Pith Number

pith:64XXDKFH

pith:2010:64XXDKFHHNKQHMQ4FJ7CIRIJJL

not attested not anchored not stored refs pending

A Golod-Shafarevich Equality and p-Tower Groups

Cam McLeman

arxiv:1008.3002 v1 · 2010-08-18 · math.NT · 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{64XXDKFHHNKQHMQ4FJ7CIRIJJL}

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	2026-05-18T04:42:03.751644Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f72f71a8a73b5503b21c2a7e2445094af75d8f78c6d4182fb742d145f39c4d4f

Aliases

arxiv: 1008.3002 · arxiv_version: 1008.3002v1 · doi: 10.48550/arxiv.1008.3002 · pith_short_12: 64XXDKFHHNKQ · pith_short_16: 64XXDKFHHNKQHMQ4 · pith_short_8: 64XXDKFH

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/64XXDKFHHNKQHMQ4FJ7CIRIJJL \
  | 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: f72f71a8a73b5503b21c2a7e2445094af75d8f78c6d4182fb742d145f39c4d4f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "392754130b8275f64e0dade4e0ab16f815a71b6585c985a301534c39a84d61d1",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2010-08-18T03:31:07Z",
    "title_canon_sha256": "fca6d9d916a67f3f3a63a93408285cbf64c1cb5f8cd069787590a37a9ca72c29"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1008.3002",
    "kind": "arxiv",
    "version": 1
  }
}