Pith Number

pith:U7ZTBDY3

pith:2015:U7ZTBDY3MP5EZUVFXQT6ARJON2

not attested not anchored not stored refs pending

Soficity, short cycles and the Higman group

Harald A. Helfgott, Kate Juschenko

arxiv:1512.02135 v4 · 2015-12-07 · math.GR · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U7ZTBDY3MP5EZUVFXQT6ARJON2}

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	2026-05-18T00:31:36.489954Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7f3308f1b63fa4cd2a5bc27e0452e6e83f954d935ecde2c5bbe47cfc877b5d9

Aliases

arxiv: 1512.02135 · arxiv_version: 1512.02135v4 · doi: 10.48550/arxiv.1512.02135 · pith_short_12: U7ZTBDY3MP5E · pith_short_16: U7ZTBDY3MP5EZUVF · pith_short_8: U7ZTBDY3

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/U7ZTBDY3MP5EZUVFXQT6ARJON2 \
  | 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: a7f3308f1b63fa4cd2a5bc27e0452e6e83f954d935ecde2c5bbe47cfc877b5d9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3222676ba5dad0bfd98c07aa239a58195f8e8d9d10af8ee73a1454b013f1319b",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2015-12-07T17:36:03Z",
    "title_canon_sha256": "f9af65cfebb445588df98e6a74a95d90c4e9cf30b78e9a9e0ade881aeac7abf3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.02135",
    "kind": "arxiv",
    "version": 4
  }
}