Pith Number

pith:6MG7COWP

pith:2012:6MG7COWPXQYOUW64PSSCA6SAGB

not attested not anchored not stored refs pending

Dehn Functions, the Word Problem, and the Bounded Word Problem For Decidable Group Presentations

Desmond Cummins

arxiv:1212.2024 v2 · 2012-12-10 · 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{6MG7COWPXQYOUW64PSSCA6SAGB}

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	2026-05-18T03:36:26.590634Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f30df13acfbc30ea5bdc7ca4207a40304e9c829ef56dbc8ea928923ac16eb0ed

Aliases

arxiv: 1212.2024 · arxiv_version: 1212.2024v2 · doi: 10.48550/arxiv.1212.2024 · pith_short_12: 6MG7COWPXQYO · pith_short_16: 6MG7COWPXQYOUW64 · pith_short_8: 6MG7COWP

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/6MG7COWPXQYOUW64PSSCA6SAGB \
  | 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: f30df13acfbc30ea5bdc7ca4207a40304e9c829ef56dbc8ea928923ac16eb0ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "478768d14dfd5fa1a524448a5763604ad10bb951be6b24727324e86dc6a5ca76",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-12-10T10:26:18Z",
    "title_canon_sha256": "f48cb20b92f40c90a2b40a2b3b7b7fc83eb0ab8bcdca1849d5e2179f5d69779f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2024",
    "kind": "arxiv",
    "version": 2
  }
}