Pith Number

pith:XT3DSGXU

pith:2025:XT3DSGXUEGKTUKAXPSE5HIVUOJ

not attested not anchored not stored refs pending

Interpolating chromatic and homomorphism thresholds

Hong Liu, Mingyuan Rong, Xinqi Huang, Zixiang Xu

arxiv:2502.09576 v1 · 2025-02-13 · 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{XT3DSGXUEGKTUKAXPSE5HIVUOJ}

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.

Cited by

1 paper in Pith

Chromatic thresholds for pairs of graphs

Receipt and verification

First computed	2026-07-05T10:13:59.555807Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bcf6391af421953a28177c89d3a2b472648a130fef040ac319f1f935f7658034

Aliases

arxiv: 2502.09576 · arxiv_version: 2502.09576v1 · doi: 10.48550/arxiv.2502.09576 · pith_short_12: XT3DSGXUEGKT · pith_short_16: XT3DSGXUEGKTUKAX · pith_short_8: XT3DSGXU

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/XT3DSGXUEGKTUKAXPSE5HIVUOJ \
  | 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: bcf6391af421953a28177c89d3a2b472648a130fef040ac319f1f935f7658034

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b14fe618352b5b3b5adc8e0a51a08b8c5623fbae1b2ffee82e8fa3980a923dfd",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-02-13T18:34:43Z",
    "title_canon_sha256": "c1c49f4706d4eb13bd006016d8738969f69dec11c5d0feb86bfd6aed87ff90e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.09576",
    "kind": "arxiv",
    "version": 1
  }
}