{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:OLTXWFR2IVLCFGMWE7LLN4FC5O","short_pith_number":"pith:OLTXWFR2","canonical_record":{"source":{"id":"hep-th/0508019","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2005-08-03T00:08:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ac68ab5ecc8d87d1f1ae48f6e0028e1f048e903a647ad981677b1d4be2f086ff","abstract_canon_sha256":"ddaed29de3e14d406b08d5891e66930e6e75bee22291a6ad21993d0ea5c9ab5c"},"schema_version":"1.0"},"canonical_sha256":"72e77b163a455622999627d6b6f0a2eb96cc2520585d1f59dd78cff3262ad76e","source":{"kind":"arxiv","id":"hep-th/0508019","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0508019","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0508019v3","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0508019","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"OLTXWFR2IVLC","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"pith_short_16","alias_value":"OLTXWFR2IVLCFGMW","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"pith_short_8","alias_value":"OLTXWFR2","created_at":"2026-07-04T16:56:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:OLTXWFR2IVLCFGMWE7LLN4FC5O","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0508019","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2005-08-03T00:08:50Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ac68ab5ecc8d87d1f1ae48f6e0028e1f048e903a647ad981677b1d4be2f086ff","abstract_canon_sha256":"ddaed29de3e14d406b08d5891e66930e6e75bee22291a6ad21993d0ea5c9ab5c"},"schema_version":"1.0"},"canonical_sha256":"72e77b163a455622999627d6b6f0a2eb96cc2520585d1f59dd78cff3262ad76e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:56:17.107098Z","signature_b64":"eDdNoYazEt/5DFhBVujYgZYl59+W2/eF7dusVFiKLb1WJjgKGG0XcgC0aSwSsl3o3bD8LousnCmDDO2sW2DYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72e77b163a455622999627d6b6f0a2eb96cc2520585d1f59dd78cff3262ad76e","last_reissued_at":"2026-07-04T16:56:17.106730Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:56:17.106730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0508019","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T16:56:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXg6FnBCO9Gh2LN2/5K5Fs7sx0PWeSlwOcRNvxlkV5c6yk/BYxxtnaOD7tMfZUeWYj+ofqLGBiDHPUEwRp5rDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:43:08.351887Z"},"content_sha256":"fc745f997e12ac66f5d0975b971dec17cff4cc5dee8e3b3b7a6d11096181da05","schema_version":"1.0","event_id":"sha256:fc745f997e12ac66f5d0975b971dec17cff4cc5dee8e3b3b7a6d11096181da05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:OLTXWFR2IVLCFGMWE7LLN4FC5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation","license":"","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Gaston Giribet","submitted_at":"2005-08-03T00:08:50Z","abstract_excerpt":"It is well known that five-point function in Liouville field theory provides a representation of solutions of the SL(2,R)_k Knizhnik-Zamolodchikov equation at the level of four-point function. Here, we make use of such representation to study some aspects of the spectral flow symmetry of sl(2)_k affine algebra and its action on the observables of the WZNW theory. To illustrate the usefulness of this method we rederive the three-point function that violates the winding number in SL(2,R) in a very succinct way. In addition, we prove several identities holding between exact solutions of the Knizh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0508019","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0508019/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:56:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7yW0QCrwaZZ48Ijbe81fXft3NTYLJLSUxmZBQDe8xrVcCmXvBNgS11tJpPj6gZ49cyRkAHGIXKGHO9ArsQMCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:43:08.352643Z"},"content_sha256":"7530dca18d4e2f1f716c771e1ca68a9e941b05bba788c00a314eefebe684dc86","schema_version":"1.0","event_id":"sha256:7530dca18d4e2f1f716c771e1ca68a9e941b05bba788c00a314eefebe684dc86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O/bundle.json","state_url":"https://pith.science/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O/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":"2026-08-18T18:43:08Z","links":{"resolver":"https://pith.science/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O","bundle":"https://pith.science/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O/bundle.json","state":"https://pith.science/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OLTXWFR2IVLCFGMWE7LLN4FC5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:OLTXWFR2IVLCFGMWE7LLN4FC5O","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":"ddaed29de3e14d406b08d5891e66930e6e75bee22291a6ad21993d0ea5c9ab5c","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2005-08-03T00:08:50Z","title_canon_sha256":"ac68ab5ecc8d87d1f1ae48f6e0028e1f048e903a647ad981677b1d4be2f086ff"},"schema_version":"1.0","source":{"id":"hep-th/0508019","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0508019","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0508019v3","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0508019","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"OLTXWFR2IVLC","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"pith_short_16","alias_value":"OLTXWFR2IVLCFGMW","created_at":"2026-07-04T16:56:17Z"},{"alias_kind":"pith_short_8","alias_value":"OLTXWFR2","created_at":"2026-07-04T16:56:17Z"}],"graph_snapshots":[{"event_id":"sha256:7530dca18d4e2f1f716c771e1ca68a9e941b05bba788c00a314eefebe684dc86","target":"graph","created_at":"2026-07-04T16:56:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0508019/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is well known that five-point function in Liouville field theory provides a representation of solutions of the SL(2,R)_k Knizhnik-Zamolodchikov equation at the level of four-point function. Here, we make use of such representation to study some aspects of the spectral flow symmetry of sl(2)_k affine algebra and its action on the observables of the WZNW theory. To illustrate the usefulness of this method we rederive the three-point function that violates the winding number in SL(2,R) in a very succinct way. In addition, we prove several identities holding between exact solutions of the Knizh","authors_text":"Gaston Giribet","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2005-08-03T00:08:50Z","title":"On Spectral Flow Symmetry and Knizhnik-Zamolodchikov Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0508019","kind":"arxiv","version":3},"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:fc745f997e12ac66f5d0975b971dec17cff4cc5dee8e3b3b7a6d11096181da05","target":"record","created_at":"2026-07-04T16:56:17Z","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":"ddaed29de3e14d406b08d5891e66930e6e75bee22291a6ad21993d0ea5c9ab5c","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2005-08-03T00:08:50Z","title_canon_sha256":"ac68ab5ecc8d87d1f1ae48f6e0028e1f048e903a647ad981677b1d4be2f086ff"},"schema_version":"1.0","source":{"id":"hep-th/0508019","kind":"arxiv","version":3}},"canonical_sha256":"72e77b163a455622999627d6b6f0a2eb96cc2520585d1f59dd78cff3262ad76e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72e77b163a455622999627d6b6f0a2eb96cc2520585d1f59dd78cff3262ad76e","first_computed_at":"2026-07-04T16:56:17.106730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:56:17.106730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eDdNoYazEt/5DFhBVujYgZYl59+W2/eF7dusVFiKLb1WJjgKGG0XcgC0aSwSsl3o3bD8LousnCmDDO2sW2DYCw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:56:17.107098Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0508019","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc745f997e12ac66f5d0975b971dec17cff4cc5dee8e3b3b7a6d11096181da05","sha256:7530dca18d4e2f1f716c771e1ca68a9e941b05bba788c00a314eefebe684dc86"],"state_sha256":"a11792be312f4d8f5061c5bf4da96ce2e622adc2e7f8307c9f27db81951e64df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lU49uRoNqMu7oMP+uoCIjIIN225pA8AG/mVjQW+WsrdBkgCfmw/fAb1u10EWnwQ5yIdFJsVQx/OPAdekj5FyBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:43:08.357527Z","bundle_sha256":"536bfdba658513b5e4f34a5253831a6498d14a0f6a749823df24158dba3f24d7"}}