{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:GCDTWHLIGJSURTE47Q3ULNKWEN","short_pith_number":"pith:GCDTWHLI","canonical_record":{"source":{"id":"2603.21189","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-03-22T12:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"ef9f397071098183ca88a02aa77cfff59826879dd19fa50d3e43fdc0712a3002","abstract_canon_sha256":"a041f42a4035c10dc713f78cf6d218f82cce6bd8a9c855acb1944c6c1cac1d5e"},"schema_version":"1.0"},"canonical_sha256":"30873b1d68326548cc9cfc3745b556236fc16d4a0931f27b269360a683b98873","source":{"kind":"arxiv","id":"2603.21189","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.21189","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"2603.21189v2","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.21189","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"GCDTWHLIGJSU","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"pith_short_16","alias_value":"GCDTWHLIGJSURTE4","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"pith_short_8","alias_value":"GCDTWHLI","created_at":"2026-05-20T00:03:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:GCDTWHLIGJSURTE47Q3ULNKWEN","target":"record","payload":{"canonical_record":{"source":{"id":"2603.21189","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-03-22T12:22:39Z","cross_cats_sorted":[],"title_canon_sha256":"ef9f397071098183ca88a02aa77cfff59826879dd19fa50d3e43fdc0712a3002","abstract_canon_sha256":"a041f42a4035c10dc713f78cf6d218f82cce6bd8a9c855acb1944c6c1cac1d5e"},"schema_version":"1.0"},"canonical_sha256":"30873b1d68326548cc9cfc3745b556236fc16d4a0931f27b269360a683b98873","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T00:03:08.997128Z","signature_b64":"MR+OqOcDXVJnorAcBESzGn+0PGN5QqHWxfTOVZnOKhe8+V9wcfQXbrDthadFxOKw6UKGfKeEK3dthx9i0E0GBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30873b1d68326548cc9cfc3745b556236fc16d4a0931f27b269360a683b98873","last_reissued_at":"2026-05-20T00:03:08.996275Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T00:03:08.996275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2603.21189","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":"2026-05-20T00:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1DIKeDE547wXEPlIZvhPKfnJaJW/5rBsFKgd2CDDh7nEBJ4FQvpL/X2khqzc2bkh87Hnf3fnepM6cnKcW4r/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:34:53.384131Z"},"content_sha256":"ec01fd28a4abbf65600907ddf58e0d0e88a83ad722574b0ef0546214ddbe45d4","schema_version":"1.0","event_id":"sha256:ec01fd28a4abbf65600907ddf58e0d0e88a83ad722574b0ef0546214ddbe45d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:GCDTWHLIGJSURTE47Q3ULNKWEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangulating surfaces quasi-isometrically","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Agelos Georgakopoulos, Federico Vigolo","submitted_at":"2026-03-22T12:22:39Z","abstract_excerpt":"We prove that if a complete Riemannian surface $(\\Sigma,d_\\Sigma)$ is quasi-isometric to some bounded degree graph $G$, then $\\Sigma$ admits a triangulation whose 1-skeleton is quasi-isometric to it when equipped with the simplicial metric. We study several variants of the problem, and identify the right condition making it an if and only if statement."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21189","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2603.21189/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-20T00:03:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xrTRBohAnKlnkuKt/K24ebJLxEZgbac+l8QZYVHjKleCc2u/nXFJOBD0sp8K4Wh2kZO9ylg7xuJ/HPf68YaSBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:34:53.384885Z"},"content_sha256":"1601dee37cc3c017f85f3576ae95e5e7bd1aca22328f50de56e8992f5948338f","schema_version":"1.0","event_id":"sha256:1601dee37cc3c017f85f3576ae95e5e7bd1aca22328f50de56e8992f5948338f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCDTWHLIGJSURTE47Q3ULNKWEN/bundle.json","state_url":"https://pith.science/pith/GCDTWHLIGJSURTE47Q3ULNKWEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCDTWHLIGJSURTE47Q3ULNKWEN/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":"2026-05-27T16:34:53Z","links":{"resolver":"https://pith.science/pith/GCDTWHLIGJSURTE47Q3ULNKWEN","bundle":"https://pith.science/pith/GCDTWHLIGJSURTE47Q3ULNKWEN/bundle.json","state":"https://pith.science/pith/GCDTWHLIGJSURTE47Q3ULNKWEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCDTWHLIGJSURTE47Q3ULNKWEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:GCDTWHLIGJSURTE47Q3ULNKWEN","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":"a041f42a4035c10dc713f78cf6d218f82cce6bd8a9c855acb1944c6c1cac1d5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-03-22T12:22:39Z","title_canon_sha256":"ef9f397071098183ca88a02aa77cfff59826879dd19fa50d3e43fdc0712a3002"},"schema_version":"1.0","source":{"id":"2603.21189","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.21189","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"arxiv_version","alias_value":"2603.21189v2","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.21189","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"pith_short_12","alias_value":"GCDTWHLIGJSU","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"pith_short_16","alias_value":"GCDTWHLIGJSURTE4","created_at":"2026-05-20T00:03:08Z"},{"alias_kind":"pith_short_8","alias_value":"GCDTWHLI","created_at":"2026-05-20T00:03:08Z"}],"graph_snapshots":[{"event_id":"sha256:1601dee37cc3c017f85f3576ae95e5e7bd1aca22328f50de56e8992f5948338f","target":"graph","created_at":"2026-05-20T00:03:08Z","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/2603.21189/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that if a complete Riemannian surface $(\\Sigma,d_\\Sigma)$ is quasi-isometric to some bounded degree graph $G$, then $\\Sigma$ admits a triangulation whose 1-skeleton is quasi-isometric to it when equipped with the simplicial metric. We study several variants of the problem, and identify the right condition making it an if and only if statement.","authors_text":"Agelos Georgakopoulos, Federico Vigolo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-03-22T12:22:39Z","title":"Triangulating surfaces quasi-isometrically"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21189","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:ec01fd28a4abbf65600907ddf58e0d0e88a83ad722574b0ef0546214ddbe45d4","target":"record","created_at":"2026-05-20T00:03:08Z","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":"a041f42a4035c10dc713f78cf6d218f82cce6bd8a9c855acb1944c6c1cac1d5e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2026-03-22T12:22:39Z","title_canon_sha256":"ef9f397071098183ca88a02aa77cfff59826879dd19fa50d3e43fdc0712a3002"},"schema_version":"1.0","source":{"id":"2603.21189","kind":"arxiv","version":2}},"canonical_sha256":"30873b1d68326548cc9cfc3745b556236fc16d4a0931f27b269360a683b98873","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30873b1d68326548cc9cfc3745b556236fc16d4a0931f27b269360a683b98873","first_computed_at":"2026-05-20T00:03:08.996275Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:08.996275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MR+OqOcDXVJnorAcBESzGn+0PGN5QqHWxfTOVZnOKhe8+V9wcfQXbrDthadFxOKw6UKGfKeEK3dthx9i0E0GBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:08.997128Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.21189","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec01fd28a4abbf65600907ddf58e0d0e88a83ad722574b0ef0546214ddbe45d4","sha256:1601dee37cc3c017f85f3576ae95e5e7bd1aca22328f50de56e8992f5948338f"],"state_sha256":"53048cf56118afd512b23844fff1fec1a9c2c27f62a260e1fcb747a69e0d3d7e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"32ynoVU9Gm6nkngmGSJdUfHtrX4dfOTiVoaOH8IjX1SgY4hT91FhbQnSFySO6hsYIYvS29tUnAHHlSQat4C2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:34:53.388869Z","bundle_sha256":"ebcdcb6e200acc3a1e21ff6fe1828c23a42e4c34e36088ce3b6f40045bd09f18"}}