{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2RUIIYC7MLP7FQ7JWCZ2TL7LGY","short_pith_number":"pith:2RUIIYC7","canonical_record":{"source":{"id":"2405.04208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-07T11:21:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6f345775713511ad087d373b681997793bfcdc4afeaf9ff19dee83b8b23ddc5b","abstract_canon_sha256":"924e5ec7562c62b0b13e4799eef5e6f6070fa5bcca461161f34558690edeada9"},"schema_version":"1.0"},"canonical_sha256":"d46884605f62dff2c3e9b0b3a9afeb363619997112c41bef2465295dd861de1e","source":{"kind":"arxiv","id":"2405.04208","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.04208","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"2405.04208v2","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04208","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"2RUIIYC7MLP7","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"pith_short_16","alias_value":"2RUIIYC7MLP7FQ7J","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"pith_short_8","alias_value":"2RUIIYC7","created_at":"2026-07-05T11:05:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2RUIIYC7MLP7FQ7JWCZ2TL7LGY","target":"record","payload":{"canonical_record":{"source":{"id":"2405.04208","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-07T11:21:41Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"6f345775713511ad087d373b681997793bfcdc4afeaf9ff19dee83b8b23ddc5b","abstract_canon_sha256":"924e5ec7562c62b0b13e4799eef5e6f6070fa5bcca461161f34558690edeada9"},"schema_version":"1.0"},"canonical_sha256":"d46884605f62dff2c3e9b0b3a9afeb363619997112c41bef2465295dd861de1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:05:32.973567Z","signature_b64":"FW881cFNXlxPv3Z9cyqgrPq8eeQBD0vlLeCY99+VgbaMJAlYyxZ4fK6JhdANAdhkbqwIjWUzpKQitVWSWhYkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d46884605f62dff2c3e9b0b3a9afeb363619997112c41bef2465295dd861de1e","last_reissued_at":"2026-07-05T11:05:32.973026Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:05:32.973026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.04208","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":"2026-07-05T11:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TjLI/s/dDdU68RFt+5yKsVPTlgaTZPncKkygjExD+GkRTvHjdOl0lol1DtjGJ0vZli3PiQ8blX7HXdYgqwvRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T03:14:54.869336Z"},"content_sha256":"0d04c8332b149329287d89d9e1fabc68b8a755b615135ba0010681c0cb5b2d33","schema_version":"1.0","event_id":"sha256:0d04c8332b149329287d89d9e1fabc68b8a755b615135ba0010681c0cb5b2d33"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2RUIIYC7MLP7FQ7JWCZ2TL7LGY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Collapsing immortal K\\\"ahler-Ricci flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Hans-Joachim Hein, Man-Chun Lee, Valentino Tosatti","submitted_at":"2024-05-07T11:21:41Z","abstract_excerpt":"We consider the K\\\"ahler-Ricci flow on compact K\\\"ahler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the singular fibers. This follows from an asymptotic expansion for the evolving metrics, in the spirit of recent work of the first and third-named authors on collapsing Calabi-Yau metrics, and proves two conjectures of Song and Tian."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04208","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/2405.04208/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":"2026-07-05T11:05:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nHHu0aWgoMtsFpk0xzIvDVuu+9rT/It/eEFu4WJ6rxpoenv8jV2w1AIiJeRftEmoYsBz4OQRNhnwJM0DZpr/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T03:14:54.869712Z"},"content_sha256":"19cd337f759784643e16c0622bc49c60035c779d0a8f54d8e14289d8a17b1b65","schema_version":"1.0","event_id":"sha256:19cd337f759784643e16c0622bc49c60035c779d0a8f54d8e14289d8a17b1b65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY/bundle.json","state_url":"https://pith.science/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY/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":"2026-07-22T03:14:54Z","links":{"resolver":"https://pith.science/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY","bundle":"https://pith.science/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY/bundle.json","state":"https://pith.science/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2RUIIYC7MLP7FQ7JWCZ2TL7LGY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2RUIIYC7MLP7FQ7JWCZ2TL7LGY","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":"924e5ec7562c62b0b13e4799eef5e6f6070fa5bcca461161f34558690edeada9","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-07T11:21:41Z","title_canon_sha256":"6f345775713511ad087d373b681997793bfcdc4afeaf9ff19dee83b8b23ddc5b"},"schema_version":"1.0","source":{"id":"2405.04208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.04208","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"arxiv_version","alias_value":"2405.04208v2","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04208","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"pith_short_12","alias_value":"2RUIIYC7MLP7","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"pith_short_16","alias_value":"2RUIIYC7MLP7FQ7J","created_at":"2026-07-05T11:05:32Z"},{"alias_kind":"pith_short_8","alias_value":"2RUIIYC7","created_at":"2026-07-05T11:05:32Z"}],"graph_snapshots":[{"event_id":"sha256:19cd337f759784643e16c0622bc49c60035c779d0a8f54d8e14289d8a17b1b65","target":"graph","created_at":"2026-07-05T11:05:32Z","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/2405.04208/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the K\\\"ahler-Ricci flow on compact K\\\"ahler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the singular fibers. This follows from an asymptotic expansion for the evolving metrics, in the spirit of recent work of the first and third-named authors on collapsing Calabi-Yau metrics, and proves two conjectures of Song and Tian.","authors_text":"Hans-Joachim Hein, Man-Chun Lee, Valentino Tosatti","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-07T11:21:41Z","title":"Collapsing immortal K\\\"ahler-Ricci flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04208","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":"sha256:0d04c8332b149329287d89d9e1fabc68b8a755b615135ba0010681c0cb5b2d33","target":"record","created_at":"2026-07-05T11:05:32Z","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":"924e5ec7562c62b0b13e4799eef5e6f6070fa5bcca461161f34558690edeada9","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-07T11:21:41Z","title_canon_sha256":"6f345775713511ad087d373b681997793bfcdc4afeaf9ff19dee83b8b23ddc5b"},"schema_version":"1.0","source":{"id":"2405.04208","kind":"arxiv","version":2}},"canonical_sha256":"d46884605f62dff2c3e9b0b3a9afeb363619997112c41bef2465295dd861de1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d46884605f62dff2c3e9b0b3a9afeb363619997112c41bef2465295dd861de1e","first_computed_at":"2026-07-05T11:05:32.973026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:32.973026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FW881cFNXlxPv3Z9cyqgrPq8eeQBD0vlLeCY99+VgbaMJAlYyxZ4fK6JhdANAdhkbqwIjWUzpKQitVWSWhYkCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:32.973567Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.04208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d04c8332b149329287d89d9e1fabc68b8a755b615135ba0010681c0cb5b2d33","sha256:19cd337f759784643e16c0622bc49c60035c779d0a8f54d8e14289d8a17b1b65"],"state_sha256":"5474acc9132bf33245e523ea1b234fdf590f013d696995d3d0ecf944782bec89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"msfk5lKtTpkGfi88kF9yleFv/qtkU/BGojPvG2cML68Qt6QiJ1t2+8Z9vR6Efko6vNx30GhVrvP73FtezOcCDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T03:14:54.871875Z","bundle_sha256":"2f7e03564c163578f30a1a0918b26d04d6e9e799005fb01ebe6d678d8c0328dc"}}