Pith Number

pith:KCAQFJ3A

pith:2009:KCAQFJ3A3EALIEHAG5AWWKCICF

not attested not anchored not stored refs pending

The Non-Commutative Cycle Lemma

Craig Armstrong, James A. Mingo, Jennifer C. H. Wilson, Roland Speicher

arxiv:0903.4601 v2 · 2009-03-26 · math.CO · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KCAQFJ3A3EALIEHAG5AWWKCICF}

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	2026-05-18T03:42:32.498471Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

508102a760d900b410e037416b28481157106abb79d56074908295092d318a29

Aliases

arxiv: 0903.4601 · arxiv_version: 0903.4601v2 · doi: 10.48550/arxiv.0903.4601 · pith_short_12: KCAQFJ3A3EAL · pith_short_16: KCAQFJ3A3EALIEHA · pith_short_8: KCAQFJ3A

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/KCAQFJ3A3EALIEHAG5AWWKCICF \
  | 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: 508102a760d900b410e037416b28481157106abb79d56074908295092d318a29

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d4d80f99cebe61049f16d26320afb26ae4ef1bc03435cd6008fda5e7a00f613",
    "cross_cats_sorted": [
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2009-03-26T14:52:57Z",
    "title_canon_sha256": "461853a0d6c72af34695f236a1d4a50688453cdf2220de2ab9dda63c13335494"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0903.4601",
    "kind": "arxiv",
    "version": 2
  }
}