Pith Number

pith:S6K37YNG

pith:2019:S6K37YNG7DYYFE4J2MOIQZLG3Z

not attested not anchored not stored refs pending

A short proof of Greenberg's Theorem

Gareth A. Jones

arxiv:1908.06675 v2 · 2019-08-19 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{S6K37YNG7DYYFE4J2MOIQZLG3Z}

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	2026-07-05T00:26:09.906623Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9795bfe1a6f8f1829389d31c886566de792fc9a901ea82a986ddc4e83fdfde2b

Aliases

arxiv: 1908.06675 · arxiv_version: 1908.06675v2 · doi: 10.48550/arxiv.1908.06675 · pith_short_12: S6K37YNG7DYY · pith_short_16: S6K37YNG7DYYFE4J · pith_short_8: S6K37YNG

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/S6K37YNG7DYYFE4J2MOIQZLG3Z \
  | 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: 9795bfe1a6f8f1829389d31c886566de792fc9a901ea82a986ddc4e83fdfde2b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4e85f3953099e9e79586c6950075eafd5d27c94a1d4d10629314ba9e5ee2644",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-08-19T10:04:10Z",
    "title_canon_sha256": "f0db5bf78528695cf8d1370329ecf0e47444672649a5d15a6f4e96d177dce89f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06675",
    "kind": "arxiv",
    "version": 2
  }
}