Pith Number

pith:EUZSTD4X

pith:2011:EUZSTD4XUCDZIMDBRAH6DI5ZBZ

not attested not anchored not stored refs pending

Proximality and pure point spectrum for tiling dynamical systems

Johannes Kellendonk, Marcy Barge

arxiv:1108.4065 v1 · 2011-08-19 · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EUZSTD4XUCDZIMDBRAH6DI5ZBZ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T04:14:56.259490Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2533298f97a087943061880fe1a3b90e52eedb1b4e73728ec048ab0b814431bf

Aliases

arxiv: 1108.4065 · arxiv_version: 1108.4065v1 · doi: 10.48550/arxiv.1108.4065 · pith_short_12: EUZSTD4XUCDZ · pith_short_16: EUZSTD4XUCDZIMDB · pith_short_8: EUZSTD4X

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/EUZSTD4XUCDZIMDBRAH6DI5ZBZ \
  | 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: 2533298f97a087943061880fe1a3b90e52eedb1b4e73728ec048ab0b814431bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b06ede8d33722d5b2f4f08f488af66439dadccf14c19a95fa4b0a9c5e81b0f50",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-08-19T22:20:21Z",
    "title_canon_sha256": "d536fa63c2789b2feef7310fb74a6c88dea48c1efb8db29d56629876ef94bbd0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1108.4065",
    "kind": "arxiv",
    "version": 1
  }
}