Pith Number

pith:X6USANQ3

pith:2019:X6USANQ33OG462WD2WUK7ZMYO6

not attested not anchored not stored refs pending

The $k$-Dimensional Weisfeiler-Leman Algorithm

Neil Immerman, Rik Sengupta

arxiv:1907.09582 v1 · 2019-07-22 · cs.CC · cs.DS · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{X6USANQ33OG462WD2WUK7ZMYO6}

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.

Cited by

1 paper in Pith

A Hierarchy of Tinhofer Graphs: Separations and Membership Testing

Receipt and verification

First computed	2026-05-17T23:39:52.860288Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bfa920361bdb8dcf6ac3d5a8afe598778af4f5cbc5692942cb5a0a4f50709031

Aliases

arxiv: 1907.09582 · arxiv_version: 1907.09582v1 · doi: 10.48550/arxiv.1907.09582 · pith_short_12: X6USANQ33OG4 · pith_short_16: X6USANQ33OG462WD · pith_short_8: X6USANQ3

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/X6USANQ33OG462WD2WUK7ZMYO6 \
  | 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: bfa920361bdb8dcf6ac3d5a8afe598778af4f5cbc5692942cb5a0a4f50709031

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b90a6a70ea404ea439f914af245391b0eb71a0e11fb8ea81299c4793be021a1",
    "cross_cats_sorted": [
      "cs.DS",
      "math.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "2019-07-22T21:16:29Z",
    "title_canon_sha256": "4a10d685869b12f34e171cdbb1c9f48a8aaa684d2645eb73ba724ca36c194030"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1907.09582",
    "kind": "arxiv",
    "version": 1
  }
}