Pith Number

pith:JPTO7NAT

pith:2010:JPTO7NATXUK55ICFZFYDCA5KZG

not attested not anchored not stored refs pending

Nielsen equivalence in small cancellation groups

Ilya Kapovich, Richard Weidmann

arxiv:1011.5862 v3 · 2010-11-26 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JPTO7NATXUK55ICFZFYDCA5KZG}

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	2026-05-18T02:23:17.435331Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4be6efb413bd15dea045c9703103aac993e88fb7b1ae55571932d3a26e4e879e

Aliases

arxiv: 1011.5862 · arxiv_version: 1011.5862v3 · doi: 10.48550/arxiv.1011.5862 · pith_short_12: JPTO7NATXUK5 · pith_short_16: JPTO7NATXUK55ICF · pith_short_8: JPTO7NAT

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/JPTO7NATXUK55ICFZFYDCA5KZG \
  | 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: 4be6efb413bd15dea045c9703103aac993e88fb7b1ae55571932d3a26e4e879e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d5016e950c240226e891cc10763a5128b7486e90d200a16b4c416ae6b11aaf3",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-11-26T19:23:44Z",
    "title_canon_sha256": "5859f3bea2f94a6ebba4defc64395ca9739e387cfa00ad0d59e2077f7a2afb03"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.5862",
    "kind": "arxiv",
    "version": 3
  }
}