Pith Number

pith:3FZO34RC

pith:2010:3FZO34RCSO7HLWAEO6CHUXOPQQ

not attested not anchored not stored refs pending

On properties not inherited by monoids from their Schutzenberger groups

Ant\'onio Malheiro, Robert Gray, Stephen J Pride

arxiv:1012.2049 v1 · 2010-12-09 · 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{3FZO34RCSO7HLWAEO6CHUXOPQQ}

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	2026-05-18T00:41:54.184249Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d972edf22293be75d80477847a5dcf84177808f126fa7e47368c3935f7ca0bbe

Aliases

arxiv: 1012.2049 · arxiv_version: 1012.2049v1 · doi: 10.48550/arxiv.1012.2049 · pith_short_12: 3FZO34RCSO7H · pith_short_16: 3FZO34RCSO7HLWAE · pith_short_8: 3FZO34RC

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/3FZO34RCSO7HLWAEO6CHUXOPQQ \
  | 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: d972edf22293be75d80477847a5dcf84177808f126fa7e47368c3935f7ca0bbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d82ac06d44f902a228b574c327bdc4ca70d99ea23ce6b7b4a412aef69bd581b1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-12-09T16:54:25Z",
    "title_canon_sha256": "3e084e5d95d4d8020962ed00c0bdea0ade2a959b646be78380be5cd2c793c820"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2049",
    "kind": "arxiv",
    "version": 1
  }
}