Pith Number

pith:NC4IJ7L6

pith:2019:NC4IJ7L6JBNVCZWRN4HD72JP7B

not attested not anchored not stored refs pending

Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity

Jinkai Li

arxiv:1906.08712 v1 · 2019-06-20 · 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{NC4IJ7L6JBNVCZWRN4HD72JP7B}

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	2026-07-05T01:03:59.558886Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68b884fd7e485b5166d16f0e3fe92ff87660374896904eaf7a3ad6e8338ec873

Aliases

arxiv: 1906.08712 · arxiv_version: 1906.08712v1 · doi: 10.48550/arxiv.1906.08712 · pith_short_12: NC4IJ7L6JBNV · pith_short_16: NC4IJ7L6JBNVCZWR · pith_short_8: NC4IJ7L6

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/NC4IJ7L6JBNVCZWRN4HD72JP7B \
  | 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: 68b884fd7e485b5166d16f0e3fe92ff87660374896904eaf7a3ad6e8338ec873

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9925f299fb7d3bb32f2b7d7b6eb8ffc726232a6e24ace2a4c1789e30a7b5ca8b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-06-20T15:57:32Z",
    "title_canon_sha256": "810934481b4835277b9bfde487dd9322afe9132899e4ff58a4223dec93088ab5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1906.08712",
    "kind": "arxiv",
    "version": 1
  }
}