Pith Number

pith:WL5SYZ42

pith:2016:WL5SYZ427PBTP37OIE54MTUC66

not attested not anchored not stored refs pending

Ramanujan Graphs in Polynomial Time

Michael B. Cohen

arxiv:1604.03544 v1 · 2016-04-12 · cs.DS · 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{WL5SYZ427PBTP37OIE54MTUC66}

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	2026-05-18T01:17:13.197230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2fb2c679afbc337efee413bc64e82f7b80bd121cf43d140806a69afae4997ea

Aliases

arxiv: 1604.03544 · arxiv_version: 1604.03544v1 · doi: 10.48550/arxiv.1604.03544 · pith_short_12: WL5SYZ427PBT · pith_short_16: WL5SYZ427PBTP37O · pith_short_8: WL5SYZ42

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/WL5SYZ427PBTP37OIE54MTUC66 \
  | 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: b2fb2c679afbc337efee413bc64e82f7b80bd121cf43d140806a69afae4997ea

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2206cd60d2b7713c0f0027ccd29a872e733462fb63d11e3a65c82b2ba611814a",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2016-04-12T19:59:18Z",
    "title_canon_sha256": "05fa1b4207e168961a738bf01cc7789cbe0b9fe64e522d46fbe55ac1318b1d06"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.03544",
    "kind": "arxiv",
    "version": 1
  }
}