{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CBRKEZV3AJRUD5YVRSX5R22RA2","short_pith_number":"pith:CBRKEZV3","canonical_record":{"source":{"id":"1810.07676","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:24:24Z","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"title_canon_sha256":"ad9f7b95b55226ca9498a60e6d8a55f3d9ec37530701d74f66ce980b61e5bf23","abstract_canon_sha256":"9ef68d8b948b9df23a453c34b498e79eeed1ff52ac160799ffb1edab8c159b85"},"schema_version":"1.0"},"canonical_sha256":"1062a266bb026341f7158cafd8eb51068ada6161114f490aa6757a8e41a495bb","source":{"kind":"arxiv","id":"1810.07676","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07676","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07676v2","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07676","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"CBRKEZV3AJRU","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CBRKEZV3AJRUD5YV","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CBRKEZV3","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CBRKEZV3AJRUD5YVRSX5R22RA2","target":"record","payload":{"canonical_record":{"source":{"id":"1810.07676","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:24:24Z","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"title_canon_sha256":"ad9f7b95b55226ca9498a60e6d8a55f3d9ec37530701d74f66ce980b61e5bf23","abstract_canon_sha256":"9ef68d8b948b9df23a453c34b498e79eeed1ff52ac160799ffb1edab8c159b85"},"schema_version":"1.0"},"canonical_sha256":"1062a266bb026341f7158cafd8eb51068ada6161114f490aa6757a8e41a495bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:06.471335Z","signature_b64":"2zWUPKmZdXMbJ7GY9AN3Fb2mFZSQgeRS14VLbj+k3od0CyXl6IlImgJT5lnK6ItDy+sGRm7KqL03X/aroU7RDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1062a266bb026341f7158cafd8eb51068ada6161114f490aa6757a8e41a495bb","last_reissued_at":"2026-05-17T23:48:06.470925Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:06.470925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.07676","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":"2026-05-17T23:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A9nZB1zXfhEm4EK01nLjU1qFFPTqluw0MbLhuuc17WsUDYisG0obrHPlRqawlr+IG/cI2K6Ou7g3zOcQqKZSCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:18:44.481733Z"},"content_sha256":"fc056bd49bca15e4c85db5e260dba007b68b2052f4d99b9127e0de4a6675e17f","schema_version":"1.0","event_id":"sha256:fc056bd49bca15e4c85db5e260dba007b68b2052f4d99b9127e0de4a6675e17f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CBRKEZV3AJRUD5YVRSX5R22RA2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The MacMahon R-matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, H. Awata, H. Kanno, K. Suetake, Y. Zenkevich","submitted_at":"2018-10-17T17:24:24Z","abstract_excerpt":"We introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters $q$, $t^{-1}$ and $\\frac{t}{q}$. We construct the intertwining operator for a tensor product of the horizontal Fock representation and the vertical MacMahon representation and show that the intertwiners are permuted using the MacMahon $R$-matrix."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07676","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":"2026-05-17T23:48:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbG36miCg6UKQKlahUrD0yrgpA5It/TcBu3GUZoFBEoRWO1TzbsawIRCeYw8JYpI9E16LApe3trCwBG3Et+aBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T05:18:44.482467Z"},"content_sha256":"6c101c4dec2e17bcf0644817b3e5b5627f58bd8e23527f8333287e183a1dd553","schema_version":"1.0","event_id":"sha256:6c101c4dec2e17bcf0644817b3e5b5627f58bd8e23527f8333287e183a1dd553"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CBRKEZV3AJRUD5YVRSX5R22RA2/bundle.json","state_url":"https://pith.science/pith/CBRKEZV3AJRUD5YVRSX5R22RA2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CBRKEZV3AJRUD5YVRSX5R22RA2/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":"2026-05-26T05:18:44Z","links":{"resolver":"https://pith.science/pith/CBRKEZV3AJRUD5YVRSX5R22RA2","bundle":"https://pith.science/pith/CBRKEZV3AJRUD5YVRSX5R22RA2/bundle.json","state":"https://pith.science/pith/CBRKEZV3AJRUD5YVRSX5R22RA2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CBRKEZV3AJRUD5YVRSX5R22RA2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CBRKEZV3AJRUD5YVRSX5R22RA2","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":"9ef68d8b948b9df23a453c34b498e79eeed1ff52ac160799ffb1edab8c159b85","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:24:24Z","title_canon_sha256":"ad9f7b95b55226ca9498a60e6d8a55f3d9ec37530701d74f66ce980b61e5bf23"},"schema_version":"1.0","source":{"id":"1810.07676","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07676","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07676v2","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07676","created_at":"2026-05-17T23:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"CBRKEZV3AJRU","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CBRKEZV3AJRUD5YV","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CBRKEZV3","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:6c101c4dec2e17bcf0644817b3e5b5627f58bd8e23527f8333287e183a1dd553","target":"graph","created_at":"2026-05-17T23:48:06Z","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 introduce an $R$-matrix acting on the tensor product of MacMahon representations of Ding-Iohara-Miki (DIM) algebra $U_{q,t}(\\widehat{\\widehat{\\mathfrak{gl}}}_1)$. This $R$-matrix acts on pairs of $3d$ Young diagrams and retains the nice symmetry of the DIM algebra under the permutation of three deformation parameters $q$, $t^{-1}$ and $\\frac{t}{q}$. We construct the intertwining operator for a tensor product of the horizontal Fock representation and the vertical MacMahon representation and show that the intertwiners are permuted using the MacMahon $R$-matrix.","authors_text":"A. Mironov, A. Morozov, H. Awata, H. Kanno, K. Suetake, Y. Zenkevich","cross_cats":["math-ph","math.MP","math.QA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:24:24Z","title":"The MacMahon R-matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07676","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:fc056bd49bca15e4c85db5e260dba007b68b2052f4d99b9127e0de4a6675e17f","target":"record","created_at":"2026-05-17T23:48:06Z","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":"9ef68d8b948b9df23a453c34b498e79eeed1ff52ac160799ffb1edab8c159b85","cross_cats_sorted":["math-ph","math.MP","math.QA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-10-17T17:24:24Z","title_canon_sha256":"ad9f7b95b55226ca9498a60e6d8a55f3d9ec37530701d74f66ce980b61e5bf23"},"schema_version":"1.0","source":{"id":"1810.07676","kind":"arxiv","version":2}},"canonical_sha256":"1062a266bb026341f7158cafd8eb51068ada6161114f490aa6757a8e41a495bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1062a266bb026341f7158cafd8eb51068ada6161114f490aa6757a8e41a495bb","first_computed_at":"2026-05-17T23:48:06.470925Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:06.470925Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2zWUPKmZdXMbJ7GY9AN3Fb2mFZSQgeRS14VLbj+k3od0CyXl6IlImgJT5lnK6ItDy+sGRm7KqL03X/aroU7RDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:06.471335Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07676","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc056bd49bca15e4c85db5e260dba007b68b2052f4d99b9127e0de4a6675e17f","sha256:6c101c4dec2e17bcf0644817b3e5b5627f58bd8e23527f8333287e183a1dd553"],"state_sha256":"ac57e138254527e4f1ff5aadbc34fd2ca144439e7f92075821c6fcc9a99ad637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NMl36wXnZLRKJd3lOVXr3KFO+jXJbEyak3yPKv8u0qkjwTph9UrY/RtBclBCw39jM5hOqCbpdTcz9pxfrX+OCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T05:18:44.486198Z","bundle_sha256":"ead9445ff1b5b37e4fce8c4c2cd1e71c0ae24d0bd3e6a2356d599c39081ee2c0"}}