Pith Number

pith:MWJSW32R

pith:2019:MWJSW32RWV534YUTZ2HHSL7PT5

not attested not anchored not stored refs pending

Proof of Brouwers Conjecture (BC) for all graphs with number of vertices n > n_0 assuming that BC holds for n< n_0 for some n_0

Alexander Pchelintsev, Llohann D. Speran\c{c}a, Vladimir Blinovsky

arxiv:1908.08534 v7 · 2019-08-22 · 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{MWJSW32RWV534YUTZ2HHSL7PT5}

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	2026-07-05T10:52:07.213114Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab

Aliases

arxiv: 1908.08534 · arxiv_version: 1908.08534v7 · doi: 10.48550/arxiv.1908.08534 · pith_short_12: MWJSW32RWV53 · pith_short_16: MWJSW32RWV534YUT · pith_short_8: MWJSW32R

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/MWJSW32RWV534YUTZ2HHSL7PT5 \
  | 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: 65932b6f51b57bbe6293ce8e792fef9f4d4bca67479103a627d1e82a9e6c90ab

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0d88d13b9e30168d4ff3b4242380d6c235169e7f400c6356a620fe1f6f694b3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2019-08-22T20:42:51Z",
    "title_canon_sha256": "7ae70edd1d429b905a8f11c1e065339d5ee97415eef9431cf97d6a05887ff84d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.08534",
    "kind": "arxiv",
    "version": 7
  }
}