Pith Number

pith:NTLY2IAU

pith:2012:NTLY2IAUUTTHXUSUT2WNAONJ7W

not attested not anchored not stored refs pending

Some remarks on Euler's totient function

Rodney Coleman (LJK)

arxiv:1207.4446 v1 · 2012-07-18 · 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{NTLY2IAUUTTHXUSUT2WNAONJ7W}

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	2026-05-18T03:50:38.234167Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6cd78d2014a4e67bd2549eacd039a9fda333cea33e6d43eb13a8e563c51855d9

Aliases

arxiv: 1207.4446 · arxiv_version: 1207.4446v1 · doi: 10.48550/arxiv.1207.4446 · pith_short_12: NTLY2IAUUTTH · pith_short_16: NTLY2IAUUTTHXUSU · pith_short_8: NTLY2IAU

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/NTLY2IAUUTTHXUSUT2WNAONJ7W \
  | 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: 6cd78d2014a4e67bd2549eacd039a9fda333cea33e6d43eb13a8e563c51855d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3b0a686c997c9bbdd679b3808dea0e31d621cae882f882c96c2f0f9faaa015dc",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-07-18T19:03:01Z",
    "title_canon_sha256": "cc19810bb2255b24d5c2c1998f2627ba4a9b1cb65317d330655e4b46725e808b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.4446",
    "kind": "arxiv",
    "version": 1
  }
}