Pith Number

pith:4GZGQB7Y

pith:1997:4GZGQB7YKVHPS4IRBQKJBRXMZK

not attested not anchored not stored refs pending

An Algebraic Invariant for Substitution Tiling Systems

Charles Radin, Lorenzo Sadun

arxiv:math/9712264 v1 · 1997-12-24 · math.DS · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4GZGQB7YKVHPS4IRBQKJBRXMZK}

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	2026-05-18T00:11:12.099538Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1b26807f8554ef971110c1490c6eccaa5851e8c21b61cfeb0477b49cd47c46f

Aliases

arxiv: math/9712264 · arxiv_version: math/9712264v1 · doi: 10.48550/arxiv.math/9712264 · pith_short_12: 4GZGQB7YKVHP · pith_short_16: 4GZGQB7YKVHPS4IR · pith_short_8: 4GZGQB7Y

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/4GZGQB7YKVHPS4IRBQKJBRXMZK \
  | 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: e1b26807f8554ef971110c1490c6eccaa5851e8c21b61cfeb0477b49cd47c46f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5877ebb7605151190963e25726698300d1dba5ee3dd134f16aad8091c3930cb8",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "1997-12-24T17:54:12Z",
    "title_canon_sha256": "33cdf4fa2b00a1a5f47c879a032f5134c1765b0e6afd72050aafb5a69cce51cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9712264",
    "kind": "arxiv",
    "version": 1
  }
}