Pith Number

pith:JVU3PTRC

pith:2012:JVU3PTRC6VQ7ABYMGPXONEZU5P

not attested not anchored not stored refs pending

A fundamental inequality between products of $x^p - 1$

Keiichi Watanabe

arxiv:1207.0701 v1 · 2012-07-02 · math.CA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JVU3PTRC6VQ7ABYMGPXONEZU5P}

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	2026-05-18T03:51:49.231006Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d69b7ce22f561f0070c33eee69334ebda3e1074b8b0fe7934f51b8214e22f82

Aliases

arxiv: 1207.0701 · arxiv_version: 1207.0701v1 · doi: 10.48550/arxiv.1207.0701 · pith_short_12: JVU3PTRC6VQ7 · pith_short_16: JVU3PTRC6VQ7ABYM · pith_short_8: JVU3PTRC

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/JVU3PTRC6VQ7ABYMGPXONEZU5P \
  | 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: 4d69b7ce22f561f0070c33eee69334ebda3e1074b8b0fe7934f51b8214e22f82

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "732dd426e3acf6296e0dd606e1d9044ab0556dff49c4b4f922fd18d3baafef8f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2012-07-02T13:26:34Z",
    "title_canon_sha256": "425cd23c5792411d3bbcfefa0da2c982f2fb8c8c58520438c756cacf82afed63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0701",
    "kind": "arxiv",
    "version": 1
  }
}