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Let $\\mathfrak{D}$ be a collection of klt pairs $(X, \\Delta)$ satisfying the following properties: (1) $X$ is a projective $3$-fold, (2) $\\Delta$ is an $\\mathbb{R}$-divisor with coefficients in $I$, (3) $K_X+\\Delta\\equiv 0$, and (4) $-K_X$ is ample. Then the set $\\{\\mbox{vol}_X(-K_X) \\ | \\ (X, \\Delta)\\in\\mathfrak{D}\\mbox{ for some }\\Delta\\}$ is bounded from above."},"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":"1808.02102","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-08-06T20:41:56Z","cross_cats_sorted":[],"title_canon_sha256":"5a4388225577a21e8739fcb08eac04994fadc74202536a630f82bffc0807ed20","abstract_canon_sha256":"64431000483739ef117e1fb09c6534b7e24e3960f959e37b58d0d5594a8be5e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:06.461978Z","signature_b64":"/K23dIPWXvFv5Hc0ZYoh/IPuHfYPPCch+rLbsdTnxnJ+jA5CjftqlktTff4rY0Y8lthzzteOCLGOd+hXuAjdBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"122b61e5b4b833d4d5201801fecc41c0ca705838fdfcc98bb6c31fdd905ca93b","last_reissued_at":"2026-05-17T23:53:06.461448Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:06.461448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the boundedness of anti-canonical volumes of singular Fano $3$-folds in characteristic $p>5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Omprokash Das","submitted_at":"2018-08-06T20:41:56Z","abstract_excerpt":"In this article we prove the following version of the Weak-BAB conjecture for $3$-folds in char $p>5$: Fix a DCC set $I\\subset [0, 1)$ and an algebraically closed field $k$ of characteristic $p>5$. Let $\\mathfrak{D}$ be a collection of klt pairs $(X, \\Delta)$ satisfying the following properties: (1) $X$ is a projective $3$-fold, (2) $\\Delta$ is an $\\mathbb{R}$-divisor with coefficients in $I$, (3) $K_X+\\Delta\\equiv 0$, and (4) $-K_X$ is ample. Then the set $\\{\\mbox{vol}_X(-K_X) \\ | \\ (X, \\Delta)\\in\\mathfrak{D}\\mbox{ for some }\\Delta\\}$ is bounded from above."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02102","kind":"arxiv","version":4},"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":"1808.02102","created_at":"2026-05-17T23:53:06.461539+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.02102v4","created_at":"2026-05-17T23:53:06.461539+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.02102","created_at":"2026-05-17T23:53:06.461539+00:00"},{"alias_kind":"pith_short_12","alias_value":"CIVWDZNUXAZ5","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"CIVWDZNUXAZ5JVJA","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"CIVWDZNU","created_at":"2026-05-18T12:32:16.446611+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/CIVWDZNUXAZ5JVJADAA75TCBYD","json":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD.json","graph_json":"https://pith.science/api/pith-number/CIVWDZNUXAZ5JVJADAA75TCBYD/graph.json","events_json":"https://pith.science/api/pith-number/CIVWDZNUXAZ5JVJADAA75TCBYD/events.json","paper":"https://pith.science/paper/CIVWDZNU"},"agent_actions":{"view_html":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD","download_json":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD.json","view_paper":"https://pith.science/paper/CIVWDZNU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.02102&json=true","fetch_graph":"https://pith.science/api/pith-number/CIVWDZNUXAZ5JVJADAA75TCBYD/graph.json","fetch_events":"https://pith.science/api/pith-number/CIVWDZNUXAZ5JVJADAA75TCBYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD/action/storage_attestation","attest_author":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD/action/author_attestation","sign_citation":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD/action/citation_signature","submit_replication":"https://pith.science/pith/CIVWDZNUXAZ5JVJADAA75TCBYD/action/replication_record"}},"created_at":"2026-05-17T23:53:06.461539+00:00","updated_at":"2026-05-17T23:53:06.461539+00:00"}