Pith Number

pith:X3KY6IMK

pith:2026:X3KY6IMK6AMGLK6VQCWTTN5DX2

not attested not anchored not stored refs pending

Set-defined graph classes: $\chi$-boundedness meets tropical algebra

John Sylvester, Samuel Braunfeld, Sarosh Adenwalla, Tom\'a\v{s} Hons, Viktor Zamaraev

arxiv:2607.23754 v1 · 2026-07-26 · cs.DM · 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{X3KY6IMK6AMGLK6VQCWTTN5DX2}

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	2026-07-28T01:23:09.562400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bed58f218af01865abd580ad39b7a3be97c9efd34810cb6a062835dbe102fa60

Aliases

arxiv: 2607.23754 · arxiv_version: 2607.23754v1 · doi: 10.48550/arxiv.2607.23754 · pith_short_12: X3KY6IMK6AMG · pith_short_16: X3KY6IMK6AMGLK6V · pith_short_8: X3KY6IMK

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/X3KY6IMK6AMGLK6VQCWTTN5DX2 \
  | 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: bed58f218af01865abd580ad39b7a3be97c9efd34810cb6a062835dbe102fa60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "86303dbd67cc5e0d6db439389c6346b711aa8afc2a45e1b587954e4e0eda08cc",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DM",
    "submitted_at": "2026-07-26T16:58:48Z",
    "title_canon_sha256": "e8158a113066a739f9460eb7e91a6e83eebf0fa8c4a59ebcb2469431162cbeeb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.23754",
    "kind": "arxiv",
    "version": 1
  }
}