Pith Number

pith:RNR3FUIG

pith:1999:RNR3FUIG6LTKZUPBS4TVBAJOMX

not attested not anchored not stored refs pending

The Multiplicities of a Dual-thin Q-polynomial Association Scheme

Bruce E. Sagan, IV, John S. Caughman

arxiv:math/9907079 v1 · 1999-07-12 · 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{RNR3FUIG6LTKZUPBS4TVBAJOMX}

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	2026-05-18T03:47:10.479813Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b63b2d106f2e6acd1e1972750812e65ea61583e2e7678392c25ddaa6402cd7b

Aliases

arxiv: math/9907079 · arxiv_version: math/9907079v1 · doi: 10.48550/arxiv.math/9907079 · pith_short_12: RNR3FUIG6LTK · pith_short_16: RNR3FUIG6LTKZUPB · pith_short_8: RNR3FUIG

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/RNR3FUIG6LTKZUPBS4TVBAJOMX \
  | 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: 8b63b2d106f2e6acd1e1972750812e65ea61583e2e7678392c25ddaa6402cd7b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4f326687da25b22311beff05689c7557b549770b21ec58baebd4d4a3396aeee7",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "1999-07-12T20:24:49Z",
    "title_canon_sha256": "8e7ee9336606cac25d67f08b4d9c192449be141a16f4c3e03d5a374b4a7d73b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9907079",
    "kind": "arxiv",
    "version": 1
  }
}