Pith Number

pith:VIPYC37G

pith:1999:VIPYC37GELGEXH2OGU7DPMPZZE

not attested not anchored not stored refs pending

The number of solutions of phi(x)=m

Kevin Ford

arxiv:math/9907204 v1 · 1999-07-01 · 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{VIPYC37GELGEXH2OGU7DPMPZZE}

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	2026-05-18T01:05:32.777814Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

aa1f816fe622cc4b9f4e353e37b1f9c93025e05aae301d549b84279e376ad45d

Aliases

arxiv: math/9907204 · arxiv_version: math/9907204v1 · doi: 10.48550/arxiv.math/9907204 · pith_short_12: VIPYC37GELGE · pith_short_16: VIPYC37GELGEXH2O · pith_short_8: VIPYC37G

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/VIPYC37GELGEXH2OGU7DPMPZZE \
  | 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: aa1f816fe622cc4b9f4e353e37b1f9c93025e05aae301d549b84279e376ad45d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e752deb46576ee0872a6c60b30f1e4784059e635dca267723af04ae20d14ad8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "1999-07-01T00:00:00Z",
    "title_canon_sha256": "3c640b5bcb02e66567019acc519a164c0a85359c4d5b1204293580f59bac7d05"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907204",
    "kind": "arxiv",
    "version": 1
  }
}