Pith Number

pith:B4JXIIE5

pith:2010:B4JXIIE5AT6SFQ7FIEMHIXPRB7

not attested not anchored not stored refs pending

Explicit examples of equivalence relations and factors with prescribed fundamental group and outer automorphism group

Steven Deprez

arxiv:1010.3612 v2 · 2010-10-18 · math.OA · math.DS · 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{B4JXIIE5AT6SFQ7FIEMHIXPRB7}

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	2026-05-18T04:00:16.092005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0f1374209d04fd22c3e54118745df10ff6a1d4b188d6aac3f09753c5b689b212

Aliases

arxiv: 1010.3612 · arxiv_version: 1010.3612v2 · doi: 10.48550/arxiv.1010.3612 · pith_short_12: B4JXIIE5AT6S · pith_short_16: B4JXIIE5AT6SFQ7F · pith_short_8: B4JXIIE5

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/B4JXIIE5AT6SFQ7FIEMHIXPRB7 \
  | 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: 0f1374209d04fd22c3e54118745df10ff6a1d4b188d6aac3f09753c5b689b212

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b12742a519689dbb9f8879110c44a937de5245db34864660bc67f30bfb5363d7",
    "cross_cats_sorted": [
      "math.DS",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OA",
    "submitted_at": "2010-10-18T14:32:32Z",
    "title_canon_sha256": "4eb756e873fae4a731b69307d0dbb40019ea3a07b4466acf02e261e2d2cb8eba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3612",
    "kind": "arxiv",
    "version": 2
  }
}