{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SGXFNZGE6KKS3S72HVM6Y4EIWY","short_pith_number":"pith:SGXFNZGE","canonical_record":{"source":{"id":"1605.00449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-02T12:03:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5ec327b5a03ef16d2cbb4d4c1f9412f5cdca634de92e6b24e20029e487aa1e23","abstract_canon_sha256":"4a5bf190a299f1d4354944dac4a9fbc45b49cbed78a4633c95f9616d68c1b5d9"},"schema_version":"1.0"},"canonical_sha256":"91ae56e4c4f2952dcbfa3d59ec7088b63127d866128bb17831ee2fa13c23ab16","source":{"kind":"arxiv","id":"1605.00449","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00449","created_at":"2026-05-18T00:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00449v2","created_at":"2026-05-18T00:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00449","created_at":"2026-05-18T00:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"SGXFNZGE6KKS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SGXFNZGE6KKS3S72","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SGXFNZGE","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SGXFNZGE6KKS3S72HVM6Y4EIWY","target":"record","payload":{"canonical_record":{"source":{"id":"1605.00449","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-02T12:03:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"5ec327b5a03ef16d2cbb4d4c1f9412f5cdca634de92e6b24e20029e487aa1e23","abstract_canon_sha256":"4a5bf190a299f1d4354944dac4a9fbc45b49cbed78a4633c95f9616d68c1b5d9"},"schema_version":"1.0"},"canonical_sha256":"91ae56e4c4f2952dcbfa3d59ec7088b63127d866128bb17831ee2fa13c23ab16","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:46.644338Z","signature_b64":"OD9vUdq98YSW68wFQ/Zvor66W6FxujGfBzEyb8iI6MQP7PuQ4AjSQTSLQqJ2E30J9oWgWnWievcOp+R2DdkkBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91ae56e4c4f2952dcbfa3d59ec7088b63127d866128bb17831ee2fa13c23ab16","last_reissued_at":"2026-05-18T00:42:46.643607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:46.643607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.00449","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":"2026-05-18T00:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P0LEg/xYSBnePDFNBjc7lY/+Uns6i+OsrctXR7wUxrpWYDbLzN0Fld0kftb/pmjc+TxlcDNzwL0ptdM6hQOXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T23:41:32.173966Z"},"content_sha256":"1f7d873013f3ae8fc5a6f2325e8086ce12f62353bc3eb4abe29505c708005efb","schema_version":"1.0","event_id":"sha256:1f7d873013f3ae8fc5a6f2325e8086ce12f62353bc3eb4abe29505c708005efb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SGXFNZGE6KKS3S72HVM6Y4EIWY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasiconformal Teichmuller theory as an analytical foundation for two-dimensional conformal field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CV","authors_text":"David Radnell, Eric Schippers, Wolfgang Staubach","submitted_at":"2016-05-02T12:03:22Z","abstract_excerpt":"The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmuller theory and geometric function theory.\n  In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called Weil-Petersson class paramet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00449","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":"2026-05-18T00:42:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ozNgoUOfSIrklRAY1g2Mm8rFyd/EEpXvbTbPi+ETwp7pQjbAWaxb2cnZ4U7UZzUOIHYOxXE1A3uN+MALXLkyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T23:41:32.174587Z"},"content_sha256":"a019f958803aab7bfc2849dc66956ec3b45c1589abe995a8c7d35d3bb9ff31ef","schema_version":"1.0","event_id":"sha256:a019f958803aab7bfc2849dc66956ec3b45c1589abe995a8c7d35d3bb9ff31ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY/bundle.json","state_url":"https://pith.science/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY/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":"2026-07-03T23:41:32Z","links":{"resolver":"https://pith.science/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY","bundle":"https://pith.science/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY/bundle.json","state":"https://pith.science/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SGXFNZGE6KKS3S72HVM6Y4EIWY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SGXFNZGE6KKS3S72HVM6Y4EIWY","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":"4a5bf190a299f1d4354944dac4a9fbc45b49cbed78a4633c95f9616d68c1b5d9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-02T12:03:22Z","title_canon_sha256":"5ec327b5a03ef16d2cbb4d4c1f9412f5cdca634de92e6b24e20029e487aa1e23"},"schema_version":"1.0","source":{"id":"1605.00449","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00449","created_at":"2026-05-18T00:42:46Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00449v2","created_at":"2026-05-18T00:42:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00449","created_at":"2026-05-18T00:42:46Z"},{"alias_kind":"pith_short_12","alias_value":"SGXFNZGE6KKS","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SGXFNZGE6KKS3S72","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SGXFNZGE","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:a019f958803aab7bfc2849dc66956ec3b45c1589abe995a8c7d35d3bb9ff31ef","target":"graph","created_at":"2026-05-18T00:42:46Z","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":"The functorial mathematical definition of conformal field theory was first formulated approximately 30 years ago. The underlying geometric category is based on the moduli space of Riemann surfaces with parametrized boundary components and the sewing operation. We survey the recent and careful study of these objects, which has led to significant connections with quasiconformal Teichmuller theory and geometric function theory.\n  In particular we propose that the natural analytic setting for conformal field theory is the moduli space of Riemann surfaces with so-called Weil-Petersson class paramet","authors_text":"David Radnell, Eric Schippers, Wolfgang Staubach","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-02T12:03:22Z","title":"Quasiconformal Teichmuller theory as an analytical foundation for two-dimensional conformal field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00449","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":"sha256:1f7d873013f3ae8fc5a6f2325e8086ce12f62353bc3eb4abe29505c708005efb","target":"record","created_at":"2026-05-18T00:42:46Z","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":"4a5bf190a299f1d4354944dac4a9fbc45b49cbed78a4633c95f9616d68c1b5d9","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-05-02T12:03:22Z","title_canon_sha256":"5ec327b5a03ef16d2cbb4d4c1f9412f5cdca634de92e6b24e20029e487aa1e23"},"schema_version":"1.0","source":{"id":"1605.00449","kind":"arxiv","version":2}},"canonical_sha256":"91ae56e4c4f2952dcbfa3d59ec7088b63127d866128bb17831ee2fa13c23ab16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91ae56e4c4f2952dcbfa3d59ec7088b63127d866128bb17831ee2fa13c23ab16","first_computed_at":"2026-05-18T00:42:46.643607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:46.643607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OD9vUdq98YSW68wFQ/Zvor66W6FxujGfBzEyb8iI6MQP7PuQ4AjSQTSLQqJ2E30J9oWgWnWievcOp+R2DdkkBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:46.644338Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00449","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f7d873013f3ae8fc5a6f2325e8086ce12f62353bc3eb4abe29505c708005efb","sha256:a019f958803aab7bfc2849dc66956ec3b45c1589abe995a8c7d35d3bb9ff31ef"],"state_sha256":"812d7cc3ce49ca3b97c33c367d4068a83f0e333123bd1bbbde481fe8281d47b4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gxPEw6vOJoD+Rw8UIl5ATIIokZByunrcJzIZPThusVcb3xbh5QFSuiDMq20VCAMBPvRcu00q5J/f4M3wZn9EDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T23:41:32.177687Z","bundle_sha256":"a454fe1db7ae6512a9b523f91871fdc126f8837de1f04fdf957664b8e4e8ebbb"}}