Pith Number

pith:NKK3NAIF

pith:2012:NKK3NAIFQMIZNQTXYIVQXF3NQE

not attested not anchored not stored refs pending

Mixing actions of countable groups are almost free

Robin Tucker-Drob

arxiv:1208.0655 v1 · 2012-08-03 · 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{NKK3NAIFQMIZNQTXYIVQXF3NQE}

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	2026-05-18T03:49:32.089401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a95b68105831196c277c22b0b976d8123e882d9ec08ed1658875934dadf9aff

Aliases

arxiv: 1208.0655 · arxiv_version: 1208.0655v1 · doi: 10.48550/arxiv.1208.0655 · pith_short_12: NKK3NAIFQMIZ · pith_short_16: NKK3NAIFQMIZNQTX · pith_short_8: NKK3NAIF

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/NKK3NAIFQMIZNQTXYIVQXF3NQE \
  | 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: 6a95b68105831196c277c22b0b976d8123e882d9ec08ed1658875934dadf9aff

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d5abe122f59c2a369e4af933fa94b37f7d72bef0cf46dea8c0a64a6dd89538b2",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-08-03T05:03:48Z",
    "title_canon_sha256": "a20e1c0d490872cc6a3dac4c7efe8d6efe7957c2f782ff865aec095eed2a7a20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1208.0655",
    "kind": "arxiv",
    "version": 1
  }
}