Pith Number

pith:MNG2QTEH

pith:2010:MNG2QTEH6KFNUCMQZUVIGY4HCR

not attested not anchored not stored refs pending

On Avoiding Sufficiently Long Abelian Squares

Elyot Grant

arxiv:1012.0524 v1 · 2010-12-02 · math.CO · cs.DM

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MNG2QTEH6KFNUCMQZUVIGY4HCR}

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	2026-05-18T04:34:17.732183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

634da84c87f28ada0990cd2a836387144e49b19a5d6ac39775ad6b3368991f15

Aliases

arxiv: 1012.0524 · arxiv_version: 1012.0524v1 · doi: 10.48550/arxiv.1012.0524 · pith_short_12: MNG2QTEH6KFN · pith_short_16: MNG2QTEH6KFNUCMQ · pith_short_8: MNG2QTEH

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/MNG2QTEH6KFNUCMQZUVIGY4HCR \
  | 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: 634da84c87f28ada0990cd2a836387144e49b19a5d6ac39775ad6b3368991f15

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0230d0537575279bb7fb9f38dbb1aeeff2d73c9df9b2bfcce89ccf67263fe646",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-12-02T18:04:54Z",
    "title_canon_sha256": "86adc715162734f583b91df95c04ab21eb5672acea4842488edaa659be713b20"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0524",
    "kind": "arxiv",
    "version": 1
  }
}