{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YCS4TE7OYGGN76R6343N5NY6BF","short_pith_number":"pith:YCS4TE7O","canonical_record":{"source":{"id":"1311.7069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-11-27T18:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f939fad81808d03f0e6c3e7a83ebdd9d6deb771750a077bab1879e9f5629f40","abstract_canon_sha256":"9932a780bcc7b21e5529607ddf723cda03a1f3ac09381095cd43274923eeffcd"},"schema_version":"1.0"},"canonical_sha256":"c0a5c993eec18cdffa3edf36deb71e095885f8a24a0fb1d145a2c52c8b2d4f57","source":{"kind":"arxiv","id":"1311.7069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7069","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7069v1","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7069","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"YCS4TE7OYGGN","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YCS4TE7OYGGN76R6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YCS4TE7O","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YCS4TE7OYGGN76R6343N5NY6BF","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-11-27T18:53:39Z","cross_cats_sorted":[],"title_canon_sha256":"1f939fad81808d03f0e6c3e7a83ebdd9d6deb771750a077bab1879e9f5629f40","abstract_canon_sha256":"9932a780bcc7b21e5529607ddf723cda03a1f3ac09381095cd43274923eeffcd"},"schema_version":"1.0"},"canonical_sha256":"c0a5c993eec18cdffa3edf36deb71e095885f8a24a0fb1d145a2c52c8b2d4f57","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:26.005669Z","signature_b64":"en1fwJhV5mqJJWh3lYatFGhVsjKc/r16DgGcoxwbmfqV6tA5EuDHyy7fTW5cGyUGrixF7qMKct2tKt8d7SkJAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0a5c993eec18cdffa3edf36deb71e095885f8a24a0fb1d145a2c52c8b2d4f57","last_reissued_at":"2026-05-18T02:48:26.005192Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:26.005192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7069","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":"2026-05-18T02:48:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHWmRjHR9SQl4YnHT/3i9wGIoWKOeWihI0g5t+L33Tp1D0hZaoaLyCr8OHpGO30q2WR9jPtU4q4WdiUDSEeRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:19:25.718495Z"},"content_sha256":"fe5f2a511d994a70f914da32191c58a4a741d26190f43e554b2bff683ee13615","schema_version":"1.0","event_id":"sha256:fe5f2a511d994a70f914da32191c58a4a741d26190f43e554b2bff683ee13615"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YCS4TE7OYGGN76R6343N5NY6BF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, D. Galakhov","submitted_at":"2013-11-27T18:53:39Z","abstract_excerpt":"A recent claim that the S-duality between 4d SUSY gauge theories, which is AGT related to the modular transformations of 2d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to the commutation relation [P,Q]=-i\\hbar between the check-operator monodromies of the exponential resolvent operator in the underlying Dotsenko-Fateev matrix models and beta-ensembles. To this end, we treat the conformal blocks as eigenfunctions of the monodromy check operators, what is especially simple in the case of one-point toric block. The kernel of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7069","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":"2026-05-18T02:48:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pB5U9FTF0pn7LWZpuqpEmFf+6o7yVZMePruSRjzja4YakjzwZHIkQsePmdoypZnyb38+gq/FiLm58qB66X/tDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:19:25.719179Z"},"content_sha256":"39172b563d03a121249e2253b196c28d8c5efe9b21c42bf5ac5a31b47c9fa934","schema_version":"1.0","event_id":"sha256:39172b563d03a121249e2253b196c28d8c5efe9b21c42bf5ac5a31b47c9fa934"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCS4TE7OYGGN76R6343N5NY6BF/bundle.json","state_url":"https://pith.science/pith/YCS4TE7OYGGN76R6343N5NY6BF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCS4TE7OYGGN76R6343N5NY6BF/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":"2026-05-26T03:19:25Z","links":{"resolver":"https://pith.science/pith/YCS4TE7OYGGN76R6343N5NY6BF","bundle":"https://pith.science/pith/YCS4TE7OYGGN76R6343N5NY6BF/bundle.json","state":"https://pith.science/pith/YCS4TE7OYGGN76R6343N5NY6BF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCS4TE7OYGGN76R6343N5NY6BF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YCS4TE7OYGGN76R6343N5NY6BF","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":"9932a780bcc7b21e5529607ddf723cda03a1f3ac09381095cd43274923eeffcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-11-27T18:53:39Z","title_canon_sha256":"1f939fad81808d03f0e6c3e7a83ebdd9d6deb771750a077bab1879e9f5629f40"},"schema_version":"1.0","source":{"id":"1311.7069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7069","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7069v1","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7069","created_at":"2026-05-18T02:48:26Z"},{"alias_kind":"pith_short_12","alias_value":"YCS4TE7OYGGN","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YCS4TE7OYGGN76R6","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YCS4TE7O","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:39172b563d03a121249e2253b196c28d8c5efe9b21c42bf5ac5a31b47c9fa934","target":"graph","created_at":"2026-05-18T02:48:26Z","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":"A recent claim that the S-duality between 4d SUSY gauge theories, which is AGT related to the modular transformations of 2d conformal blocks, is no more than an ordinary Fourier transform at the perturbative level, is further traced down to the commutation relation [P,Q]=-i\\hbar between the check-operator monodromies of the exponential resolvent operator in the underlying Dotsenko-Fateev matrix models and beta-ensembles. To this end, we treat the conformal blocks as eigenfunctions of the monodromy check operators, what is especially simple in the case of one-point toric block. The kernel of th","authors_text":"A. Mironov, A. Morozov, D. Galakhov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-11-27T18:53:39Z","title":"S-Duality and Modular Transformation as a non-perturbative deformation of the ordinary pq-duality"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7069","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:fe5f2a511d994a70f914da32191c58a4a741d26190f43e554b2bff683ee13615","target":"record","created_at":"2026-05-18T02:48:26Z","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":"9932a780bcc7b21e5529607ddf723cda03a1f3ac09381095cd43274923eeffcd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-11-27T18:53:39Z","title_canon_sha256":"1f939fad81808d03f0e6c3e7a83ebdd9d6deb771750a077bab1879e9f5629f40"},"schema_version":"1.0","source":{"id":"1311.7069","kind":"arxiv","version":1}},"canonical_sha256":"c0a5c993eec18cdffa3edf36deb71e095885f8a24a0fb1d145a2c52c8b2d4f57","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a5c993eec18cdffa3edf36deb71e095885f8a24a0fb1d145a2c52c8b2d4f57","first_computed_at":"2026-05-18T02:48:26.005192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:26.005192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"en1fwJhV5mqJJWh3lYatFGhVsjKc/r16DgGcoxwbmfqV6tA5EuDHyy7fTW5cGyUGrixF7qMKct2tKt8d7SkJAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:26.005669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe5f2a511d994a70f914da32191c58a4a741d26190f43e554b2bff683ee13615","sha256:39172b563d03a121249e2253b196c28d8c5efe9b21c42bf5ac5a31b47c9fa934"],"state_sha256":"349b1fecc7de3bece56b07ddd5174b8e88261f37038997157795abbca0e144b7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0yM4+FfuJHt4nzzUzBnLqKLaN7li1rA2d5Zp7LLBBnK0CAOBQ5rTmVlD22ll69vYm9HlsvchP8XelGdUOzWSDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:19:25.722716Z","bundle_sha256":"7aebb07c5848be879fbf1e5e1d59ba6745b699b6923691c0aef4ea73f58e6029"}}