Pith Number

pith:HHOULELY

pith:2026:HHOULELY55VAVEPLYKRNPOD5NO

not attested not anchored not stored refs pending

Optimal Small Set Expanders and Their Codes

Marcelo Fiori, Mauricio Velasco, Pedro Raigorodsky, Tristram Bogart

arxiv:2606.23579 v1 · 2026-06-22 · math.CO · cs.CR · cs.IT · math.IT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HHOULELY55VAVEPLYKRNPOD5NO}

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	2026-06-23T03:14:31.375342Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

39dd459178ef6a0a91ebc2a2d7b87d6baf10f6a134034f81273ac1bab4012dcc

Aliases

arxiv: 2606.23579 · arxiv_version: 2606.23579v1 · doi: 10.48550/arxiv.2606.23579 · pith_short_12: HHOULELY55VA · pith_short_16: HHOULELY55VAVEPL · pith_short_8: HHOULELY

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/HHOULELY55VAVEPLYKRNPOD5NO \
  | 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: 39dd459178ef6a0a91ebc2a2d7b87d6baf10f6a134034f81273ac1bab4012dcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1c2cd49936bba7c5ca516dd0dea2e679e61eaac7cf852c429014a7500db2e0ba",
    "cross_cats_sorted": [
      "cs.CR",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-06-22T16:46:20Z",
    "title_canon_sha256": "857769cc5e66f30da2627e76cce8e4d84c05708fabc051c509ed3540bc5edfa9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.23579",
    "kind": "arxiv",
    "version": 1
  }
}