Pith Number

pith:W6O2HH43

pith:2012:W6O2HH43ZZNU5J5GGK7UG6YXQU

not attested not anchored not stored refs pending

Open subgroups of free topological groups

Jeremy Brazas

arxiv:1209.5486 v2 · 2012-09-25 · math.AT · math.GN

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W6O2HH43ZZNU5J5GGK7UG6YXQU}

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	2026-05-18T02:49:46.185363Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b79da39f9bce5b4ea7a632bf437b178506211d629a3a9bf007332ec75dc9e151

Aliases

arxiv: 1209.5486 · arxiv_version: 1209.5486v2 · doi: 10.48550/arxiv.1209.5486 · pith_short_12: W6O2HH43ZZNU · pith_short_16: W6O2HH43ZZNU5J5G · pith_short_8: W6O2HH43

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/W6O2HH43ZZNU5J5GGK7UG6YXQU \
  | 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: b79da39f9bce5b4ea7a632bf437b178506211d629a3a9bf007332ec75dc9e151

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5da718e00376ae67c4b0a69f2314407f0f9f9bb62976d85eee021530d79f7a94",
    "cross_cats_sorted": [
      "math.GN"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2012-09-25T03:19:12Z",
    "title_canon_sha256": "4925423b791ffe2451d021a0e0f5b38d1ac9f3afb263c28b8de7e46ff1587eff"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5486",
    "kind": "arxiv",
    "version": 2
  }
}