Pith Number

pith:W7G5QMG3

pith:2015:W7G5QMG3B2HFMI7IZLCKNFVC6N

not attested not anchored not stored refs pending

Variations on average character degrees and $p$-nilpotence

Mark L. Lewis

arxiv:1507.00309 v1 · 2015-07-01 · 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{W7G5QMG3B2HFMI7IZLCKNFVC6N}

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	2026-05-18T01:37:29.219144Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b7cdd830db0e8e5623e8cac4a696a2f3605a59ab4ce872c995050e231e06925f

Aliases

arxiv: 1507.00309 · arxiv_version: 1507.00309v1 · doi: 10.48550/arxiv.1507.00309 · pith_short_12: W7G5QMG3B2HF · pith_short_16: W7G5QMG3B2HFMI7I · pith_short_8: W7G5QMG3

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/W7G5QMG3B2HFMI7IZLCKNFVC6N \
  | 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: b7cdd830db0e8e5623e8cac4a696a2f3605a59ab4ce872c995050e231e06925f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8b572c02723b28fb9bf061594b41e30da524923dc0a2b553fda6f3f67b6494b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-07-01T18:35:43Z",
    "title_canon_sha256": "d5c4f52209508f42263c8e6bfc9a13e4625e1187faa55d52b160a7161e4d19d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.00309",
    "kind": "arxiv",
    "version": 1
  }
}