{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:S2Z6SODUFGTNOX7AQ3FOF4H3HD","short_pith_number":"pith:S2Z6SODU","schema_version":"1.0","canonical_sha256":"96b3e9387429a6d75fe086cae2f0fb38e1dd65f726b7c45a6332182ebd79fe02","source":{"kind":"arxiv","id":"2310.06820","version":1},"attestation_state":"computed","paper":{"title":"Counting Calabi-Yau Threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Andreas Schachner, Jakob Moritz, Liam McAllister, Mike Stillman, Naomi Gendler, Nate MacFadden, Richard Nally","submitted_at":"2023-10-10T17:48:00Z","abstract_excerpt":"We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we prove that the number of distinct simply connected Calabi-Yau threefold hypersurfaces resulting from triangulations of four-dimensional reflexive polytopes is 4, 27, 183, 1,184 and 8,036 at $h^{1,1}$ = 1, 2, 3, 4, and 5, respectively. We also establish that there are ten equivalence classes of Wall data of non-simply connected Calabi-Yau threefolds from the Kreuzer-Skarke list. Finally, we give a provisional count o"},"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":"2310.06820","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-10-10T17:48:00Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"13eb9c1ee846f55ad9d18ba43519a013c0535475b6876f3b6b391fb19f94107c","abstract_canon_sha256":"77a7ed75d9a79a84f13c4e800882b524b676bd9a4d3ce32cb5ee4c4303e46b1f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:59:24.545076Z","signature_b64":"qhIX2R4cs0TFAmLDn90FGgnQcHTl1MDvHhcFF3dtGuQ25GNYIPPjtOqgdbfaurNbyd4Gqs8uEtf7OizrrBlxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96b3e9387429a6d75fe086cae2f0fb38e1dd65f726b7c45a6332182ebd79fe02","last_reissued_at":"2026-07-05T06:59:24.544634Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:59:24.544634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counting Calabi-Yau Threefolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"hep-th","authors_text":"Andreas Schachner, Jakob Moritz, Liam McAllister, Mike Stillman, Naomi Gendler, Nate MacFadden, Richard Nally","submitted_at":"2023-10-10T17:48:00Z","abstract_excerpt":"We enumerate topologically-inequivalent compact Calabi-Yau threefold hypersurfaces. By computing arithmetic and algebraic invariants and the Gopakumar-Vafa invariants of curves, we prove that the number of distinct simply connected Calabi-Yau threefold hypersurfaces resulting from triangulations of four-dimensional reflexive polytopes is 4, 27, 183, 1,184 and 8,036 at $h^{1,1}$ = 1, 2, 3, 4, and 5, respectively. We also establish that there are ten equivalence classes of Wall data of non-simply connected Calabi-Yau threefolds from the Kreuzer-Skarke list. Finally, we give a provisional count o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.06820","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/2310.06820/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":"2310.06820","created_at":"2026-07-05T06:59:24.544690+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.06820v1","created_at":"2026-07-05T06:59:24.544690+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.06820","created_at":"2026-07-05T06:59:24.544690+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2Z6SODUFGTN","created_at":"2026-07-05T06:59:24.544690+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2Z6SODUFGTNOX7A","created_at":"2026-07-05T06:59:24.544690+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2Z6SODU","created_at":"2026-07-05T06:59:24.544690+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.05280","citing_title":"Kaleidoscopes, Waves and the Prepotential","ref_index":27,"is_internal_anchor":false},{"citing_arxiv_id":"2605.27770","citing_title":"Sampling Triangulations and Calabi-Yau Threefolds with Autoregressive GNNs","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2605.30259","citing_title":"Late-time Quantum Vacuum Decay and its Cosmological Implications","ref_index":15,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD","json":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD.json","graph_json":"https://pith.science/api/pith-number/S2Z6SODUFGTNOX7AQ3FOF4H3HD/graph.json","events_json":"https://pith.science/api/pith-number/S2Z6SODUFGTNOX7AQ3FOF4H3HD/events.json","paper":"https://pith.science/paper/S2Z6SODU"},"agent_actions":{"view_html":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD","download_json":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD.json","view_paper":"https://pith.science/paper/S2Z6SODU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.06820&json=true","fetch_graph":"https://pith.science/api/pith-number/S2Z6SODUFGTNOX7AQ3FOF4H3HD/graph.json","fetch_events":"https://pith.science/api/pith-number/S2Z6SODUFGTNOX7AQ3FOF4H3HD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD/action/storage_attestation","attest_author":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD/action/author_attestation","sign_citation":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD/action/citation_signature","submit_replication":"https://pith.science/pith/S2Z6SODUFGTNOX7AQ3FOF4H3HD/action/replication_record"}},"created_at":"2026-07-05T06:59:24.544690+00:00","updated_at":"2026-07-05T06:59:24.544690+00:00"}