Pith Number

pith:NCEJWITR

pith:2013:NCEJWITRC43PYDT66ISV6VCDQN

not attested not anchored not stored refs pending

The Gale-Berlekamp game for Hadamard matrices

Teodor Banica

arxiv:1306.6003 v4 · 2013-06-25 · math.CO · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NCEJWITRC43PYDT66ISV6VCDQN}

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	2026-05-18T02:32:22.641839Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68889b22711736fc0e7ef2255f54438347caf2d5eff1e66fa1fe2a800c8879b4

Aliases

arxiv: 1306.6003 · arxiv_version: 1306.6003v4 · doi: 10.48550/arxiv.1306.6003 · pith_short_12: NCEJWITRC43P · pith_short_16: NCEJWITRC43PYDT6 · pith_short_8: NCEJWITR

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/NCEJWITRC43PYDT66ISV6VCDQN \
  | 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: 68889b22711736fc0e7ef2255f54438347caf2d5eff1e66fa1fe2a800c8879b4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "33de07afb359452f590662c019cf591b717763ffbd8af7905b23d448c0cba760",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-06-25T15:37:32Z",
    "title_canon_sha256": "c73457f405a8426f412dd4251af990e068bf294c4263535bf9a412df70ac0992"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.6003",
    "kind": "arxiv",
    "version": 4
  }
}