Pith Number

pith:4OAJ23GJ

pith:2015:4OAJ23GJ4VFLMRWDXJNUNWMSFZ

not attested not anchored not stored refs pending

The Z-cubes: a hypercube variant with small diameter

Xuding Zhu

arxiv:1509.06884 v1 · 2015-09-23 · 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{4OAJ23GJ4VFLMRWDXJNUNWMSFZ}

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	2026-05-18T01:32:17.647492Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e3809d6cc9e54ab646c3ba5b46d9922e699b8107cbdd5fcca4e4481127ca7f33

Aliases

arxiv: 1509.06884 · arxiv_version: 1509.06884v1 · doi: 10.48550/arxiv.1509.06884 · pith_short_12: 4OAJ23GJ4VFL · pith_short_16: 4OAJ23GJ4VFLMRWD · pith_short_8: 4OAJ23GJ

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/4OAJ23GJ4VFLMRWDXJNUNWMSFZ \
  | 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: e3809d6cc9e54ab646c3ba5b46d9922e699b8107cbdd5fcca4e4481127ca7f33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "796e621c88c7e2f554e67f694cd2b2b39e43ba4a5ce4f809afae97dd04380db5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2015-09-23T08:41:25Z",
    "title_canon_sha256": "daa6f6335d6656666c2ec064cad5a6757b4635f4cc1a0d5d0601a50f3a63cde4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06884",
    "kind": "arxiv",
    "version": 1
  }
}