Pith Number

pith:WW5LSZGP

pith:2015:WW5LSZGPPJOVMYFZWI2SQFEECG

not attested not anchored not stored refs pending

On vanishing criteria that control finite group structure

Julian Brough

arxiv:1509.06571 v1 · 2015-09-22 · 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{WW5LSZGPPJOVMYFZWI2SQFEECG}

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	2026-05-18T01:32:19.868721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b5bab964cf7a5d5660b9b2352814841190eefd1b64e22b2c256960492785e0c4

Aliases

arxiv: 1509.06571 · arxiv_version: 1509.06571v1 · doi: 10.48550/arxiv.1509.06571 · pith_short_12: WW5LSZGPPJOV · pith_short_16: WW5LSZGPPJOVMYFZ · pith_short_8: WW5LSZGP

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/WW5LSZGPPJOVMYFZWI2SQFEECG \
  | 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: b5bab964cf7a5d5660b9b2352814841190eefd1b64e22b2c256960492785e0c4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "651ef43334d7ed415912f207db8cd7fccbfbe700670c6e34934e2e0661c78995",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-09-22T12:37:10Z",
    "title_canon_sha256": "bf789ca1819cee0426e85c8b0b0b17fef90ce4ef37a504c9c675d4f1ba1ed9b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.06571",
    "kind": "arxiv",
    "version": 1
  }
}