{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:P5W5LAQQPEPLGCYTJLGRQKFIRH","short_pith_number":"pith:P5W5LAQQ","canonical_record":{"source":{"id":"0910.3607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-19T16:48:55Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"6712e2f56a3cb2d95aea213cb7b158f91929d11e654b156e3ed12f0ae2f08d41","abstract_canon_sha256":"a3d334d6dad4521fe3e2515b090bce9382b513d0936395d7ce74130ab1d66289"},"schema_version":"1.0"},"canonical_sha256":"7f6dd58210791eb30b134acd1828a889f2ccdbe8ffe141125d5e3417469b2da4","source":{"kind":"arxiv","id":"0910.3607","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3607","created_at":"2026-05-18T04:23:34Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3607v2","created_at":"2026-05-18T04:23:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3607","created_at":"2026-05-18T04:23:34Z"},{"alias_kind":"pith_short_12","alias_value":"P5W5LAQQPEPL","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P5W5LAQQPEPLGCYT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P5W5LAQQ","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:P5W5LAQQPEPLGCYTJLGRQKFIRH","target":"record","payload":{"canonical_record":{"source":{"id":"0910.3607","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-19T16:48:55Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"6712e2f56a3cb2d95aea213cb7b158f91929d11e654b156e3ed12f0ae2f08d41","abstract_canon_sha256":"a3d334d6dad4521fe3e2515b090bce9382b513d0936395d7ce74130ab1d66289"},"schema_version":"1.0"},"canonical_sha256":"7f6dd58210791eb30b134acd1828a889f2ccdbe8ffe141125d5e3417469b2da4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:23:34.410114Z","signature_b64":"H6i+rSewqd48wRizSIoarPl2mO5H/a9kQfSy3VUaWpfzNiLVrATb5zoaJzwwOi/WI6ekxKUhaWpvw2WQ7pZMCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f6dd58210791eb30b134acd1828a889f2ccdbe8ffe141125d5e3417469b2da4","last_reissued_at":"2026-05-18T04:23:34.409617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:23:34.409617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.3607","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":"2026-05-18T04:23:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yTAUkV8qOfv6ZMwQ/HJu7YAy8B95Lzu3tHes7S6KJtfjwrDkzlA+lO/T1WZRHbitHukNhwDF7F9vsopc7nqhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:40:18.912407Z"},"content_sha256":"00e2f8eb486dc8b7dac556dc2302f2da089064c91588dc7cf4475b9c6f57bc97","schema_version":"1.0","event_id":"sha256:00e2f8eb486dc8b7dac556dc2302f2da089064c91588dc7cf4475b9c6f57bc97"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:P5W5LAQQPEPLGCYTJLGRQKFIRH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multigraded Factorial Rings and Fano varieties with torus action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Elaine Herppich, Hendrik S\\\"u{\\ss}, Juergen Hausen","submitted_at":"2009-10-19T16:48:55Z","abstract_excerpt":"In a first result, we describe all finitely generated factorial algebras over an algebraically closed field of characteristic zero that come with an effective multigrading of complexity one by means of generators and relations. This enables us to construct systematically varieties with free divisor class group and a complexity one torus action via their Cox rings. For the Fano varieties of this type that have a free divisor class group of rank one, we provide explicit bounds for the number of possible deformation types depending on the dimension and the index of the Picard group in the divisor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3607","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":"2026-05-18T04:23:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sjOZe1V7+Lx3pukXykDKPnlpPSlSsaaB8rni3xeM5LkueHYvq8f3dzko8/GQ9MH3pTMbTVT1SC1tm2p8aC1lDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:40:18.912825Z"},"content_sha256":"4d62d8af5c5fd15e6e7e17641e1cb7d287d605dfb9ffb06f448ab4bbed7fd3f8","schema_version":"1.0","event_id":"sha256:4d62d8af5c5fd15e6e7e17641e1cb7d287d605dfb9ffb06f448ab4bbed7fd3f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH/bundle.json","state_url":"https://pith.science/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH/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":"2026-06-23T02:40:18Z","links":{"resolver":"https://pith.science/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH","bundle":"https://pith.science/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH/bundle.json","state":"https://pith.science/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5W5LAQQPEPLGCYTJLGRQKFIRH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:P5W5LAQQPEPLGCYTJLGRQKFIRH","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":"a3d334d6dad4521fe3e2515b090bce9382b513d0936395d7ce74130ab1d66289","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-19T16:48:55Z","title_canon_sha256":"6712e2f56a3cb2d95aea213cb7b158f91929d11e654b156e3ed12f0ae2f08d41"},"schema_version":"1.0","source":{"id":"0910.3607","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.3607","created_at":"2026-05-18T04:23:34Z"},{"alias_kind":"arxiv_version","alias_value":"0910.3607v2","created_at":"2026-05-18T04:23:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.3607","created_at":"2026-05-18T04:23:34Z"},{"alias_kind":"pith_short_12","alias_value":"P5W5LAQQPEPL","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"P5W5LAQQPEPLGCYT","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"P5W5LAQQ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:4d62d8af5c5fd15e6e7e17641e1cb7d287d605dfb9ffb06f448ab4bbed7fd3f8","target":"graph","created_at":"2026-05-18T04:23:34Z","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":"In a first result, we describe all finitely generated factorial algebras over an algebraically closed field of characteristic zero that come with an effective multigrading of complexity one by means of generators and relations. This enables us to construct systematically varieties with free divisor class group and a complexity one torus action via their Cox rings. For the Fano varieties of this type that have a free divisor class group of rank one, we provide explicit bounds for the number of possible deformation types depending on the dimension and the index of the Picard group in the divisor","authors_text":"Elaine Herppich, Hendrik S\\\"u{\\ss}, Juergen Hausen","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-19T16:48:55Z","title":"Multigraded Factorial Rings and Fano varieties with torus action"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.3607","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":"sha256:00e2f8eb486dc8b7dac556dc2302f2da089064c91588dc7cf4475b9c6f57bc97","target":"record","created_at":"2026-05-18T04:23:34Z","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":"a3d334d6dad4521fe3e2515b090bce9382b513d0936395d7ce74130ab1d66289","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2009-10-19T16:48:55Z","title_canon_sha256":"6712e2f56a3cb2d95aea213cb7b158f91929d11e654b156e3ed12f0ae2f08d41"},"schema_version":"1.0","source":{"id":"0910.3607","kind":"arxiv","version":2}},"canonical_sha256":"7f6dd58210791eb30b134acd1828a889f2ccdbe8ffe141125d5e3417469b2da4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f6dd58210791eb30b134acd1828a889f2ccdbe8ffe141125d5e3417469b2da4","first_computed_at":"2026-05-18T04:23:34.409617Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:34.409617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H6i+rSewqd48wRizSIoarPl2mO5H/a9kQfSy3VUaWpfzNiLVrATb5zoaJzwwOi/WI6ekxKUhaWpvw2WQ7pZMCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:34.410114Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.3607","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00e2f8eb486dc8b7dac556dc2302f2da089064c91588dc7cf4475b9c6f57bc97","sha256:4d62d8af5c5fd15e6e7e17641e1cb7d287d605dfb9ffb06f448ab4bbed7fd3f8"],"state_sha256":"0c61a2731481a18dc602ef1a8406d472ba119982dfed662b0a9f27c45f556342"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yrLTwAHLudt5OSmNUqVs0eFSBcAzSIxgJIB9dmz9XVp12CTkplygJvoy5Mk8BGr49UzQu1Ri74SGJ2BzbUy1Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:40:18.915000Z","bundle_sha256":"4d0e617bdbfafe99df8ec8caae4a15399acf578af3ac4ca97b87a13546e81138"}}