Pith Number

pith:23WRNEZR

pith:2013:23WRNEZRMMYK5FXD7RNPIYFRFQ

not attested not anchored not stored refs pending

Estimates for spectral density functions of matrices over C[Z^d]

Wolfgang Lueck

arxiv:1310.8564 v2 · 2013-10-31 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{23WRNEZRMMYK5FXD7RNPIYFRFQ}

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	2026-05-18T02:39:09.016195Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d6ed1693316330ae96e3fc5af460b12c24f28a2dcdeb4f35f43a1cca8ed52fb7

Aliases

arxiv: 1310.8564 · arxiv_version: 1310.8564v2 · doi: 10.48550/arxiv.1310.8564 · pith_short_12: 23WRNEZRMMYK · pith_short_16: 23WRNEZRMMYK5FXD · pith_short_8: 23WRNEZR

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/23WRNEZRMMYK5FXD7RNPIYFRFQ \
  | 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: d6ed1693316330ae96e3fc5af460b12c24f28a2dcdeb4f35f43a1cca8ed52fb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efbb3a1e089989a136b25d937fa240939133020763d8c62ac503699e5114e21a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-10-31T15:56:55Z",
    "title_canon_sha256": "af670f5d2767a27769fa8be998ec29cfa370a9baa286a592b36ff6f7f18f5d83"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1310.8564",
    "kind": "arxiv",
    "version": 2
  }
}