Pith Number

pith:QNNUDZEQ

pith:2012:QNNUDZEQDTSXSOSFGCMOJ5IGS4

not attested not anchored not stored refs pending

Surface subgroups from linear programming

Alden Walker, Danny Calegari

arxiv:1212.2618 v2 · 2012-12-11 · math.GR · math.DS · 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{QNNUDZEQDTSXSOSFGCMOJ5IGS4}

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	2026-05-18T01:28:21.404215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

835b41e4901ce5793a453098e4f506970979fa7a23609995016f08f56842d3fb

Aliases

arxiv: 1212.2618 · arxiv_version: 1212.2618v2 · doi: 10.48550/arxiv.1212.2618 · pith_short_12: QNNUDZEQDTSX · pith_short_16: QNNUDZEQDTSXSOSF · pith_short_8: QNNUDZEQ

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/QNNUDZEQDTSXSOSFGCMOJ5IGS4 \
  | 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: 835b41e4901ce5793a453098e4f506970979fa7a23609995016f08f56842d3fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "584cd6a6bddac77eaaf08ca8905f4dc59a7335a70ceb4854379bc29afeb0e152",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-12-11T20:37:00Z",
    "title_canon_sha256": "d6761f571a0b34cb05b393ef2727ee37d1a633d9067311bc4938b26b6818991c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.2618",
    "kind": "arxiv",
    "version": 2
  }
}