Pith Number

pith:PWNZ3S7Z

pith:2025:PWNZ3S7ZB5BO7LL5GY63PSAAZB

not attested not anchored not stored refs pending

Analyticity and asymptotic behavior of solutions to the compressible Navier-Stokes-Korteweg equations with the zero sound speed in scaling critical spaces

Ryosuke Nakasato, Takayuki Kobayashi

arxiv:2506.01573 v1 · 2025-06-02 · 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{PWNZ3S7ZB5BO7LL5GY63PSAAZB}

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	2026-07-05T11:14:16.112788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7d9b9dcbf90f42efad7d363db7c800c84677fe5be5a569d645d39bfbd900abc5

Aliases

arxiv: 2506.01573 · arxiv_version: 2506.01573v1 · doi: 10.48550/arxiv.2506.01573 · pith_short_12: PWNZ3S7ZB5BO · pith_short_16: PWNZ3S7ZB5BO7LL5 · pith_short_8: PWNZ3S7Z

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/PWNZ3S7ZB5BO7LL5GY63PSAAZB \
  | 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: 7d9b9dcbf90f42efad7d363db7c800c84677fe5be5a569d645d39bfbd900abc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df9dacaf0bf96759f4389851a7fe1f4b23fdd9c514a9a755af8937eabbba01e0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-06-02T11:57:20Z",
    "title_canon_sha256": "a97b86aa526a75d7f3c975d4837427fae10f7a30adff966b8e66184cb5c61ba1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.01573",
    "kind": "arxiv",
    "version": 1
  }
}