Pith Number

pith:KFULLNH7

pith:2012:KFULLNH7ZPB7YTHKXGPTNXS77Z

not attested not anchored not stored refs pending

Cohomology of the Pinwheel Tiling

Benjamin Whitehead, Dirk Frettl\"oh, Michael F. Whittaker

arxiv:1212.4401 v1 · 2012-12-18 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KFULLNH7ZPB7YTHKXGPTNXS77Z}

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	2026-05-18T02:42:15.221055Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5168b5b4ffcbc3fc4ceab99f36de5ffe6f6c07a255a8f09821212c0e89a28a4c

Aliases

arxiv: 1212.4401 · arxiv_version: 1212.4401v1 · doi: 10.48550/arxiv.1212.4401 · pith_short_12: KFULLNH7ZPB7 · pith_short_16: KFULLNH7ZPB7YTHK · pith_short_8: KFULLNH7

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/KFULLNH7ZPB7YTHKXGPTNXS77Z \
  | 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: 5168b5b4ffcbc3fc4ceab99f36de5ffe6f6c07a255a8f09821212c0e89a28a4c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4d806760900b062fd44ced5607cd3657de82f3d9504fe31f5df58837d40e4849",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-12-18T16:02:18Z",
    "title_canon_sha256": "b365f45b92ec61743a6a5d0cf148e346ce6a6cbe7919a943586022d7d14d3950"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.4401",
    "kind": "arxiv",
    "version": 1
  }
}