{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UOT47Q6B3NGUSJ4L6QZYP2N6XH","short_pith_number":"pith:UOT47Q6B","canonical_record":{"source":{"id":"1003.2944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-15T15:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"fd205b400915379a13b96da9cef7564068ff17dded509345a2e1c5bc57c2b563","abstract_canon_sha256":"569af2d0ce734ceb6974e158cff0515b4fd8978ec83a51e4ba5f7ec8b14c6b01"},"schema_version":"1.0"},"canonical_sha256":"a3a7cfc3c1db4d49278bf43387e9beb9e37c8bfdd518d24c788aa78a75ebfd13","source":{"kind":"arxiv","id":"1003.2944","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2944","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2944v2","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2944","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"UOT47Q6B3NGU","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOT47Q6B3NGUSJ4L","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOT47Q6B","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UOT47Q6B3NGUSJ4L6QZYP2N6XH","target":"record","payload":{"canonical_record":{"source":{"id":"1003.2944","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-15T15:45:46Z","cross_cats_sorted":[],"title_canon_sha256":"fd205b400915379a13b96da9cef7564068ff17dded509345a2e1c5bc57c2b563","abstract_canon_sha256":"569af2d0ce734ceb6974e158cff0515b4fd8978ec83a51e4ba5f7ec8b14c6b01"},"schema_version":"1.0"},"canonical_sha256":"a3a7cfc3c1db4d49278bf43387e9beb9e37c8bfdd518d24c788aa78a75ebfd13","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:59.401228Z","signature_b64":"9mrZrBXKkXH7Wyfmp7ulgt94Vk58E+HRFdmhbWIzQXZ7E55dAJkuPUWfR+k05uzUoOF3+55Z1SNGTvs//YPKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3a7cfc3c1db4d49278bf43387e9beb9e37c8bfdd518d24c788aa78a75ebfd13","last_reissued_at":"2026-05-18T03:50:59.400434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:59.400434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1003.2944","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":"2026-05-18T03:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t43C1E+zG05fVZgLTVhkrkkRPA4Zqbsf7KYdckDwjnHd5bsMBwHhZQ/4R6Gy0hXY29GAnWVl4pbf83u+GiCTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:15:44.684672Z"},"content_sha256":"34f65f3f24f90a1c8c94d48c6d3f70168d16db9451c8371cf40bcc4ff70c3f67","schema_version":"1.0","event_id":"sha256:34f65f3f24f90a1c8c94d48c6d3f70168d16db9451c8371cf40bcc4ff70c3f67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UOT47Q6B3NGUSJ4L6QZYP2N6XH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the perimeters of simple polygons contained in a plane convex body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Zsolt L\\'angi","submitted_at":"2010-03-15T15:45:46Z","abstract_excerpt":"A simple n-gon is a polygon with n edges such that each vertex belongs to exactly two edges and every other point belongs to at most one edge. Brass, Moser and Pach asked the following question: For n > 3 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet, Hansen and Messine answered this question, and showed that the supremum is the perimeter of an isosceles triangle inscribed in the disk, with an edge of multiplicity n-2. L\\'angi generalized their result for polygons contained in a hyperbolic disk. In this note we find the supremum of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2944","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":"2026-05-18T03:50:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ggyIajJ0pX42WBu2j4HbFwiXV8ByB2FElF7bLn7PZAiEx1ag/ETsw+JkqUv229xj7PZ8M7WA8loyP3KQEi6ACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T12:15:44.685019Z"},"content_sha256":"367914f21a8a883eeeca1a630bdac5a5a45a4fe7bda470f2ac30e81c50598d33","schema_version":"1.0","event_id":"sha256:367914f21a8a883eeeca1a630bdac5a5a45a4fe7bda470f2ac30e81c50598d33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH/bundle.json","state_url":"https://pith.science/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH/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":"2026-06-21T12:15:44Z","links":{"resolver":"https://pith.science/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH","bundle":"https://pith.science/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH/bundle.json","state":"https://pith.science/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UOT47Q6B3NGUSJ4L6QZYP2N6XH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UOT47Q6B3NGUSJ4L6QZYP2N6XH","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":"569af2d0ce734ceb6974e158cff0515b4fd8978ec83a51e4ba5f7ec8b14c6b01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-15T15:45:46Z","title_canon_sha256":"fd205b400915379a13b96da9cef7564068ff17dded509345a2e1c5bc57c2b563"},"schema_version":"1.0","source":{"id":"1003.2944","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.2944","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"arxiv_version","alias_value":"1003.2944v2","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2944","created_at":"2026-05-18T03:50:59Z"},{"alias_kind":"pith_short_12","alias_value":"UOT47Q6B3NGU","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UOT47Q6B3NGUSJ4L","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UOT47Q6B","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:367914f21a8a883eeeca1a630bdac5a5a45a4fe7bda470f2ac30e81c50598d33","target":"graph","created_at":"2026-05-18T03:50:59Z","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":"A simple n-gon is a polygon with n edges such that each vertex belongs to exactly two edges and every other point belongs to at most one edge. Brass, Moser and Pach asked the following question: For n > 3 odd, what is the maximum perimeter of a simple n-gon contained in a Euclidean unit disk? In 2009, Audet, Hansen and Messine answered this question, and showed that the supremum is the perimeter of an isosceles triangle inscribed in the disk, with an edge of multiplicity n-2. L\\'angi generalized their result for polygons contained in a hyperbolic disk. In this note we find the supremum of the ","authors_text":"Zsolt L\\'angi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-15T15:45:46Z","title":"On the perimeters of simple polygons contained in a plane convex body"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2944","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":"sha256:34f65f3f24f90a1c8c94d48c6d3f70168d16db9451c8371cf40bcc4ff70c3f67","target":"record","created_at":"2026-05-18T03:50:59Z","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":"569af2d0ce734ceb6974e158cff0515b4fd8978ec83a51e4ba5f7ec8b14c6b01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2010-03-15T15:45:46Z","title_canon_sha256":"fd205b400915379a13b96da9cef7564068ff17dded509345a2e1c5bc57c2b563"},"schema_version":"1.0","source":{"id":"1003.2944","kind":"arxiv","version":2}},"canonical_sha256":"a3a7cfc3c1db4d49278bf43387e9beb9e37c8bfdd518d24c788aa78a75ebfd13","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3a7cfc3c1db4d49278bf43387e9beb9e37c8bfdd518d24c788aa78a75ebfd13","first_computed_at":"2026-05-18T03:50:59.400434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:59.400434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mrZrBXKkXH7Wyfmp7ulgt94Vk58E+HRFdmhbWIzQXZ7E55dAJkuPUWfR+k05uzUoOF3+55Z1SNGTvs//YPKAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:59.401228Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.2944","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34f65f3f24f90a1c8c94d48c6d3f70168d16db9451c8371cf40bcc4ff70c3f67","sha256:367914f21a8a883eeeca1a630bdac5a5a45a4fe7bda470f2ac30e81c50598d33"],"state_sha256":"776242d79c62fc23c3f8aedf893ce86234c2dfd34d168eca34e904ddcae8ccc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mGkcOfXclQYOg9gKUCFi4n46ewH9+ujjDyY54gLR1/q1jYfJ3pix0U5QPyICMz+1eL9+UmlqLWDr9kwwaTDtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T12:15:44.686970Z","bundle_sha256":"04a11e37c0fcf2607c6b232aba1ef5569a9b32dc085c54f0dc1c46dd43caeb91"}}