Pith Number

pith:GW56UUYR

pith:2026:GW56UUYRAFOS4OZTIMIAQGCA7T

not attested not anchored not stored refs pending

Multiphase formulation of the Vlasov-Navier-Stokes equations

Valentin Lemarie (LAMA)

arxiv:2606.30022 v1 · 2026-06-29 · math.AP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GW56UUYRAFOS4OZTIMIAQGCA7T}

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	2026-06-30T02:17:46.401182Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35bbea5311015d2e3b334310081840fccf57e4fcd3b5a00d167d24d82971da83

Aliases

arxiv: 2606.30022 · arxiv_version: 2606.30022v1 · doi: 10.48550/arxiv.2606.30022 · pith_short_12: GW56UUYRAFOS · pith_short_16: GW56UUYRAFOS4OZT · pith_short_8: GW56UUYR

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/GW56UUYRAFOS4OZTIMIAQGCA7T \
  | 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: 35bbea5311015d2e3b334310081840fccf57e4fcd3b5a00d167d24d82971da83

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b4194c55edee81a217baf36d7c3e03e92e8d3e98d54f4a9ab5a2f75e0f80f8be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-06-29T09:25:17Z",
    "title_canon_sha256": "a9bb0ca332f33bdc14043bed6bccb3d9eb2385c7fad7695fb4ff54a7e9a8c181"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.30022",
    "kind": "arxiv",
    "version": 1
  }
}