{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LVEKYQRPBHVK6OWB5BAMMXY4RP","short_pith_number":"pith:LVEKYQRP","canonical_record":{"source":{"id":"1707.00834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"1ebf94d952be93cf916370dc167376e5baf29333cf61865a1e2213c24c345548","abstract_canon_sha256":"6dc0916bde49e8eb0a1cb3423d328e9a263aed637e6edc94212b72ccf9675106"},"schema_version":"1.0"},"canonical_sha256":"5d48ac422f09eaaf3ac1e840c65f1c8bf53839e83849bdea7d65402a2a273009","source":{"kind":"arxiv","id":"1707.00834","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00834","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00834v2","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00834","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"LVEKYQRPBHVK","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LVEKYQRPBHVK6OWB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LVEKYQRP","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LVEKYQRPBHVK6OWB5BAMMXY4RP","target":"record","payload":{"canonical_record":{"source":{"id":"1707.00834","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:27:43Z","cross_cats_sorted":[],"title_canon_sha256":"1ebf94d952be93cf916370dc167376e5baf29333cf61865a1e2213c24c345548","abstract_canon_sha256":"6dc0916bde49e8eb0a1cb3423d328e9a263aed637e6edc94212b72ccf9675106"},"schema_version":"1.0"},"canonical_sha256":"5d48ac422f09eaaf3ac1e840c65f1c8bf53839e83849bdea7d65402a2a273009","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:53.649838Z","signature_b64":"T7R7/mFR+P8JWddKYQfxbJPnsMjNms9s8A/twbUTqdjTulEaVzN1dbJ6Fg1LIeza57BwRnmIPsa7ZRJ+DWI+Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d48ac422f09eaaf3ac1e840c65f1c8bf53839e83849bdea7d65402a2a273009","last_reissued_at":"2026-05-18T00:40:53.649308Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:53.649308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.00834","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RF5ocNc/fYSRkrMYDOQpjTZY1Z3H7MAcr9m+e+RsVieWAv/KFhmL21EODLTihusKCudawcHE0jviqxy5/UK+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:25:46.579513Z"},"content_sha256":"a84710dcbf1dbf1ef1acc786a158fa3eeb64799d58f59438933f347653cb93dc","schema_version":"1.0","event_id":"sha256:a84710dcbf1dbf1ef1acc786a158fa3eeb64799d58f59438933f347653cb93dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LVEKYQRPBHVK6OWB5BAMMXY4RP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The minimal model program for b-log canonical divisors and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Basil Nanayakkara, Boris Lerner, Colin Ingalls, Daniel Chan, Kelly Jabbusch, Kenneth Chan, Louis de Thanhoffer de V\\\"olcsey, Michel Van den Bergh, Rajesh Kulkarni, S\\'andor J Kov\\'acs, Shinnosuke Okawa","submitted_at":"2017-07-04T07:27:43Z","abstract_excerpt":"We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work in the setting of the b-log MMP. If we assume that the log MMP terminates, then so does the b- log MMP. Furthermore, the b-log MMP includes both the log MMP and the equivariant MMP as special cases. There are various interesting b-log varieties arising from different objects, including the Brauer pairs, or \"non-commutative algebraic varieties which are finit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00834","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":"2026-05-18T00:40:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IUF+CM8kxjrqbZG5X8fA7u+Tpto78IN9oTeSzRqEn+Tc1zy71gJHcDgOyPfbd7dUWa+pybvZKoSng5vw7VAHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:25:46.580076Z"},"content_sha256":"66c3312c9a09a848c56fd9a76518aaf6411efac499944c946820da766f1e576c","schema_version":"1.0","event_id":"sha256:66c3312c9a09a848c56fd9a76518aaf6411efac499944c946820da766f1e576c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP/bundle.json","state_url":"https://pith.science/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP/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":"2026-05-28T15:25:46Z","links":{"resolver":"https://pith.science/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP","bundle":"https://pith.science/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP/bundle.json","state":"https://pith.science/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LVEKYQRPBHVK6OWB5BAMMXY4RP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LVEKYQRPBHVK6OWB5BAMMXY4RP","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":"6dc0916bde49e8eb0a1cb3423d328e9a263aed637e6edc94212b72ccf9675106","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:27:43Z","title_canon_sha256":"1ebf94d952be93cf916370dc167376e5baf29333cf61865a1e2213c24c345548"},"schema_version":"1.0","source":{"id":"1707.00834","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.00834","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1707.00834v2","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00834","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"LVEKYQRPBHVK","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LVEKYQRPBHVK6OWB","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LVEKYQRP","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:66c3312c9a09a848c56fd9a76518aaf6411efac499944c946820da766f1e576c","target":"graph","created_at":"2026-05-18T00:40:53Z","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 discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log varieties. We show that the main theorems of the log MMP work in the setting of the b-log MMP. If we assume that the log MMP terminates, then so does the b- log MMP. Furthermore, the b-log MMP includes both the log MMP and the equivariant MMP as special cases. There are various interesting b-log varieties arising from different objects, including the Brauer pairs, or \"non-commutative algebraic varieties which are finit","authors_text":"Basil Nanayakkara, Boris Lerner, Colin Ingalls, Daniel Chan, Kelly Jabbusch, Kenneth Chan, Louis de Thanhoffer de V\\\"olcsey, Michel Van den Bergh, Rajesh Kulkarni, S\\'andor J Kov\\'acs, Shinnosuke Okawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:27:43Z","title":"The minimal model program for b-log canonical divisors and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00834","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:a84710dcbf1dbf1ef1acc786a158fa3eeb64799d58f59438933f347653cb93dc","target":"record","created_at":"2026-05-18T00:40:53Z","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":"6dc0916bde49e8eb0a1cb3423d328e9a263aed637e6edc94212b72ccf9675106","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-04T07:27:43Z","title_canon_sha256":"1ebf94d952be93cf916370dc167376e5baf29333cf61865a1e2213c24c345548"},"schema_version":"1.0","source":{"id":"1707.00834","kind":"arxiv","version":2}},"canonical_sha256":"5d48ac422f09eaaf3ac1e840c65f1c8bf53839e83849bdea7d65402a2a273009","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d48ac422f09eaaf3ac1e840c65f1c8bf53839e83849bdea7d65402a2a273009","first_computed_at":"2026-05-18T00:40:53.649308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:53.649308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T7R7/mFR+P8JWddKYQfxbJPnsMjNms9s8A/twbUTqdjTulEaVzN1dbJ6Fg1LIeza57BwRnmIPsa7ZRJ+DWI+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:53.649838Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.00834","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a84710dcbf1dbf1ef1acc786a158fa3eeb64799d58f59438933f347653cb93dc","sha256:66c3312c9a09a848c56fd9a76518aaf6411efac499944c946820da766f1e576c"],"state_sha256":"5f119686e11f4a16788ac0e511f614351f5b02a8659503197241e050dbbed2cd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2A0dvAbJqtNUKYL/Qx314Dt7OTr2vornchECCb3B7sacgtiNh/y8AG9mCcX6E4A9YAhnTJbcqzBIifmP3te2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:25:46.583476Z","bundle_sha256":"e6b58daaabd2f83b53778bf0e4a551d28ee2826d6380effc83c70cb8c4693b4a"}}