Pith Number

pith:D2G5QDLH

pith:2018:D2G5QDLHIH2NCSLDFTKRDGPDGE

not attested not anchored not stored refs pending

A family of four-variable expanders with quadratic growth

Mehdi Makhul

arxiv:1805.04292 v1 · 2018-05-11 · math.CO · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{D2G5QDLHIH2NCSLDFTKRDGPDGE}

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	2026-05-17T23:44:59.556783Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1e8dd80d6741f4d149632cd51199e33113f3e992fe894737b32c6276645c167e

Aliases

arxiv: 1805.04292 · arxiv_version: 1805.04292v1 · doi: 10.48550/arxiv.1805.04292 · pith_short_12: D2G5QDLHIH2N · pith_short_16: D2G5QDLHIH2NCSLD · pith_short_8: D2G5QDLH

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/D2G5QDLHIH2NCSLDFTKRDGPDGE \
  | 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: 1e8dd80d6741f4d149632cd51199e33113f3e992fe894737b32c6276645c167e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "01066554d54d3ac3d0b831c1a68db22e50764d4f0d45201303a4fff8da8f3614",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2018-05-11T09:39:00Z",
    "title_canon_sha256": "38a1a27a8598d40c6ae669ff81fcad91754ee119c5802fc4d4256e033abae0e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.04292",
    "kind": "arxiv",
    "version": 1
  }
}