{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:VD3D7XWAU26A462MY4OL7M4GWI","short_pith_number":"pith:VD3D7XWA","canonical_record":{"source":{"id":"1012.5554","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-27T02:16:54Z","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"be7fdf0d05e358ca5eafdc17c8899c82558b774a846a14bdfe14cad0c2c02d51","abstract_canon_sha256":"a8348690469a58ff999b6d41d3f38a50324cf5a4c95e9e0bf2af29d17cde3346"},"schema_version":"1.0"},"canonical_sha256":"a8f63fdec0a6bc0e7b4cc71cbfb386b22841b031117d85563d0e38be127e2320","source":{"kind":"arxiv","id":"1012.5554","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5554","created_at":"2026-05-18T02:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5554v2","created_at":"2026-05-18T02:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5554","created_at":"2026-05-18T02:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"VD3D7XWAU26A","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VD3D7XWAU26A462M","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VD3D7XWA","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:VD3D7XWAU26A462MY4OL7M4GWI","target":"record","payload":{"canonical_record":{"source":{"id":"1012.5554","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-27T02:16:54Z","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"title_canon_sha256":"be7fdf0d05e358ca5eafdc17c8899c82558b774a846a14bdfe14cad0c2c02d51","abstract_canon_sha256":"a8348690469a58ff999b6d41d3f38a50324cf5a4c95e9e0bf2af29d17cde3346"},"schema_version":"1.0"},"canonical_sha256":"a8f63fdec0a6bc0e7b4cc71cbfb386b22841b031117d85563d0e38be127e2320","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:17.534664Z","signature_b64":"2i4pF1M1ZtbGQFM7knSY302WxXudKTONMMJpraYV9rkcyOCERi0xG0UjZizTB9Tv0+1Bh0rkI4MO06vajDMWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8f63fdec0a6bc0e7b4cc71cbfb386b22841b031117d85563d0e38be127e2320","last_reissued_at":"2026-05-18T02:04:17.533890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:17.533890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.5554","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":"2026-05-18T02:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TWE/d8AmExTysCjjaFs0EZj3Z2YMwbIU+eMNGOuzeKKiLt3pKfi73iuqML1TzwVqhZYom/Lix6EWgv0s5MUlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:09:58.910906Z"},"content_sha256":"7ffb014d2748ecbcc6149916ab45c11d0a5c5cc52767147496fd1e8927e81ad0","schema_version":"1.0","event_id":"sha256:7ffb014d2748ecbcc6149916ab45c11d0a5c5cc52767147496fd1e8927e81ad0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:VD3D7XWAU26A462MY4OL7M4GWI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized string equations for double Hurwitz numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Kanehisa Takasaki","submitted_at":"2010-12-27T02:16:54Z","abstract_excerpt":"The generating function of double Hurwitz numbers is known to become a tau function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators turn out to satisfy a set of generalized string equations. These generalized string equations resemble those of $c = 1$ string theory except that the Orlov-Schulman operators are contained therein in an exponentiated form. These equations are derived from a set of intertwining relations for fermiom bilinears in a two-dimensional free fermion system. The intertwiner is constructed from a fermionic counterpart of the cut-and-join operator. A c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5554","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":"2026-05-18T02:04:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zMjgCCfayHJr6WWiNtJWd6KmrdIS7pVB/yTFj1otORlKAjMIlbR3nX5VzK1lb0F10xNmk/ucHeXkzy+kOnglDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T05:09:58.911305Z"},"content_sha256":"7237ecc41415cb0188e426dd667df94843ae9418245b1cc7777eea72b2b4046a","schema_version":"1.0","event_id":"sha256:7237ecc41415cb0188e426dd667df94843ae9418245b1cc7777eea72b2b4046a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VD3D7XWAU26A462MY4OL7M4GWI/bundle.json","state_url":"https://pith.science/pith/VD3D7XWAU26A462MY4OL7M4GWI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VD3D7XWAU26A462MY4OL7M4GWI/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":"2026-06-02T05:09:58Z","links":{"resolver":"https://pith.science/pith/VD3D7XWAU26A462MY4OL7M4GWI","bundle":"https://pith.science/pith/VD3D7XWAU26A462MY4OL7M4GWI/bundle.json","state":"https://pith.science/pith/VD3D7XWAU26A462MY4OL7M4GWI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VD3D7XWAU26A462MY4OL7M4GWI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:VD3D7XWAU26A462MY4OL7M4GWI","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":"a8348690469a58ff999b6d41d3f38a50324cf5a4c95e9e0bf2af29d17cde3346","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-27T02:16:54Z","title_canon_sha256":"be7fdf0d05e358ca5eafdc17c8899c82558b774a846a14bdfe14cad0c2c02d51"},"schema_version":"1.0","source":{"id":"1012.5554","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5554","created_at":"2026-05-18T02:04:17Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5554v2","created_at":"2026-05-18T02:04:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5554","created_at":"2026-05-18T02:04:17Z"},{"alias_kind":"pith_short_12","alias_value":"VD3D7XWAU26A","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"VD3D7XWAU26A462M","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"VD3D7XWA","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:7237ecc41415cb0188e426dd667df94843ae9418245b1cc7777eea72b2b4046a","target":"graph","created_at":"2026-05-18T02:04:17Z","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 generating function of double Hurwitz numbers is known to become a tau function of the Toda hierarchy. The associated Lax and Orlov-Schulman operators turn out to satisfy a set of generalized string equations. These generalized string equations resemble those of $c = 1$ string theory except that the Orlov-Schulman operators are contained therein in an exponentiated form. These equations are derived from a set of intertwining relations for fermiom bilinears in a two-dimensional free fermion system. The intertwiner is constructed from a fermionic counterpart of the cut-and-join operator. A c","authors_text":"Kanehisa Takasaki","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-27T02:16:54Z","title":"Generalized string equations for double Hurwitz numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5554","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":"sha256:7ffb014d2748ecbcc6149916ab45c11d0a5c5cc52767147496fd1e8927e81ad0","target":"record","created_at":"2026-05-18T02:04:17Z","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":"a8348690469a58ff999b6d41d3f38a50324cf5a4c95e9e0bf2af29d17cde3346","cross_cats_sorted":["hep-th","math.MP","math.QA","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-12-27T02:16:54Z","title_canon_sha256":"be7fdf0d05e358ca5eafdc17c8899c82558b774a846a14bdfe14cad0c2c02d51"},"schema_version":"1.0","source":{"id":"1012.5554","kind":"arxiv","version":2}},"canonical_sha256":"a8f63fdec0a6bc0e7b4cc71cbfb386b22841b031117d85563d0e38be127e2320","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8f63fdec0a6bc0e7b4cc71cbfb386b22841b031117d85563d0e38be127e2320","first_computed_at":"2026-05-18T02:04:17.533890Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:17.533890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2i4pF1M1ZtbGQFM7knSY302WxXudKTONMMJpraYV9rkcyOCERi0xG0UjZizTB9Tv0+1Bh0rkI4MO06vajDMWCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:17.534664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5554","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ffb014d2748ecbcc6149916ab45c11d0a5c5cc52767147496fd1e8927e81ad0","sha256:7237ecc41415cb0188e426dd667df94843ae9418245b1cc7777eea72b2b4046a"],"state_sha256":"f7c7141a52659fb3c010bfa0d200bb28d6706242d9782d43491e613dc885a986"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTTnjY4KjRXApaIgGOmAVkUJyUHujTXsMIjSu5Wtpybr446w5fInib0I7rw7faj6We3C2/gt5lBmWIn36qxeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T05:09:58.913283Z","bundle_sha256":"bb27f3fa8f7f376238c70b9e5eb86774365692f3fe607089c2fffc8a94ffbf5f"}}