Pith Number

pith:UKEHQ5GK

pith:2021:UKEHQ5GKGOEQS7YOE7UFNWKSM7

not attested not anchored not stored refs pending

The commutator subgroups of free groups and surface groups

Andrew Putman

arxiv:2101.05905 v2 · 2021-01-14 · math.GT · 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{UKEHQ5GKGOEQS7YOE7UFNWKSM7}

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	2026-07-05T04:40:43.597681Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a2887874ca3389097f0e27e856d95267fce7b350d3594bae33d60dee6c6d336d

Aliases

arxiv: 2101.05905 · arxiv_version: 2101.05905v2 · doi: 10.48550/arxiv.2101.05905 · pith_short_12: UKEHQ5GKGOEQ · pith_short_16: UKEHQ5GKGOEQS7YO · pith_short_8: UKEHQ5GK

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/UKEHQ5GKGOEQS7YOE7UFNWKSM7 \
  | 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: a2887874ca3389097f0e27e856d95267fce7b350d3594bae33d60dee6c6d336d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faebdadea8eb61f75ad5be879bc34399030ba7f8e3b4f1bfc23f36067bd9b6f7",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2021-01-14T23:19:51Z",
    "title_canon_sha256": "b135f46232bf9d26bdaa898cd976651b6baeef8a6667050b12648770f0793874"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2101.05905",
    "kind": "arxiv",
    "version": 2
  }
}