}$ for finitely many elements $f_1,\\dots,f_n$ that generate the ideal $(1)=A\\subseteq A$. We use homotopy type theory together with three axioms as the internal language of a (higher) Zariski topos. One of our main contributions is the use of higher","authors_text":"Felix Cherubini, Matthias Hutzler, Thierry Coquand","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-30T18:23:04Z","title":"A Foundation for Synthetic Algebraic Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.00073","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:aa8f2ec7d60b135137ac98f0eaf08c2256a4e463278d5814d8491d4d667b843a","target":"record","created_at":"2026-07-05T10:16:06Z","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":"d7ae1c54e318b244d55aa5ed803c53b988299f0bcb24fe3959936303ed240c09","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2023-06-30T18:23:04Z","title_canon_sha256":"0d2124331e8342f822f181574d11db49aa5382ca9c4ead455879bbb6f5bfbb1e"},"schema_version":"1.0","source":{"id":"2307.00073","kind":"arxiv","version":2}},"canonical_sha256":"ff1cc949ddc70c34308d56c91208e4b33d3ecfc99015697d97c7e39f927cdb25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff1cc949ddc70c34308d56c91208e4b33d3ecfc99015697d97c7e39f927cdb25","first_computed_at":"2026-07-05T10:16:06.153984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:16:06.153984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iebNuZw+naRRV3NJC8rWItr3Ug5s2egKb74nTNkWgsRjKKY//1BzYSRM33Y6z1aAI7Y6qGyvjxo00NyYouG2Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:16:06.154435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.00073","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa8f2ec7d60b135137ac98f0eaf08c2256a4e463278d5814d8491d4d667b843a","sha256:71595391c54d4bd4f6cc2d2c0c9f1de998f9095a6bb2ee550121d4ed8054deba"],"state_sha256":"94ee30f8ea5a50ed4769e8420a639c2ec808aaf7e635a9102c5a375c2e2c9fbd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NutYjYvzqhtcRKNU4oqJ3h9Wq0eBjPjrnj7jZVMvnLc/uQ9FjGuW+EaqoRgQtOfDP1D6cWg/qCs3XezUCbC0Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T17:00:13.725344Z","bundle_sha256":"267b67b669ecc1f6e1b3fb931a48cecaae14fea50f19e0c2a31a26f00f87932a"}}