Pith Number

pith:N73CGXFB

pith:2012:N73CGXFBRTLZ6SY2LBH5PUNFRI

not attested not anchored not stored refs pending

A New Proof of the Flat Wall Theorem

Ken-ichi Kawarabayashi, Paul Wollan, Robin Thomas

arxiv:1207.6927 v3 · 2012-07-30 · 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{N73CGXFBRTLZ6SY2LBH5PUNFRI}

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	2026-05-18T01:07:57.177718Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ff6235ca18cd79f4b1a584fd7d1a58a2d36cb5964dd015b58018b985913659d

Aliases

arxiv: 1207.6927 · arxiv_version: 1207.6927v3 · doi: 10.48550/arxiv.1207.6927 · pith_short_12: N73CGXFBRTLZ · pith_short_16: N73CGXFBRTLZ6SY2 · pith_short_8: N73CGXFB

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/N73CGXFBRTLZ6SY2LBH5PUNFRI \
  | 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: 6ff6235ca18cd79f4b1a584fd7d1a58a2d36cb5964dd015b58018b985913659d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd02e9385179152cc2dc42b5e97f08db0be250189e8536b73f89ee457035a4de",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-07-30T13:03:28Z",
    "title_canon_sha256": "7f246e62fb43a7dbc87da838c470abb223afebce17cefbadb2f18248b93d73ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.6927",
    "kind": "arxiv",
    "version": 3
  }
}