Pith Number

pith:CU7RWXFB

pith:2018:CU7RWXFBE5HBCJJR25XPWWKJE3

not attested not anchored not stored refs pending

Ramanujan graphs in cryptography

Anamaria Costache, Anna Pusk\'as, Brooke Feigon, Kristin Lauter, Maike Massierer

arxiv:1806.05709 v2 · 2018-06-14 · math.NT · cs.CR · 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{CU7RWXFBE5HBCJJR25XPWWKJE3}

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	2026-05-17T23:58:08.582186Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

153f1b5ca1274e112531d76efb594926fcf99adb4ae602e1d4e69c393ef2aead

Aliases

arxiv: 1806.05709 · arxiv_version: 1806.05709v2 · doi: 10.48550/arxiv.1806.05709 · pith_short_12: CU7RWXFBE5HB · pith_short_16: CU7RWXFBE5HBCJJR · pith_short_8: CU7RWXFB

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/CU7RWXFBE5HBCJJR25XPWWKJE3 \
  | 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: 153f1b5ca1274e112531d76efb594926fcf99adb4ae602e1d4e69c393ef2aead

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9aa1170b54a2406e3f0602373ea92f1075f79c39e3f559de661b2cbb33b1e86d",
    "cross_cats_sorted": [
      "cs.CR",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2018-06-14T19:16:04Z",
    "title_canon_sha256": "da39cc83f873d277e180e4ffca7796d56f9c0eb0847df1c7f427a522d68cd91b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1806.05709",
    "kind": "arxiv",
    "version": 2
  }
}