{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2006:YUHFUN3MAEG2AQS67RR7NWOOW7","short_pith_number":"pith:YUHFUN3M","schema_version":"1.0","canonical_sha256":"c50e5a376c010da0425efc63f6d9ceb7e4f06167c2ed6e6ba9fa6f9b1e33a302","source":{"kind":"arxiv","id":"math/0604231","version":2},"attestation_state":"computed","paper":{"title":"Convex projective structures on Gromov--Thurston manifolds","license":"","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.DG","authors_text":"Michael Kapovich","submitted_at":"2006-04-11T01:33:58Z","abstract_excerpt":"We consider Gromov-Thurston examples of negatively curved n-manifolds which do not admit metrics of constant sectional curvature. We show that for each n some of the Gromov-Thurston manifolds admit strictly convex real-projective structures."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"math/0604231","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.DG","submitted_at":"2006-04-11T01:33:58Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"02ed8cb1c9c3d47c2858336a41921b1db13035e0922a0ec495039ee4d21e7ff1","abstract_canon_sha256":"bf86739952326ecc4fcfb703955d1e604659b7cd7c5c0793312f0a531a4b1b05"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.630212Z","signature_b64":"m2N+b1yK0RyFlaq//XTi0Q4WyTCxTuhrhhYqSfGGmdDytAIgQadyx9szHK9I45WNwzwX4HoIA1YTxcsJ292ZBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c50e5a376c010da0425efc63f6d9ceb7e4f06167c2ed6e6ba9fa6f9b1e33a302","last_reissued_at":"2026-05-18T02:37:59.629877Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.629877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex projective structures on Gromov--Thurston manifolds","license":"","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.DG","authors_text":"Michael Kapovich","submitted_at":"2006-04-11T01:33:58Z","abstract_excerpt":"We consider Gromov-Thurston examples of negatively curved n-manifolds which do not admit metrics of constant sectional curvature. We show that for each n some of the Gromov-Thurston manifolds admit strictly convex real-projective structures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0604231","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"math/0604231","created_at":"2026-05-18T02:37:59.629927+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0604231v2","created_at":"2026-05-18T02:37:59.629927+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0604231","created_at":"2026-05-18T02:37:59.629927+00:00"},{"alias_kind":"pith_short_12","alias_value":"YUHFUN3MAEG2","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_16","alias_value":"YUHFUN3MAEG2AQS6","created_at":"2026-05-18T12:25:54.717736+00:00"},{"alias_kind":"pith_short_8","alias_value":"YUHFUN3M","created_at":"2026-05-18T12:25:54.717736+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7","json":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7.json","graph_json":"https://pith.science/api/pith-number/YUHFUN3MAEG2AQS67RR7NWOOW7/graph.json","events_json":"https://pith.science/api/pith-number/YUHFUN3MAEG2AQS67RR7NWOOW7/events.json","paper":"https://pith.science/paper/YUHFUN3M"},"agent_actions":{"view_html":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7","download_json":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7.json","view_paper":"https://pith.science/paper/YUHFUN3M","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0604231&json=true","fetch_graph":"https://pith.science/api/pith-number/YUHFUN3MAEG2AQS67RR7NWOOW7/graph.json","fetch_events":"https://pith.science/api/pith-number/YUHFUN3MAEG2AQS67RR7NWOOW7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7/action/storage_attestation","attest_author":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7/action/author_attestation","sign_citation":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7/action/citation_signature","submit_replication":"https://pith.science/pith/YUHFUN3MAEG2AQS67RR7NWOOW7/action/replication_record"}},"created_at":"2026-05-18T02:37:59.629927+00:00","updated_at":"2026-05-18T02:37:59.629927+00:00"}