Pith Number

pith:F4NDQXEU

pith:2011:F4NDQXEU6BCI2PZKJAAQ3IHDGR

not attested not anchored not stored refs pending

Global symmetric classical and strong solutions of the full compressible Navier-Stokes equations with vacuum and large initial data

Changjiang Zhu, Huanyao Wen

arxiv:1109.5328 v2 · 2011-09-25 · 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{F4NDQXEU6BCI2PZKJAAQ3IHDGR}

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	2026-05-18T03:57:38.801028Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2f1a385c94f0448d3f2a48010da0e334560f36dee14f6674fd89ab90fce55144

Aliases

arxiv: 1109.5328 · arxiv_version: 1109.5328v2 · doi: 10.48550/arxiv.1109.5328 · pith_short_12: F4NDQXEU6BCI · pith_short_16: F4NDQXEU6BCI2PZK · pith_short_8: F4NDQXEU

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/F4NDQXEU6BCI2PZKJAAQ3IHDGR \
  | 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: 2f1a385c94f0448d3f2a48010da0e334560f36dee14f6674fd89ab90fce55144

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68bcef0dc7d4085232a56753d7ba7efb6f7c5f30d219ccbd6676d49d18c2fb76",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-09-25T06:54:17Z",
    "title_canon_sha256": "213f2cee0e4324a1fdf5482fe938ec4527cade26ca6cf9712028c4acecdba8c9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.5328",
    "kind": "arxiv",
    "version": 2
  }
}