Pith Number

pith:KTR2LGBU

pith:2024:KTR2LGBUX2EPCAN73LRB6YJFMR

not attested not anchored not stored refs pending

Beyond chromatic threshold via the $(p,q)$-theorem, and a sharp blow-up phenomenon

Chong Shangguan, Hong Liu, Jozef Skokan, Zixiang Xu

arxiv:2403.17910 v3 · 2024-03-26 · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KTR2LGBUX2EPCAN73LRB6YJFMR}

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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.

Cited by

1 paper in Pith

Chromatic thresholds for pairs of graphs

Receipt and verification

First computed	2026-07-05T08:59:26.770926Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54e3a59834be88f101bfdae21f61256447c27e98857e51a7f29f348de66f78f5

Aliases

arxiv: 2403.17910 · arxiv_version: 2403.17910v3 · doi: 10.48550/arxiv.2403.17910 · pith_short_12: KTR2LGBUX2EP · pith_short_16: KTR2LGBUX2EPCAN7 · pith_short_8: KTR2LGBU

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/KTR2LGBUX2EPCAN73LRB6YJFMR \
  | 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: 54e3a59834be88f101bfdae21f61256447c27e98857e51a7f29f348de66f78f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "700a7943c1be8bb2db6ebc21b933a7a4ceccafee2d211e19b37d0336c1a11014",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2024-03-26T17:47:00Z",
    "title_canon_sha256": "0068bb83ad92accbd05f4b7f592084838838e3b51c252a9cbf8a3f8c32febce9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2403.17910",
    "kind": "arxiv",
    "version": 3
  }
}