Pith Number

pith:KA3L3L5U

pith:2012:KA3L3L5UBKDIGNR26BC7L3DK6X

not attested not anchored not stored refs pending

On some Liouville Type Theorems for the Compressible Navier-Stokes Equations

Dong Li, Xinwei Yu

arxiv:1209.3718 v1 · 2012-09-17 · 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{KA3L3L5UBKDIGNR26BC7L3DK6X}

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	2026-05-18T03:45:23.646349Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5036bdafb40a8683363af045f5ec6af5e6c94b9001cdb0f2d312040b5b4d6247

Aliases

arxiv: 1209.3718 · arxiv_version: 1209.3718v1 · doi: 10.48550/arxiv.1209.3718 · pith_short_12: KA3L3L5UBKDI · pith_short_16: KA3L3L5UBKDIGNR2 · pith_short_8: KA3L3L5U

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/KA3L3L5UBKDIGNR26BC7L3DK6X \
  | 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: 5036bdafb40a8683363af045f5ec6af5e6c94b9001cdb0f2d312040b5b4d6247

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd36b4aa554ad146b0776f45de27d19cdafc37546185ee1def92cd34c3127012",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2012-09-17T16:54:49Z",
    "title_canon_sha256": "a81c24174f046f898ed394ca3c1c17b27afb05d3193b9d6593e63616d86abe0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3718",
    "kind": "arxiv",
    "version": 1
  }
}