Pith Number

pith:XWJ45JXI

pith:2015:XWJ45JXI6F5WOWOH4KECHRDW5D

not attested not anchored not stored refs pending

A family of measures on symmetric groups and the field with one element

Jeffrey C. Lagarias

arxiv:1505.05745 v3 · 2015-05-21 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XWJ45JXI6F5WOWOH4KECHRDW5D}

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	2026-05-18T00:25:44.611778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bd93cea6e8f17b6759c7e28823c476e8f91a2d85ffc7b04c2f76747ce3b9f7d3

Aliases

arxiv: 1505.05745 · arxiv_version: 1505.05745v3 · doi: 10.48550/arxiv.1505.05745 · pith_short_12: XWJ45JXI6F5W · pith_short_16: XWJ45JXI6F5WOWOH · pith_short_8: XWJ45JXI

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/XWJ45JXI6F5WOWOH4KECHRDW5D \
  | 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: bd93cea6e8f17b6759c7e28823c476e8f91a2d85ffc7b04c2f76747ce3b9f7d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6f0e765e3467f8a8b23bc01ca054d85ef2aa4c5ac9d9a5fd4661de2759fc136d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-05-21T14:06:11Z",
    "title_canon_sha256": "041bd6935864ba0bdcd66af0d6c475561afc004ab160e27bc5c2ff760b0fb71b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.05745",
    "kind": "arxiv",
    "version": 3
  }
}