Pith Number

pith:UPG6PL4F

pith:2019:UPG6PL4FQNCRYDIXQZKLA4HPRE

not attested not anchored not stored refs pending

Optimal time-decay estimates for the compressible Navier-Stokes-Poisson equations without additional smallness assumptions

Weixuan Shi

arxiv:1908.01209 v1 · 2019-08-03 · 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{UPG6PL4FQNCRYDIXQZKLA4HPRE}

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	2026-07-04T23:51:28.030303Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3cde7af8583451c0d178654b070ef89000ed9f065cfd6e3d85951bf08b7b4f8

Aliases

arxiv: 1908.01209 · arxiv_version: 1908.01209v1 · doi: 10.48550/arxiv.1908.01209 · pith_short_12: UPG6PL4FQNCR · pith_short_16: UPG6PL4FQNCRYDIX · pith_short_8: UPG6PL4F

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/UPG6PL4FQNCRYDIXQZKLA4HPRE \
  | 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: a3cde7af8583451c0d178654b070ef89000ed9f065cfd6e3d85951bf08b7b4f8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ad909616a332529e92930482e1df7c919eefedf6c4792dc68d45a2f578062eef",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2019-08-03T18:04:07Z",
    "title_canon_sha256": "d1b6a720b882f57e662349ac354ba5ec675d79b04495b8bcae19547805a2a7d8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.01209",
    "kind": "arxiv",
    "version": 1
  }
}