Pith Number

pith:VCP52Q7L

pith:2001:VCP52Q7LI46ZFZHLGRUYP7MWTX

not attested not anchored not stored refs pending

Lacunary matrices

Asma Harcharras, Krzysztof Oleszkiewicz, Stefan Neuwirth

arxiv:math/0102211 v1 · 2001-02-27 · math.FA · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VCP52Q7LI46ZFZHLGRUYP7MWTX}

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	2026-05-18T00:37:49.250357Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a89fdd43eb473d92e4eb346987fd969dd3516cafe60201c7f2100b54b3f3b253

Aliases

arxiv: math/0102211 · arxiv_version: math/0102211v1 · doi: 10.48550/arxiv.math/0102211 · pith_short_12: VCP52Q7LI46Z · pith_short_16: VCP52Q7LI46ZFZHL · pith_short_8: VCP52Q7L

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/VCP52Q7LI46ZFZHLGRUYP7MWTX \
  | 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: a89fdd43eb473d92e4eb346987fd969dd3516cafe60201c7f2100b54b3f3b253

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7d8f490cf1bddc8dd02ee45191f5e9b17a43fbfeb96a0fffa69dbb402e4e1b7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.FA",
    "submitted_at": "2001-02-27T14:29:36Z",
    "title_canon_sha256": "695061ae73bd939116f13f76f1ead24d0e36a5cb4cc92def9a099accc5d68327"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0102211",
    "kind": "arxiv",
    "version": 1
  }
}