{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:O26X6VLZHCLNAEZ4TU3AC73HD5","short_pith_number":"pith:O26X6VLZ","canonical_record":{"source":{"id":"1009.0897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-05T08:32:53Z","cross_cats_sorted":[],"title_canon_sha256":"8dc52cb5a50ea720417ba157a037ed82883637dfe311c83ca012b4ed14bf62f3","abstract_canon_sha256":"e2054a4fa8968fb331cbab775bb5e465af79182d687cd733b8261d7b757f3293"},"schema_version":"1.0"},"canonical_sha256":"76bd7f55793896d0133c9d36017f671f42f4fedc7cf030103799a13afdeac081","source":{"kind":"arxiv","id":"1009.0897","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0897","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0897v2","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0897","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"O26X6VLZHCLN","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O26X6VLZHCLNAEZ4","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O26X6VLZ","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:O26X6VLZHCLNAEZ4TU3AC73HD5","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-05T08:32:53Z","cross_cats_sorted":[],"title_canon_sha256":"8dc52cb5a50ea720417ba157a037ed82883637dfe311c83ca012b4ed14bf62f3","abstract_canon_sha256":"e2054a4fa8968fb331cbab775bb5e465af79182d687cd733b8261d7b757f3293"},"schema_version":"1.0"},"canonical_sha256":"76bd7f55793896d0133c9d36017f671f42f4fedc7cf030103799a13afdeac081","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:07.564751Z","signature_b64":"bF1ANwbILVObJJVX0kgOdRELIIAnluzWdAMfQI55kEVWJBHinAtzTH1pJlgOtbLIbPsJ385pTU/ZSr/9wg4zCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76bd7f55793896d0133c9d36017f671f42f4fedc7cf030103799a13afdeac081","last_reissued_at":"2026-05-18T00:33:07.564077Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:07.564077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0897","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":"2026-05-18T00:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a3oYqCPtsYT2/8837shVA966yOq5xVkJ4nEp+xxnM9gGIctrnVLUl6hyvi/5GCGrv27XTG05Mv4qOGsTX1cNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:46:07.829675Z"},"content_sha256":"3fde0b2a415696702c8873e6b50608fb814860afbd88e8a4bf606f430a4b3006","schema_version":"1.0","event_id":"sha256:3fde0b2a415696702c8873e6b50608fb814860afbd88e8a4bf606f430a4b3006"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:O26X6VLZHCLNAEZ4TU3AC73HD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A simple proof of the isoperimetric theorem for the hyperbolic plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"A. Skopenkov","submitted_at":"2010-09-05T08:32:53Z","abstract_excerpt":"In this pedagogical note we present a short proof of the following main result of arxiv.org/abs/0911.5319, and clarify its relation to the isoperimetric problem.\n  On the hyperbolic plane consider triangles ABC with fixed lengths of AB and AC. The maximal area of these triangles is attained for the triangle ABC such that \\angle A=\\angle B+\\angle C.\n  The proof is essentially the same as in the above-cited paper. However, since the result is beautiful and important, a short proof cleared of unnecessary details could be interesting for a reader. The note is accessible for students familiar with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0897","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":"2026-05-18T00:33:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4SPemMgiL0d+SZIgsyvnj3BKgoDwbly7z0Zp6Ccg8hqNYTBw6wYJBY1vWkIMFZ0AmtvZ9jSUtBrAEZyaQZsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T20:46:07.830420Z"},"content_sha256":"04bc1f59199381b23a822521d1cf18bcdc7257c17f75fe21451dd763e195afa3","schema_version":"1.0","event_id":"sha256:04bc1f59199381b23a822521d1cf18bcdc7257c17f75fe21451dd763e195afa3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O26X6VLZHCLNAEZ4TU3AC73HD5/bundle.json","state_url":"https://pith.science/pith/O26X6VLZHCLNAEZ4TU3AC73HD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O26X6VLZHCLNAEZ4TU3AC73HD5/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":"2026-06-11T20:46:07Z","links":{"resolver":"https://pith.science/pith/O26X6VLZHCLNAEZ4TU3AC73HD5","bundle":"https://pith.science/pith/O26X6VLZHCLNAEZ4TU3AC73HD5/bundle.json","state":"https://pith.science/pith/O26X6VLZHCLNAEZ4TU3AC73HD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O26X6VLZHCLNAEZ4TU3AC73HD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:O26X6VLZHCLNAEZ4TU3AC73HD5","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":"e2054a4fa8968fb331cbab775bb5e465af79182d687cd733b8261d7b757f3293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-05T08:32:53Z","title_canon_sha256":"8dc52cb5a50ea720417ba157a037ed82883637dfe311c83ca012b4ed14bf62f3"},"schema_version":"1.0","source":{"id":"1009.0897","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0897","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0897v2","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0897","created_at":"2026-05-18T00:33:07Z"},{"alias_kind":"pith_short_12","alias_value":"O26X6VLZHCLN","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"O26X6VLZHCLNAEZ4","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"O26X6VLZ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:04bc1f59199381b23a822521d1cf18bcdc7257c17f75fe21451dd763e195afa3","target":"graph","created_at":"2026-05-18T00:33:07Z","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":"In this pedagogical note we present a short proof of the following main result of arxiv.org/abs/0911.5319, and clarify its relation to the isoperimetric problem.\n  On the hyperbolic plane consider triangles ABC with fixed lengths of AB and AC. The maximal area of these triangles is attained for the triangle ABC such that \\angle A=\\angle B+\\angle C.\n  The proof is essentially the same as in the above-cited paper. However, since the result is beautiful and important, a short proof cleared of unnecessary details could be interesting for a reader. The note is accessible for students familiar with ","authors_text":"A. Skopenkov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-05T08:32:53Z","title":"A simple proof of the isoperimetric theorem for the hyperbolic plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0897","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":"sha256:3fde0b2a415696702c8873e6b50608fb814860afbd88e8a4bf606f430a4b3006","target":"record","created_at":"2026-05-18T00:33:07Z","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":"e2054a4fa8968fb331cbab775bb5e465af79182d687cd733b8261d7b757f3293","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-09-05T08:32:53Z","title_canon_sha256":"8dc52cb5a50ea720417ba157a037ed82883637dfe311c83ca012b4ed14bf62f3"},"schema_version":"1.0","source":{"id":"1009.0897","kind":"arxiv","version":2}},"canonical_sha256":"76bd7f55793896d0133c9d36017f671f42f4fedc7cf030103799a13afdeac081","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76bd7f55793896d0133c9d36017f671f42f4fedc7cf030103799a13afdeac081","first_computed_at":"2026-05-18T00:33:07.564077Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:07.564077Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bF1ANwbILVObJJVX0kgOdRELIIAnluzWdAMfQI55kEVWJBHinAtzTH1pJlgOtbLIbPsJ385pTU/ZSr/9wg4zCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:07.564751Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0897","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3fde0b2a415696702c8873e6b50608fb814860afbd88e8a4bf606f430a4b3006","sha256:04bc1f59199381b23a822521d1cf18bcdc7257c17f75fe21451dd763e195afa3"],"state_sha256":"8c5f550470c24a68b92248031ac4f11f5c6f796b1283bb164e077c4c8a04a3ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Lp8lFJ3bPYJ8E6DGmwvK38uD5rnav2y4Q/3n+SAS6xlRiFLVPTwYitHVKaM9/7hOVV2vlKwUl2dllAQTIXsBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T20:46:07.834575Z","bundle_sha256":"b9d8284c8b441fe86afa67239788f5ad6077fec4fd6fb68f75f120bb2b3645c7"}}