Pith Number

pith:XQ3DAC6V

pith:2026:XQ3DAC6VQ7ZCJXXHB3HSXBZ3UM

not attested not anchored not stored refs pending

Frieze patterns and aperiodic tilings of the plane

Dirk Frettl\"oh, Jan Maz\'{a}\v{c}

arxiv:2607.21348 v1 · 2026-07-23 · math.CO · 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{XQ3DAC6VQ7ZCJXXHB3HSXBZ3UM}

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	2026-07-24T01:24:27.019097Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc36300bd587f224dee70ecf2b873ba30448b4c530e333c9cbfb5c4839ff611f

Aliases

arxiv: 2607.21348 · arxiv_version: 2607.21348v1 · doi: 10.48550/arxiv.2607.21348 · pith_short_12: XQ3DAC6VQ7ZC · pith_short_16: XQ3DAC6VQ7ZCJXXH · pith_short_8: XQ3DAC6V

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/XQ3DAC6VQ7ZCJXXHB3HSXBZ3UM \
  | 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: bc36300bd587f224dee70ecf2b873ba30448b4c530e333c9cbfb5c4839ff611f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a8a47737be05651e8d24211c2c908c7286fc1b5ec9638721839d888b466a752",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-07-23T14:14:22Z",
    "title_canon_sha256": "04ff62530d9a94fad4d5d11429371f2f66f6a7269844da99e66f6e9e9d635c52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.21348",
    "kind": "arxiv",
    "version": 1
  }
}