{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:XJJ3OWXC6FQ6M34Y37LMLX5F72","short_pith_number":"pith:XJJ3OWXC","canonical_record":{"source":{"id":"1811.00088","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-31T19:52:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"615c74d1f5e047918dae9b5d35a128ec18ae0b4b665f2ba84382fcae3ebb82e6","abstract_canon_sha256":"3c482cef939d3a81c871d4d9f51536ee81cc8854f288cbe189e08fa36e094f1b"},"schema_version":"1.0"},"canonical_sha256":"ba53b75ae2f161e66f98dfd6c5dfa5fea67ff19d29cee3194834075ea3b85e37","source":{"kind":"arxiv","id":"1811.00088","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00088","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00088v2","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00088","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"XJJ3OWXC6FQ6","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_16","alias_value":"XJJ3OWXC6FQ6M34Y","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_8","alias_value":"XJJ3OWXC","created_at":"2026-07-05T01:50:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:XJJ3OWXC6FQ6M34Y37LMLX5F72","target":"record","payload":{"canonical_record":{"source":{"id":"1811.00088","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-31T19:52:14Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"615c74d1f5e047918dae9b5d35a128ec18ae0b4b665f2ba84382fcae3ebb82e6","abstract_canon_sha256":"3c482cef939d3a81c871d4d9f51536ee81cc8854f288cbe189e08fa36e094f1b"},"schema_version":"1.0"},"canonical_sha256":"ba53b75ae2f161e66f98dfd6c5dfa5fea67ff19d29cee3194834075ea3b85e37","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:50:14.419264Z","signature_b64":"Ju3cbk8u/BauqK1uFC+Vvm1mBh1FpqrvGyhjXtcxmqKNjmyla7LFImrlIhWVQWMTSI6CoR3rBakLMdcMt+bRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba53b75ae2f161e66f98dfd6c5dfa5fea67ff19d29cee3194834075ea3b85e37","last_reissued_at":"2026-07-05T01:50:14.418932Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:50:14.418932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.00088","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":"2026-07-05T01:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3IluK1HJViUdkl4gOsOuwhMRJ72jIssDcy6ImHr3H1uCwapEpZTqvgDG5vgOonH98lZV7tQFra+wszYD6DhIBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:55:37.096049Z"},"content_sha256":"e378be83f67b20d4062f86ce2b43386e01a8e30e6f8a6e897ed41370cf3b8bb3","schema_version":"1.0","event_id":"sha256:e378be83f67b20d4062f86ce2b43386e01a8e30e6f8a6e897ed41370cf3b8bb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:XJJ3OWXC6FQ6M34Y37LMLX5F72","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Applications of the moduli continuity method to log K-stable pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AG","authors_text":"Cristiano Spotti, Jesus Martinez-Garcia, Patricio Gallardo","submitted_at":"2018-10-31T19:52:14Z","abstract_excerpt":"The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of K\\\"ahler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting' to describe explicitly some compact moduli spaces of K-polystable log Fano pairs. We focus on situations when the angle of singularities is perturbed in an interval sufficiently close to one, by considering constructions arising from Geometric Invariant Theory. More precisely, we discuss the cases of pairs given by cubic surfaces with anticanonical sections"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00088","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1811.00088/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:50:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"any6WrDkgrZ0/E0qfal+fimJXLm5VKIPUiSOqVSUv9MTxvzZKfPIDeG/3uPlr3roQDf0oAjNFA4dZRdNYxQLCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T17:55:37.096650Z"},"content_sha256":"b049fb5fa9340d2e3661d6d46d899516f831164b9da5d7009df248bf87048c8a","schema_version":"1.0","event_id":"sha256:b049fb5fa9340d2e3661d6d46d899516f831164b9da5d7009df248bf87048c8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72/bundle.json","state_url":"https://pith.science/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72/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":"2026-08-04T17:55:37Z","links":{"resolver":"https://pith.science/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72","bundle":"https://pith.science/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72/bundle.json","state":"https://pith.science/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XJJ3OWXC6FQ6M34Y37LMLX5F72/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XJJ3OWXC6FQ6M34Y37LMLX5F72","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":"3c482cef939d3a81c871d4d9f51536ee81cc8854f288cbe189e08fa36e094f1b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-31T19:52:14Z","title_canon_sha256":"615c74d1f5e047918dae9b5d35a128ec18ae0b4b665f2ba84382fcae3ebb82e6"},"schema_version":"1.0","source":{"id":"1811.00088","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00088","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00088v2","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00088","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_12","alias_value":"XJJ3OWXC6FQ6","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_16","alias_value":"XJJ3OWXC6FQ6M34Y","created_at":"2026-07-05T01:50:14Z"},{"alias_kind":"pith_short_8","alias_value":"XJJ3OWXC","created_at":"2026-07-05T01:50:14Z"}],"graph_snapshots":[{"event_id":"sha256:b049fb5fa9340d2e3661d6d46d899516f831164b9da5d7009df248bf87048c8a","target":"graph","created_at":"2026-07-05T01:50:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1811.00088/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of K\\\"ahler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting' to describe explicitly some compact moduli spaces of K-polystable log Fano pairs. We focus on situations when the angle of singularities is perturbed in an interval sufficiently close to one, by considering constructions arising from Geometric Invariant Theory. More precisely, we discuss the cases of pairs given by cubic surfaces with anticanonical sections","authors_text":"Cristiano Spotti, Jesus Martinez-Garcia, Patricio Gallardo","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-31T19:52:14Z","title":"Applications of the moduli continuity method to log K-stable pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00088","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:e378be83f67b20d4062f86ce2b43386e01a8e30e6f8a6e897ed41370cf3b8bb3","target":"record","created_at":"2026-07-05T01:50:14Z","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":"3c482cef939d3a81c871d4d9f51536ee81cc8854f288cbe189e08fa36e094f1b","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-10-31T19:52:14Z","title_canon_sha256":"615c74d1f5e047918dae9b5d35a128ec18ae0b4b665f2ba84382fcae3ebb82e6"},"schema_version":"1.0","source":{"id":"1811.00088","kind":"arxiv","version":2}},"canonical_sha256":"ba53b75ae2f161e66f98dfd6c5dfa5fea67ff19d29cee3194834075ea3b85e37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba53b75ae2f161e66f98dfd6c5dfa5fea67ff19d29cee3194834075ea3b85e37","first_computed_at":"2026-07-05T01:50:14.418932Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:50:14.418932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ju3cbk8u/BauqK1uFC+Vvm1mBh1FpqrvGyhjXtcxmqKNjmyla7LFImrlIhWVQWMTSI6CoR3rBakLMdcMt+bRAA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:50:14.419264Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.00088","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e378be83f67b20d4062f86ce2b43386e01a8e30e6f8a6e897ed41370cf3b8bb3","sha256:b049fb5fa9340d2e3661d6d46d899516f831164b9da5d7009df248bf87048c8a"],"state_sha256":"64c4c3bd4b424a6a06901459c8b2fc3ac540fc87118bdd0534ea7b4b78b07aa8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P6Dxnu0ZfuwKSrUGCpUTh5K5wA5k28zJNaGVwicSG5dvG0an791xhmOk64JuEIkGLzPxkYdDupdh4kPGqv7ZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T17:55:37.104034Z","bundle_sha256":"3db5667d6c89442b0f65c078567c5cdc61179705a3e50d0364f4459454c5f7fd"}}