Pith Number

pith:VQOXQ7ZR

pith:2011:VQOXQ7ZR5SCMVVKVJTR2R467YH

not attested not anchored not stored refs pending

A geometric proof of the Affability Theorem for planar tilings

\'Alvaro Lozano Rojo, Fernando Alcalde Cuesta, Pablo Gonz\'alez Sequeiros

arxiv:1112.2125 v3 · 2011-12-09 · 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{VQOXQ7ZR5SCMVVKVJTR2R467YH}

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	2026-05-18T02:52:14.535084Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ac1d787f31ec84cad5554ce3a8f3dfc1faff368c1a9e09d9c8ce9916b9916e43

Aliases

arxiv: 1112.2125 · arxiv_version: 1112.2125v3 · doi: 10.48550/arxiv.1112.2125 · pith_short_12: VQOXQ7ZR5SCM · pith_short_16: VQOXQ7ZR5SCMVVKV · pith_short_8: VQOXQ7ZR

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/VQOXQ7ZR5SCMVVKVJTR2R467YH \
  | 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: ac1d787f31ec84cad5554ce3a8f3dfc1faff368c1a9e09d9c8ce9916b9916e43

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c888d91604b8ce21adf505a06f334b27e7da75f094fd80f06a2684811372603a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-12-09T15:42:21Z",
    "title_canon_sha256": "a05f61be7b4a89722a128cd198a40598c2ccc87d5837b3e30f369414bbd4b384"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2125",
    "kind": "arxiv",
    "version": 3
  }
}