Pith Number

pith:RINAX5SJ

pith:2025:RINAX5SJSNFP7HV4VUATSTQ2ON

not attested not anchored not stored refs pending

A note on the spectral radius and $[a,b]$-factor of graphs

Dandan Fan, Huiqiu Lin, Yinfen Zhu

arxiv:2509.00769 v2 · 2025-08-31 · math.SP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{RINAX5SJSNFP7HV4VUATSTQ2ON}

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	2026-07-05T12:03:52.457829Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a1a0bf649934aff9ebcad01394e1a7376dd33599eb265f3119df28e0077f66b

Aliases

arxiv: 2509.00769 · arxiv_version: 2509.00769v2 · doi: 10.48550/arxiv.2509.00769 · pith_short_12: RINAX5SJSNFP · pith_short_16: RINAX5SJSNFP7HV4 · pith_short_8: RINAX5SJ

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/RINAX5SJSNFP7HV4VUATSTQ2ON \
  | 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: 8a1a0bf649934aff9ebcad01394e1a7376dd33599eb265f3119df28e0077f66b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a6181c5ce2fa12e48043cd03e4a53964adc264ed284438df29f5caf132efd2f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SP",
    "submitted_at": "2025-08-31T09:47:17Z",
    "title_canon_sha256": "04881e5057e797b2037ce5532b0dfe236caab69eedaa7e04fabbb8cfdd7ef608"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.00769",
    "kind": "arxiv",
    "version": 2
  }
}