{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2001:KKJCVMCKXFKRYK3UZFZVI75B7Q","short_pith_number":"pith:KKJCVMCK","schema_version":"1.0","canonical_sha256":"52922ab04ab9551c2b74c973547fa1fc2f1ec7e141b9bde92cdb70755e83a68a","source":{"kind":"arxiv","id":"math/0108037","version":1},"attestation_state":"computed","paper":{"title":"Examples of Type IV unprojection","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Miles Reid","submitted_at":"2001-08-06T14:05:26Z","abstract_excerpt":"I show that the weighted projective line PP(2,3) has an embedding PP(2,3) into PP(4,5,6,9) whose image Gamma is contained in a quasismooth K3 hypersurface X_24 in PP(4,5,6,9). The pair (Gamma in X_24) unprojects to the codimension 4 K3 surface Y in PP(4,5,5,6,7,8,9) with\n Basket = [1/2(1,1), 1/5(1,4), 1/5(2,3), 1/9(4,5)],\n Hilbert Numerator = 1 - t^12 - t^13 - 2t^14 - 2t^15 - 2t^16 - t^17\n  + t^19 + 2t^20 + 3t^21 + 4t^2 + 3t^23 + ..\n (this example is called Altinok4(111) in the Magma K3 database). The local coordinates at the third centre P_3 = 1/5(2,3) of Y are of weight 7 and 8 (rather than "},"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":"math/0108037","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-08-06T14:05:26Z","cross_cats_sorted":[],"title_canon_sha256":"c0683eb957eca92d96321cd3afa2e745879c540f64f7d9d87746e950dd1c94b9","abstract_canon_sha256":"7cc6358e6ac77c4de719db04df9638cf0ce5d0cf3dfee0053d8ff65ac02f2793"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:37.615769Z","signature_b64":"lw3pfW4f1DYkIRfwFnH6vio8TKCnTxKCXBItYnp8FQK9ucPvjAoUUaalSRFTdvL836lPZ34IqIGU4S/IZe6dCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52922ab04ab9551c2b74c973547fa1fc2f1ec7e141b9bde92cdb70755e83a68a","last_reissued_at":"2026-05-18T01:05:37.615166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:37.615166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Examples of Type IV unprojection","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Miles Reid","submitted_at":"2001-08-06T14:05:26Z","abstract_excerpt":"I show that the weighted projective line PP(2,3) has an embedding PP(2,3) into PP(4,5,6,9) whose image Gamma is contained in a quasismooth K3 hypersurface X_24 in PP(4,5,6,9). The pair (Gamma in X_24) unprojects to the codimension 4 K3 surface Y in PP(4,5,5,6,7,8,9) with\n Basket = [1/2(1,1), 1/5(1,4), 1/5(2,3), 1/9(4,5)],\n Hilbert Numerator = 1 - t^12 - t^13 - 2t^14 - 2t^15 - 2t^16 - t^17\n  + t^19 + 2t^20 + 3t^21 + 4t^2 + 3t^23 + ..\n (this example is called Altinok4(111) in the Magma K3 database). The local coordinates at the third centre P_3 = 1/5(2,3) of Y are of weight 7 and 8 (rather than "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0108037","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":""},"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":"math/0108037","created_at":"2026-05-18T01:05:37.615262+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0108037v1","created_at":"2026-05-18T01:05:37.615262+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0108037","created_at":"2026-05-18T01:05:37.615262+00:00"},{"alias_kind":"pith_short_12","alias_value":"KKJCVMCKXFKR","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_16","alias_value":"KKJCVMCKXFKRYK3U","created_at":"2026-05-18T12:25:50.254431+00:00"},{"alias_kind":"pith_short_8","alias_value":"KKJCVMCK","created_at":"2026-05-18T12:25:50.254431+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q","json":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q.json","graph_json":"https://pith.science/api/pith-number/KKJCVMCKXFKRYK3UZFZVI75B7Q/graph.json","events_json":"https://pith.science/api/pith-number/KKJCVMCKXFKRYK3UZFZVI75B7Q/events.json","paper":"https://pith.science/paper/KKJCVMCK"},"agent_actions":{"view_html":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q","download_json":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q.json","view_paper":"https://pith.science/paper/KKJCVMCK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0108037&json=true","fetch_graph":"https://pith.science/api/pith-number/KKJCVMCKXFKRYK3UZFZVI75B7Q/graph.json","fetch_events":"https://pith.science/api/pith-number/KKJCVMCKXFKRYK3UZFZVI75B7Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q/action/storage_attestation","attest_author":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q/action/author_attestation","sign_citation":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q/action/citation_signature","submit_replication":"https://pith.science/pith/KKJCVMCKXFKRYK3UZFZVI75B7Q/action/replication_record"}},"created_at":"2026-05-18T01:05:37.615262+00:00","updated_at":"2026-05-18T01:05:37.615262+00:00"}