{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CREYA5TXF5QMDJVPBZZUHPBQOL","short_pith_number":"pith:CREYA5TX","canonical_record":{"source":{"id":"1505.04412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-17T16:05:34Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4a552faae66397aa32b490ea11dcef1647b6f85890a1a978872a8d4bba9233e8","abstract_canon_sha256":"fe6920f6c9d22dfec06a53d2794984d57279dbbf2919f80bfcbaf9e3128bf211"},"schema_version":"1.0"},"canonical_sha256":"14498076772f60c1a6af0e7343bc3072df481a40bcd644f64cf11ef6871fcd18","source":{"kind":"arxiv","id":"1505.04412","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04412","created_at":"2026-05-18T01:24:24Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04412v2","created_at":"2026-05-18T01:24:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04412","created_at":"2026-05-18T01:24:24Z"},{"alias_kind":"pith_short_12","alias_value":"CREYA5TXF5QM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CREYA5TXF5QMDJVP","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CREYA5TX","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CREYA5TXF5QMDJVPBZZUHPBQOL","target":"record","payload":{"canonical_record":{"source":{"id":"1505.04412","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-17T16:05:34Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"4a552faae66397aa32b490ea11dcef1647b6f85890a1a978872a8d4bba9233e8","abstract_canon_sha256":"fe6920f6c9d22dfec06a53d2794984d57279dbbf2919f80bfcbaf9e3128bf211"},"schema_version":"1.0"},"canonical_sha256":"14498076772f60c1a6af0e7343bc3072df481a40bcd644f64cf11ef6871fcd18","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:24.856080Z","signature_b64":"iGvYS7JbZM1SfiUaM1s3hvfNN60CI7AW/BzKPu07mUNHd3Ga6AxGaTTq9NuLvKCrfgqyfeWDpw3y/wpINRnwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14498076772f60c1a6af0e7343bc3072df481a40bcd644f64cf11ef6871fcd18","last_reissued_at":"2026-05-18T01:24:24.855402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:24.855402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.04412","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zfbcWuyqpepjIc7JSzkcB+9FI/vrNWnWHMXjc6ym349MWIj9jxLHGlxW4jvyHiZnOt+WFaal/qL90U0A16drBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:49:11.977576Z"},"content_sha256":"29e732085b9deac1eeba357ab49e15fea3a4c6676b8908bcd18956430d7ea65e","schema_version":"1.0","event_id":"sha256:29e732085b9deac1eeba357ab49e15fea3a4c6676b8908bcd18956430d7ea65e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CREYA5TXF5QMDJVPBZZUHPBQOL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hyperbolization of cusps with convex boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.MG","authors_text":"Fran\\c{c}ois Fillastre, Giona Veronelli, Ivan Izmestiev","submitted_at":"2015-05-17T16:05:34Z","abstract_excerpt":"We prove that for every metric on the torus with curvature bounded from below by -1 in the sense of Alexandrov there exists a hyperbolic cusp with convex boundary such that the induced metric on the boundary is the given metric. The proof is by polyhedral approximation. This was the last open case of a general theorem: every metric with curvature bounded from below on a compact surface is isometric to a convex surface in a 3-dimensional space form."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04412","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:24:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w/Z/B/rKzCkbyvbOob9ElWwin0sQZ+m+wpuiMufimkI7TpOactoI8sqPc4yX965cYwYlSHagieGEDhP6FpqMAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T15:49:11.977920Z"},"content_sha256":"2690ea03e5db5d10d31f6890b330c858524dbcba1bb8fb08e5225147672cf332","schema_version":"1.0","event_id":"sha256:2690ea03e5db5d10d31f6890b330c858524dbcba1bb8fb08e5225147672cf332"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CREYA5TXF5QMDJVPBZZUHPBQOL/bundle.json","state_url":"https://pith.science/pith/CREYA5TXF5QMDJVPBZZUHPBQOL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CREYA5TXF5QMDJVPBZZUHPBQOL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T15:49:11Z","links":{"resolver":"https://pith.science/pith/CREYA5TXF5QMDJVPBZZUHPBQOL","bundle":"https://pith.science/pith/CREYA5TXF5QMDJVPBZZUHPBQOL/bundle.json","state":"https://pith.science/pith/CREYA5TXF5QMDJVPBZZUHPBQOL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CREYA5TXF5QMDJVPBZZUHPBQOL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CREYA5TXF5QMDJVPBZZUHPBQOL","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":"fe6920f6c9d22dfec06a53d2794984d57279dbbf2919f80bfcbaf9e3128bf211","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-17T16:05:34Z","title_canon_sha256":"4a552faae66397aa32b490ea11dcef1647b6f85890a1a978872a8d4bba9233e8"},"schema_version":"1.0","source":{"id":"1505.04412","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.04412","created_at":"2026-05-18T01:24:24Z"},{"alias_kind":"arxiv_version","alias_value":"1505.04412v2","created_at":"2026-05-18T01:24:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.04412","created_at":"2026-05-18T01:24:24Z"},{"alias_kind":"pith_short_12","alias_value":"CREYA5TXF5QM","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CREYA5TXF5QMDJVP","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CREYA5TX","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:2690ea03e5db5d10d31f6890b330c858524dbcba1bb8fb08e5225147672cf332","target":"graph","created_at":"2026-05-18T01:24:24Z","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"},"paper":{"abstract_excerpt":"We prove that for every metric on the torus with curvature bounded from below by -1 in the sense of Alexandrov there exists a hyperbolic cusp with convex boundary such that the induced metric on the boundary is the given metric. The proof is by polyhedral approximation. This was the last open case of a general theorem: every metric with curvature bounded from below on a compact surface is isometric to a convex surface in a 3-dimensional space form.","authors_text":"Fran\\c{c}ois Fillastre, Giona Veronelli, Ivan Izmestiev","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-17T16:05:34Z","title":"Hyperbolization of cusps with convex boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.04412","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":"sha256:29e732085b9deac1eeba357ab49e15fea3a4c6676b8908bcd18956430d7ea65e","target":"record","created_at":"2026-05-18T01:24:24Z","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":"fe6920f6c9d22dfec06a53d2794984d57279dbbf2919f80bfcbaf9e3128bf211","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-17T16:05:34Z","title_canon_sha256":"4a552faae66397aa32b490ea11dcef1647b6f85890a1a978872a8d4bba9233e8"},"schema_version":"1.0","source":{"id":"1505.04412","kind":"arxiv","version":2}},"canonical_sha256":"14498076772f60c1a6af0e7343bc3072df481a40bcd644f64cf11ef6871fcd18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14498076772f60c1a6af0e7343bc3072df481a40bcd644f64cf11ef6871fcd18","first_computed_at":"2026-05-18T01:24:24.855402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:24.855402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iGvYS7JbZM1SfiUaM1s3hvfNN60CI7AW/BzKPu07mUNHd3Ga6AxGaTTq9NuLvKCrfgqyfeWDpw3y/wpINRnwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:24.856080Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.04412","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29e732085b9deac1eeba357ab49e15fea3a4c6676b8908bcd18956430d7ea65e","sha256:2690ea03e5db5d10d31f6890b330c858524dbcba1bb8fb08e5225147672cf332"],"state_sha256":"91240210bec28afa90fd9c3b0b973750225d036d10d876fef0a3f110fe263dce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/wmmgcjUEsde2SOaiVQyYlzpiwKf3DjjP7febosRuA6sk2i3Ej9+EQHb6JHn26lfC73U2AcGEZcOyM14jryGBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T15:49:11.979910Z","bundle_sha256":"ec548dffd71c09a64327c8107590dd4c4f428530275499ca2893de27918bb11b"}}