Pith Number

pith:TYP5QPAL

pith:2026:TYP5QPALUPZJ5ZQVYRPOIIOUNZ

not attested not anchored not stored refs pending

The $k$-out-of-$n$ picture-hanging puzzle: shorter solutions for small $k$ and $n-k$

Tom Verhoeff

arxiv:2605.27617 v1 · 2026-05-26 · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TYP5QPALUPZJ5ZQVYRPOIIOUNZ}

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	2026-05-28T01:04:18.385193Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e1fd83c0ba3f29ee615c45ee421d46e5929bb58e3d508b3225d3109ed385e86

Aliases

arxiv: 2605.27617 · arxiv_version: 2605.27617v1 · doi: 10.48550/arxiv.2605.27617 · pith_short_12: TYP5QPALUPZJ · pith_short_16: TYP5QPALUPZJ5ZQV · pith_short_8: TYP5QPAL

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/TYP5QPALUPZJ5ZQVYRPOIIOUNZ \
  | 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: 9e1fd83c0ba3f29ee615c45ee421d46e5929bb58e3d508b3225d3109ed385e86

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8a1d3dfd85f336718edbeaa9f3352d0c73b84c330eace29edff7f262132b78b0",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://creativecommons.org/licenses/by-sa/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-26T19:31:30Z",
    "title_canon_sha256": "2017c92543f880cb2fbecf3d46a130fa5d13c0f0fcd23b48c398ef6c40a8b1fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.27617",
    "kind": "arxiv",
    "version": 1
  }
}