{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:3T6UPOJEVEBYLGDQVCYEFK7YC5","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":"852902dd17d30470dc5c8fb3185cb2d311566bb0461b7f612b4a90bfc6d19164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T06:01:42Z","title_canon_sha256":"4897dc7e13f016f6f2a69701c92a26ca97c06ecc472319a8ccf1b0a8d8a15b1f"},"schema_version":"1.0","source":{"id":"2605.13881","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.13881","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"arxiv_version","alias_value":"2605.13881v1","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13881","created_at":"2026-05-17T23:39:19Z"},{"alias_kind":"pith_short_12","alias_value":"3T6UPOJEVEBY","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"3T6UPOJEVEBYLGDQ","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"3T6UPOJE","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:5fafdd61bb5791b63540be2959c983d92523295e4b9ed01cc573c2dbf5d2ff98","target":"graph","created_at":"2026-05-17T23:39:19Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The set of Iitaka volumes of a given set of pairs of varieties satisfies the DCC property; this generalizes previous results of Birkar and Li about usual pairs to the real coefficient case and establishes similar results on generalised pairs under natural boundedness assumptions."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"Natural boundedness assumptions are required for technical reasons when treating generalised pairs."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The DCC property for Iitaka volumes holds for real-coefficient pairs and for generalized pairs with natural boundedness assumptions."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The set of Iitaka volumes for pairs of varieties satisfies the descending chain condition with real coefficients."}],"snapshot_sha256":"661adf676a22c632cf87fb9e7dc33c054671d5a4155b8cdd90e0e2bc7db400d6"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We investigate the DCC property of the set of Iitaka volumes of a given set of pairs of varieties. We both generalize previous results of Birkar and Li about usual pairs to the real coefficient case, and also establish similar results on generalised pairs, where some natural boundedness assumptions are required for technical reasons.","authors_text":"Pinxian Bie","cross_cats":[],"headline":"The set of Iitaka volumes for pairs of varieties satisfies the descending chain condition with real coefficients.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T06:01:42Z","title":"On the DCC Property of Iitaka Volume with Real Coefficients and Generalised Pairs"},"references":{"count":32,"internal_anchors":1,"resolved_work":32,"sample":[{"cited_arxiv_id":"math/9903060","doi":"","is_internal_anchor":true,"ref_index":1,"title":"The Adjunction Conjecture and its applications","work_id":"a47ef837-e79f-4e57-88d6-f583b6104cc0","year":1999},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Florin Ambro, The moduli b -divisor of an lc-trivial fibration , Compos. Math. 141 (2005), no. 2, 385--403","work_id":"f336f5c2-4a85-44c4-9c60-e6f0a8d0b525","year":2005},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type , J. Amer. Math. Soc. 23 (2010), no. 2, 405--468","work_id":"798fc7b3-2fb3-4a3a-b01d-35ee92ea8f77","year":2010},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"C. Birkar and C. D. Hacon, Variations of generalised pairs, arXiv:2204.10456 (2022)","work_id":"78843fb5-74c2-4041-822a-49f2eb2627b8","year":2022},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Birkar, Existence of log canonical flips and a special LMMP , Pub","work_id":"f2c8db14-2890-4b18-aeb0-a5b1bd24adfc","year":2012}],"snapshot_sha256":"db9d175ad9e2e47b15b1e7450a35410e93d6adac55c72f2c5875315e1cdffb53"},"source":{"id":"2605.13881","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-15T06:06:32.306215Z","id":"f5313054-f643-40ff-94fc-617fd666d363","model_set":{"reader":"grok-4.3"},"one_line_summary":"The DCC property for Iitaka volumes holds for real-coefficient pairs and for generalized pairs with natural boundedness assumptions.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The set of Iitaka volumes for pairs of varieties satisfies the descending chain condition with real coefficients.","strongest_claim":"The set of Iitaka volumes of a given set of pairs of varieties satisfies the DCC property; this generalizes previous results of Birkar and Li about usual pairs to the real coefficient case and establishes similar results on generalised pairs under natural boundedness assumptions.","weakest_assumption":"Natural boundedness assumptions are required for technical reasons when treating generalised pairs."}},"verdict_id":"f5313054-f643-40ff-94fc-617fd666d363"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2ed044488af73ce6632323fe87ac1ce68bbdb13160563639038f4a0687f128ea","target":"record","created_at":"2026-05-17T23:39:19Z","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":"852902dd17d30470dc5c8fb3185cb2d311566bb0461b7f612b4a90bfc6d19164","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-05-11T06:01:42Z","title_canon_sha256":"4897dc7e13f016f6f2a69701c92a26ca97c06ecc472319a8ccf1b0a8d8a15b1f"},"schema_version":"1.0","source":{"id":"2605.13881","kind":"arxiv","version":1}},"canonical_sha256":"dcfd47b924a903859870a8b042abf8174e8bf9f77a413b4a6c9ee8a0362eca01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dcfd47b924a903859870a8b042abf8174e8bf9f77a413b4a6c9ee8a0362eca01","first_computed_at":"2026-05-17T23:39:19.184375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:19.184375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gEZvUyS/GkwU99g+qiIxyuonAoUACmui7SlAYTNUjuMSPQ/Lsi6yY+qVeOM7Q4a+OBNx0q3AhCEShB+JiMeMAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:19.185113Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13881","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ed044488af73ce6632323fe87ac1ce68bbdb13160563639038f4a0687f128ea","sha256:5fafdd61bb5791b63540be2959c983d92523295e4b9ed01cc573c2dbf5d2ff98"],"state_sha256":"43c2fc6989a317329d450169681fb23931aa35d351c24bbd4070eedbb299347d"}