Pith Number

pith:YL6TDZAU

pith:1999:YL6TDZAUCKIHCWMTSC7XPZW4VR

not attested not anchored not stored refs pending

Taylor-Kubo Formula for Turbulent Diffusion in a Non-Mixing Flow with Long-Range Correlation

Albert C. Fannjiang, Tomasz Komorowski

arxiv:math/9906050 v1 · 1999-06-08 · math.PR · 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{YL6TDZAUCKIHCWMTSC7XPZW4VR}

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	2026-05-18T01:05:32.951354Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2fd31e414129071599390bf77e6dcac755086308818fd6dbbbb8d050fe6246d

Aliases

arxiv: math/9906050 · arxiv_version: math/9906050v1 · doi: 10.48550/arxiv.math/9906050 · pith_short_12: YL6TDZAUCKIH · pith_short_16: YL6TDZAUCKIHCWMT · pith_short_8: YL6TDZAU

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/YL6TDZAUCKIHCWMTSC7XPZW4VR \
  | 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: c2fd31e414129071599390bf77e6dcac755086308818fd6dbbbb8d050fe6246d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca8d146189dc3e7c0c7deb6bd4d50d8e1d581e381cc17ec08565b8e43c76629c",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-06-08T20:24:36Z",
    "title_canon_sha256": "68e3b9d034092e989784610ac4b8f67fd3e8e1256daec9cdf9d29014129acd92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9906050",
    "kind": "arxiv",
    "version": 1
  }
}