Pith Number

pith:ZFQM2TIH

pith:2008:ZFQM2TIHASBUHVRSIYWZ57GIM2

not attested not anchored not stored refs pending

Asymptotic Behaviour of Random Vandermonde Matrices with Entries on the Unit Circle

Merouane Debbah, {\O}yvind Ryan

arxiv:0802.3570 v3 · 2008-02-25 · cs.IT · math.IT

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZFQM2TIHASBUHVRSIYWZ57GIM2}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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.

Receipt and verification

First computed	2026-05-18T01:09:24.527466Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c960cd4d07048343d632462d9efcc866b9951c4ff1d7e5f4eb69444a24a5e4f0

Aliases

arxiv: 0802.3570 · arxiv_version: 0802.3570v3 · doi: 10.48550/arxiv.0802.3570 · pith_short_12: ZFQM2TIHASBU · pith_short_16: ZFQM2TIHASBUHVRS · pith_short_8: ZFQM2TIH

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/ZFQM2TIHASBUHVRSIYWZ57GIM2 \
  | 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: c960cd4d07048343d632462d9efcc866b9951c4ff1d7e5f4eb69444a24a5e4f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a4bff966f65be59b5e75a113cd635a288eefe880fa4b54426ac08c6b1a2ee917",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2008-02-25T09:06:13Z",
    "title_canon_sha256": "3b550a78f40d78bf879f5abd4a89c34628be92bff0ba6248764adfc5b0773b55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0802.3570",
    "kind": "arxiv",
    "version": 3
  }
}