{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2ETVNU3MG2QO22AFKKQ62ZQWWU","short_pith_number":"pith:2ETVNU3M","canonical_record":{"source":{"id":"1804.05302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-15T03:59:01Z","cross_cats_sorted":[],"title_canon_sha256":"a0ead92aea24833f5df483b7232e8b63133d6b883cbaa7447e77bc7e3fe3b647","abstract_canon_sha256":"043bb13dc67d0fbf7fc0a5d5f9cd6fdc26e11e00c8cc08926e53b671bbc670ab"},"schema_version":"1.0"},"canonical_sha256":"d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733","source":{"kind":"arxiv","id":"1804.05302","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05302","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05302v2","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05302","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"2ETVNU3MG2QO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2ETVNU3MG2QO22AF","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2ETVNU3M","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2ETVNU3MG2QO22AFKKQ62ZQWWU","target":"record","payload":{"canonical_record":{"source":{"id":"1804.05302","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-15T03:59:01Z","cross_cats_sorted":[],"title_canon_sha256":"a0ead92aea24833f5df483b7232e8b63133d6b883cbaa7447e77bc7e3fe3b647","abstract_canon_sha256":"043bb13dc67d0fbf7fc0a5d5f9cd6fdc26e11e00c8cc08926e53b671bbc670ab"},"schema_version":"1.0"},"canonical_sha256":"d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:55.202932Z","signature_b64":"nGiSGY2aPWGjhTghbQbSNrv84V+sdnoR/wjRKq8ZviZnF4DZONd5Dxg4Vs7VQv81wqHmcjpIS3oFc3gm21z3Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733","last_reissued_at":"2026-05-18T00:07:55.202217Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:55.202217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.05302","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":"2026-05-18T00:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gr7onksZug0aYKATxf03W0UvoAKdLb15g1PW0oItORJutyr3xkdFP4fTYsRyZQUPJnu7w8qJb7YxJys3xphkBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:23:16.791869Z"},"content_sha256":"9eb2dec4387c3c8091b1502872fe2c50aab216e1b0b79521a62baea27c9d1578","schema_version":"1.0","event_id":"sha256:9eb2dec4387c3c8091b1502872fe2c50aab216e1b0b79521a62baea27c9d1578"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2ETVNU3MG2QO22AFKKQ62ZQWWU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric Fano contractions associated to long extremal rays","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hiroshi Sato, Osamu Fujino","submitted_at":"2018-04-15T03:59:01Z","abstract_excerpt":"We show that a toric Fano contraction associated to an extremal ray whose length is greater than the dimension of its fiber is a projective space bundle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05302","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":"2026-05-18T00:07:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zbJ1ovUAvT5TbLgg085DyMx0t0HJYX77Y4IKieBpfMPazNejsWdgBVXag7s/eSj1kPRl3Rg1Ex9dHzWgjuDHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T10:23:16.792204Z"},"content_sha256":"8669a6c379a0cdf2b1804287fa73dcf98139a78612794b46d9696278a51af475","schema_version":"1.0","event_id":"sha256:8669a6c379a0cdf2b1804287fa73dcf98139a78612794b46d9696278a51af475"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU/bundle.json","state_url":"https://pith.science/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU/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":"2026-06-29T10:23:16Z","links":{"resolver":"https://pith.science/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU","bundle":"https://pith.science/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU/bundle.json","state":"https://pith.science/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ETVNU3MG2QO22AFKKQ62ZQWWU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2ETVNU3MG2QO22AFKKQ62ZQWWU","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":"043bb13dc67d0fbf7fc0a5d5f9cd6fdc26e11e00c8cc08926e53b671bbc670ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-15T03:59:01Z","title_canon_sha256":"a0ead92aea24833f5df483b7232e8b63133d6b883cbaa7447e77bc7e3fe3b647"},"schema_version":"1.0","source":{"id":"1804.05302","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.05302","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"arxiv_version","alias_value":"1804.05302v2","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.05302","created_at":"2026-05-18T00:07:55Z"},{"alias_kind":"pith_short_12","alias_value":"2ETVNU3MG2QO","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2ETVNU3MG2QO22AF","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2ETVNU3M","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:8669a6c379a0cdf2b1804287fa73dcf98139a78612794b46d9696278a51af475","target":"graph","created_at":"2026-05-18T00:07:55Z","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":"We show that a toric Fano contraction associated to an extremal ray whose length is greater than the dimension of its fiber is a projective space bundle.","authors_text":"Hiroshi Sato, Osamu Fujino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-15T03:59:01Z","title":"Toric Fano contractions associated to long extremal rays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05302","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":"sha256:9eb2dec4387c3c8091b1502872fe2c50aab216e1b0b79521a62baea27c9d1578","target":"record","created_at":"2026-05-18T00:07:55Z","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":"043bb13dc67d0fbf7fc0a5d5f9cd6fdc26e11e00c8cc08926e53b671bbc670ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-04-15T03:59:01Z","title_canon_sha256":"a0ead92aea24833f5df483b7232e8b63133d6b883cbaa7447e77bc7e3fe3b647"},"schema_version":"1.0","source":{"id":"1804.05302","kind":"arxiv","version":2}},"canonical_sha256":"d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d12756d36c36a0ed680552a1ed6616b52d001a34740b3a04f0a004012bc0a733","first_computed_at":"2026-05-18T00:07:55.202217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:55.202217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nGiSGY2aPWGjhTghbQbSNrv84V+sdnoR/wjRKq8ZviZnF4DZONd5Dxg4Vs7VQv81wqHmcjpIS3oFc3gm21z3Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:55.202932Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.05302","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9eb2dec4387c3c8091b1502872fe2c50aab216e1b0b79521a62baea27c9d1578","sha256:8669a6c379a0cdf2b1804287fa73dcf98139a78612794b46d9696278a51af475"],"state_sha256":"f941d8a0d5665c5a0a68c418f027876e05fd2f685a44062f5d8cabe568a6ae9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TBgJ8XTyOhiUbvtZo3cmOgdCTNjod5PYiArBiJGQp8mO7mXKJoZeM7T8USppDe6Ai1dqcpROBYkniYYJim7HCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T10:23:16.794217Z","bundle_sha256":"295c94ce7a6649e2154baf99f8d423f44fc863903d3f2be89928144fb56a17ac"}}