Pith Number

pith:AXHCSN35

pith:2010:AXHCSN35F7QR7KXMHRDO2TWZAO

not attested not anchored not stored refs pending

Ramanujan graphs of very large girth based on octonions

Jean-Pierre Tillich, Xavier Dahan

arxiv:1011.2642 v5 · 2010-11-11 · 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{AXHCSN35F7QR7KXMHRDO2TWZAO}

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	2026-05-18T04:03:17.698926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05ce29377d2fe11faaec3c46ed4ed90382f594a28cb191797206877639b3c7b7

Aliases

arxiv: 1011.2642 · arxiv_version: 1011.2642v5 · doi: 10.48550/arxiv.1011.2642 · pith_short_12: AXHCSN35F7QR · pith_short_16: AXHCSN35F7QR7KXM · pith_short_8: AXHCSN35

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/AXHCSN35F7QR7KXMHRDO2TWZAO \
  | 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: 05ce29377d2fe11faaec3c46ed4ed90382f594a28cb191797206877639b3c7b7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1dac5dee385486faefff1466a518d8965e7f64203515974579389d40e1236095",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-11-11T13:03:24Z",
    "title_canon_sha256": "8eed4be7e10031729f87ad547bfd5930371f11e099c76aac4def0d1ed4ef919b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1011.2642",
    "kind": "arxiv",
    "version": 5
  }
}