Pith Number

pith:WH7ZSEYY

pith:2026:WH7ZSEYY6C6ZAM23AWASE3Q5LU

not attested not anchored not stored refs pending

A Simple Sub-Polynomial Degree Coboundary Expander

Arka Ray, Max Hopkins

arxiv:2605.22173 v1 · 2026-05-21 · math.CO · cs.CC · 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{WH7ZSEYY6C6ZAM23AWASE3Q5LU}

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	2026-05-22T01:04:30.155607Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1ff991318f0bd90335b0581226e1d5d133d22f1e996aac935457d37b0d4e9d8

Aliases

arxiv: 2605.22173 · arxiv_version: 2605.22173v1 · doi: 10.48550/arxiv.2605.22173 · pith_short_12: WH7ZSEYY6C6Z · pith_short_16: WH7ZSEYY6C6ZAM23 · pith_short_8: WH7ZSEYY

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/WH7ZSEYY6C6ZAM23AWASE3Q5LU \
  | 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: b1ff991318f0bd90335b0581226e1d5d133d22f1e996aac935457d37b0d4e9d8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "432efab58a38450725762df68b15503a2082bfb9d747125bdfa7e4b985cff35c",
    "cross_cats_sorted": [
      "cs.CC",
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-21T08:43:32Z",
    "title_canon_sha256": "0ff31bbd8fcca2512c8c9ecc038635b6c3a9a2d0b729df4793cd29c433d13e47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22173",
    "kind": "arxiv",
    "version": 1
  }
}