Pith Number

pith:UJ4CE22A

pith:2004:UJ4CE22AGPYMR4B3UBL42YSR2K

not attested not anchored not stored refs pending

Phase transition of the largest eigenvalue for non-null complex sample covariance matrices

Gerard Ben Arous, Jinho Baik, Sandrine Peche

arxiv:math/0403022 v2 · 2004-03-01 · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UJ4CE22AGPYMR4B3UBL42YSR2K}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

4 papers in Pith

Spectral phase transitions and trainability in neural network learning dynamics

A Borodin-Okounkov-Geronimo-Case identity for tilted Toeplitz minors

Pseudorandom Dynamics in the SYK Model and Cryptographic Censorship in JT Gravity

Principal Components Decomposition of Fraction of Variance Explained in High Dimensional Linear Models with Strong Correlation

Receipt and verification

First computed	2026-07-04T14:38:16.657708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a278226b4033f0c8f03ba057cd6251d28c2cb96f1cc55b61d58e431885372d31

Aliases

arxiv: math/0403022 · arxiv_version: math/0403022v2 · doi: 10.48550/arxiv.math/0403022 · pith_short_12: UJ4CE22AGPYM · pith_short_16: UJ4CE22AGPYMR4B3 · pith_short_8: UJ4CE22A

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/UJ4CE22AGPYMR4B3UBL42YSR2K \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a278226b4033f0c8f03ba057cd6251d28c2cb96f1cc55b61d58e431885372d31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ea4f998ba2961f32f2cd052435e6ebb30438ad38b971e4234ff444f9dccb966",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-03-01T18:18:03Z",
    "title_canon_sha256": "7ecba2c1302f9a79e8487c7e1caebfc20a88c74632d2155c8b28128e4e897602"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0403022",
    "kind": "arxiv",
    "version": 2
  }
}