Pith Number

pith:USMWBTMQ

pith:2025:USMWBTMQZ43NBU4EPKS47PUUXA

not attested not anchored not stored refs pending

Undecidability of Translational Tiling of the Plane with Four Tiles

Chao Yang, Zhujun Zhang

arxiv:2506.19295 v1 · 2025-06-24 · math.CO · cs.CG · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{USMWBTMQZ43NBU4EPKS47PUUXA}

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	2026-07-05T11:26:12.853988Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a49960cd90cf36d0d3847aa5cfbe94b833ea771427049e30963a30fda840a637

Aliases

arxiv: 2506.19295 · arxiv_version: 2506.19295v1 · doi: 10.48550/arxiv.2506.19295 · pith_short_12: USMWBTMQZ43N · pith_short_16: USMWBTMQZ43NBU4E · pith_short_8: USMWBTMQ

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/USMWBTMQZ43NBU4EPKS47PUUXA \
  | 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: a49960cd90cf36d0d3847aa5cfbe94b833ea771427049e30963a30fda840a637

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4cc16405c3a2d1954d15a4355d48ea2eefc2e4f8bdc0358a091479f0ad2ba99",
    "cross_cats_sorted": [
      "cs.CG",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2025-06-24T04:00:41Z",
    "title_canon_sha256": "a503ab857d6a578ea60cea504b95a168d8f423f9b0f7b6562023c59b05166e98"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.19295",
    "kind": "arxiv",
    "version": 1
  }
}