Pith Number

pith:O2V4M32D

pith:2014:O2V4M32DFDZEWQ5YQ7RXYTBJCX

not attested not anchored not stored refs pending

A theorem on roots of unity and a combinatorial principle

Daniel Nett, Simon Lentner

arxiv:1409.5822 v2 · 2014-09-19 · math.QA · math.CO · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{O2V4M32DFDZEWQ5YQ7RXYTBJCX}

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	2026-05-18T02:39:55.356678Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76abc66f4328f24b43b887e37c4c2915e4fdbde8f57a4a5b154b3c28721bf3c7

Aliases

arxiv: 1409.5822 · arxiv_version: 1409.5822v2 · doi: 10.48550/arxiv.1409.5822 · pith_short_12: O2V4M32DFDZE · pith_short_16: O2V4M32DFDZEWQ5Y · pith_short_8: O2V4M32D

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/O2V4M32DFDZEWQ5YQ7RXYTBJCX \
  | 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: 76abc66f4328f24b43b887e37c4c2915e4fdbde8f57a4a5b154b3c28721bf3c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "628b786ed357abebc270d298eb1e186209116d56c28b0cafe4d3cbc968ca78d6",
    "cross_cats_sorted": [
      "math.CO",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2014-09-19T21:44:24Z",
    "title_canon_sha256": "f7c91019a448087893d3397d8303fb0e7b1f13589f53bdb9c5fb5f2ce9d0e5c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5822",
    "kind": "arxiv",
    "version": 2
  }
}