Pith Number

pith:FNQFW6DS

pith:2026:FNQFW6DSH6LSOMRSLY4LNRDBK3

not attested not anchored not stored refs pending

Modeling Equations in Wave-Particle Turbulence Simulation

Gaocheng Liu, Kun Xu, Xiaojian Yang

arxiv:2607.10176 v1 · 2026-07-11 · physics.flu-dyn · 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{FNQFW6DSH6LSOMRSLY4LNRDBK3}

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	2026-07-14T01:20:28.895239Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2b605b78723f972732325e38b6c46156e71f58ea58ef47d2ae011fa00a3704eb

Aliases

arxiv: 2607.10176 · arxiv_version: 2607.10176v1 · doi: 10.48550/arxiv.2607.10176 · pith_short_12: FNQFW6DSH6LS · pith_short_16: FNQFW6DSH6LSOMRS · pith_short_8: FNQFW6DS

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/FNQFW6DSH6LSOMRSLY4LNRDBK3 \
  | 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: 2b605b78723f972732325e38b6c46156e71f58ea58ef47d2ae011fa00a3704eb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "708b068cf69355d806c1fd34c8b943924fd8354c02a84e338ca5325c60bd7449",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2026-07-11T07:42:44Z",
    "title_canon_sha256": "b76784dd5cda4d474c905c13f6a6aa9967457eaa47ffbada106df6cc63fbc29d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.10176",
    "kind": "arxiv",
    "version": 1
  }
}