Pith Number

pith:NKZ2E2WI

pith:2007:NKZ2E2WIYOWNWWMGCZO6DPZNZW

not attested not anchored not stored refs pending

Pattern equivariant functions, deformations and equivalence of tiling spaces

Johannes Kellendonk

arxiv:math/0703156 v1 · 2007-03-06 · 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{NKZ2E2WIYOWNWWMGCZO6DPZNZW}

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.

Cited by

1 paper in Pith

Exact renormalisation for patch frequencies in inflation systems

Receipt and verification

First computed	2026-07-04T14:59:57.966566Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ab3a26ac8c3acdb5986165de1bf2dcda2ee8766af7e1628aaeea119ca5fbbb3

Aliases

arxiv: math/0703156 · arxiv_version: math/0703156v1 · doi: 10.48550/arxiv.math/0703156 · pith_short_12: NKZ2E2WIYOWN · pith_short_16: NKZ2E2WIYOWNWWMG · pith_short_8: NKZ2E2WI

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/NKZ2E2WIYOWNWWMGCZO6DPZNZW \
  | 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: 6ab3a26ac8c3acdb5986165de1bf2dcda2ee8766af7e1628aaeea119ca5fbbb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3bd10518186c2c961ac6aeb7f7de45d40a97330f2ba92a15381fe388c0ebcab4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2007-03-06T14:53:36Z",
    "title_canon_sha256": "5fc835fc983d3bbce36bfd2bf97a56e990759bcb8cdf6237a45d0c7751de50fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0703156",
    "kind": "arxiv",
    "version": 1
  }
}