{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KSAJTVSJSADMG3DL743S56GVBM","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":"0e111dfd9ba9c337ef570e8d2ef6f92ed66a21e22b3ee09afd14eb78131c46e7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-12T16:02:02Z","title_canon_sha256":"9ccc939d91e486ff527ae92edbe8194ba746887d27835ac5a865e2367dd4c8d5"},"schema_version":"1.0","source":{"id":"2408.06250","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.06250","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"arxiv_version","alias_value":"2408.06250v4","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.06250","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_12","alias_value":"KSAJTVSJSADM","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_16","alias_value":"KSAJTVSJSADMG3DL","created_at":"2026-07-05T11:22:31Z"},{"alias_kind":"pith_short_8","alias_value":"KSAJTVSJ","created_at":"2026-07-05T11:22:31Z"}],"graph_snapshots":[{"event_id":"sha256:dbaa1fcf2a2a0d176470db1a24686b60920250ff66cd9a3495a2f659cc5460ff","target":"graph","created_at":"2026-07-05T11:22:31Z","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/2408.06250/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $X$ be a smooth complex quasi-projective variety and $\\Gamma=\\pi_1(X)$. Let $\\chi \\colon \\Gamma \\to \\mathbb{R}$ be an additive character. We prove that the ray $[\\chi]$ does not belong to the BNS set $\\Sigma(\\Gamma)$ if and only if it comes as a pullback along an algebraic fibration $f \\colon X \\to \\mathcal{C}$ over a quasi-projective hyperbolic orbicurve $\\mathcal{C}$. We also prove that if $\\pi_1(X)$ admits a solvable quotient which is not virtually nilpotent, there exists a finite \\'etale cover $X_1 \\to X$ and a fibration $f \\colon X_1 \\to \\mathcal{C}$ over a quasi-projective hyperbolic","authors_text":"Vasily Rogov","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-12T16:02:02Z","title":"The Bieri-Neumann-Strebel sets of quasi-projective groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.06250","kind":"arxiv","version":4},"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":"sha256:92b9dee76d21daf3a3b0cc7cc0ef9fd28d77bbb45ee5546b719e82dd43e9eb58","target":"record","created_at":"2026-07-05T11:22:31Z","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":"0e111dfd9ba9c337ef570e8d2ef6f92ed66a21e22b3ee09afd14eb78131c46e7","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2024-08-12T16:02:02Z","title_canon_sha256":"9ccc939d91e486ff527ae92edbe8194ba746887d27835ac5a865e2367dd4c8d5"},"schema_version":"1.0","source":{"id":"2408.06250","kind":"arxiv","version":4}},"canonical_sha256":"548099d6499006c36c6bff372ef8d50b3aabdcf442ed1d3d302bd976874ea3c6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"548099d6499006c36c6bff372ef8d50b3aabdcf442ed1d3d302bd976874ea3c6","first_computed_at":"2026-07-05T11:22:31.719142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:31.719142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tw1BDxpXsVjj1PZDydo2NzlQe8fUEUTxKVfONvXQNO5CTYaHSAbtzKy6ETl/MOHNodnH79rOXquVgAQKtWZgCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:31.719789Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.06250","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92b9dee76d21daf3a3b0cc7cc0ef9fd28d77bbb45ee5546b719e82dd43e9eb58","sha256:dbaa1fcf2a2a0d176470db1a24686b60920250ff66cd9a3495a2f659cc5460ff"],"state_sha256":"e9f37754c4f4b85c250df3a2e6de848cf81991413db37ea35291082145331a6a"}