Pith Number

pith:NBCKGK5V

pith:2026:NBCKGK5V2FN66ZXC7QGPBEYJ2J

not attested not anchored not stored refs pending

Stallings foldings for rational subsets of automatic groups

Andrew Duncan, Dominik Francoeur, John R. Britnell, Luc\'{i}a Asencio-Mart\'in, Sarah Rees

arxiv:2607.26284 v1 · 2026-07-28 · 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{NBCKGK5V2FN66ZXC7QGPBEYJ2J}

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	2026-07-30T01:17:55.055473Z
Builder	pith-number-builder-2026-05-17-v1
Signature	unsigned_v0
Schema	pith-number/v1.0

Canonical hash

6844a32bb5d15bef66e2fc0cf09309d25fc6b4ed9e0e624a72bb273c9c9a2a96

Aliases

arxiv: 2607.26284 · arxiv_version: 2607.26284v1 · doi: 10.48550/arxiv.2607.26284 · pith_short_12: NBCKGK5V2FN6 · pith_short_16: NBCKGK5V2FN66ZXC · pith_short_8: NBCKGK5V

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/NBCKGK5V2FN66ZXC7QGPBEYJ2J \
  | 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: 6844a32bb5d15bef66e2fc0cf09309d25fc6b4ed9e0e624a72bb273c9c9a2a96

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "785df9602693a2f16436bac3230588e56f906014a5bc819fb0428b03eec7bd00",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2026-07-28T21:26:07Z",
    "title_canon_sha256": "62d71d61ce7dbd34fb605e8ceeda8fc9118349cb630a2019213a0e4d9cca2316"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.26284",
    "kind": "arxiv",
    "version": 1
  }
}