Pith Number

pith:LGXW64F6

pith:2025:LGXW64F67YXEOU4IJPKK4B2ZHI

not attested not anchored not stored refs pending

On the two-dimensional Navier-Stokes equations with horizontal viscosity

Chongsheng Cao, Yanqiu Guo

arxiv:2507.02775 v1 · 2025-07-03 · 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{LGXW64F67YXEOU4IJPKK4B2ZHI}

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	2026-07-05T11:31:34.477230Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

59af6f70befe2e4753884bd4ae07593a35f9d68d7777b2b7787ca1423f0395a7

Aliases

arxiv: 2507.02775 · arxiv_version: 2507.02775v1 · doi: 10.48550/arxiv.2507.02775 · pith_short_12: LGXW64F67YXE · pith_short_16: LGXW64F67YXEOU4I · pith_short_8: LGXW64F6

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/LGXW64F67YXEOU4IJPKK4B2ZHI \
  | 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: 59af6f70befe2e4753884bd4ae07593a35f9d68d7777b2b7787ca1423f0395a7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8eeb414da147f5473bcfc5bc38e57abd3a8100f9d1835803a5018f4fa098a9ae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-03T16:36:18Z",
    "title_canon_sha256": "011cf346dcaef3dd181f0e3e2346b7c4d811dd9ff03d02a017b3381ffc0615ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.02775",
    "kind": "arxiv",
    "version": 1
  }
}