Pith Number

pith:ICRIHHPU

pith:2026:ICRIHHPUH6YPPU5PJEEN7ZRKD2

not attested not anchored not stored refs pending

Chromatic thresholds for linear equations and recurrence

Hong Liu, Ningyuan Yang, Shengtong Zhang, Zhuo Wu

arxiv:2603.05490 v2 · 2026-03-05 · 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{ICRIHHPUH6YPPU5PJEEN7ZRKD2}

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

3 papers in Pith

Linear equations and chromatic thresholds in $B_h$ sets

Chromatic thresholds for pairs of graphs

Receipt and verification

First computed	2026-07-01T00:17:10.655262Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

40a2839df43fb0f7d3af4908dfe62a1eb6bd6ba4715e1144f5e96171256f1371

Aliases

arxiv: 2603.05490 · arxiv_version: 2603.05490v2 · doi: 10.48550/arxiv.2603.05490 · pith_short_12: ICRIHHPUH6YP · pith_short_16: ICRIHHPUH6YPPU5P · pith_short_8: ICRIHHPU

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/ICRIHHPUH6YPPU5PJEEN7ZRKD2 \
  | 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: 40a2839df43fb0f7d3af4908dfe62a1eb6bd6ba4715e1144f5e96171256f1371

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0fadeef1b00575a3f48556f9b09da0744f7395c733a8454f17fd26139588940",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-03-05T18:56:15Z",
    "title_canon_sha256": "c06533c167569794df77ca1baa972eaec8ff70ec02dbfafc90b9b99cf99a3e64"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.05490",
    "kind": "arxiv",
    "version": 2
  }
}