Pith Number

pith:AL3BP4PU

pith:2014:AL3BP4PUYBE7DOQUQWE64TGWIJ

not attested not anchored not stored refs pending

Stability of coefficients in the Kronecker product of a hook and a rectangle

Bill Hallahan, Cristina Ballantine

arxiv:1412.1431 v1 · 2014-12-03 · 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{AL3BP4PUYBE7DOQUQWE64TGWIJ}

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	2026-05-18T02:32:12.502381Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02f617f1f4c049f1ba148589ee4cd642417c97b1ee2c13335fd9b20d2f729be1

Aliases

arxiv: 1412.1431 · arxiv_version: 1412.1431v1 · doi: 10.48550/arxiv.1412.1431 · pith_short_12: AL3BP4PUYBE7 · pith_short_16: AL3BP4PUYBE7DOQU · pith_short_8: AL3BP4PU

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/AL3BP4PUYBE7DOQUQWE64TGWIJ \
  | 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: 02f617f1f4c049f1ba148589ee4cd642417c97b1ee2c13335fd9b20d2f729be1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f5511f7d23f726d9b1333425e5f04388034df681818a2f2bfbd9211c2a2cdc4b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-03T18:38:39Z",
    "title_canon_sha256": "c26886698fff5fcaefa50bc2b9ddcdab3661f9e1aa8bf36512e78a35afc1e977"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.1431",
    "kind": "arxiv",
    "version": 1
  }
}