Pith Number

pith:QP642U3I

pith:2015:QP642U3I5DJUHTI4K6GHY7ANI6

not attested not anchored not stored refs pending

Crystallization of space: Space-time fractals from fractal arithmetic

Diederik Aerts, Maciej Kuna, Marek Czachor

arxiv:1506.00487 v3 · 2015-06-01 · gr-qc · math-ph · math.MP · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{QP642U3I5DJUHTI4K6GHY7ANI6}

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	2026-05-18T01:22:21.115238Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83fdcd5368e8d343cd1c578c7c7c0d4782df5b0f137f48d375d036538b289ce8

Aliases

arxiv: 1506.00487 · arxiv_version: 1506.00487v3 · doi: 10.48550/arxiv.1506.00487 · pith_short_12: QP642U3I5DJU · pith_short_16: QP642U3I5DJUHTI4 · pith_short_8: QP642U3I

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/QP642U3I5DJUHTI4K6GHY7ANI6 \
  | 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: 83fdcd5368e8d343cd1c578c7c7c0d4782df5b0f137f48d375d036538b289ce8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d10265f5a9c0a0e19a38545d6d26bacc7b1adf2a678882a80dec3d086d59201a",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-06-01T13:28:56Z",
    "title_canon_sha256": "891734d652d292b4a0320abf20a9900f55bcbdac1899040b87f95db300d34e23"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00487",
    "kind": "arxiv",
    "version": 3
  }
}