Pith Number

pith:A3WWBQ4D

pith:2017:A3WWBQ4DR6GPFXVCIZODDHFKVQ

not attested not anchored not stored refs pending

Uniform rank gradient, cost and local-global convergence

L\'aszl\'o M\'arton T\'oth, Mikl\'os Ab\'ert

arxiv:1710.10431 v2 · 2017-10-28 · math.GR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{A3WWBQ4DR6GPFXVCIZODDHFKVQ}

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	2026-05-18T00:29:08.034692Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

06ed60c3838f8cf2dea2465c319caaac3c95993ea663df553cd6c96cfc980871

Aliases

arxiv: 1710.10431 · arxiv_version: 1710.10431v2 · doi: 10.48550/arxiv.1710.10431 · pith_short_12: A3WWBQ4DR6GP · pith_short_16: A3WWBQ4DR6GPFXVC · pith_short_8: A3WWBQ4D

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/A3WWBQ4DR6GPFXVCIZODDHFKVQ \
  | 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: 06ed60c3838f8cf2dea2465c319caaac3c95993ea663df553cd6c96cfc980871

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6b5658c1e113380ea8810256f8af0337e17db72c27ae443aba91bb7a1dd1a4f4",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2017-10-28T09:15:30Z",
    "title_canon_sha256": "bd6f55f23cdbb4c8c61138839b3aa45e2c8828fe1336a3ac928b6444e02f2e58"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1710.10431",
    "kind": "arxiv",
    "version": 2
  }
}