Pith Number

pith:N4JXJVDI

pith:2026:N4JXJVDICDBTX3ULTITVRP2OF3

not attested not anchored not stored refs pending

A linear upper bound on the $\mathbb{Z}_p$-Ramsey number of graphs with sufficiently large $2$-packing

Andrew Simmons, Emily Heath

arxiv:2605.21817 v1 · 2026-05-20 · 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{N4JXJVDICDBTX3ULTITVRP2OF3}

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	2026-05-22T01:04:09.182823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6f1374d46810c33bee8b9a2758bf4e2ed19aee8c7e1eac75226e46ff5078e312

Aliases

arxiv: 2605.21817 · arxiv_version: 2605.21817v1 · doi: 10.48550/arxiv.2605.21817 · pith_short_12: N4JXJVDICDBT · pith_short_16: N4JXJVDICDBTX3UL · pith_short_8: N4JXJVDI

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/N4JXJVDICDBTX3ULTITVRP2OF3 \
  | 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: 6f1374d46810c33bee8b9a2758bf4e2ed19aee8c7e1eac75226e46ff5078e312

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1aac11ded0c05237123afa382f9bb7ac38a99cf0d31865501ed69d94fe84cc95",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-20T23:38:08Z",
    "title_canon_sha256": "514e3ed1d37b478fdd989908d640fd0a9591454f9710be7b11bc11d34170d825"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.21817",
    "kind": "arxiv",
    "version": 1
  }
}