Pith Number

pith:VMNZPKRN

pith:2009:VMNZPKRNVSRXSFQPLYJV2LTIWU

not attested not anchored not stored refs pending

Geodesic rewriting systems and pregroups

Alexei Miasnikov, Andrew J. Duncan, Volker Diekert

arxiv:0906.2223 v1 · 2009-06-11 · 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{VMNZPKRNVSRXSFQPLYJV2LTIWU}

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	2026-05-18T03:41:01.685370Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ab1b97aa2daca379160f5e135d2e68b53d52a3fc2b5ec3507f215c855b47beb0

Aliases

arxiv: 0906.2223 · arxiv_version: 0906.2223v1 · doi: 10.48550/arxiv.0906.2223 · pith_short_12: VMNZPKRNVSRX · pith_short_16: VMNZPKRNVSRXSFQP · pith_short_8: VMNZPKRN

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/VMNZPKRNVSRXSFQPLYJV2LTIWU \
  | 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: ab1b97aa2daca379160f5e135d2e68b53d52a3fc2b5ec3507f215c855b47beb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd9635ea11697db2554c88b28a132fc305d02d5ac818e5d79dbf441190428cfa",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-06-11T22:36:05Z",
    "title_canon_sha256": "6e598994e3bb2aa529b435b51e36b3eb321a9f5947cb0541d924c2522793b13d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.2223",
    "kind": "arxiv",
    "version": 1
  }
}