Pith Number

pith:AS54WBCY

pith:2026:AS54WBCYDWD6EGWKL3SVTBRA6W

not attested not anchored not stored refs pending

Global weak solutions to the isentropic compressible Navier-Stokes equations with vacuum and unbounded density in a half-plane under Dirichlet boundary conditions

Shuai Wang, Xin Zhong

arxiv:2601.11852 v3 · 2026-01-17 · 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{AS54WBCYDWD6EGWKL3SVTBRA6W}

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	2026-06-04T01:08:40.119979Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04bbcb04581d87e21aca5ee5598620f5b4fbfbef31dcefd72d8dd6b00028085f

Aliases

arxiv: 2601.11852 · arxiv_version: 2601.11852v3 · doi: 10.48550/arxiv.2601.11852 · pith_short_12: AS54WBCYDWD6 · pith_short_16: AS54WBCYDWD6EGWK · pith_short_8: AS54WBCY

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/AS54WBCYDWD6EGWKL3SVTBRA6W \
  | 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: 04bbcb04581d87e21aca5ee5598620f5b4fbfbef31dcefd72d8dd6b00028085f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78265333e404581399dae30d6b930786f3207e1e270c1d0b47c801df6a8a5ec5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-01-17T00:44:22Z",
    "title_canon_sha256": "34205ef7c728b2e636ac0c0c308b3b0eedce3a0e3e9143212d1a3c7cfceba192"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.11852",
    "kind": "arxiv",
    "version": 3
  }
}