{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:B6RWNQDBCPHRE3HZFQX4QA2IJ6","short_pith_number":"pith:B6RWNQDB","schema_version":"1.0","canonical_sha256":"0fa366c06113cf126cf92c2fc803484fbe2af1026b02f2efd856ad9ed10d2f9a","source":{"kind":"arxiv","id":"2412.03203","version":1},"attestation_state":"computed","paper":{"title":"A Foundation for Synthetic Stone Duality","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Felix Cherubini, Freek Geerligs, Hugo Moeneclaey, Thierry Coquand","submitted_at":"2024-12-04T10:42:13Z","abstract_excerpt":"The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski topos. In this paper we apply such techniques to the higher topos corresponding to the light condensed sets of Dustin Clausen and Peter Scholze. This seems to be an appropriate setting to develop synthetic topology, similar to the work of Mart\\'in Escard\\'o. To reason internally about light condensed sets, we use homotopy type theory extended with 4 axioms. Our axioms are strong enough to prove Markov's principle, LL"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2412.03203","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.LO","submitted_at":"2024-12-04T10:42:13Z","cross_cats_sorted":[],"title_canon_sha256":"634bbfaa73a48fcb36663d08ba61ddfcb5e53ed818528379b062cc68cb14f0fd","abstract_canon_sha256":"eb501347e7ea1e333460a46b6ba8070d69105982fb18f872967d6978283c4517"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:44:26.367729Z","signature_b64":"viVSBZDfiCLZZST33aGFJBejYDSJTQJa8kiTzwVNGubngt9HRuVTD4S1XRZaUV8FvqZKP3Uoc/4JlFAZImKYAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0fa366c06113cf126cf92c2fc803484fbe2af1026b02f2efd856ad9ed10d2f9a","last_reissued_at":"2026-07-05T09:44:26.367218Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:44:26.367218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Foundation for Synthetic Stone Duality","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Felix Cherubini, Freek Geerligs, Hugo Moeneclaey, Thierry Coquand","submitted_at":"2024-12-04T10:42:13Z","abstract_excerpt":"The language of homotopy type theory has proved to be appropriate as an internal language for various higher toposes, for example with Synthetic Algebraic Geometry for the Zariski topos. In this paper we apply such techniques to the higher topos corresponding to the light condensed sets of Dustin Clausen and Peter Scholze. This seems to be an appropriate setting to develop synthetic topology, similar to the work of Mart\\'in Escard\\'o. To reason internally about light condensed sets, we use homotopy type theory extended with 4 axioms. Our axioms are strong enough to prove Markov's principle, LL"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.03203","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.03203/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2412.03203","created_at":"2026-07-05T09:44:26.367280+00:00"},{"alias_kind":"arxiv_version","alias_value":"2412.03203v1","created_at":"2026-07-05T09:44:26.367280+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.03203","created_at":"2026-07-05T09:44:26.367280+00:00"},{"alias_kind":"pith_short_12","alias_value":"B6RWNQDBCPHR","created_at":"2026-07-05T09:44:26.367280+00:00"},{"alias_kind":"pith_short_16","alias_value":"B6RWNQDBCPHRE3HZ","created_at":"2026-07-05T09:44:26.367280+00:00"},{"alias_kind":"pith_short_8","alias_value":"B6RWNQDB","created_at":"2026-07-05T09:44:26.367280+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.15126","citing_title":"Constructive higher sheaf models with applications to synthetic mathematics","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2605.15126","citing_title":"Constructive higher sheaf models with applications to synthetic mathematics","ref_index":10,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6","json":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6.json","graph_json":"https://pith.science/api/pith-number/B6RWNQDBCPHRE3HZFQX4QA2IJ6/graph.json","events_json":"https://pith.science/api/pith-number/B6RWNQDBCPHRE3HZFQX4QA2IJ6/events.json","paper":"https://pith.science/paper/B6RWNQDB"},"agent_actions":{"view_html":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6","download_json":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6.json","view_paper":"https://pith.science/paper/B6RWNQDB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2412.03203&json=true","fetch_graph":"https://pith.science/api/pith-number/B6RWNQDBCPHRE3HZFQX4QA2IJ6/graph.json","fetch_events":"https://pith.science/api/pith-number/B6RWNQDBCPHRE3HZFQX4QA2IJ6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6/action/storage_attestation","attest_author":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6/action/author_attestation","sign_citation":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6/action/citation_signature","submit_replication":"https://pith.science/pith/B6RWNQDBCPHRE3HZFQX4QA2IJ6/action/replication_record"}},"created_at":"2026-07-05T09:44:26.367280+00:00","updated_at":"2026-07-05T09:44:26.367280+00:00"}