Pith Number

pith:KGXANOKU

pith:2012:KGXANOKUADZVZAGMMMGDAYFBX7

not attested not anchored not stored refs pending

Context-Free Groups and Their Structure Trees

Armin Wei\ss, Volker Diekert

arxiv:1202.3276 v5 · 2012-02-15 · 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{KGXANOKUADZVZAGMMMGDAYFBX7}

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	2026-05-18T03:06:43.117113Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

51ae06b95400f35c80cc630c3060a1bff642d7b3737bc92f991b9d59d0fdee17

Aliases

arxiv: 1202.3276 · arxiv_version: 1202.3276v5 · doi: 10.48550/arxiv.1202.3276 · pith_short_12: KGXANOKUADZV · pith_short_16: KGXANOKUADZVZAGM · pith_short_8: KGXANOKU

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/KGXANOKUADZVZAGMMMGDAYFBX7 \
  | 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: 51ae06b95400f35c80cc630c3060a1bff642d7b3737bc92f991b9d59d0fdee17

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "30be0ea51a2508700784c4aa9aa9b07c6e6b11dbb34e5736b2cea05619aa7e68",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-02-15T11:09:09Z",
    "title_canon_sha256": "f538c7129016cb33fd2128ed0f47466823cdc6a64bd5fdf910cc6a89ee434516"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.3276",
    "kind": "arxiv",
    "version": 5
  }
}