Pith Number

pith:R3N5JWRZ

pith:2018:R3N5JWRZ6DTTIHSQBPUNVESSGD

not attested not anchored not stored refs pending

An Overview of Complex Fractal Dimensions: From Fractal Strings to Fractal Drums, and Back

Michel L. Lapidus

arxiv:1803.10399 v2 · 2018-03-28 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{R3N5JWRZ6DTTIHSQBPUNVESSGD}

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	2026-05-18T00:04:44.918455Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8edbd4da39f0e7341e500be8da925230d873b98223dd74fbe8e2666e422bb888

Aliases

arxiv: 1803.10399 · arxiv_version: 1803.10399v2 · doi: 10.48550/arxiv.1803.10399 · pith_short_12: R3N5JWRZ6DTT · pith_short_16: R3N5JWRZ6DTTIHSQ · pith_short_8: R3N5JWRZ

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/R3N5JWRZ6DTTIHSQBPUNVESSGD \
  | 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: 8edbd4da39f0e7341e500be8da925230d873b98223dd74fbe8e2666e422bb888

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "03bd63f5d858fb33e8174e4f69de77124ca9600b022f696d71205231988d9a3e",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-03-28T03:25:12Z",
    "title_canon_sha256": "7f640dacb4429e2c2ea743b0ef20aa09d276313b04e434880ba165d00c2c7b1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1803.10399",
    "kind": "arxiv",
    "version": 2
  }
}