{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:VD6WCJ6BZVOEO5OMFUGM7ZW63P","short_pith_number":"pith:VD6WCJ6B","canonical_record":{"source":{"id":"math/0409560","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2004-09-28T19:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcc119e31ce315372250fec26cb9359a90a6c88201873d963546c531037ce8c1","abstract_canon_sha256":"9a52b1fa455c973ba5a8ffbde91677afced5f36d2803d26730826213d3090114"},"schema_version":"1.0"},"canonical_sha256":"a8fd6127c1cd5c4775cc2d0ccfe6dedbf3e3fdcecfe90a8b6307233ede596614","source":{"kind":"arxiv","id":"math/0409560","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409560","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409560v3","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409560","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"VD6WCJ6BZVOE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"VD6WCJ6BZVOEO5OM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"VD6WCJ6B","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:VD6WCJ6BZVOEO5OMFUGM7ZW63P","target":"record","payload":{"canonical_record":{"source":{"id":"math/0409560","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2004-09-28T19:01:42Z","cross_cats_sorted":[],"title_canon_sha256":"bcc119e31ce315372250fec26cb9359a90a6c88201873d963546c531037ce8c1","abstract_canon_sha256":"9a52b1fa455c973ba5a8ffbde91677afced5f36d2803d26730826213d3090114"},"schema_version":"1.0"},"canonical_sha256":"a8fd6127c1cd5c4775cc2d0ccfe6dedbf3e3fdcecfe90a8b6307233ede596614","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:54.624771Z","signature_b64":"ZXg5vGJVCyoQjlKJ/kwDzdYrPucCgCOrRmLgvIVuwbIa1daDvm1j3FHpzd78vw6E8ZcnV/8DLtsbmpd2ls0jCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8fd6127c1cd5c4775cc2d0ccfe6dedbf3e3fdcecfe90a8b6307233ede596614","last_reissued_at":"2026-05-18T02:54:54.624209Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:54.624209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0409560","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:54:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9FxO7zbXy66n9WtMUAlDznpJ2+n6pq3w3rLAI0xn7HGZP+e1TbTt3+ZIeyADMrFC1yjrcRvNTy/QNYgT4sJdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:07:38.428462Z"},"content_sha256":"b0434392dde6b9112e7e6f9274b5b4158f3ebf87940dd36c0cb58a393526461e","schema_version":"1.0","event_id":"sha256:b0434392dde6b9112e7e6f9274b5b4158f3ebf87940dd36c0cb58a393526461e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:VD6WCJ6BZVOEO5OMFUGM7ZW63P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Hyperbolic Surface With A Square Grid Net","license":"","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Lukas Geyer, Sergei Merenkov","submitted_at":"2004-09-28T19:01:42Z","abstract_excerpt":"We prove the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage of the extended real line under the projection map is homeomorphic to the square grid in the plane. This answers a question raised by \\`E. B. Vinberg."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409560","kind":"arxiv","version":3},"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":"2026-05-18T02:54:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpNMOsuvJxTUhSNrh9AOKZO6Vj2XTC4FzRogWWtC1TUtpKyDj4COtYhEXX4ywuv6YOXPMy+pCbvPld3uPRCkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T21:07:38.428810Z"},"content_sha256":"95d4066892fe4ceaf3f86b970e98863493d22ea35ff66cc1b33734413f564b78","schema_version":"1.0","event_id":"sha256:95d4066892fe4ceaf3f86b970e98863493d22ea35ff66cc1b33734413f564b78"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P/bundle.json","state_url":"https://pith.science/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P/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":"2026-07-01T21:07:38Z","links":{"resolver":"https://pith.science/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P","bundle":"https://pith.science/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P/bundle.json","state":"https://pith.science/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VD6WCJ6BZVOEO5OMFUGM7ZW63P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:VD6WCJ6BZVOEO5OMFUGM7ZW63P","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":"9a52b1fa455c973ba5a8ffbde91677afced5f36d2803d26730826213d3090114","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2004-09-28T19:01:42Z","title_canon_sha256":"bcc119e31ce315372250fec26cb9359a90a6c88201873d963546c531037ce8c1"},"schema_version":"1.0","source":{"id":"math/0409560","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0409560","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/0409560v3","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0409560","created_at":"2026-05-18T02:54:54Z"},{"alias_kind":"pith_short_12","alias_value":"VD6WCJ6BZVOE","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"VD6WCJ6BZVOEO5OM","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"VD6WCJ6B","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:95d4066892fe4ceaf3f86b970e98863493d22ea35ff66cc1b33734413f564b78","target":"graph","created_at":"2026-05-18T02:54:54Z","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 the existence of a hyperbolic surface spread over the sphere for which the projection map has all its singular values on the extended real line, and such that the preimage of the extended real line under the projection map is homeomorphic to the square grid in the plane. This answers a question raised by \\`E. B. Vinberg.","authors_text":"Lukas Geyer, Sergei Merenkov","cross_cats":[],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2004-09-28T19:01:42Z","title":"A Hyperbolic Surface With A Square Grid Net"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409560","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:b0434392dde6b9112e7e6f9274b5b4158f3ebf87940dd36c0cb58a393526461e","target":"record","created_at":"2026-05-18T02:54:54Z","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":"9a52b1fa455c973ba5a8ffbde91677afced5f36d2803d26730826213d3090114","cross_cats_sorted":[],"license":"","primary_cat":"math.CV","submitted_at":"2004-09-28T19:01:42Z","title_canon_sha256":"bcc119e31ce315372250fec26cb9359a90a6c88201873d963546c531037ce8c1"},"schema_version":"1.0","source":{"id":"math/0409560","kind":"arxiv","version":3}},"canonical_sha256":"a8fd6127c1cd5c4775cc2d0ccfe6dedbf3e3fdcecfe90a8b6307233ede596614","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8fd6127c1cd5c4775cc2d0ccfe6dedbf3e3fdcecfe90a8b6307233ede596614","first_computed_at":"2026-05-18T02:54:54.624209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:54.624209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZXg5vGJVCyoQjlKJ/kwDzdYrPucCgCOrRmLgvIVuwbIa1daDvm1j3FHpzd78vw6E8ZcnV/8DLtsbmpd2ls0jCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:54.624771Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0409560","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0434392dde6b9112e7e6f9274b5b4158f3ebf87940dd36c0cb58a393526461e","sha256:95d4066892fe4ceaf3f86b970e98863493d22ea35ff66cc1b33734413f564b78"],"state_sha256":"2640e8e32d2b4e297bda07dd7b464d79a2492000453acf29acf8ed0296c74d0c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nT88pCi8ttjqX55yjhT7Y5AvWfo5hRXkJWXU8qgEaDJa9iHqqk+cV5GmM3QkdkV5u1IzDM4LFLlTGl9sivvCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T21:07:38.430768Z","bundle_sha256":"cd2b47a2d468c209b9a4c1a65b38ccec069e4884eff65dca9783f4aafc45dfa2"}}