Pith Number

pith:SQJ5ROZG

pith:2019:SQJ5ROZG5WYCIZW2XBML5Q5JEL

not attested not anchored not stored refs pending

Explicit near-Ramanujan graphs of every degree

Pedro Paredes, Ryan O'Donnell, Sidhanth Mohanty

arxiv:1909.06988 v3 · 2019-09-16 · cs.DS · cs.DM · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SQJ5ROZG5WYCIZW2XBML5Q5JEL}

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	2026-07-05T05:19:31.951413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9413d8bb26edb02466dab858bec3a922fd86de91a6348553bb08be1192e12df7

Aliases

arxiv: 1909.06988 · arxiv_version: 1909.06988v3 · doi: 10.48550/arxiv.1909.06988 · pith_short_12: SQJ5ROZG5WYC · pith_short_16: SQJ5ROZG5WYCIZW2 · pith_short_8: SQJ5ROZG

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/SQJ5ROZG5WYCIZW2XBML5Q5JEL \
  | 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: 9413d8bb26edb02466dab858bec3a922fd86de91a6348553bb08be1192e12df7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6d452649b8b559bb34eb679ab846db9d01e1e3268c96484bf62763e9feb01d8e",
    "cross_cats_sorted": [
      "cs.DM",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2019-09-16T05:03:38Z",
    "title_canon_sha256": "8b3d93a1ed3e1cb8074eeb22e6d8f1ded4003006142dd96e14ef49fe1b04f75a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1909.06988",
    "kind": "arxiv",
    "version": 3
  }
}