Pith Number

pith:N42E3SDO

pith:2026:N42E3SDOCD4H4URMBBIZUOTPOR

not attested not anchored not stored refs pending

Spectral extremal results for triangle-free graphs with chromatic number at least four

Huiqiu Lin, Yinfen Zhu

arxiv:2605.14627 v1 · 2026-05-14 · 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{N42E3SDOCD4H4URMBBIZUOTPOR}

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	2026-05-17T23:39:04.005737Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f344dc86e10f87e522c08519a3a6f744d0b333974bc2cc2ee7692a9b60a51b0

Aliases

arxiv: 2605.14627 · arxiv_version: 2605.14627v1 · doi: 10.48550/arxiv.2605.14627 · pith_short_12: N42E3SDOCD4H · pith_short_16: N42E3SDOCD4H4URM · pith_short_8: N42E3SDO

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/N42E3SDOCD4H4URMBBIZUOTPOR \
  | 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: 6f344dc86e10f87e522c08519a3a6f744d0b333974bc2cc2ee7692a9b60a51b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c3b36734a9f04bc8487dbfb4b2622104439d07ede79d9658f2689e4bbd7bee00",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-14T09:40:29Z",
    "title_canon_sha256": "4df2c5b157e3dbbbc2c13fa96a9c328bc3f56171aa388ba15589c59577cdbe22"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14627",
    "kind": "arxiv",
    "version": 1
  }
}