Pith Number

pith:U3YAN2TI

pith:2017:U3YAN2TIBPAMMXP42GKCBB3Y6J

not attested not anchored not stored refs pending

The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation

Edriss S. Titi, Jinkai Li

arxiv:1706.08885 v1 · 2017-06-26 · math.AP · physics.ao-ph · physics.flu-dyn · physics.geo-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U3YAN2TIBPAMMXP42GKCBB3Y6J}

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	2026-05-18T00:41:30.701870Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a6f006ea680bc0c65dfcd194208778f24be25ec932f0ca7bcf9897a5fb33d6e0

Aliases

arxiv: 1706.08885 · arxiv_version: 1706.08885v1 · doi: 10.48550/arxiv.1706.08885 · pith_short_12: U3YAN2TIBPAM · pith_short_16: U3YAN2TIBPAMMXP4 · pith_short_8: U3YAN2TI

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/U3YAN2TIBPAMMXP42GKCBB3Y6J \
  | 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: a6f006ea680bc0c65dfcd194208778f24be25ec932f0ca7bcf9897a5fb33d6e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c0c688f5e723b8ce8b92549b6d40e2d3f741886f64f079c3fbd508191c4cd1f9",
    "cross_cats_sorted": [
      "physics.ao-ph",
      "physics.flu-dyn",
      "physics.geo-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-06-26T13:06:24Z",
    "title_canon_sha256": "f8c0a21b8d210282a2db2062f31eaacbb671940e5ef239cf6f01a66926709312"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1706.08885",
    "kind": "arxiv",
    "version": 1
  }
}