{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TH76I477XWICOLKLEHLDSVFORA","short_pith_number":"pith:TH76I477","canonical_record":{"source":{"id":"1201.3816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:09:45Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7b55f8bb840f42f8bd5d9d9903b282c1d9f55b374395b35af7a7146eca578110","abstract_canon_sha256":"d5b5c128bddc344ada6ab2a3122adc45cd53c03aba5903b5c8001bd996d0dce7"},"schema_version":"1.0"},"canonical_sha256":"99ffe473ffbd90272d4b21d63954ae883e53bb27f31063512b1edbe9c83b5d00","source":{"kind":"arxiv","id":"1201.3816","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3816","created_at":"2026-05-18T03:52:01Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3816v1","created_at":"2026-05-18T03:52:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3816","created_at":"2026-05-18T03:52:01Z"},{"alias_kind":"pith_short_12","alias_value":"TH76I477XWIC","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TH76I477XWICOLKL","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TH76I477","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TH76I477XWICOLKLEHLDSVFORA","target":"record","payload":{"canonical_record":{"source":{"id":"1201.3816","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:09:45Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"7b55f8bb840f42f8bd5d9d9903b282c1d9f55b374395b35af7a7146eca578110","abstract_canon_sha256":"d5b5c128bddc344ada6ab2a3122adc45cd53c03aba5903b5c8001bd996d0dce7"},"schema_version":"1.0"},"canonical_sha256":"99ffe473ffbd90272d4b21d63954ae883e53bb27f31063512b1edbe9c83b5d00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:52:01.214243Z","signature_b64":"JbXnRR7cHU69po3LFciUXUluF/AmLfNdhYFFFHiUw021FzZDgZMcdEFpieCWwslOS43w4PSPGX5t3FHQqXtnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99ffe473ffbd90272d4b21d63954ae883e53bb27f31063512b1edbe9c83b5d00","last_reissued_at":"2026-05-18T03:52:01.213328Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:52:01.213328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.3816","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":"2026-05-18T03:52:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m4f+wymhGa1l6YIRRpCfXHyfw0iVcSfxuIk/sGse14RezkrJ7m0PFHm5392vHNyppm+b5tpTSDEHP2Dq6tvVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:56:04.218280Z"},"content_sha256":"cb43a729040ccc5618900f5c7c138321e82a3ec13001cca28adb64a23abd0dae","schema_version":"1.0","event_id":"sha256:cb43a729040ccc5618900f5c7c138321e82a3ec13001cca28adb64a23abd0dae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TH76I477XWICOLKLEHLDSVFORA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Central Limit Theorems for Radial Random Walks on $p\\times q$ Matrices for $p\\to\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.PR","authors_text":"Michael Voit","submitted_at":"2012-01-18T15:09:45Z","abstract_excerpt":"Let $\\nu\\in M^1([0,\\infty[)$ be a fixed probability measure. For each dimension $p\\in\\b N$, let $(X_n^p)_{n\\ge1}$ be i.i.d. $\\b R^p$-valued radial random variables with radial distribution $\\nu$. We derive two central limit theorems for $ \\|X_1^p+...+X_n^p\\|_2$ for $n,p\\to\\infty$ with normal limits. The first CLT for $n>>p$ follows from known estimates of convergence in the CLT on $\\b R^p$, while the second CLT for $n<<p$ will be a consequence of asymptotic properties of Bessel convolutions. Both limit theorems are considered also for $U(p)$-invariant random walks on the space of $p\\times q$ m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3816","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":"2026-05-18T03:52:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+7sXNmyS66GbDjDvh26/5yxJ4u8vvO+7dY+qY3C7dl6/NxnXWZteB6CZtQN9Ouifsz1JbxlxLMqD3rHBb7mBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:56:04.219011Z"},"content_sha256":"45460a7ac526ca5ecd5ac360b1c7e23b878571fa7618e0d61a4b1c5d457a06ef","schema_version":"1.0","event_id":"sha256:45460a7ac526ca5ecd5ac360b1c7e23b878571fa7618e0d61a4b1c5d457a06ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TH76I477XWICOLKLEHLDSVFORA/bundle.json","state_url":"https://pith.science/pith/TH76I477XWICOLKLEHLDSVFORA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TH76I477XWICOLKLEHLDSVFORA/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":"2026-06-08T20:56:04Z","links":{"resolver":"https://pith.science/pith/TH76I477XWICOLKLEHLDSVFORA","bundle":"https://pith.science/pith/TH76I477XWICOLKLEHLDSVFORA/bundle.json","state":"https://pith.science/pith/TH76I477XWICOLKLEHLDSVFORA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TH76I477XWICOLKLEHLDSVFORA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TH76I477XWICOLKLEHLDSVFORA","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":"d5b5c128bddc344ada6ab2a3122adc45cd53c03aba5903b5c8001bd996d0dce7","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:09:45Z","title_canon_sha256":"7b55f8bb840f42f8bd5d9d9903b282c1d9f55b374395b35af7a7146eca578110"},"schema_version":"1.0","source":{"id":"1201.3816","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.3816","created_at":"2026-05-18T03:52:01Z"},{"alias_kind":"arxiv_version","alias_value":"1201.3816v1","created_at":"2026-05-18T03:52:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.3816","created_at":"2026-05-18T03:52:01Z"},{"alias_kind":"pith_short_12","alias_value":"TH76I477XWIC","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TH76I477XWICOLKL","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TH76I477","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:45460a7ac526ca5ecd5ac360b1c7e23b878571fa7618e0d61a4b1c5d457a06ef","target":"graph","created_at":"2026-05-18T03:52:01Z","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"},"paper":{"abstract_excerpt":"Let $\\nu\\in M^1([0,\\infty[)$ be a fixed probability measure. For each dimension $p\\in\\b N$, let $(X_n^p)_{n\\ge1}$ be i.i.d. $\\b R^p$-valued radial random variables with radial distribution $\\nu$. We derive two central limit theorems for $ \\|X_1^p+...+X_n^p\\|_2$ for $n,p\\to\\infty$ with normal limits. The first CLT for $n>>p$ follows from known estimates of convergence in the CLT on $\\b R^p$, while the second CLT for $n<<p$ will be a consequence of asymptotic properties of Bessel convolutions. Both limit theorems are considered also for $U(p)$-invariant random walks on the space of $p\\times q$ m","authors_text":"Michael Voit","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:09:45Z","title":"Central Limit Theorems for Radial Random Walks on $p\\times q$ Matrices for $p\\to\\infty$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.3816","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:cb43a729040ccc5618900f5c7c138321e82a3ec13001cca28adb64a23abd0dae","target":"record","created_at":"2026-05-18T03:52:01Z","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":"d5b5c128bddc344ada6ab2a3122adc45cd53c03aba5903b5c8001bd996d0dce7","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-01-18T15:09:45Z","title_canon_sha256":"7b55f8bb840f42f8bd5d9d9903b282c1d9f55b374395b35af7a7146eca578110"},"schema_version":"1.0","source":{"id":"1201.3816","kind":"arxiv","version":1}},"canonical_sha256":"99ffe473ffbd90272d4b21d63954ae883e53bb27f31063512b1edbe9c83b5d00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99ffe473ffbd90272d4b21d63954ae883e53bb27f31063512b1edbe9c83b5d00","first_computed_at":"2026-05-18T03:52:01.213328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:01.213328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JbXnRR7cHU69po3LFciUXUluF/AmLfNdhYFFFHiUw021FzZDgZMcdEFpieCWwslOS43w4PSPGX5t3FHQqXtnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:01.214243Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.3816","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb43a729040ccc5618900f5c7c138321e82a3ec13001cca28adb64a23abd0dae","sha256:45460a7ac526ca5ecd5ac360b1c7e23b878571fa7618e0d61a4b1c5d457a06ef"],"state_sha256":"64b3adf5042e7827b6934a29c8ecc2d7bca1049d7cdfed1647f178278de1e9d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ruIlJ+Ov9mmFpJBoTvO+35dr9tw6sceKa57nqVXuFaH/Cpx2373RV6Ni6K2d3lyVs+NDVnpU7wYv3BK8J41gBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:56:04.223361Z","bundle_sha256":"c087a761c9395cb208a37890b5d94a5a1ab9769639a31bbc9afe2b86c8facd21"}}