Pith Number

pith:P3QFOZWL

pith:2012:P3QFOZWLEOMRNM6KL26VLXWSR2

not attested not anchored not stored refs pending

Aperiodic tilings of manifolds of intermediate growth

Micha{\l} Marcinkowski, Piotr W. Nowak

arxiv:1205.0495 v2 · 2012-05-02 · math.GR · math.DS · math.GT · 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{P3QFOZWLEOMRNM6KL26VLXWSR2}

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	2026-05-18T02:47:23.303592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ee05766cb239916b3ca5ebd55ded28ea577e3c2abb2f696a56ced6ce465cdcc

Aliases

arxiv: 1205.0495 · arxiv_version: 1205.0495v2 · doi: 10.48550/arxiv.1205.0495 · pith_short_12: P3QFOZWLEOMR · pith_short_16: P3QFOZWLEOMRNM6K · pith_short_8: P3QFOZWL

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/P3QFOZWLEOMRNM6KL26VLXWSR2 \
  | 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: 7ee05766cb239916b3ca5ebd55ded28ea577e3c2abb2f696a56ced6ce465cdcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9b40db5ae1ced87661ac403e0c29981c11d0539ee2a4d5fcb22bd79bb7d0c58d",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2012-05-02T17:23:53Z",
    "title_canon_sha256": "b0b2f6ba72913d55fb231c352851790ec38b793436c6c4ca271e91f054121c6c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0495",
    "kind": "arxiv",
    "version": 2
  }
}