{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:G4GUXWKCOY2AWE3BYHIYMWGW7Z","short_pith_number":"pith:G4GUXWKC","canonical_record":{"source":{"id":"1109.4699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-22T04:27:49Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ab4af397d8cc7fae9f9e48ac03a4804ac297244936fb44e501bfd48b18ada7eb","abstract_canon_sha256":"4889b9cd546c29d945a0f37395862aee75968096cf8ed7702c830a519c4cb63c"},"schema_version":"1.0"},"canonical_sha256":"370d4bd94276340b1361c1d18658d6fe7f0c1a158014c34582a6227ce4dae378","source":{"kind":"arxiv","id":"1109.4699","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4699","created_at":"2026-05-18T04:12:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4699v2","created_at":"2026-05-18T04:12:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4699","created_at":"2026-05-18T04:12:31Z"},{"alias_kind":"pith_short_12","alias_value":"G4GUXWKCOY2A","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4GUXWKCOY2AWE3B","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4GUXWKC","created_at":"2026-05-18T12:26:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:G4GUXWKCOY2AWE3BYHIYMWGW7Z","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-22T04:27:49Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"ab4af397d8cc7fae9f9e48ac03a4804ac297244936fb44e501bfd48b18ada7eb","abstract_canon_sha256":"4889b9cd546c29d945a0f37395862aee75968096cf8ed7702c830a519c4cb63c"},"schema_version":"1.0"},"canonical_sha256":"370d4bd94276340b1361c1d18658d6fe7f0c1a158014c34582a6227ce4dae378","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:31.843549Z","signature_b64":"hY9SBI39hWeksv8a3WdT9n0mfmvn7mBIwR8kdI8PV+Y674YvJIjim9VX0EHsALwBEJhuBclrCG35/F49bP60Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"370d4bd94276340b1361c1d18658d6fe7f0c1a158014c34582a6227ce4dae378","last_reissued_at":"2026-05-18T04:12:31.842873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:31.842873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4699","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":"2026-05-18T04:12:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETpdvrzJmROgKjM0x928LAcKkwh63MUmLeVzSicY0lQBn9dTLWdFi6Bjpm8T4/k3mw04h8JKXziMnHEXOUw9Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:28:45.927268Z"},"content_sha256":"f3ee536988becfb51f1cdfb4364170fc0243c00791cc00f08265ae82c750968d","schema_version":"1.0","event_id":"sha256:f3ee536988becfb51f1cdfb4364170fc0243c00791cc00f08265ae82c750968d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:G4GUXWKCOY2AWE3BYHIYMWGW7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Maximal Invariants For Lorentz Wishart Models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Emanuel Ben-David","submitted_at":"2011-09-22T04:27:49Z","abstract_excerpt":"In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by means of maximal invariant statistics which are explicitly derived in the paper. The testing problems, respectively, concern the hypothesis that parameters are in a sub-Lorentz-cone, and the the hypothesis that two observations have the same parameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4699","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":"2026-05-18T04:12:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BISZcF8fsq8IbVt14pePd57MANOEX0Fc8eDe0KW/Ax/B8BMwyFJF3xathS+tSq8hFQeExWBeuxY/IkBNG5boCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:28:45.927636Z"},"content_sha256":"5d6b29f73a821629bad5206a90f63904deb4af64d00e60567bae2567fef772c5","schema_version":"1.0","event_id":"sha256:5d6b29f73a821629bad5206a90f63904deb4af64d00e60567bae2567fef772c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z/bundle.json","state_url":"https://pith.science/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z/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":"2026-07-02T09:28:45Z","links":{"resolver":"https://pith.science/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z","bundle":"https://pith.science/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z/bundle.json","state":"https://pith.science/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4GUXWKCOY2AWE3BYHIYMWGW7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:G4GUXWKCOY2AWE3BYHIYMWGW7Z","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":"4889b9cd546c29d945a0f37395862aee75968096cf8ed7702c830a519c4cb63c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-22T04:27:49Z","title_canon_sha256":"ab4af397d8cc7fae9f9e48ac03a4804ac297244936fb44e501bfd48b18ada7eb"},"schema_version":"1.0","source":{"id":"1109.4699","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4699","created_at":"2026-05-18T04:12:31Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4699v2","created_at":"2026-05-18T04:12:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4699","created_at":"2026-05-18T04:12:31Z"},{"alias_kind":"pith_short_12","alias_value":"G4GUXWKCOY2A","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"G4GUXWKCOY2AWE3B","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"G4GUXWKC","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:5d6b29f73a821629bad5206a90f63904deb4af64d00e60567bae2567fef772c5","target":"graph","created_at":"2026-05-18T04:12:31Z","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":"In this paper we consider two statistical hypotheses for the families of Wishart type distributions. These distributions are analogs of the Wishart distributions defined and parametrized over a Lorentz cone. We test these hypotheses by means of maximal invariant statistics which are explicitly derived in the paper. The testing problems, respectively, concern the hypothesis that parameters are in a sub-Lorentz-cone, and the the hypothesis that two observations have the same parameter.","authors_text":"Emanuel Ben-David","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-22T04:27:49Z","title":"Maximal Invariants For Lorentz Wishart Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4699","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:f3ee536988becfb51f1cdfb4364170fc0243c00791cc00f08265ae82c750968d","target":"record","created_at":"2026-05-18T04:12:31Z","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":"4889b9cd546c29d945a0f37395862aee75968096cf8ed7702c830a519c4cb63c","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-09-22T04:27:49Z","title_canon_sha256":"ab4af397d8cc7fae9f9e48ac03a4804ac297244936fb44e501bfd48b18ada7eb"},"schema_version":"1.0","source":{"id":"1109.4699","kind":"arxiv","version":2}},"canonical_sha256":"370d4bd94276340b1361c1d18658d6fe7f0c1a158014c34582a6227ce4dae378","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370d4bd94276340b1361c1d18658d6fe7f0c1a158014c34582a6227ce4dae378","first_computed_at":"2026-05-18T04:12:31.842873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:31.842873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hY9SBI39hWeksv8a3WdT9n0mfmvn7mBIwR8kdI8PV+Y674YvJIjim9VX0EHsALwBEJhuBclrCG35/F49bP60Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:31.843549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4699","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3ee536988becfb51f1cdfb4364170fc0243c00791cc00f08265ae82c750968d","sha256:5d6b29f73a821629bad5206a90f63904deb4af64d00e60567bae2567fef772c5"],"state_sha256":"bed2920ab0c2c152afb30455c02bef6901c13191ecadecc2db4be0a1ca4287ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LKpc6REokeOQKraOvgqUDU8xkgR6/yL+2np6cJAsJHzYJm3zEaSSDLZ27aNHdBv8Y6zi4VjgjAa3ATFhesuXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T09:28:45.929598Z","bundle_sha256":"f62c5a0804bb10098d4bb45ebf72e05d8437b533718980df5f7743c78c80eb9f"}}