Pith Number

pith:UTN2IRYH

pith:2013:UTN2IRYH7JDPXEKCRAHYY6FL5H

not attested not anchored not stored refs pending

Morley's other miracle: $\displaystyle 4^{p-1}\equiv\pm (\smallmatrix p-1 \frac{p-1}{2} \endsmallmatrix) \pmod {p^3} $

Christian Aebi, Grant Cairns

arxiv:1302.3678 v1 · 2013-02-15 · 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{UTN2IRYH7JDPXEKCRAHYY6FL5H}

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	2026-05-18T03:33:36.150718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a4dba44707fa46fb9142880f8c78abe9eb2f2def7fd27668e53aa617fa435399

Aliases

arxiv: 1302.3678 · arxiv_version: 1302.3678v1 · doi: 10.48550/arxiv.1302.3678 · pith_short_12: UTN2IRYH7JDP · pith_short_16: UTN2IRYH7JDPXEKC · pith_short_8: UTN2IRYH

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/UTN2IRYH7JDPXEKCRAHYY6FL5H \
  | 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: a4dba44707fa46fb9142880f8c78abe9eb2f2def7fd27668e53aa617fa435399

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "554427c3abd17b96d52b3198d59328a1d9e4f26a7817bec062925767d3689e91",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-02-15T05:19:59Z",
    "title_canon_sha256": "03a9775891b217d7feb45c1e4a470aaeabe2d67054027911404b7c09b7ff714d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.3678",
    "kind": "arxiv",
    "version": 1
  }
}