{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HJVRCDEYVQGFE7GKSLNO5LWBN3","short_pith_number":"pith:HJVRCDEY","canonical_record":{"source":{"id":"1711.04361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-12T21:28:05Z","cross_cats_sorted":[],"title_canon_sha256":"06791fdb04012e37775379edbb42ee9fd3377a93c4a7e70cb15f46d399d43163","abstract_canon_sha256":"1405c3ce4416ee9d16ed3e69fffc7438123285d4cfc415dcb5c6f1c91f9f0d28"},"schema_version":"1.0"},"canonical_sha256":"3a6b110c98ac0c527cca92daeeaec16ee5662f5bb2f5943a40fd013c4d6858f2","source":{"kind":"arxiv","id":"1711.04361","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04361","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04361v1","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04361","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"HJVRCDEYVQGF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HJVRCDEYVQGFE7GK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HJVRCDEY","created_at":"2026-05-18T12:31:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HJVRCDEYVQGFE7GKSLNO5LWBN3","target":"record","payload":{"canonical_record":{"source":{"id":"1711.04361","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-12T21:28:05Z","cross_cats_sorted":[],"title_canon_sha256":"06791fdb04012e37775379edbb42ee9fd3377a93c4a7e70cb15f46d399d43163","abstract_canon_sha256":"1405c3ce4416ee9d16ed3e69fffc7438123285d4cfc415dcb5c6f1c91f9f0d28"},"schema_version":"1.0"},"canonical_sha256":"3a6b110c98ac0c527cca92daeeaec16ee5662f5bb2f5943a40fd013c4d6858f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:59.909649Z","signature_b64":"ai3vuYyseU+pnjCltUYhoBaJa1BBqs1YVFNz8x6sVTxJ4LdNpI9bH0OVyLLtY3MPSFGE/NVHZFwoeYWAzqC9DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a6b110c98ac0c527cca92daeeaec16ee5662f5bb2f5943a40fd013c4d6858f2","last_reissued_at":"2026-05-18T00:00:59.909200Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:59.909200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.04361","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":"2026-05-18T00:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8mV8vu6XL0hRnTiUefnF3resnZGegxW4DVt2jc8kJRXl0t6Pqp2ssEVRTfXFwxYc9mzyShDO9fN116TWwfbiDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:00:58.545471Z"},"content_sha256":"0219795670df49d365c4ef05420d9ff90e1ea686e5cc017714c9f331d4b726c1","schema_version":"1.0","event_id":"sha256:0219795670df49d365c4ef05420d9ff90e1ea686e5cc017714c9f331d4b726c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HJVRCDEYVQGFE7GKSLNO5LWBN3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rigid Fuchsian systems in 2-dimensional conformal field theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Raoul Santachiara, Vladimir Belavin, Yoshishige Haraoka","submitted_at":"2017-11-12T21:28:05Z","abstract_excerpt":"We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of W3 Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one n-th level semi-degenerate field and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04361","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":"2026-05-18T00:00:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9piM1EAJ7qO5s4pHTCbeFspnP/cJw3zkLRK5EWkYJ86cwPB567dACPSaY5yXFGDq9qbQTPVYThJZ4480rY0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T16:00:58.545805Z"},"content_sha256":"e7d9d9a6b1f0721c698d17bc3170db855d64dc692ec5da5864b450eb4b3e4c65","schema_version":"1.0","event_id":"sha256:e7d9d9a6b1f0721c698d17bc3170db855d64dc692ec5da5864b450eb4b3e4c65"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3/bundle.json","state_url":"https://pith.science/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3/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":"2026-06-05T16:00:58Z","links":{"resolver":"https://pith.science/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3","bundle":"https://pith.science/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3/bundle.json","state":"https://pith.science/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HJVRCDEYVQGFE7GKSLNO5LWBN3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HJVRCDEYVQGFE7GKSLNO5LWBN3","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":"1405c3ce4416ee9d16ed3e69fffc7438123285d4cfc415dcb5c6f1c91f9f0d28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-12T21:28:05Z","title_canon_sha256":"06791fdb04012e37775379edbb42ee9fd3377a93c4a7e70cb15f46d399d43163"},"schema_version":"1.0","source":{"id":"1711.04361","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.04361","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1711.04361v1","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.04361","created_at":"2026-05-18T00:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"HJVRCDEYVQGF","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HJVRCDEYVQGFE7GK","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HJVRCDEY","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:e7d9d9a6b1f0721c698d17bc3170db855d64dc692ec5da5864b450eb4b3e4c65","target":"graph","created_at":"2026-05-18T00:00:59Z","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":"We investigate Fuchsian equations arising in the context of 2-dimensional conformal field theory (CFT) and we apply the Katz theory of Fucshian rigid systems to solve some of these equations. We show that the Katz theory provides a precise mathematical framework to answer the question whether the fusion rules of degenerate primary fields are enough for determining the differential equations satisfied by their correlation functions. We focus on the case of W3 Toda CFT: we argue that the differential equations arising for four-point conformal blocks with one n-th level semi-degenerate field and ","authors_text":"Raoul Santachiara, Vladimir Belavin, Yoshishige Haraoka","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-12T21:28:05Z","title":"Rigid Fuchsian systems in 2-dimensional conformal field theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.04361","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":"sha256:0219795670df49d365c4ef05420d9ff90e1ea686e5cc017714c9f331d4b726c1","target":"record","created_at":"2026-05-18T00:00:59Z","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":"1405c3ce4416ee9d16ed3e69fffc7438123285d4cfc415dcb5c6f1c91f9f0d28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-11-12T21:28:05Z","title_canon_sha256":"06791fdb04012e37775379edbb42ee9fd3377a93c4a7e70cb15f46d399d43163"},"schema_version":"1.0","source":{"id":"1711.04361","kind":"arxiv","version":1}},"canonical_sha256":"3a6b110c98ac0c527cca92daeeaec16ee5662f5bb2f5943a40fd013c4d6858f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a6b110c98ac0c527cca92daeeaec16ee5662f5bb2f5943a40fd013c4d6858f2","first_computed_at":"2026-05-18T00:00:59.909200Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:59.909200Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ai3vuYyseU+pnjCltUYhoBaJa1BBqs1YVFNz8x6sVTxJ4LdNpI9bH0OVyLLtY3MPSFGE/NVHZFwoeYWAzqC9DA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:59.909649Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.04361","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0219795670df49d365c4ef05420d9ff90e1ea686e5cc017714c9f331d4b726c1","sha256:e7d9d9a6b1f0721c698d17bc3170db855d64dc692ec5da5864b450eb4b3e4c65"],"state_sha256":"d92a2083b6285a5e2ca1e9bb8d962b4760fbd8ad7466dfb7e0f3819ea9ce973b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xbiFEjJ/WfobbwbZX9RF+U+qVQGNjgZLrJzLWcNNQZ3W3OsJB6LL0SbcsmvL7OS/4LgDCXYQ79gegYC9Vc/UDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T16:00:58.547617Z","bundle_sha256":"49e8b94fb89d6092bd0a32d38fa81f68f9310b9a7b92e6865cb4f8fcc8ac1c54"}}