Pith Number

pith:YMGH36OY

pith:2013:YMGH36OY2GRMXNOD4JHO7EUZV7

not attested not anchored not stored refs pending

Explicit formulae for spectral norms of circulant-type matrices with some given entries

Jianwei Zhou, Zhaolin Jiang

arxiv:1305.5607 v1 · 2013-05-24 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YMGH36OY2GRMXNOD4JHO7EUZV7}

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

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	2026-05-18T03:25:03.710282Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c30c7df9d8d1a2cbb5c3e24eef9299afc501c064ce8536f02f37f98404d5a3de

Aliases

arxiv: 1305.5607 · arxiv_version: 1305.5607v1 · doi: 10.48550/arxiv.1305.5607 · pith_short_12: YMGH36OY2GRM · pith_short_16: YMGH36OY2GRMXNOD · pith_short_8: YMGH36OY

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/YMGH36OY2GRMXNOD4JHO7EUZV7 \
  | 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: c30c7df9d8d1a2cbb5c3e24eef9299afc501c064ce8536f02f37f98404d5a3de

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f64543bc51c606e7e7d4843d51e70154197a6a6036f4ee08e35664d41e59520",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/3.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-05-24T02:53:48Z",
    "title_canon_sha256": "de43d108366e0d033df01d5c2bbc22abeaf80713578b03307b86d62f0d1d95d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.5607",
    "kind": "arxiv",
    "version": 1
  }
}