Pith Number

pith:YKSCOBEK

pith:2021:YKSCOBEKQJANK4CWQUJMFFZZWI

not attested not anchored not stored refs pending

Cycle type of random permutations: A toolkit

Kevin Ford

arxiv:2104.12019 v3 · 2021-04-24 · math.CO · math.GR · math.NT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YKSCOBEKQJANK4CWQUJMFFZZWI}

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	2026-07-05T04:55:14.894273Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2a427048a8240d570568512c29739b235185784a8c2e15da2032726bb07de85

Aliases

arxiv: 2104.12019 · arxiv_version: 2104.12019v3 · doi: 10.48550/arxiv.2104.12019 · pith_short_12: YKSCOBEKQJAN · pith_short_16: YKSCOBEKQJANK4CW · pith_short_8: YKSCOBEK

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/YKSCOBEKQJANK4CWQUJMFFZZWI \
  | 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: c2a427048a8240d570568512c29739b235185784a8c2e15da2032726bb07de85

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4af32388b783e8df8fb3f03dda5f928862eb90ecbe366bceedc61d3247b55ddf",
    "cross_cats_sorted": [
      "math.GR",
      "math.NT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2021-04-24T20:34:42Z",
    "title_canon_sha256": "7f3ec68916065c09c974bca2c85a5bc2c8f99224fa4057f9de4721cac8c8d20f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2104.12019",
    "kind": "arxiv",
    "version": 3
  }
}