Pith Number

pith:ZNTF3PIY

pith:2000:ZNTF3PIYG6L36QSJUI4BJPFVCP

not attested not anchored not stored refs pending

A Homeomorphism Invariant for Substitution Tiling Spaces

Charles Radin, Lorenzo Sadun, Nic Ormes

arxiv:math/0008171 v1 · 2000-08-22 · math.DS · math.AT · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZNTF3PIYG6L36QSJUI4BJPFVCP}

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	2026-05-18T00:11:07.535198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cb665dbd183797bf4249a23814bcb513d0e011110008388851019b4ed6c14a34

Aliases

arxiv: math/0008171 · arxiv_version: math/0008171v1 · doi: 10.48550/arxiv.math/0008171 · pith_short_12: ZNTF3PIYG6L3 · pith_short_16: ZNTF3PIYG6L36QSJ · pith_short_8: ZNTF3PIY

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/ZNTF3PIYG6L36QSJUI4BJPFVCP \
  | 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: cb665dbd183797bf4249a23814bcb513d0e011110008388851019b4ed6c14a34

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "41b8030c156553390f708b947f61c76263f889cbaae9f7f46fa4c06ceb87d011",
    "cross_cats_sorted": [
      "math.AT",
      "math.KT"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2000-08-22T16:54:48Z",
    "title_canon_sha256": "4828f3c711d724d5b3b536447554000aa83b7373098a82a518827d524e4a997e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0008171",
    "kind": "arxiv",
    "version": 1
  }
}