Pith Number

pith:AHZ7CO3I

pith:2013:AHZ7CO3IX7ZL7CNUH5U2NFD5PB

not attested not anchored not stored refs pending

The Minimum Spectral Radius of Graphs with the Independence Number

Xiao-Dong Zhang, Ya-Lei Jin

arxiv:1308.2075 v1 · 2013-08-09 · 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{AHZ7CO3IX7ZL7CNUH5U2NFD5PB}

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	2026-05-18T02:42:28.767526Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01f3f13b68bff2bf89b43f69a6947d78611b39ecb21b97370d18934f202d5c5e

Aliases

arxiv: 1308.2075 · arxiv_version: 1308.2075v1 · doi: 10.48550/arxiv.1308.2075 · pith_short_12: AHZ7CO3IX7ZL · pith_short_16: AHZ7CO3IX7ZL7CNU · pith_short_8: AHZ7CO3I

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/AHZ7CO3IX7ZL7CNUH5U2NFD5PB \
  | 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: 01f3f13b68bff2bf89b43f69a6947d78611b39ecb21b97370d18934f202d5c5e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4dee728dbde3675c6acb814952829c485b9546532a94120d0b32828115d12457",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-08-09T10:06:04Z",
    "title_canon_sha256": "dedc1fbde6b9a569c74eba5153116f40f79d338591cf972580247ef28cf2a15e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.2075",
    "kind": "arxiv",
    "version": 1
  }
}