Pith Number

pith:M232ZIK5

pith:2014:M232ZIK5UJJOZMAPD6NKDNRIMJ

not attested not anchored not stored refs pending

The spectral excess theorem for distance-regular graphs having distance-$d$ graph with fewer distinct eigenvalues

M.A. Fiol

arxiv:1409.5146 v1 · 2014-09-17 · 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{M232ZIK5UJJOZMAPD6NKDNRIMJ}

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	2026-05-18T02:42:36.624309Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66b7aca15da252ecb00f1f9aa1b6286265f27beac306cc537dfc0b37760988a4

Aliases

arxiv: 1409.5146 · arxiv_version: 1409.5146v1 · doi: 10.48550/arxiv.1409.5146 · pith_short_12: M232ZIK5UJJO · pith_short_16: M232ZIK5UJJOZMAP · pith_short_8: M232ZIK5

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/M232ZIK5UJJOZMAPD6NKDNRIMJ \
  | 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: 66b7aca15da252ecb00f1f9aa1b6286265f27beac306cc537dfc0b37760988a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb1c77ea006a1fa7da7b29b4ef9ff64d8ebaa170323a058f5057ea970911477c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-09-17T20:59:18Z",
    "title_canon_sha256": "d4ee007ef63142b79b1b9d56be5a66fd7de967d7fd0b1f708c062840202b5040"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1409.5146",
    "kind": "arxiv",
    "version": 1
  }
}