{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:FIR23VBVVWPBQQNQ6JNTMQDZIE","short_pith_number":"pith:FIR23VBV","canonical_record":{"source":{"id":"1603.05378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-17T07:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"b347027a20bb8ea69a38da98bdf117dca4453dc1bc2963e4810a12ac6d26206e","abstract_canon_sha256":"6673fe71d8c2df88b780c37e3e2445850be53bece10894b06925d06f2a73e1c9"},"schema_version":"1.0"},"canonical_sha256":"2a23add435ad9e1841b0f25b364079412e63314da1adc607b9619a643c76669f","source":{"kind":"arxiv","id":"1603.05378","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05378","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05378v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05378","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"FIR23VBVVWPB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FIR23VBVVWPBQQNQ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FIR23VBV","created_at":"2026-05-18T12:30:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:FIR23VBVVWPBQQNQ6JNTMQDZIE","target":"record","payload":{"canonical_record":{"source":{"id":"1603.05378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-17T07:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"b347027a20bb8ea69a38da98bdf117dca4453dc1bc2963e4810a12ac6d26206e","abstract_canon_sha256":"6673fe71d8c2df88b780c37e3e2445850be53bece10894b06925d06f2a73e1c9"},"schema_version":"1.0"},"canonical_sha256":"2a23add435ad9e1841b0f25b364079412e63314da1adc607b9619a643c76669f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:56.484380Z","signature_b64":"FSGhjvK62Oh9yOuJi8NeB8blbT1FxEFHDSm1P7MiuC/VTjYeqcD4Iz90PuEnGMxejBM5zOBn7ne2pzlxQZTeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a23add435ad9e1841b0f25b364079412e63314da1adc607b9619a643c76669f","last_reissued_at":"2026-05-18T01:18:56.483985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:56.483985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.05378","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"se2g3RNslX8yDA9xGbMsWgdY36m9cRWFx9eW4r9qKwbW6yIfdFbcGL+7P/f9jRCXcykrftKWjlYRBk1rLeI5Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:11:37.547183Z"},"content_sha256":"3a680d81f6a070cfb1c748ecf4933464f6515d325a170dcdfab61f02e52b14bb","schema_version":"1.0","event_id":"sha256:3a680d81f6a070cfb1c748ecf4933464f6515d325a170dcdfab61f02e52b14bb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:FIR23VBVVWPBQQNQ6JNTMQDZIE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Commentary on Teichm{\\\"u}ller's paper ``Vollst{\\\"a}ndige L{\\\"o}sung einer Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an extremal problem of the quasiconformal mapping)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Athanase Papadopoulos (IRMA, CUNY), Irma), Vincent Alberge (CUNY","submitted_at":"2016-03-17T07:38:12Z","abstract_excerpt":"We comment on Teichm{\\\"u}ller 's paper ''Vollst{\\\"a}ndige L{\\\"o}sung einer Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an ex-tremal problem of the quasiconformal mapping),, published in 1941. In this paper, Teichm{\\\"u}ller gives a proof of the existence of extremal quasiconformal mappings in the case of the pentagon (disc with five distinguished points on the boundary). The final version of this paper will appear as a chapter in Volume VI of the Handbook of Teichm{\\\"u}ller theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05378","kind":"arxiv","version":1},"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":"2026-05-18T01:18:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZA+VTdsIw9p355RSxZmxQjAt9HeqzbYouQGIZs80HPJ9l74iI+OiW8HC4baGTEHrJNS/CQKOUTxS3NZfSkjrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:11:37.547849Z"},"content_sha256":"424824baf618f793605a1cfd58d6c35c1a0d4a988e9c2213f3a1a1d9ab16b983","schema_version":"1.0","event_id":"sha256:424824baf618f793605a1cfd58d6c35c1a0d4a988e9c2213f3a1a1d9ab16b983"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE/bundle.json","state_url":"https://pith.science/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE/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":"2026-05-27T08:11:37Z","links":{"resolver":"https://pith.science/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE","bundle":"https://pith.science/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE/bundle.json","state":"https://pith.science/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FIR23VBVVWPBQQNQ6JNTMQDZIE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FIR23VBVVWPBQQNQ6JNTMQDZIE","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":"6673fe71d8c2df88b780c37e3e2445850be53bece10894b06925d06f2a73e1c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-17T07:38:12Z","title_canon_sha256":"b347027a20bb8ea69a38da98bdf117dca4453dc1bc2963e4810a12ac6d26206e"},"schema_version":"1.0","source":{"id":"1603.05378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.05378","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"arxiv_version","alias_value":"1603.05378v1","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.05378","created_at":"2026-05-18T01:18:56Z"},{"alias_kind":"pith_short_12","alias_value":"FIR23VBVVWPB","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FIR23VBVVWPBQQNQ","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FIR23VBV","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:424824baf618f793605a1cfd58d6c35c1a0d4a988e9c2213f3a1a1d9ab16b983","target":"graph","created_at":"2026-05-18T01:18:56Z","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 comment on Teichm{\\\"u}ller 's paper ''Vollst{\\\"a}ndige L{\\\"o}sung einer Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an ex-tremal problem of the quasiconformal mapping),, published in 1941. In this paper, Teichm{\\\"u}ller gives a proof of the existence of extremal quasiconformal mappings in the case of the pentagon (disc with five distinguished points on the boundary). The final version of this paper will appear as a chapter in Volume VI of the Handbook of Teichm{\\\"u}ller theory.","authors_text":"Athanase Papadopoulos (IRMA, CUNY), Irma), Vincent Alberge (CUNY","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-17T07:38:12Z","title":"A Commentary on Teichm{\\\"u}ller's paper ``Vollst{\\\"a}ndige L{\\\"o}sung einer Extremalaufgabe der quasikonformen Abbildung'' (Complete solution of an extremal problem of the quasiconformal mapping)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.05378","kind":"arxiv","version":1},"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":"sha256:3a680d81f6a070cfb1c748ecf4933464f6515d325a170dcdfab61f02e52b14bb","target":"record","created_at":"2026-05-18T01:18:56Z","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":"6673fe71d8c2df88b780c37e3e2445850be53bece10894b06925d06f2a73e1c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-03-17T07:38:12Z","title_canon_sha256":"b347027a20bb8ea69a38da98bdf117dca4453dc1bc2963e4810a12ac6d26206e"},"schema_version":"1.0","source":{"id":"1603.05378","kind":"arxiv","version":1}},"canonical_sha256":"2a23add435ad9e1841b0f25b364079412e63314da1adc607b9619a643c76669f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a23add435ad9e1841b0f25b364079412e63314da1adc607b9619a643c76669f","first_computed_at":"2026-05-18T01:18:56.483985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:56.483985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FSGhjvK62Oh9yOuJi8NeB8blbT1FxEFHDSm1P7MiuC/VTjYeqcD4Iz90PuEnGMxejBM5zOBn7ne2pzlxQZTeDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:56.484380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.05378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a680d81f6a070cfb1c748ecf4933464f6515d325a170dcdfab61f02e52b14bb","sha256:424824baf618f793605a1cfd58d6c35c1a0d4a988e9c2213f3a1a1d9ab16b983"],"state_sha256":"66200ffb21bbfea284480e450849e2e3f3ab9070c8a789f7c64f80a34ef37183"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZgLjzSt9P0KFJ1+PGrnCWdvKaFjUUaKSWYlLg7aytIiMCyvxBgB+9uO08sUJd0dPh4NGk/qjG4XUNocJTY+3CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:11:37.551495Z","bundle_sha256":"a99d220d61892d6a965f4deb3817ea818f54389bfbb6f6e39e439d61f9d33557"}}