{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BFYCQWNN4YZWOMWIPY4QTAGSPK","short_pith_number":"pith:BFYCQWNN","canonical_record":{"source":{"id":"0906.2853","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2009-06-16T07:33:10Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ef27802f8c2863b4b97b22f8e8912e5c5eef017e1cbee396f79357a134d933e0","abstract_canon_sha256":"d78e97585247d536603b823cb12f3e0faa827d9c8fae46e510487560801d225f"},"schema_version":"1.0"},"canonical_sha256":"09702859ade6336732c87e390980d27a8a0f2522e64bbe5dd2fcc38ac2afd91f","source":{"kind":"arxiv","id":"0906.2853","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2853","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2853v5","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2853","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"BFYCQWNN4YZW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BFYCQWNN4YZWOMWI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BFYCQWNN","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BFYCQWNN4YZWOMWIPY4QTAGSPK","target":"record","payload":{"canonical_record":{"source":{"id":"0906.2853","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2009-06-16T07:33:10Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"ef27802f8c2863b4b97b22f8e8912e5c5eef017e1cbee396f79357a134d933e0","abstract_canon_sha256":"d78e97585247d536603b823cb12f3e0faa827d9c8fae46e510487560801d225f"},"schema_version":"1.0"},"canonical_sha256":"09702859ade6336732c87e390980d27a8a0f2522e64bbe5dd2fcc38ac2afd91f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:07.343412Z","signature_b64":"xDAzOi00plyVtqfgySI7E03kztdziZ0uzqmlyB+meisDyam+upOK5vJl3YRaeG5lirnKzbLmbsNFHaBAvsxLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09702859ade6336732c87e390980d27a8a0f2522e64bbe5dd2fcc38ac2afd91f","last_reissued_at":"2026-05-18T04:24:07.342864Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:07.342864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.2853","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DrVhHIMCRVYWfp226WlkoE+XefRTu9ET9o+zR4aJuPAH8G96TdYPXH44rUENEVMReC9l/vgYxzcSy7DTzgh8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:57:33.096791Z"},"content_sha256":"cd70f69ee86283dc6cbb043d2463bad37710eb23888010f91e9cd321e8d0ab37","schema_version":"1.0","event_id":"sha256:cd70f69ee86283dc6cbb043d2463bad37710eb23888010f91e9cd321e8d0ab37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BFYCQWNN4YZWOMWIPY4QTAGSPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Mori's theorem for quasiconformal maps in the $n$-space","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Barkat Ali Bhayo, Matti Vuorinen","submitted_at":"2009-06-16T07:33:10Z","abstract_excerpt":"R. Fehlmann and M. Vuorinen proved in 1988 that Mori's constant $M(n,K)$ for $K$-quasiconformal maps of the unit ball in $\\mathbf{R}^n$ onto itself keeping the origin fixed satisfies $M(n,K) \\to 1$ when $K\\to 1 .$ We give here an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M. K. Vamanamurthy. We also give an explicit version of the Schwarz lemma for quasiconformal self-maps of the unit disk. Some experimental results are provided to compare the various "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2853","kind":"arxiv","version":5},"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":"2026-05-18T04:24:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kt0CwwwEEBIOIqRiAKPzxjjtV/g8W0XBk0aBVqoJjaU+BMKino+PjDUWz9q6Wsa9L+cHSN5rLLvyTGr4c6plCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T04:57:33.097136Z"},"content_sha256":"ad3b3a0772595b5abcd3033d8f86d3cbc67ce0e2c9e3c577acb041e647ea539b","schema_version":"1.0","event_id":"sha256:ad3b3a0772595b5abcd3033d8f86d3cbc67ce0e2c9e3c577acb041e647ea539b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK/bundle.json","state_url":"https://pith.science/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK/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":"2026-06-21T04:57:33Z","links":{"resolver":"https://pith.science/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK","bundle":"https://pith.science/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK/bundle.json","state":"https://pith.science/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BFYCQWNN4YZWOMWIPY4QTAGSPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BFYCQWNN4YZWOMWIPY4QTAGSPK","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":"d78e97585247d536603b823cb12f3e0faa827d9c8fae46e510487560801d225f","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2009-06-16T07:33:10Z","title_canon_sha256":"ef27802f8c2863b4b97b22f8e8912e5c5eef017e1cbee396f79357a134d933e0"},"schema_version":"1.0","source":{"id":"0906.2853","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2853","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2853v5","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2853","created_at":"2026-05-18T04:24:07Z"},{"alias_kind":"pith_short_12","alias_value":"BFYCQWNN4YZW","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BFYCQWNN4YZWOMWI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BFYCQWNN","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:ad3b3a0772595b5abcd3033d8f86d3cbc67ce0e2c9e3c577acb041e647ea539b","target":"graph","created_at":"2026-05-18T04:24:07Z","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":"R. Fehlmann and M. Vuorinen proved in 1988 that Mori's constant $M(n,K)$ for $K$-quasiconformal maps of the unit ball in $\\mathbf{R}^n$ onto itself keeping the origin fixed satisfies $M(n,K) \\to 1$ when $K\\to 1 .$ We give here an alternative proof of this fact, with a quantitative upper bound for the constant in terms of elementary functions. Our proof is based on a refinement of a method due to G.D. Anderson and M. K. Vamanamurthy. We also give an explicit version of the Schwarz lemma for quasiconformal self-maps of the unit disk. Some experimental results are provided to compare the various ","authors_text":"Barkat Ali Bhayo, Matti Vuorinen","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2009-06-16T07:33:10Z","title":"On Mori's theorem for quasiconformal maps in the $n$-space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2853","kind":"arxiv","version":5},"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:cd70f69ee86283dc6cbb043d2463bad37710eb23888010f91e9cd321e8d0ab37","target":"record","created_at":"2026-05-18T04:24:07Z","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":"d78e97585247d536603b823cb12f3e0faa827d9c8fae46e510487560801d225f","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.CA","submitted_at":"2009-06-16T07:33:10Z","title_canon_sha256":"ef27802f8c2863b4b97b22f8e8912e5c5eef017e1cbee396f79357a134d933e0"},"schema_version":"1.0","source":{"id":"0906.2853","kind":"arxiv","version":5}},"canonical_sha256":"09702859ade6336732c87e390980d27a8a0f2522e64bbe5dd2fcc38ac2afd91f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09702859ade6336732c87e390980d27a8a0f2522e64bbe5dd2fcc38ac2afd91f","first_computed_at":"2026-05-18T04:24:07.342864Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:07.342864Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xDAzOi00plyVtqfgySI7E03kztdziZ0uzqmlyB+meisDyam+upOK5vJl3YRaeG5lirnKzbLmbsNFHaBAvsxLCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:07.343412Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2853","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd70f69ee86283dc6cbb043d2463bad37710eb23888010f91e9cd321e8d0ab37","sha256:ad3b3a0772595b5abcd3033d8f86d3cbc67ce0e2c9e3c577acb041e647ea539b"],"state_sha256":"962fbbfaeb4d8a1954244a60b983619bd4e1b76b90d34259c256e3bcd8b6dfda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUrhYljgIpPnT7mtBzO6hw9QRbUd96ioS/wLSPBf0GVjpGCq+yv8rM7vqp2jgiHouixp1ebRrWKeHSGTTOlFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T04:57:33.099116Z","bundle_sha256":"fa7048908e617a6c311f4be95bad2e9562eefdc2aadd56b24d7627cc0dedc792"}}