Pith Number

pith:JL6WGS4Y

pith:2020:JL6WGS4Y5A3SP2QC5W2NNJ7GVT

not attested not anchored not stored refs pending

Each positive rational number has the form $\varphi(m^2)/\varphi(n^2)$

Dmitry Krachun, Zhi-Wei Sun

arxiv:2001.03736 v2 · 2020-01-11 · math.HO · 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{JL6WGS4Y5A3SP2QC5W2NNJ7GVT}

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	2026-07-05T01:45:19.228210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4afd634b98e83727ea02edb4d6a7e6ace9dca581908ebf9de330eb54a0dfd8b3

Aliases

arxiv: 2001.03736 · arxiv_version: 2001.03736v2 · doi: 10.48550/arxiv.2001.03736 · pith_short_12: JL6WGS4Y5A3S · pith_short_16: JL6WGS4Y5A3SP2QC · pith_short_8: JL6WGS4Y

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/JL6WGS4Y5A3SP2QC5W2NNJ7GVT \
  | 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: 4afd634b98e83727ea02edb4d6a7e6ace9dca581908ebf9de330eb54a0dfd8b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1012e92ad5a1a323d1f77d361736232a011f915db6d0fb38b0acba425fbebb0a",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2020-01-11T10:52:44Z",
    "title_canon_sha256": "09e2a2f66a11f30c46327be3c5f476b029a3d6acea8e4e71fdede7c45d92246d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2001.03736",
    "kind": "arxiv",
    "version": 2
  }
}