Pith Number

pith:LSTOPFIN

pith:2025:LSTOPFINGMZESYZGK4S6PVJ2CV

not attested not anchored not stored refs pending

Edge-coloring $K_{n, n}$ with no 2-colored $C_{2k}$

Deepak Bal, Patrick Bennett

arxiv:2507.13329 v1 · 2025-07-17 · 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{LSTOPFINGMZESYZGK4S6PVJ2CV}

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	2026-07-05T11:38:59.233458Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5ca6e7950d33324963265725e7d53a157f9678fd877a3984efb76c757cea3b35

Aliases

arxiv: 2507.13329 · arxiv_version: 2507.13329v1 · doi: 10.48550/arxiv.2507.13329 · pith_short_12: LSTOPFINGMZE · pith_short_16: LSTOPFINGMZESYZG · pith_short_8: LSTOPFIN

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/LSTOPFINGMZESYZGK4S6PVJ2CV \
  | 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: 5ca6e7950d33324963265725e7d53a157f9678fd877a3984efb76c757cea3b35

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4230e2eba456b9c2aa613de6187225a099e7c74d150cb5210e1c0430c0076c2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-07-17T17:47:55Z",
    "title_canon_sha256": "a8d504c40cad52f604ca117fdef3cc039ef3432291f02eb0269dd12caefa7b04"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13329",
    "kind": "arxiv",
    "version": 1
  }
}