Pith Number

pith:NVELVHEK

pith:2025:NVELVHEKTFN256YEAAKTD3VAIO

not attested not anchored not stored refs pending

Spectral extremal problems for degenerate graphs

Jiadong Wu, Liying Kang, Zhenyu Ni

arxiv:2507.12014 v1 · 2025-07-16 · 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{NVELVHEKTFN256YEAAKTD3VAIO}

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	2026-07-05T11:38:12.907947Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d48ba9c8a995baefb04001531eea043a0689c98e9e6c181b9c4fb1f7b71522e

Aliases

arxiv: 2507.12014 · arxiv_version: 2507.12014v1 · doi: 10.48550/arxiv.2507.12014 · pith_short_12: NVELVHEKTFN2 · pith_short_16: NVELVHEKTFN256YE · pith_short_8: NVELVHEK

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/NVELVHEKTFN256YEAAKTD3VAIO \
  | 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: 6d48ba9c8a995baefb04001531eea043a0689c98e9e6c181b9c4fb1f7b71522e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d04b338ac97e48de0bb00e1994925a35181380d96666ca505ee075c4b3aca64c",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-16T08:18:54Z",
    "title_canon_sha256": "a87a80980ad13c0447f181de5fd38e7b37f6032cceff30d2721b49461db898a9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.12014",
    "kind": "arxiv",
    "version": 1
  }
}