{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PKHOGQNDIB6R6YGPICZ77NJFFT","short_pith_number":"pith:PKHOGQND","canonical_record":{"source":{"id":"1305.3569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T18:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"0c766e8b587f08ecf9459aed6d0e144c7b84902485639ece0f14b7c883b1177c","abstract_canon_sha256":"35f21b719531977944eb4b2f23227b1368d1f009f13f27a64c87ca57fcab498b"},"schema_version":"1.0"},"canonical_sha256":"7a8ee341a3407d1f60cf40b3ffb5252cfe33cc8e06cbaf3b4e4808fe749dce07","source":{"kind":"arxiv","id":"1305.3569","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3569","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3569v2","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3569","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"PKHOGQNDIB6R","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PKHOGQNDIB6R6YGP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PKHOGQND","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PKHOGQNDIB6R6YGPICZ77NJFFT","target":"record","payload":{"canonical_record":{"source":{"id":"1305.3569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T18:05:29Z","cross_cats_sorted":[],"title_canon_sha256":"0c766e8b587f08ecf9459aed6d0e144c7b84902485639ece0f14b7c883b1177c","abstract_canon_sha256":"35f21b719531977944eb4b2f23227b1368d1f009f13f27a64c87ca57fcab498b"},"schema_version":"1.0"},"canonical_sha256":"7a8ee341a3407d1f60cf40b3ffb5252cfe33cc8e06cbaf3b4e4808fe749dce07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:17.519283Z","signature_b64":"fr4d1VtgysVxRWhRfTX1SRhncI6KpHI6S8bh7X+HvTWeyTse9lkkLu4r8lD44eQCHBSisewJ11PdLKhXmjN2Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a8ee341a3407d1f60cf40b3ffb5252cfe33cc8e06cbaf3b4e4808fe749dce07","last_reissued_at":"2026-05-17T23:53:17.518637Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:17.518637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.3569","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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jyg1w313yRA8DLf11EcjRoPpFerj3tX9x1qDZQHERi1BQ8MtMTny+oSRHX0nXiTN2oBFZoHOrBnfmGK98pB5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:04:06.661363Z"},"content_sha256":"c96a7501da165c8155e4d6effe9706bbeb0452d683ca3f483c7e44c538a59976","schema_version":"1.0","event_id":"sha256:c96a7501da165c8155e4d6effe9706bbeb0452d683ca3f483c7e44c538a59976"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PKHOGQNDIB6R6YGPICZ77NJFFT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Log canonical pairs with good augmented base loci","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Caucher Birkar, Zhengyu Hu","submitted_at":"2013-05-15T18:05:29Z","abstract_excerpt":"Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\\Q$-divisor, and that there is a surjective morphism $f\\colon X\\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\\sim_\\Q f^*M$ for some $\\Q$-divisor $M$, and the augmented base locus ${\\bf{B_+}}(M)$ does not contain the image of any log canonical centre of $(X,B)$. We will show that $(X,B)$ has a good log minimal model. An interesting special case is when $f$ is the identity morphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3569","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":"2026-05-17T23:53:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FkXMcZMohDI3vxFKhkJpLJ8t4aNF5mhtUGbP+P1mBcsdHDOlx0bR7n3XySPmuWK8DCcJHQutpqKvt7JdQnpYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:04:06.662055Z"},"content_sha256":"979f827a9b3d20486723b49975eca6296dc75a4075e1b726464baccecaecb997","schema_version":"1.0","event_id":"sha256:979f827a9b3d20486723b49975eca6296dc75a4075e1b726464baccecaecb997"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKHOGQNDIB6R6YGPICZ77NJFFT/bundle.json","state_url":"https://pith.science/pith/PKHOGQNDIB6R6YGPICZ77NJFFT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKHOGQNDIB6R6YGPICZ77NJFFT/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":"2026-06-07T06:04:06Z","links":{"resolver":"https://pith.science/pith/PKHOGQNDIB6R6YGPICZ77NJFFT","bundle":"https://pith.science/pith/PKHOGQNDIB6R6YGPICZ77NJFFT/bundle.json","state":"https://pith.science/pith/PKHOGQNDIB6R6YGPICZ77NJFFT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKHOGQNDIB6R6YGPICZ77NJFFT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PKHOGQNDIB6R6YGPICZ77NJFFT","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":"35f21b719531977944eb4b2f23227b1368d1f009f13f27a64c87ca57fcab498b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T18:05:29Z","title_canon_sha256":"0c766e8b587f08ecf9459aed6d0e144c7b84902485639ece0f14b7c883b1177c"},"schema_version":"1.0","source":{"id":"1305.3569","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.3569","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"arxiv_version","alias_value":"1305.3569v2","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.3569","created_at":"2026-05-17T23:53:17Z"},{"alias_kind":"pith_short_12","alias_value":"PKHOGQNDIB6R","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PKHOGQNDIB6R6YGP","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PKHOGQND","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:979f827a9b3d20486723b49975eca6296dc75a4075e1b726464baccecaecb997","target":"graph","created_at":"2026-05-17T23:53:17Z","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":"Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\\Q$-divisor, and that there is a surjective morphism $f\\colon X\\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\\sim_\\Q f^*M$ for some $\\Q$-divisor $M$, and the augmented base locus ${\\bf{B_+}}(M)$ does not contain the image of any log canonical centre of $(X,B)$. We will show that $(X,B)$ has a good log minimal model. An interesting special case is when $f$ is the identity morphism.","authors_text":"Caucher Birkar, Zhengyu Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T18:05:29Z","title":"Log canonical pairs with good augmented base loci"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3569","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:c96a7501da165c8155e4d6effe9706bbeb0452d683ca3f483c7e44c538a59976","target":"record","created_at":"2026-05-17T23:53:17Z","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":"35f21b719531977944eb4b2f23227b1368d1f009f13f27a64c87ca57fcab498b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-15T18:05:29Z","title_canon_sha256":"0c766e8b587f08ecf9459aed6d0e144c7b84902485639ece0f14b7c883b1177c"},"schema_version":"1.0","source":{"id":"1305.3569","kind":"arxiv","version":2}},"canonical_sha256":"7a8ee341a3407d1f60cf40b3ffb5252cfe33cc8e06cbaf3b4e4808fe749dce07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a8ee341a3407d1f60cf40b3ffb5252cfe33cc8e06cbaf3b4e4808fe749dce07","first_computed_at":"2026-05-17T23:53:17.518637Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:17.518637Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fr4d1VtgysVxRWhRfTX1SRhncI6KpHI6S8bh7X+HvTWeyTse9lkkLu4r8lD44eQCHBSisewJ11PdLKhXmjN2Dg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:17.519283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.3569","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c96a7501da165c8155e4d6effe9706bbeb0452d683ca3f483c7e44c538a59976","sha256:979f827a9b3d20486723b49975eca6296dc75a4075e1b726464baccecaecb997"],"state_sha256":"6e180c8725f4c0f61d7f9c28fd61a8d239a768895f338121c1628ba11aed2784"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sfjTYVUG/guCu3JIngdscXrvFOd+U2t+Sl9t5NG1wzJfX5qCHcqHaUPPhs9X2W5HlEEzKwDv2MIo3qtli0a2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:04:06.666732Z","bundle_sha256":"7c6eeb39ce09a9199db472295db36d7a904e9fcc6471e9c30309e8455774cf1d"}}