Pith Number

pith:ZXOJFRO5

pith:2005:ZXOJFRO5W35K3GNGGZQ54R3WZ4

not attested not anchored not stored refs pending

Systems of submodules and a remark by M.C.R. Butler

Markus Schmidmeier

arxiv:math/0507559 v2 · 2005-07-27 · math.RT · math.CT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZXOJFRO5W35K3GNGGZQ54R3WZ4}

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	2026-05-17T23:42:09.237913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cddc92c5ddb6faad99a63661de4776cf2e6e88cbc45c8a2f4e216a2e0af388b1

Aliases

arxiv: math/0507559 · arxiv_version: math/0507559v2 · doi: 10.48550/arxiv.math/0507559 · pith_short_12: ZXOJFRO5W35K · pith_short_16: ZXOJFRO5W35K3GNG · pith_short_8: ZXOJFRO5

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/ZXOJFRO5W35K3GNGGZQ54R3WZ4 \
  | 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: cddc92c5ddb6faad99a63661de4776cf2e6e88cbc45c8a2f4e216a2e0af388b1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7dc7a539d28748604a7d834783514ffc825df8fb4eafe3662e580bf21734b8cb",
    "cross_cats_sorted": [
      "math.CT"
    ],
    "license": "",
    "primary_cat": "math.RT",
    "submitted_at": "2005-07-27T12:47:50Z",
    "title_canon_sha256": "2308c78ae1fa2528adca510c3e9c180d359ffb4bc014f3d5267ec998b7bac380"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0507559",
    "kind": "arxiv",
    "version": 2
  }
}