Pith Number

pith:VKAMNMLY

pith:2018:VKAMNMLYGRPRL2KSMQJN4SLROE

not attested not anchored not stored refs pending

A Pascal-like Bound for the Number of Necklaces with Fixed Density

I. Heckenberger, J. Sawada

arxiv:1801.09516 v1 · 2018-01-29 · math.CO · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VKAMNMLYGRPRL2KSMQJN4SLROE}

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	2026-05-18T00:24:57.191457Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa80c6b178345f15e9526412de49717118a35b5a01d7b7cdc1a6ec91197a1210

Aliases

arxiv: 1801.09516 · arxiv_version: 1801.09516v1 · doi: 10.48550/arxiv.1801.09516 · pith_short_12: VKAMNMLYGRPR · pith_short_16: VKAMNMLYGRPRL2KS · pith_short_8: VKAMNMLY

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/VKAMNMLYGRPRL2KSMQJN4SLROE \
  | 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: aa80c6b178345f15e9526412de49717118a35b5a01d7b7cdc1a6ec91197a1210

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e2d4d2a798bfe46ca4c674a4a13ad98a72a545c87524b9d3c8109e1b569e5f3b",
    "cross_cats_sorted": [
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-01-29T14:13:33Z",
    "title_canon_sha256": "52c3958ce5a2de508d83c620619eca1cd0ab22cb0dc2340d769dffad56378607"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.09516",
    "kind": "arxiv",
    "version": 1
  }
}