Pith Number

pith:7UQ4DVTL

pith:2012:7UQ4DVTLMSVFIMZN57ZGSN3ARJ

not attested not anchored not stored refs pending

On Kruskal's theorem that every 3 x 3 x 3 array has rank at most 5

Jiaxiong Hu, Murray R. Bremner

arxiv:1209.1553 v1 · 2012-09-06 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7UQ4DVTLMSVFIMZN57ZGSN3ARJ}

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	2026-05-18T03:46:04.526620Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fd21c1d66b64aa54332deff26937608a6bac39efe4d4bcd8d8f2c31cd8958ee4

Aliases

arxiv: 1209.1553 · arxiv_version: 1209.1553v1 · doi: 10.48550/arxiv.1209.1553 · pith_short_12: 7UQ4DVTLMSVF · pith_short_16: 7UQ4DVTLMSVFIMZN · pith_short_8: 7UQ4DVTL

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/7UQ4DVTLMSVFIMZN57ZGSN3ARJ \
  | 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: fd21c1d66b64aa54332deff26937608a6bac39efe4d4bcd8d8f2c31cd8958ee4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "79d7952b3e1967104ea0822f0d9888d1b3c4d712d294238bb7a0d2c6ece5a5a9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2012-09-06T19:54:53Z",
    "title_canon_sha256": "751879f22034beb6b022483c3f80d39200b9448cbaf03b5f0c6dfe0f17894189"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1553",
    "kind": "arxiv",
    "version": 1
  }
}