{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:5X5DFQ4EAEDFCDZ642KUMNVTPP","short_pith_number":"pith:5X5DFQ4E","canonical_record":{"source":{"id":"1012.3137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-14T19:11:05Z","cross_cats_sorted":[],"title_canon_sha256":"3cf472f0a8161ef92123d4290b502c4fe725630a66fd6665f69cfe197d6e2024","abstract_canon_sha256":"04d94eb8d8cc52b51ae8af68f6f505981a01039cefbea6fd67d5955f661452e7"},"schema_version":"1.0"},"canonical_sha256":"edfa32c3840106510f3ee6954636b37beb1a4575676dbd481e5e37e812f091df","source":{"kind":"arxiv","id":"1012.3137","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3137","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3137v1","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3137","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"5X5DFQ4EAEDF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5X5DFQ4EAEDFCDZ6","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5X5DFQ4E","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:5X5DFQ4EAEDFCDZ642KUMNVTPP","target":"record","payload":{"canonical_record":{"source":{"id":"1012.3137","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-14T19:11:05Z","cross_cats_sorted":[],"title_canon_sha256":"3cf472f0a8161ef92123d4290b502c4fe725630a66fd6665f69cfe197d6e2024","abstract_canon_sha256":"04d94eb8d8cc52b51ae8af68f6f505981a01039cefbea6fd67d5955f661452e7"},"schema_version":"1.0"},"canonical_sha256":"edfa32c3840106510f3ee6954636b37beb1a4575676dbd481e5e37e812f091df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:34.396641Z","signature_b64":"qnDVaOgf4lyYX8Ww9L4gP9NimkhgGeTwOL9x1OW+lKIroY/ISPF5vv1XRcUKEZPDvCujLDy0aVybQ96+9wl2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edfa32c3840106510f3ee6954636b37beb1a4575676dbd481e5e37e812f091df","last_reissued_at":"2026-05-18T04:26:34.396113Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:34.396113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.3137","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":"2026-05-18T04:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RciALIGpLpCOxugLniENu4JrNjayv7vMhJ6ta+OgE+kQPs3PYX5lb4VKd44yBdqL2FQZToT6zNT5/ejgzaNRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:52:52.429473Z"},"content_sha256":"5246b9e95d372fd1e112398fdeefae0b7c4e8261d83c315393e354ef199e253d","schema_version":"1.0","event_id":"sha256:5246b9e95d372fd1e112398fdeefae0b7c4e8261d83c315393e354ef199e253d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:5X5DFQ4EAEDFCDZ642KUMNVTPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A direct proof of AGT conjecture at beta = 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A.Mironov, A.Morozov, Sh.Shakirov","submitted_at":"2010-12-14T19:11:05Z","abstract_excerpt":"The AGT conjecture claims an equivalence of conformal blocks in 2d CFT and sums of Nekrasov functions (instantonic sums in 4d SUSY gauge theory). The conformal blocks can be presented as Dotsenko-Fateev beta-ensembles, hence, the AGT conjecture implies the equality between Dotsenko-Fateev beta-ensembles and the Nekrasov functions. In this paper, we prove it in a particular case of beta=1 (which corresponds to c = 1 at the conformal side and to epsilon_1 + epsilon_2 = 0 at the gauge theory side) in a very direct way. The central role is played by representation of the Nekrasov functions through"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3137","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":"2026-05-18T04:26:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QhCZJwG+z2IcwtHJQekx9moZw4citBMn+SlWMyV9R+9zya90dFDtrtKqG4hv8ws3vQBu5f0NKtkd9mGrpQoJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T11:52:52.430148Z"},"content_sha256":"6999713bd25b2abb2af23254d6db0cf9b9ffbee63858a14caa392cf125dd34fc","schema_version":"1.0","event_id":"sha256:6999713bd25b2abb2af23254d6db0cf9b9ffbee63858a14caa392cf125dd34fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP/bundle.json","state_url":"https://pith.science/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP/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":"2026-05-22T11:52:52Z","links":{"resolver":"https://pith.science/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP","bundle":"https://pith.science/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP/bundle.json","state":"https://pith.science/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5X5DFQ4EAEDFCDZ642KUMNVTPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5X5DFQ4EAEDFCDZ642KUMNVTPP","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":"04d94eb8d8cc52b51ae8af68f6f505981a01039cefbea6fd67d5955f661452e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-14T19:11:05Z","title_canon_sha256":"3cf472f0a8161ef92123d4290b502c4fe725630a66fd6665f69cfe197d6e2024"},"schema_version":"1.0","source":{"id":"1012.3137","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.3137","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"arxiv_version","alias_value":"1012.3137v1","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.3137","created_at":"2026-05-18T04:26:34Z"},{"alias_kind":"pith_short_12","alias_value":"5X5DFQ4EAEDF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5X5DFQ4EAEDFCDZ6","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5X5DFQ4E","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:6999713bd25b2abb2af23254d6db0cf9b9ffbee63858a14caa392cf125dd34fc","target":"graph","created_at":"2026-05-18T04:26:34Z","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 AGT conjecture claims an equivalence of conformal blocks in 2d CFT and sums of Nekrasov functions (instantonic sums in 4d SUSY gauge theory). The conformal blocks can be presented as Dotsenko-Fateev beta-ensembles, hence, the AGT conjecture implies the equality between Dotsenko-Fateev beta-ensembles and the Nekrasov functions. In this paper, we prove it in a particular case of beta=1 (which corresponds to c = 1 at the conformal side and to epsilon_1 + epsilon_2 = 0 at the gauge theory side) in a very direct way. The central role is played by representation of the Nekrasov functions through","authors_text":"A.Mironov, A.Morozov, Sh.Shakirov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-14T19:11:05Z","title":"A direct proof of AGT conjecture at beta = 1"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.3137","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":"sha256:5246b9e95d372fd1e112398fdeefae0b7c4e8261d83c315393e354ef199e253d","target":"record","created_at":"2026-05-18T04:26:34Z","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":"04d94eb8d8cc52b51ae8af68f6f505981a01039cefbea6fd67d5955f661452e7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-12-14T19:11:05Z","title_canon_sha256":"3cf472f0a8161ef92123d4290b502c4fe725630a66fd6665f69cfe197d6e2024"},"schema_version":"1.0","source":{"id":"1012.3137","kind":"arxiv","version":1}},"canonical_sha256":"edfa32c3840106510f3ee6954636b37beb1a4575676dbd481e5e37e812f091df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edfa32c3840106510f3ee6954636b37beb1a4575676dbd481e5e37e812f091df","first_computed_at":"2026-05-18T04:26:34.396113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:34.396113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qnDVaOgf4lyYX8Ww9L4gP9NimkhgGeTwOL9x1OW+lKIroY/ISPF5vv1XRcUKEZPDvCujLDy0aVybQ96+9wl2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:34.396641Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.3137","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5246b9e95d372fd1e112398fdeefae0b7c4e8261d83c315393e354ef199e253d","sha256:6999713bd25b2abb2af23254d6db0cf9b9ffbee63858a14caa392cf125dd34fc"],"state_sha256":"c4cb79d6333e76baf3185e81bc2f2d0736896c4597078c11abcfb62bbde15fa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HHfwc93iRvERxCDHS7F4I4DeQGdOVmyI89BTHVhbyixcHn7i8G5PQzfw9zzgSsFZcDNQyJFVsHVrMDf/FUu2BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T11:52:52.433624Z","bundle_sha256":"bc059964135803a2136850f8416b0ccdfc402d31391e92381f7e18ebb6c0485a"}}