Pith Number

pith:QT2Q4ZI6

pith:2023:QT2Q4ZI67W2XVPEORNJCFJHD5H

not attested not anchored not stored refs pending

Supersaturation beyond color-critical graphs

Jie Ma, Long-tu Yuan

arxiv:2310.08081 v1 · 2023-10-12 · 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{QT2Q4ZI67W2XVPEORNJCFJHD5H}

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	2026-07-05T07:00:00.691585Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

84f50e651efdb57abc8e8b5222a4e3e9e53265ccce8b11497fe150146d6f722f

Aliases

arxiv: 2310.08081 · arxiv_version: 2310.08081v1 · doi: 10.48550/arxiv.2310.08081 · pith_short_12: QT2Q4ZI67W2X · pith_short_16: QT2Q4ZI67W2XVPEO · pith_short_8: QT2Q4ZI6

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/QT2Q4ZI67W2XVPEORNJCFJHD5H \
  | 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: 84f50e651efdb57abc8e8b5222a4e3e9e53265ccce8b11497fe150146d6f722f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a8defbbab8949d4d4ceeeb63ff6bb83dc1def6770aaa3110970197168104b2cd",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2023-10-12T07:10:22Z",
    "title_canon_sha256": "2cafd46cfe671970d6590c3a7bb2d127012c25c11821a1ae03d41ebb72f71672"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2310.08081",
    "kind": "arxiv",
    "version": 1
  }
}