Pith Number

pith:PLKH2GVO

pith:2026:PLKH2GVO2Z6FGOR3DPIG6HEALV

not attested not anchored not stored refs pending

Entropy Transference for Rainbow-$H$-Free Colourings of Random Graphs

Haixiang Zhang, Mei Lu, Mengyu Cao

arxiv:2608.04845 v1 · 2026-08-05 · 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{PLKH2GVO2Z6FGOR3DPIG6HEALV}

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	2026-08-06T01:47:23.595183Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ad47d1aaed67c533a3b1bd06f1c805d68d52a75e33cd2944885d45db816b796

Aliases

arxiv: 2608.04845 · arxiv_version: 2608.04845v1 · doi: 10.48550/arxiv.2608.04845 · pith_short_12: PLKH2GVO2Z6F · pith_short_16: PLKH2GVO2Z6FGOR3 · pith_short_8: PLKH2GVO

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/PLKH2GVO2Z6FGOR3DPIG6HEALV \
  | 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: 7ad47d1aaed67c533a3b1bd06f1c805d68d52a75e33cd2944885d45db816b796

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6fb615fcaf2e52d5625c020d8b72d9475d96cfc135e8cc5438adbecd25592d57",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-08-05T13:40:05Z",
    "title_canon_sha256": "c2c9328752af588ba6e28b6fec4ecd4eb0632ff7f03d20d3b5887d4ff239ae16"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2608.04845",
    "kind": "arxiv",
    "version": 1
  }
}