{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:CYFLGHNL3W2BUU24IMSLYLRSIL","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":"2fa5501657bc1452d61b9a9d54ebc1450f1c92084edeea7e76a221298f660e3c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2004-09-17T22:58:13Z","title_canon_sha256":"172b2e9443182cca83f7e72bd620bbe30a5169e047783bb058acdbddc3c41951"},"schema_version":"1.0","source":{"id":"math/0409311","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409311","created_at":"2026-07-04T15:39:08Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409311v3","created_at":"2026-07-04T15:39:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409311","created_at":"2026-07-04T15:39:08Z"},{"alias_kind":"pith_short_12","alias_value":"CYFLGHNL3W2B","created_at":"2026-07-04T15:39:08Z"},{"alias_kind":"pith_short_16","alias_value":"CYFLGHNL3W2BUU24","created_at":"2026-07-04T15:39:08Z"},{"alias_kind":"pith_short_8","alias_value":"CYFLGHNL","created_at":"2026-07-04T15:39:08Z"}],"graph_snapshots":[{"event_id":"sha256:b602432da0b3bc738e7096679b191873bafc3edef643ddbc305f2742d476672c","target":"graph","created_at":"2026-07-04T15:39:08Z","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/math/0409311/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Besson-Courtois-Gallot theorem is proven for noncompact finite volume Riemannian manifolds. In particular, no bounded geometry assumptions are made. This proves the minimal entropy conjecture for nonuniform rank one lattices.","authors_text":"Peter A. Storm","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2004-09-17T22:58:13Z","title":"The minimal entropy conjecture for nonuniform rank one lattices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409311","kind":"arxiv","version":3},"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:dd727bba2cd515f3449edb04ce6155bc9db32420b36f319421336f9bcdeb8786","target":"record","created_at":"2026-07-04T15:39:08Z","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":"2fa5501657bc1452d61b9a9d54ebc1450f1c92084edeea7e76a221298f660e3c","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2004-09-17T22:58:13Z","title_canon_sha256":"172b2e9443182cca83f7e72bd620bbe30a5169e047783bb058acdbddc3c41951"},"schema_version":"1.0","source":{"id":"math/0409311","kind":"arxiv","version":3}},"canonical_sha256":"160ab31dabddb41a535c4324bc2e3242e5d7ad29275e8a55abc32aab03ecdd1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"160ab31dabddb41a535c4324bc2e3242e5d7ad29275e8a55abc32aab03ecdd1a","first_computed_at":"2026-07-04T15:39:08.156709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:39:08.156709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p4o5pCAXrMKMCbYLdB1Zb8ClPxlA1HsjJqz2QsimmUIx1Pm5A/fa6LwWiUNKSRRMgQ3COyQh0Q1Em5EyIcvqAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:39:08.157059Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0409311","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd727bba2cd515f3449edb04ce6155bc9db32420b36f319421336f9bcdeb8786","sha256:b602432da0b3bc738e7096679b191873bafc3edef643ddbc305f2742d476672c"],"state_sha256":"5fc5646006509ca6979ccd10c37ca5df7eeed8e85a90c0dfd733eddb2861e94a"}