Pith Number

pith:UV7VU6FF

pith:2016:UV7VU6FFUNLPEXMBRRV3YXHZFD

not attested not anchored not stored refs pending

A note on graphs with exactly two main eigenvalues

Fenjin Liu, Jack H. Koolen, Sakander Hayat, Zhi Qiao

arxiv:1608.08702 v1 · 2016-08-31 · 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{UV7VU6FFUNLPEXMBRRV3YXHZFD}

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	2026-05-18T01:06:40.146672Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a57f5a78a5a356f25d818c6bbc5cf928dbd05f8f7f80432ae0f1164e5c430ed1

Aliases

arxiv: 1608.08702 · arxiv_version: 1608.08702v1 · doi: 10.48550/arxiv.1608.08702 · pith_short_12: UV7VU6FFUNLP · pith_short_16: UV7VU6FFUNLPEXMB · pith_short_8: UV7VU6FF

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/UV7VU6FFUNLPEXMBRRV3YXHZFD \
  | 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: a57f5a78a5a356f25d818c6bbc5cf928dbd05f8f7f80432ae0f1164e5c430ed1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3b254df2b665330434457c0839043cd956f40005bd4cb17bc281f8bb6d8a36a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-08-31T01:47:23Z",
    "title_canon_sha256": "918575c2848803ac8e9f27e67268b1fe8d7b73466970171ab3e685f54c02b7a2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.08702",
    "kind": "arxiv",
    "version": 1
  }
}