Pith Number

pith:ZGSKI563

pith:2023:ZGSKI5632QNJCPY54HVMCAQGIA

not attested not anchored not stored refs pending

New Explicit Constant-Degree Lossless Expanders

Louis Golowich

arxiv:2306.07551 v2 · 2023-06-13 · math.CO · 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{ZGSKI5632QNJCPY54HVMCAQGIA}

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

Optimal Small Set Expanders and Their Codes

Receipt and verification

First computed	2026-07-05T07:31:29.288401Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9a4a477dbd41a913f1de1eac10206400143b598756ec4bf98d58dec7fe3579e

Aliases

arxiv: 2306.07551 · arxiv_version: 2306.07551v2 · doi: 10.48550/arxiv.2306.07551 · pith_short_12: ZGSKI5632QNJ · pith_short_16: ZGSKI5632QNJCPY5 · pith_short_8: ZGSKI563

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/ZGSKI5632QNJCPY54HVMCAQGIA \
  | 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: c9a4a477dbd41a913f1de1eac10206400143b598756ec4bf98d58dec7fe3579e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8a1de6d36d85178ccadd6e1cff65c65d94e8166c7348627f9984d435a25d112",
    "cross_cats_sorted": [
      "cs.DM"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-06-13T05:52:49Z",
    "title_canon_sha256": "704003b76ef596f7424d7ea182f48cfc282ae1855d4391d9a47fb741ab24cde1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2306.07551",
    "kind": "arxiv",
    "version": 2
  }
}