{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:VKTI23JYR5PJ6MMMK6NE2HPTIJ","short_pith_number":"pith:VKTI23JY","canonical_record":{"source":{"id":"2111.05776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-10T16:30:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"42527ff9f8f70d15045915428279bce1d39581b2cd08c2541521fd7a78481159","abstract_canon_sha256":"5dbaed2f8d47f896ef48acd66c225e75a5887fb5f7d132dc38e1818458454635"},"schema_version":"1.0"},"canonical_sha256":"aaa68d6d388f5e9f318c579a4d1df3426d4449ea49e286ece2d18f8216cd26ef","source":{"kind":"arxiv","id":"2111.05776","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.05776","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"2111.05776v2","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.05776","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"VKTI23JYR5PJ","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"VKTI23JYR5PJ6MMM","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"VKTI23JY","created_at":"2026-07-05T04:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:VKTI23JYR5PJ6MMMK6NE2HPTIJ","target":"record","payload":{"canonical_record":{"source":{"id":"2111.05776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-10T16:30:04Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"42527ff9f8f70d15045915428279bce1d39581b2cd08c2541521fd7a78481159","abstract_canon_sha256":"5dbaed2f8d47f896ef48acd66c225e75a5887fb5f7d132dc38e1818458454635"},"schema_version":"1.0"},"canonical_sha256":"aaa68d6d388f5e9f318c579a4d1df3426d4449ea49e286ece2d18f8216cd26ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:29:10.529360Z","signature_b64":"mD5O7Hi0dIRsNmItHwIHBFyjIj5zOA8oj/sVeHK3nzXOfiawjGFApnvgszOA2xRwZB5lvjfk6en5E+whGBQzDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aaa68d6d388f5e9f318c579a4d1df3426d4449ea49e286ece2d18f8216cd26ef","last_reissued_at":"2026-07-05T04:29:10.528794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:29:10.528794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.05776","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":"2026-07-05T04:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GQJCXabnAOk5ntxpHtPwkkdWeYxUC7lb9QnJgcrP/jlaKgbyJ5uCNg3HvvZ4ky6EFrk+QrDFbDevSo4xx/N3BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:53:54.007924Z"},"content_sha256":"667ff6c48ce94fb49c78115a9509446871fc4659943632f51a372257176e7284","schema_version":"1.0","event_id":"sha256:667ff6c48ce94fb49c78115a9509446871fc4659943632f51a372257176e7284"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:VKTI23JYR5PJ6MMMK6NE2HPTIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spin Hurwitz theory and Miwa transform for the Schur Q-functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. Mironov, A. Morozov, A. Zhabin","submitted_at":"2021-11-10T16:30:04Z","abstract_excerpt":"Schur functions are the common eigenfunctions of generalized cut-and-join operators which form a closed algebra. They can be expressed as differential operators in time-variables and also through the eigenvalues of auxiliary $N\\times N$ matrices $X$, known as Miwa variables. Relevant for the cubic Kontsevich model and also for spin Hurwitz theory is an alternative set of Schur Q-functions. They appear in representation theory of the Sergeev group, which is a substitute of the symmetric group, related to the queer Lie superalgebras $\\mathfrak{q}(N)$.. The corresponding spin $\\hat{\\cal W}$-opera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.05776","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.05776/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":"2026-07-05T04:29:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rYcpSJCbUBPAdUWMLMzMmKCPjmeLqIgnl/6TwX34g8U6wn8oFyOds7y5H58S393PGuoiGH8zbnpaCgVlr3WjDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T03:53:54.008445Z"},"content_sha256":"ee54912565435a927353e88245d9c05c67679f9a097b8a0cde53121867e1747d","schema_version":"1.0","event_id":"sha256:ee54912565435a927353e88245d9c05c67679f9a097b8a0cde53121867e1747d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ/bundle.json","state_url":"https://pith.science/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ/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":"2026-08-06T03:53:54Z","links":{"resolver":"https://pith.science/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ","bundle":"https://pith.science/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ/bundle.json","state":"https://pith.science/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKTI23JYR5PJ6MMMK6NE2HPTIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:VKTI23JYR5PJ6MMMK6NE2HPTIJ","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":"5dbaed2f8d47f896ef48acd66c225e75a5887fb5f7d132dc38e1818458454635","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-10T16:30:04Z","title_canon_sha256":"42527ff9f8f70d15045915428279bce1d39581b2cd08c2541521fd7a78481159"},"schema_version":"1.0","source":{"id":"2111.05776","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.05776","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"arxiv_version","alias_value":"2111.05776v2","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.05776","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"pith_short_12","alias_value":"VKTI23JYR5PJ","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"VKTI23JYR5PJ6MMM","created_at":"2026-07-05T04:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"VKTI23JY","created_at":"2026-07-05T04:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:ee54912565435a927353e88245d9c05c67679f9a097b8a0cde53121867e1747d","target":"graph","created_at":"2026-07-05T04:29:10Z","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/2111.05776/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Schur functions are the common eigenfunctions of generalized cut-and-join operators which form a closed algebra. They can be expressed as differential operators in time-variables and also through the eigenvalues of auxiliary $N\\times N$ matrices $X$, known as Miwa variables. Relevant for the cubic Kontsevich model and also for spin Hurwitz theory is an alternative set of Schur Q-functions. They appear in representation theory of the Sergeev group, which is a substitute of the symmetric group, related to the queer Lie superalgebras $\\mathfrak{q}(N)$.. The corresponding spin $\\hat{\\cal W}$-opera","authors_text":"A. Mironov, A. Morozov, A. Zhabin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-10T16:30:04Z","title":"Spin Hurwitz theory and Miwa transform for the Schur Q-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.05776","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":"sha256:667ff6c48ce94fb49c78115a9509446871fc4659943632f51a372257176e7284","target":"record","created_at":"2026-07-05T04:29:10Z","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":"5dbaed2f8d47f896ef48acd66c225e75a5887fb5f7d132dc38e1818458454635","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2021-11-10T16:30:04Z","title_canon_sha256":"42527ff9f8f70d15045915428279bce1d39581b2cd08c2541521fd7a78481159"},"schema_version":"1.0","source":{"id":"2111.05776","kind":"arxiv","version":2}},"canonical_sha256":"aaa68d6d388f5e9f318c579a4d1df3426d4449ea49e286ece2d18f8216cd26ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aaa68d6d388f5e9f318c579a4d1df3426d4449ea49e286ece2d18f8216cd26ef","first_computed_at":"2026-07-05T04:29:10.528794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:29:10.528794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mD5O7Hi0dIRsNmItHwIHBFyjIj5zOA8oj/sVeHK3nzXOfiawjGFApnvgszOA2xRwZB5lvjfk6en5E+whGBQzDw==","signature_status":"signed_v1","signed_at":"2026-07-05T04:29:10.529360Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.05776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:667ff6c48ce94fb49c78115a9509446871fc4659943632f51a372257176e7284","sha256:ee54912565435a927353e88245d9c05c67679f9a097b8a0cde53121867e1747d"],"state_sha256":"c266bfc403ba4801b53e459383023dada6e10c9daf76b25a253efb99e25c3bea"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1OeYhubDVnQj3X+m+WKoOYTunh73PF1mko3DyGjvnd1dSxNiy+2/FYHYT81AB7JBqn5uDWJO0mUcCMCmJTUADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T03:53:54.012059Z","bundle_sha256":"29a921cba1e2ede23468cb6d44ec0e73d680d751752796deb2f219a5f7246fe1"}}