{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZBM2DEXUDIBDHLOTANMDCQWCEG","short_pith_number":"pith:ZBM2DEXU","canonical_record":{"source":{"id":"1609.01799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-07T01:38:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1d527fe5273acfb00580c1739b7488e79ed3d278b3539beeefe6ce8b5a4b0d91","abstract_canon_sha256":"d8e2bf4ad7fc53b6fdaeeaf1edb872927c2551164adbf236243ca0c63844fa94"},"schema_version":"1.0"},"canonical_sha256":"c859a192f41a0233add303583142c221a59c08f21a1121b805ab8ca6b6cdfb59","source":{"kind":"arxiv","id":"1609.01799","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01799","created_at":"2026-05-18T01:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01799v1","created_at":"2026-05-18T01:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01799","created_at":"2026-05-18T01:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZBM2DEXUDIBD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZBM2DEXUDIBDHLOT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZBM2DEXU","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZBM2DEXUDIBDHLOTANMDCQWCEG","target":"record","payload":{"canonical_record":{"source":{"id":"1609.01799","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-07T01:38:55Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"1d527fe5273acfb00580c1739b7488e79ed3d278b3539beeefe6ce8b5a4b0d91","abstract_canon_sha256":"d8e2bf4ad7fc53b6fdaeeaf1edb872927c2551164adbf236243ca0c63844fa94"},"schema_version":"1.0"},"canonical_sha256":"c859a192f41a0233add303583142c221a59c08f21a1121b805ab8ca6b6cdfb59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:10.071393Z","signature_b64":"3DozXal9R0c9c8498JqoP0GtiPAViVHz/uZKXuQx6SrnsbSUnfKDAQQGG84FizW8YTQE8dfGvD0ys0bsq9GUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c859a192f41a0233add303583142c221a59c08f21a1121b805ab8ca6b6cdfb59","last_reissued_at":"2026-05-18T01:05:10.070681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:10.070681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.01799","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":"2026-05-18T01:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2xDAnCU+talqU43t+TuTvFZqnf/FSzchSgqO76xnGgZygaPj/V1w2vjM2ltVjCLlYeV8ID6MxJAtZcYpgBd3Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:17:25.353609Z"},"content_sha256":"c592d6a8cd23e042c1af4c662a45215260d7d06eee75ec8ae5578e27942a3fa5","schema_version":"1.0","event_id":"sha256:c592d6a8cd23e042c1af4c662a45215260d7d06eee75ec8ae5578e27942a3fa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZBM2DEXUDIBDHLOTANMDCQWCEG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Differential relations for the largest root distribution of complex non-central Wishart matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Akimichi Takemura, Raimundas Vidunas","submitted_at":"2016-09-07T01:38:55Z","abstract_excerpt":"A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density function is derived (for m=2,3) or conjectured."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01799","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":""},"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":"2026-05-18T01:05:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2oHUMjIwHtJLAmFGoEWTJpSZf96fnvwzlhK2qdQZlgvj2YY/d5+73NLzfhbERpc32IFpvfMcB0uzYvXxY+uFDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:17:25.353953Z"},"content_sha256":"cd43453a49b63f46d8b754d0ff938c7e789a4f5e40d3a57f1935a4c311bb4b5f","schema_version":"1.0","event_id":"sha256:cd43453a49b63f46d8b754d0ff938c7e789a4f5e40d3a57f1935a4c311bb4b5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG/bundle.json","state_url":"https://pith.science/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG/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":"2026-06-04T19:17:25Z","links":{"resolver":"https://pith.science/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG","bundle":"https://pith.science/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG/bundle.json","state":"https://pith.science/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBM2DEXUDIBDHLOTANMDCQWCEG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZBM2DEXUDIBDHLOTANMDCQWCEG","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":"d8e2bf4ad7fc53b6fdaeeaf1edb872927c2551164adbf236243ca0c63844fa94","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-07T01:38:55Z","title_canon_sha256":"1d527fe5273acfb00580c1739b7488e79ed3d278b3539beeefe6ce8b5a4b0d91"},"schema_version":"1.0","source":{"id":"1609.01799","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.01799","created_at":"2026-05-18T01:05:10Z"},{"alias_kind":"arxiv_version","alias_value":"1609.01799v1","created_at":"2026-05-18T01:05:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.01799","created_at":"2026-05-18T01:05:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZBM2DEXUDIBD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZBM2DEXUDIBDHLOT","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZBM2DEXU","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:cd43453a49b63f46d8b754d0ff938c7e789a4f5e40d3a57f1935a4c311bb4b5f","target":"graph","created_at":"2026-05-18T01:05:10Z","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"},"paper":{"abstract_excerpt":"A holonomic system for the probability density function of the largest eigenvalue of a non-central complex Wishart distribution with identity covariance matrix is derived. Furthermore a new determinantal formula for the probability density function is derived (for m=2,3) or conjectured.","authors_text":"Akimichi Takemura, Raimundas Vidunas","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-07T01:38:55Z","title":"Differential relations for the largest root distribution of complex non-central Wishart matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.01799","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:c592d6a8cd23e042c1af4c662a45215260d7d06eee75ec8ae5578e27942a3fa5","target":"record","created_at":"2026-05-18T01:05:10Z","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":"d8e2bf4ad7fc53b6fdaeeaf1edb872927c2551164adbf236243ca0c63844fa94","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-09-07T01:38:55Z","title_canon_sha256":"1d527fe5273acfb00580c1739b7488e79ed3d278b3539beeefe6ce8b5a4b0d91"},"schema_version":"1.0","source":{"id":"1609.01799","kind":"arxiv","version":1}},"canonical_sha256":"c859a192f41a0233add303583142c221a59c08f21a1121b805ab8ca6b6cdfb59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c859a192f41a0233add303583142c221a59c08f21a1121b805ab8ca6b6cdfb59","first_computed_at":"2026-05-18T01:05:10.070681Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:10.070681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3DozXal9R0c9c8498JqoP0GtiPAViVHz/uZKXuQx6SrnsbSUnfKDAQQGG84FizW8YTQE8dfGvD0ys0bsq9GUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:10.071393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.01799","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c592d6a8cd23e042c1af4c662a45215260d7d06eee75ec8ae5578e27942a3fa5","sha256:cd43453a49b63f46d8b754d0ff938c7e789a4f5e40d3a57f1935a4c311bb4b5f"],"state_sha256":"731c103ad15ed72db34ebe1038efd60ca89df3cbca3a6da3f7f3b43469d8d486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"20+c3LEILNhMpH+9nN0CLppcQsnTDGH3FoJXMXt8Ta41t7of2XhbpKNSIHtEYPGEMqeVEwEMu6xCHOYfCpbGBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:17:25.355961Z","bundle_sha256":"d1f22a097b7d4cfe60947c17185c47d3c48a040b156b02ad235a4d720472d3a9"}}