{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:65XDEUK5K6MSYN72IQZLHFU6PB","short_pith_number":"pith:65XDEUK5","canonical_record":{"source":{"id":"1107.4149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-21T03:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"eaef3050e41d97fc80b58b1ad0d80b891ad226a89bf621ee4db3b9999dcdfe79","abstract_canon_sha256":"66bac6d1db2281330f52b61223ca5f10c98837a2e3bc7ddc8b316da4bebf42dd"},"schema_version":"1.0"},"canonical_sha256":"f76e32515d57992c37fa4432b3969e7852faf065b00c9bda2e51999ba55e9f4f","source":{"kind":"arxiv","id":"1107.4149","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4149","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4149v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4149","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"65XDEUK5K6MS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"65XDEUK5K6MSYN72","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"65XDEUK5","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:65XDEUK5K6MSYN72IQZLHFU6PB","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4149","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-21T03:18:17Z","cross_cats_sorted":[],"title_canon_sha256":"eaef3050e41d97fc80b58b1ad0d80b891ad226a89bf621ee4db3b9999dcdfe79","abstract_canon_sha256":"66bac6d1db2281330f52b61223ca5f10c98837a2e3bc7ddc8b316da4bebf42dd"},"schema_version":"1.0"},"canonical_sha256":"f76e32515d57992c37fa4432b3969e7852faf065b00c9bda2e51999ba55e9f4f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:12.329973Z","signature_b64":"DsSMM3B+qH1Q3/+vQ40hzBi0KW9Lyvwrx4ySN7aEQowdumy7KFpVhjKaOG7XWs59WlVUYoBTU8a+/pbhdelwCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f76e32515d57992c37fa4432b3969e7852faf065b00c9bda2e51999ba55e9f4f","last_reissued_at":"2026-05-18T03:55:12.329549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:12.329549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4149","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":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l/5OUDwnyA91I3/iURJndp2DOpSQCetjEMC//i7z6DTcRIy0sNgfQaViwSaBgolGi4z1xSTv5J5JWlmqckXNCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:00:39.716653Z"},"content_sha256":"28f20c0e63a1ea6ab699faf37a0d787e0584f3c8c1454737188473d0b3253731","schema_version":"1.0","event_id":"sha256:28f20c0e63a1ea6ab699faf37a0d787e0584f3c8c1454737188473d0b3253731"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:65XDEUK5K6MSYN72IQZLHFU6PB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Finiteness of B-representation and Semi-log Canonical Abundance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Chenyang Xu, Christopher Hacon","submitted_at":"2011-07-21T03:18:17Z","abstract_excerpt":"We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by the abundance conjecture for log canonical pairs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4149","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":"2026-05-18T03:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/6bQIHZMH63Qj09PeCk7WTy0zfg04Khl07Ju+e1331pN6RBn4oVYxXIf7II9/xGGKhuPLFfbOalnJ1e9tbBIAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T20:00:39.717499Z"},"content_sha256":"a727af15e49c3b1c69cd81c7e87418630e84b2d063df91d7826a5ac607b81921","schema_version":"1.0","event_id":"sha256:a727af15e49c3b1c69cd81c7e87418630e84b2d063df91d7826a5ac607b81921"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/65XDEUK5K6MSYN72IQZLHFU6PB/bundle.json","state_url":"https://pith.science/pith/65XDEUK5K6MSYN72IQZLHFU6PB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/65XDEUK5K6MSYN72IQZLHFU6PB/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":"2026-06-05T20:00:39Z","links":{"resolver":"https://pith.science/pith/65XDEUK5K6MSYN72IQZLHFU6PB","bundle":"https://pith.science/pith/65XDEUK5K6MSYN72IQZLHFU6PB/bundle.json","state":"https://pith.science/pith/65XDEUK5K6MSYN72IQZLHFU6PB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/65XDEUK5K6MSYN72IQZLHFU6PB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:65XDEUK5K6MSYN72IQZLHFU6PB","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":"66bac6d1db2281330f52b61223ca5f10c98837a2e3bc7ddc8b316da4bebf42dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-21T03:18:17Z","title_canon_sha256":"eaef3050e41d97fc80b58b1ad0d80b891ad226a89bf621ee4db3b9999dcdfe79"},"schema_version":"1.0","source":{"id":"1107.4149","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4149","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4149v2","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4149","created_at":"2026-05-18T03:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"65XDEUK5K6MS","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"65XDEUK5K6MSYN72","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"65XDEUK5","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:a727af15e49c3b1c69cd81c7e87418630e84b2d063df91d7826a5ac607b81921","target":"graph","created_at":"2026-05-18T03:55:12Z","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 give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by the abundance conjecture for log canonical pairs.","authors_text":"Chenyang Xu, Christopher Hacon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-21T03:18:17Z","title":"On Finiteness of B-representation and Semi-log Canonical Abundance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4149","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":"sha256:28f20c0e63a1ea6ab699faf37a0d787e0584f3c8c1454737188473d0b3253731","target":"record","created_at":"2026-05-18T03:55:12Z","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":"66bac6d1db2281330f52b61223ca5f10c98837a2e3bc7ddc8b316da4bebf42dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-21T03:18:17Z","title_canon_sha256":"eaef3050e41d97fc80b58b1ad0d80b891ad226a89bf621ee4db3b9999dcdfe79"},"schema_version":"1.0","source":{"id":"1107.4149","kind":"arxiv","version":2}},"canonical_sha256":"f76e32515d57992c37fa4432b3969e7852faf065b00c9bda2e51999ba55e9f4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f76e32515d57992c37fa4432b3969e7852faf065b00c9bda2e51999ba55e9f4f","first_computed_at":"2026-05-18T03:55:12.329549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:12.329549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DsSMM3B+qH1Q3/+vQ40hzBi0KW9Lyvwrx4ySN7aEQowdumy7KFpVhjKaOG7XWs59WlVUYoBTU8a+/pbhdelwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:12.329973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4149","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:28f20c0e63a1ea6ab699faf37a0d787e0584f3c8c1454737188473d0b3253731","sha256:a727af15e49c3b1c69cd81c7e87418630e84b2d063df91d7826a5ac607b81921"],"state_sha256":"0abe1d62886aca5d44d6d6e56b9735110a5caf83fe36487604a5caa7e72013f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VUgvfjFR1dJZ+GFiWcjVmI9NsEAYgy4+rCN0AHMTNv5FTBcZCYidxVviM7ykcYVdT4bqdx4VJbr0ec8S/2bnBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T20:00:39.721814Z","bundle_sha256":"2b1e70a3025dcb15e7f088b48183064a7f322824b51ceafec9f96a8f57607c2b"}}