Pith Number

pith:KK5H3F3X

pith:2021:KK5H3F3X7V4UEE4SGFA2XYINN2

not attested not anchored not stored refs pending

Well-Posedness and Exponential Decay for the Navier-Stokes Equations of Viscous Compressible Heat-Conductive Fluids with Vacuum

Hao Xu, Jianwen Zhang, Suhua Lai

arxiv:2103.16332 v3 · 2021-03-30 · 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{KK5H3F3X7V4UEE4SGFA2XYINN2}

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	2026-07-05T03:26:16.026332Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26

Aliases

arxiv: 2103.16332 · arxiv_version: 2103.16332v3 · doi: 10.48550/arxiv.2103.16332 · pith_short_12: KK5H3F3X7V4U · pith_short_16: KK5H3F3X7V4UEE4S · pith_short_8: KK5H3F3X

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/KK5H3F3X7V4UEE4SGFA2XYINN2 \
  | 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: 52ba7d9777fd794213923141abe10d6e8d1af2e57e363643caa1e5a6aadf4a26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8d582ddf03346e288b418cc326d6f026f49676c2b9fe074caec7df0cbb667970",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2021-03-30T13:27:56Z",
    "title_canon_sha256": "f41a0c71e4af4392316c57fb711040001a1e7bb1195bc2fd81cd81bf75a8d1a0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.16332",
    "kind": "arxiv",
    "version": 3
  }
}