Pith Number

pith:VN2SFJ2X

pith:2012:VN2SFJ2XZLVT4D4P7JRZMMNTRC

not attested not anchored not stored refs pending

Condition Numbers of Random Toeplitz and Circulant Matrices

Guoliang Qian, Victor Y. Pan

arxiv:1212.4551 v1 · 2012-12-19 · math.NA · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VN2SFJ2XZLVT4D4P7JRZMMNTRC}

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	2026-05-18T03:38:12.056196Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab7522a757caeb3e0f8ffa639631b388857a99e188868c7a62e8a5c0b46c067f

Aliases

arxiv: 1212.4551 · arxiv_version: 1212.4551v1 · doi: 10.48550/arxiv.1212.4551 · pith_short_12: VN2SFJ2XZLVT · pith_short_16: VN2SFJ2XZLVT4D4P · pith_short_8: VN2SFJ2X

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/VN2SFJ2XZLVT4D4P7JRZMMNTRC \
  | 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: ab7522a757caeb3e0f8ffa639631b388857a99e188868c7a62e8a5c0b46c067f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a4c81a7c7f99796ab452c01af2b843e1f449f3374df67bd4985de55cd2408b0",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2012-12-19T01:33:03Z",
    "title_canon_sha256": "d10bb4e1a5661664fbb00f7e354ad053ea1b8d7dffb8e7a775076e0bac0cc15d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4551",
    "kind": "arxiv",
    "version": 1
  }
}