{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"16390a3598444bdbf92bcfe75778d79322b16324be68e827ea68d0bcd6c29e7e","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"8c6edca7459e3c4340ef3acc3757ec590d3bc9c16b7f05f7ed9d1c69e54a0052","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"qft.string-vacua.landscape-finiteness","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"String theory offers many ways to curl up extra dimensions. Whether the number of distinct low-energy universes is finite is unknown.","posed_since":"","precise":"Determine whether the set of string compactifications to 4D with a bounded number of light fields and effective theories valid below a fixed cutoff is finite, including whether the number of topologically distinct Calabi-Yau threefolds is finite.","problem_ref":null,"references":"","settled_by":"A finiteness theorem for all compactifications below a fixed cutoff, or an infinite family of distinct consistent vacua.","status_note":"Finiteness of tadpole-bounded flux vacua on a fixed Calabi-Yau orientifold was proven with tame geometry (Bakker, Grimm, Schnell, Tsimerman 2021); finiteness of Calabi-Yau threefold topologies remains open.","title":"Is the number of string vacua finite","topic_ref":"925c6562a6d5b6dc4a9070f6df384c4141e0b53a77a35c230ef4f29c1888453c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"650fbc5425def5b9314cb4fd17a24badf28972fd510a000b2562b34f2276c5c7","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"21b30204260e99768d6724e11f226e639490214c1b832353985149e375011861","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"sLc_WVG-P8mYAOPkq9lBr_me7iR_d4Z3MFJkT80jHJa4byLRFJROR2eIEXdkg3tsCQKeeQwQhhvfcPAFtL63CQ"},"schema":"pubphys.envelope/1"},"record_hash":"650fbc5425def5b9314cb4fd17a24badf28972fd510a000b2562b34f2276c5c7","leaf_index":1959}