{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5R5PI5KCY32LRTP2BFFQ2UKXVG","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":"abfb830d68d10b60efb0995ab4d6691ecf61ac5c6f1b7d515c9a5e2534ac6fd6","cross_cats_sorted":["math.CV","math.DG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-08T13:54:51Z","title_canon_sha256":"58aa69356a50358ec5014f805498197f9cfd6fa7bff71e947a8dc54cebd9e688"},"schema_version":"1.0","source":{"id":"2505.05250","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.05250","created_at":"2026-07-05T11:45:57Z"},{"alias_kind":"arxiv_version","alias_value":"2505.05250v2","created_at":"2026-07-05T11:45:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.05250","created_at":"2026-07-05T11:45:57Z"},{"alias_kind":"pith_short_12","alias_value":"5R5PI5KCY32L","created_at":"2026-07-05T11:45:57Z"},{"alias_kind":"pith_short_16","alias_value":"5R5PI5KCY32LRTP2","created_at":"2026-07-05T11:45:57Z"},{"alias_kind":"pith_short_8","alias_value":"5R5PI5KC","created_at":"2026-07-05T11:45:57Z"}],"graph_snapshots":[{"event_id":"sha256:02eda481b7d14d5ad04c9d8a58f015872f40f73fbcf4cb989f82baf8195fce4c","target":"graph","created_at":"2026-07-05T11:45:57Z","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/2505.05250/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the non-vanishing conjecture implies the abundance conjecture when $\\nu\\leq 1$. We also prove the abundance conjecture in dimension $\\leq 5$ when $\\kappa\\geq 0$ and $\\nu\\leq 1$ unconditionally.","authors_text":"Jihao Liu, Zheng Xu","cross_cats":["math.CV","math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-08T13:54:51Z","title":"Non-vanishing implies numerical dimension one abundance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.05250","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:de05b04b70d0b35690cc978390ecdb28c6ab128a74a1e6352c8611fdb51cb193","target":"record","created_at":"2026-07-05T11:45:57Z","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":"abfb830d68d10b60efb0995ab4d6691ecf61ac5c6f1b7d515c9a5e2534ac6fd6","cross_cats_sorted":["math.CV","math.DG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.AG","submitted_at":"2025-05-08T13:54:51Z","title_canon_sha256":"58aa69356a50358ec5014f805498197f9cfd6fa7bff71e947a8dc54cebd9e688"},"schema_version":"1.0","source":{"id":"2505.05250","kind":"arxiv","version":2}},"canonical_sha256":"ec7af47542c6f4b8cdfa094b0d5157a98d4eb5cc1ed6799b65f93077d6f71079","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec7af47542c6f4b8cdfa094b0d5157a98d4eb5cc1ed6799b65f93077d6f71079","first_computed_at":"2026-07-05T11:45:57.968231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:57.968231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l1fEIsHyHxP8ktcR/8G0tCq8xB2xWFHikQuAVgP7x5tR4vQwHcK+BrEPtTXn29dQtjD3+nl1hEKA8YU5kNvFCg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:57.968766Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.05250","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de05b04b70d0b35690cc978390ecdb28c6ab128a74a1e6352c8611fdb51cb193","sha256:02eda481b7d14d5ad04c9d8a58f015872f40f73fbcf4cb989f82baf8195fce4c"],"state_sha256":"91ecac969bafb3a456788abf55d3e70e8f01d38a41f6e21033452d8fd700f47a"}