Pith Number

pith:3V4S63VQ

pith:2018:3V4S63VQTPVKAPZSR3ATGHRMYQ

not attested not anchored not stored refs pending

Bell polynomials and Brownian bridge in Spectral Gravity models on multifractal Robertson-Walker cosmologies

Farzad Fathizadeh, Matilde Marcolli, Yeorgia Kafkoulis

arxiv:1811.02972 v1 · 2018-11-07 · math-ph · gr-qc · hep-th · 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{3V4S63VQTPVKAPZSR3ATGHRMYQ}

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	2026-05-18T00:01:20.250477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

dd792f6eb09beaa03f328ec1331e2cc42cdf9575a2275c8de31109350e99d0d4

Aliases

arxiv: 1811.02972 · arxiv_version: 1811.02972v1 · doi: 10.48550/arxiv.1811.02972 · pith_short_12: 3V4S63VQTPVK · pith_short_16: 3V4S63VQTPVKAPZS · pith_short_8: 3V4S63VQ

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/3V4S63VQTPVKAPZSR3ATGHRMYQ \
  | 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: dd792f6eb09beaa03f328ec1331e2cc42cdf9575a2275c8de31109350e99d0d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4efb20a28e25486058946f44822527edb2dc29af2cdc85a65c9a0466a0b3b1d",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2018-11-07T16:34:48Z",
    "title_canon_sha256": "d627fef2a9f5e8e923197373359f92abb072d193dd51379f97fa11a3d7c0dc71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1811.02972",
    "kind": "arxiv",
    "version": 1
  }
}