Pith Number

pith:NWLOWOEZ

pith:2006:NWLOWOEZZCM36ECL3WX4ZAGZRJ

not attested not anchored not stored refs pending

Random quotients of the modular group are rigid and essentially incompressible

Ilya Kapovich, Paul Schupp

arxiv:math/0604343 v1 · 2006-04-14 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWLOWOEZZCM36ECL3WX4ZAGZRJ}

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	2026-05-18T04:20:50.183626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d96eb3899c899bf104bddafcc80d98a627ba6b6f43a94bd9b1a76bd18ac7847

Aliases

arxiv: math/0604343 · arxiv_version: math/0604343v1 · doi: 10.48550/arxiv.math/0604343 · pith_short_12: NWLOWOEZZCM3 · pith_short_16: NWLOWOEZZCM36ECL · pith_short_8: NWLOWOEZ

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/NWLOWOEZZCM36ECL3WX4ZAGZRJ \
  | 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: 6d96eb3899c899bf104bddafcc80d98a627ba6b6f43a94bd9b1a76bd18ac7847

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5d5cab59d15c4a9d892ed8c704eafbcd1d32ac92105ce558320042692fb945f",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-04-14T20:15:12Z",
    "title_canon_sha256": "501bbf696797ed298379583737b23712c58b83df4e9dd37a559a911f12f9f099"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0604343",
    "kind": "arxiv",
    "version": 1
  }
}