{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GTUUCNEMETNGTSKTRNFJ6B5VG6","short_pith_number":"pith:GTUUCNEM","canonical_record":{"source":{"id":"1104.4268","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-21T14:03:47Z","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"title_canon_sha256":"a7969a3aa48a3878271467cd240aed47a777aa0e12624ed00743ed9a22ee8a39","abstract_canon_sha256":"83729743c8ac4ba5d7424f9fc22868bb4c78a9995fd057eccea9007a122a477e"},"schema_version":"1.0"},"canonical_sha256":"34e941348c24da69c9538b4a9f07b53791a291c58cd3ea78e02c2173eafa73ca","source":{"kind":"arxiv","id":"1104.4268","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4268","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4268v3","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4268","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"GTUUCNEMETNG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GTUUCNEMETNGTSKT","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GTUUCNEM","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GTUUCNEMETNGTSKTRNFJ6B5VG6","target":"record","payload":{"canonical_record":{"source":{"id":"1104.4268","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-21T14:03:47Z","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"title_canon_sha256":"a7969a3aa48a3878271467cd240aed47a777aa0e12624ed00743ed9a22ee8a39","abstract_canon_sha256":"83729743c8ac4ba5d7424f9fc22868bb4c78a9995fd057eccea9007a122a477e"},"schema_version":"1.0"},"canonical_sha256":"34e941348c24da69c9538b4a9f07b53791a291c58cd3ea78e02c2173eafa73ca","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:45.808084Z","signature_b64":"beOIYcp+TE1+kPquhukVU0fevUrkkmCWzootHHf8tCgC9BHRGx/vJSUbOlQ55M1ZajJN+JqkpHN+OSKjFcxPDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34e941348c24da69c9538b4a9f07b53791a291c58cd3ea78e02c2173eafa73ca","last_reissued_at":"2026-05-18T03:21:45.807571Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:45.807571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.4268","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gWVsydW7RfxF51K6gJnME4GDd/tulmbPIp8ijBRpngIRTynYZO9BzAPaJwtya2yUJq8t+GX+sN5vFYMI2FozDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:44:37.275498Z"},"content_sha256":"6af61a74546eaf3c3dbe50d22bf27c9d3de17fa6df7f1cd361bd23ffbb78181b","schema_version":"1.0","event_id":"sha256:6af61a74546eaf3c3dbe50d22bf27c9d3de17fa6df7f1cd361bd23ffbb78181b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GTUUCNEMETNGTSKTRNFJ6B5VG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear PDEs for gap probabilities in random matrices and KP theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR","nlin.SI"],"primary_cat":"math-ph","authors_text":"M. Adler, M. Cafasso, P. van Moerbeke","submitted_at":"2011-04-21T14:03:47Z","abstract_excerpt":"Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are intimately related to wave functions for polynomial (Gel'fand-Dickey reductions) or rational reductions of the KP-hierarchy; their Fredholm determinant also satisfies linear PDEs (Virasoro constraints), yielding, in a systematic way, non-linear PDEs for the Fredholm determinant of such kernels. Examples include Fredholm determinants giving the gap probability of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4268","kind":"arxiv","version":3},"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":"2026-05-18T03:21:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ElN0abYtcvvRIiMsB6W3V/w3w+5EXOo76EFetd5kaHK8zyd77MHnuSYG5G33Gkc8mJDeJWOfY+nWgbWX23EeDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T15:44:37.275845Z"},"content_sha256":"bfb416e964350cfa4200ad11498f1e5b8e18deaee39ae549afd187d67d8933ed","schema_version":"1.0","event_id":"sha256:bfb416e964350cfa4200ad11498f1e5b8e18deaee39ae549afd187d67d8933ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6/bundle.json","state_url":"https://pith.science/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6/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":"2026-06-04T15:44:37Z","links":{"resolver":"https://pith.science/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6","bundle":"https://pith.science/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6/bundle.json","state":"https://pith.science/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GTUUCNEMETNGTSKTRNFJ6B5VG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GTUUCNEMETNGTSKTRNFJ6B5VG6","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":"83729743c8ac4ba5d7424f9fc22868bb4c78a9995fd057eccea9007a122a477e","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-21T14:03:47Z","title_canon_sha256":"a7969a3aa48a3878271467cd240aed47a777aa0e12624ed00743ed9a22ee8a39"},"schema_version":"1.0","source":{"id":"1104.4268","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4268","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4268v3","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4268","created_at":"2026-05-18T03:21:45Z"},{"alias_kind":"pith_short_12","alias_value":"GTUUCNEMETNG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GTUUCNEMETNGTSKT","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GTUUCNEM","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:bfb416e964350cfa4200ad11498f1e5b8e18deaee39ae549afd187d67d8933ed","target":"graph","created_at":"2026-05-18T03:21:45Z","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":"Airy and Pearcey-like kernels and generalizations arising in random matrix theory are expressed as double integrals of ratios of exponentials, possibly multiplied with a rational function. In this work it is shown that such kernels are intimately related to wave functions for polynomial (Gel'fand-Dickey reductions) or rational reductions of the KP-hierarchy; their Fredholm determinant also satisfies linear PDEs (Virasoro constraints), yielding, in a systematic way, non-linear PDEs for the Fredholm determinant of such kernels. Examples include Fredholm determinants giving the gap probability of","authors_text":"M. Adler, M. Cafasso, P. van Moerbeke","cross_cats":["math.MP","math.PR","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-21T14:03:47Z","title":"Nonlinear PDEs for gap probabilities in random matrices and KP theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4268","kind":"arxiv","version":3},"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":"sha256:6af61a74546eaf3c3dbe50d22bf27c9d3de17fa6df7f1cd361bd23ffbb78181b","target":"record","created_at":"2026-05-18T03:21:45Z","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":"83729743c8ac4ba5d7424f9fc22868bb4c78a9995fd057eccea9007a122a477e","cross_cats_sorted":["math.MP","math.PR","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-04-21T14:03:47Z","title_canon_sha256":"a7969a3aa48a3878271467cd240aed47a777aa0e12624ed00743ed9a22ee8a39"},"schema_version":"1.0","source":{"id":"1104.4268","kind":"arxiv","version":3}},"canonical_sha256":"34e941348c24da69c9538b4a9f07b53791a291c58cd3ea78e02c2173eafa73ca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34e941348c24da69c9538b4a9f07b53791a291c58cd3ea78e02c2173eafa73ca","first_computed_at":"2026-05-18T03:21:45.807571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:45.807571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"beOIYcp+TE1+kPquhukVU0fevUrkkmCWzootHHf8tCgC9BHRGx/vJSUbOlQ55M1ZajJN+JqkpHN+OSKjFcxPDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:45.808084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4268","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6af61a74546eaf3c3dbe50d22bf27c9d3de17fa6df7f1cd361bd23ffbb78181b","sha256:bfb416e964350cfa4200ad11498f1e5b8e18deaee39ae549afd187d67d8933ed"],"state_sha256":"e964b8a89d6e1df9aa488ab934a810197d71b0726596e27fbd3805b338ee521e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l6CWU/GI+AJsJQo+NNQiQtnrcPC7ESdfxnLcNU8+qT5hfwLFpp6VF17ODZ3ll5RIqPxkpsyooVlH0fTUgBhtAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T15:44:37.277808Z","bundle_sha256":"05ddb31a53446c0a754dd24f46bf1a128a25e1e40bbb1c013baf9661d769f628"}}