{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EKLX36AU6CTCCSYJI52REOX345","short_pith_number":"pith:EKLX36AU","canonical_record":{"source":{"id":"1912.00635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-02T08:50:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b5352c020f509f273b689c2c818758055b845cd8a3cd2ec555cca9a9659c0336","abstract_canon_sha256":"4e72d6a2143b3d12c33fae8bb298f49fe791da2d8f6400e316dab2cffd9f27ad"},"schema_version":"1.0"},"canonical_sha256":"22977df814f0a6214b094775123afbe770d21ed80435026d2f85adb72cc0bee4","source":{"kind":"arxiv","id":"1912.00635","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00635","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00635v1","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00635","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"EKLX36AU6CTC","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"pith_short_16","alias_value":"EKLX36AU6CTCCSYJ","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"pith_short_8","alias_value":"EKLX36AU","created_at":"2026-07-05T00:48:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EKLX36AU6CTCCSYJI52REOX345","target":"record","payload":{"canonical_record":{"source":{"id":"1912.00635","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-02T08:50:33Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b5352c020f509f273b689c2c818758055b845cd8a3cd2ec555cca9a9659c0336","abstract_canon_sha256":"4e72d6a2143b3d12c33fae8bb298f49fe791da2d8f6400e316dab2cffd9f27ad"},"schema_version":"1.0"},"canonical_sha256":"22977df814f0a6214b094775123afbe770d21ed80435026d2f85adb72cc0bee4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:48:01.215814Z","signature_b64":"iWdgFUyt8N6JL5guDUK/3+b6y+V8BvSpvmUDGTV8rLxxWIfbF7qOZ0A7g9caxWBzTuHXo6Lds/F3AXM8257aCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22977df814f0a6214b094775123afbe770d21ed80435026d2f85adb72cc0bee4","last_reissued_at":"2026-07-05T00:48:01.215366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:48:01.215366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.00635","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":"2026-07-05T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vx/dHrB+q+xx2mWs45jZje2LokyGAdH22fgsWb6+RuKMda4fk1CYrz84VrwDtkhOaDxuJuL7P5/kQ4qXonIBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:16:44.573521Z"},"content_sha256":"dd97288d4325a127a6577e3916550eb8c9cded5fb2162e93863559c25d10dc8e","schema_version":"1.0","event_id":"sha256:dd97288d4325a127a6577e3916550eb8c9cded5fb2162e93863559c25d10dc8e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EKLX36AU6CTCCSYJI52REOX345","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hook variables: cut-and-join operators and $\\tau$-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","submitted_at":"2019-12-02T08:50:33Z","abstract_excerpt":"Young diagrams can be parameterized with the help of hook variables, which is well known but never studied in big detail. We demonstrate that this is the most adequate parameterization for many physical applications: from the Schur functions, conventional, skew and shifted, which all satisfy their own kinds of determinant formulas in these coordinates, to KP/Toda integrability and related basis of cut-and-join $\\hat W$-operators, which are both actually expressed through the single-hook diagrams. In particular, we discuss a new type of multi-component KP $\\tau$-functions, Matisse $\\tau$-functi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00635","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.00635/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":"2026-07-05T00:48:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RJE8LTX4tQWkKApfAlDEJB17pWHq/jT3ZzOh37tmrMTg5X2g60YihD2cX06EtoR/+6Y5/BuXJrQMsmiFu9NhCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T23:16:44.573906Z"},"content_sha256":"70697ca87a3a2b959ebf20d2cc51115c9de9f72b3d33346695e2d2f076f7e6be","schema_version":"1.0","event_id":"sha256:70697ca87a3a2b959ebf20d2cc51115c9de9f72b3d33346695e2d2f076f7e6be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKLX36AU6CTCCSYJI52REOX345/bundle.json","state_url":"https://pith.science/pith/EKLX36AU6CTCCSYJI52REOX345/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKLX36AU6CTCCSYJI52REOX345/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":"2026-08-05T23:16:44Z","links":{"resolver":"https://pith.science/pith/EKLX36AU6CTCCSYJI52REOX345","bundle":"https://pith.science/pith/EKLX36AU6CTCCSYJI52REOX345/bundle.json","state":"https://pith.science/pith/EKLX36AU6CTCCSYJI52REOX345/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKLX36AU6CTCCSYJI52REOX345/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EKLX36AU6CTCCSYJI52REOX345","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":"4e72d6a2143b3d12c33fae8bb298f49fe791da2d8f6400e316dab2cffd9f27ad","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-02T08:50:33Z","title_canon_sha256":"b5352c020f509f273b689c2c818758055b845cd8a3cd2ec555cca9a9659c0336"},"schema_version":"1.0","source":{"id":"1912.00635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00635","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00635v1","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00635","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"pith_short_12","alias_value":"EKLX36AU6CTC","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"pith_short_16","alias_value":"EKLX36AU6CTCCSYJ","created_at":"2026-07-05T00:48:01Z"},{"alias_kind":"pith_short_8","alias_value":"EKLX36AU","created_at":"2026-07-05T00:48:01Z"}],"graph_snapshots":[{"event_id":"sha256:70697ca87a3a2b959ebf20d2cc51115c9de9f72b3d33346695e2d2f076f7e6be","target":"graph","created_at":"2026-07-05T00:48:01Z","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/1912.00635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Young diagrams can be parameterized with the help of hook variables, which is well known but never studied in big detail. We demonstrate that this is the most adequate parameterization for many physical applications: from the Schur functions, conventional, skew and shifted, which all satisfy their own kinds of determinant formulas in these coordinates, to KP/Toda integrability and related basis of cut-and-join $\\hat W$-operators, which are both actually expressed through the single-hook diagrams. In particular, we discuss a new type of multi-component KP $\\tau$-functions, Matisse $\\tau$-functi","authors_text":"A. Mironov, A. Morozov","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-02T08:50:33Z","title":"Hook variables: cut-and-join operators and $\\tau$-functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00635","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:dd97288d4325a127a6577e3916550eb8c9cded5fb2162e93863559c25d10dc8e","target":"record","created_at":"2026-07-05T00:48:01Z","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":"4e72d6a2143b3d12c33fae8bb298f49fe791da2d8f6400e316dab2cffd9f27ad","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2019-12-02T08:50:33Z","title_canon_sha256":"b5352c020f509f273b689c2c818758055b845cd8a3cd2ec555cca9a9659c0336"},"schema_version":"1.0","source":{"id":"1912.00635","kind":"arxiv","version":1}},"canonical_sha256":"22977df814f0a6214b094775123afbe770d21ed80435026d2f85adb72cc0bee4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22977df814f0a6214b094775123afbe770d21ed80435026d2f85adb72cc0bee4","first_computed_at":"2026-07-05T00:48:01.215366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:48:01.215366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iWdgFUyt8N6JL5guDUK/3+b6y+V8BvSpvmUDGTV8rLxxWIfbF7qOZ0A7g9caxWBzTuHXo6Lds/F3AXM8257aCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:48:01.215814Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.00635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd97288d4325a127a6577e3916550eb8c9cded5fb2162e93863559c25d10dc8e","sha256:70697ca87a3a2b959ebf20d2cc51115c9de9f72b3d33346695e2d2f076f7e6be"],"state_sha256":"f3a639e428eb0a1bf8b5fd65a701ddaecc56b7b86b61573be39ac2f87af45ae8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yj8qxTZQAya03UlsW5USvLcCzanaXNmbZsxxw5xE1VRE8LSCBDyptQSVvH9hIv5vbPWVocUVcehbh+IsORsWBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T23:16:44.576848Z","bundle_sha256":"1e85bc2721c9eddc2410609af1b503ac8eb4cc8ebd894cf7f12e0c55a57a8439"}}