Pith Number

pith:ALAP3OPQ

pith:2017:ALAP3OPQ5OBXJXEA7VXOJ4VBNW

not attested not anchored not stored refs pending

Magic squares with all subsquares of possible orders based on extended Langford sequences

Ming Zhong, Wen Li, Yong Zhang

arxiv:1712.05560 v1 · 2017-12-15 · 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{ALAP3OPQ5OBXJXEA7VXOJ4VBNW}

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	2026-05-18T00:27:56.182339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02c0fdb9f0eb8374dc80fd6ee4f2a16d96657b54a9058b6b999eb0f29e10d0af

Aliases

arxiv: 1712.05560 · arxiv_version: 1712.05560v1 · doi: 10.48550/arxiv.1712.05560 · pith_short_12: ALAP3OPQ5OBX · pith_short_16: ALAP3OPQ5OBXJXEA · pith_short_8: ALAP3OPQ

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/ALAP3OPQ5OBXJXEA7VXOJ4VBNW \
  | 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: 02c0fdb9f0eb8374dc80fd6ee4f2a16d96657b54a9058b6b999eb0f29e10d0af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f6adb67159782728485365c2212c95795f0360eaf320d8eafea7a7df5c113e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2017-12-15T07:00:29Z",
    "title_canon_sha256": "c19677298a844c8d04a21109cfbbe6f8b2a15389e9ef825312b29375bbde54e6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.05560",
    "kind": "arxiv",
    "version": 1
  }
}