Pith Number

pith:5ZQEJKOV

pith:2026:5ZQEJKOV6XC7J7OMXYBXZKPNDU

not attested not anchored not stored refs pending

C4-face-magic labeling on a 4x4 Klein bottle grid graph

Stephen J. Curran, Timothy Myers

arxiv:2606.06817 v1 · 2026-06-05 · 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{5ZQEJKOV6XC7J7OMXYBXZKPNDU}

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	2026-06-08T01:04:29.649983Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ee6044a9d5f5c5f4fdccbe037ca9ed1d11733945dc838e2636afca032dc9dd10

Aliases

arxiv: 2606.06817 · arxiv_version: 2606.06817v1 · doi: 10.48550/arxiv.2606.06817 · pith_short_12: 5ZQEJKOV6XC7 · pith_short_16: 5ZQEJKOV6XC7J7OM · pith_short_8: 5ZQEJKOV

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/5ZQEJKOV6XC7J7OMXYBXZKPNDU \
  | 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: ee6044a9d5f5c5f4fdccbe037ca9ed1d11733945dc838e2636afca032dc9dd10

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "251ed5e8c457d64f36871f3c50160eb63a0705368114886e9735057cce70deb5",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-05T01:40:16Z",
    "title_canon_sha256": "1440a9f6564e84106b8315364f24dab486222f50ea11a7761cd3b0316da1208b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.06817",
    "kind": "arxiv",
    "version": 1
  }
}