Pith Number

pith:Q4A5NTYG

pith:2015:Q4A5NTYGALTRZKXA5RNWPJFRH4

not attested not anchored not stored refs pending

Fitting heights of solvable groups with no nontrivial prime power character degrees

Mark L. Lewis

arxiv:1506.07148 v1 · 2015-06-23 · 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{Q4A5NTYGALTRZKXA5RNWPJFRH4}

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	2026-05-18T01:40:55.048306Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8701d6cf0602e71caae0ec5b67a4b13f1bf85ccd712e4c5314575211e92fd3d1

Aliases

arxiv: 1506.07148 · arxiv_version: 1506.07148v1 · doi: 10.48550/arxiv.1506.07148 · pith_short_12: Q4A5NTYGALTR · pith_short_16: Q4A5NTYGALTRZKXA · pith_short_8: Q4A5NTYG

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/Q4A5NTYGALTRZKXA5RNWPJFRH4 \
  | 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: 8701d6cf0602e71caae0ec5b67a4b13f1bf85ccd712e4c5314575211e92fd3d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8e0a3ebb5e09816887500f8ff7c7c3a72767396ba7a4c7522d0961b980351ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-06-23T19:24:47Z",
    "title_canon_sha256": "b4f16eef521075ff68fea15d03b358c6f81e80a5715d9608afab43ec1952c3a8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.07148",
    "kind": "arxiv",
    "version": 1
  }
}