{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FM6GNJIBBA2HE5LDYERSIA7CL7","short_pith_number":"pith:FM6GNJIB","canonical_record":{"source":{"id":"1409.8433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-30T08:37:01Z","cross_cats_sorted":[],"title_canon_sha256":"dcf35f1b1fbad5fae0d5159523757f6ad9c240c3e778ee6a936a5d7df53ca967","abstract_canon_sha256":"00657342a3742005d0b136f994075c86954c535c03c7bc3ab3d35816efca5bdc"},"schema_version":"1.0"},"canonical_sha256":"2b3c66a5010834727563c1232403e25fe4cbaaf9d55ef08d2ed60594b9429b90","source":{"kind":"arxiv","id":"1409.8433","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8433","created_at":"2026-05-18T02:19:43Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8433v2","created_at":"2026-05-18T02:19:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8433","created_at":"2026-05-18T02:19:43Z"},{"alias_kind":"pith_short_12","alias_value":"FM6GNJIBBA2H","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FM6GNJIBBA2HE5LD","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FM6GNJIB","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FM6GNJIBBA2HE5LDYERSIA7CL7","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-30T08:37:01Z","cross_cats_sorted":[],"title_canon_sha256":"dcf35f1b1fbad5fae0d5159523757f6ad9c240c3e778ee6a936a5d7df53ca967","abstract_canon_sha256":"00657342a3742005d0b136f994075c86954c535c03c7bc3ab3d35816efca5bdc"},"schema_version":"1.0"},"canonical_sha256":"2b3c66a5010834727563c1232403e25fe4cbaaf9d55ef08d2ed60594b9429b90","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:43.742519Z","signature_b64":"NDIb4zNGY7XEvqhWrSormd1Z+46nkFbzPWNeIGAPLF6hOtEQ1RmWl29R1CSGVaPH5CCVjI9Lh/0LI62bb8IFBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b3c66a5010834727563c1232403e25fe4cbaaf9d55ef08d2ed60594b9429b90","last_reissued_at":"2026-05-18T02:19:43.742099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:43.742099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8433","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMKl9T0ubOD6dHutD1sB59yFNEF/rp1sq0NILiFqLqQME6tMmbD5ef6ilk6ZUVeLHS/qKiu5X08bFBedyWWSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:48:05.118573Z"},"content_sha256":"1f30ed5f156502acb783c202716ffd4b515399f486111f8dc1de195c408ab102","schema_version":"1.0","event_id":"sha256:1f30ed5f156502acb783c202716ffd4b515399f486111f8dc1de195c408ab102"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FM6GNJIBBA2HE5LDYERSIA7CL7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Around the Mukai conjecture for Fano manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Kento Fujita","submitted_at":"2014-09-30T08:37:01Z","abstract_excerpt":"As a generalization of the Mukai conjecture, we conjecture that the Fano manifolds $X$ which satisfy the property $\\rho_X(r_X-1)\\geq\\dim X-1$ have very special structure, where $\\rho_X$ is the Picard number of $X$ and $r_X$ is the index of $X$. In this paper, we classify those $X$ if $\\rho_X\\leq 3$ or $\\dim X\\leq 5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8433","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NLOvnCqO9LxIPDUrNuKJfqzcNZoOjKv/Ys40ShakmM1oFhAzB+xkah/dG02NXRuDuyLGrA8OKf5dyjNlSx30Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:48:05.119197Z"},"content_sha256":"53bed2537711c2e9554382ccbb1276313c9b7f166572b021980037e8b9d4b743","schema_version":"1.0","event_id":"sha256:53bed2537711c2e9554382ccbb1276313c9b7f166572b021980037e8b9d4b743"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FM6GNJIBBA2HE5LDYERSIA7CL7/bundle.json","state_url":"https://pith.science/pith/FM6GNJIBBA2HE5LDYERSIA7CL7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FM6GNJIBBA2HE5LDYERSIA7CL7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T11:48:05Z","links":{"resolver":"https://pith.science/pith/FM6GNJIBBA2HE5LDYERSIA7CL7","bundle":"https://pith.science/pith/FM6GNJIBBA2HE5LDYERSIA7CL7/bundle.json","state":"https://pith.science/pith/FM6GNJIBBA2HE5LDYERSIA7CL7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FM6GNJIBBA2HE5LDYERSIA7CL7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FM6GNJIBBA2HE5LDYERSIA7CL7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"00657342a3742005d0b136f994075c86954c535c03c7bc3ab3d35816efca5bdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-30T08:37:01Z","title_canon_sha256":"dcf35f1b1fbad5fae0d5159523757f6ad9c240c3e778ee6a936a5d7df53ca967"},"schema_version":"1.0","source":{"id":"1409.8433","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8433","created_at":"2026-05-18T02:19:43Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8433v2","created_at":"2026-05-18T02:19:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8433","created_at":"2026-05-18T02:19:43Z"},{"alias_kind":"pith_short_12","alias_value":"FM6GNJIBBA2H","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FM6GNJIBBA2HE5LD","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FM6GNJIB","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:53bed2537711c2e9554382ccbb1276313c9b7f166572b021980037e8b9d4b743","target":"graph","created_at":"2026-05-18T02:19:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"As a generalization of the Mukai conjecture, we conjecture that the Fano manifolds $X$ which satisfy the property $\\rho_X(r_X-1)\\geq\\dim X-1$ have very special structure, where $\\rho_X$ is the Picard number of $X$ and $r_X$ is the index of $X$. In this paper, we classify those $X$ if $\\rho_X\\leq 3$ or $\\dim X\\leq 5$.","authors_text":"Kento Fujita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-30T08:37:01Z","title":"Around the Mukai conjecture for Fano manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8433","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1f30ed5f156502acb783c202716ffd4b515399f486111f8dc1de195c408ab102","target":"record","created_at":"2026-05-18T02:19:43Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"00657342a3742005d0b136f994075c86954c535c03c7bc3ab3d35816efca5bdc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-09-30T08:37:01Z","title_canon_sha256":"dcf35f1b1fbad5fae0d5159523757f6ad9c240c3e778ee6a936a5d7df53ca967"},"schema_version":"1.0","source":{"id":"1409.8433","kind":"arxiv","version":2}},"canonical_sha256":"2b3c66a5010834727563c1232403e25fe4cbaaf9d55ef08d2ed60594b9429b90","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b3c66a5010834727563c1232403e25fe4cbaaf9d55ef08d2ed60594b9429b90","first_computed_at":"2026-05-18T02:19:43.742099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:43.742099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NDIb4zNGY7XEvqhWrSormd1Z+46nkFbzPWNeIGAPLF6hOtEQ1RmWl29R1CSGVaPH5CCVjI9Lh/0LI62bb8IFBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:43.742519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8433","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f30ed5f156502acb783c202716ffd4b515399f486111f8dc1de195c408ab102","sha256:53bed2537711c2e9554382ccbb1276313c9b7f166572b021980037e8b9d4b743"],"state_sha256":"ffc43c9e5180c50d79e0214dc9c92427260e1fddd5d60c52294951bf8b6a1cd1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JxomU9p8SCf9ijjGi0JgAvFjLdv8Br5cYcDi/a5dLx6agZbpohZN7hoP473f9K/6svCqpX5UdTa0omBbYhnRAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:48:05.121525Z","bundle_sha256":"febb8b9a643ed0a6a52cf558c5da3b479f9847f61fd200ce1709a6b6058615b9"}}