Pith Number

pith:DDL6AORZ

pith:2025:DDL6AORZJLUJGRZJFWAKENEGW2

not attested not anchored not stored refs pending

Global existence and optimal time-decay rates of the compressible Navier-Stokes equations with density-dependent viscosities

Anchun Ni, Jie Fan, Xiangdi Huang

arxiv:2507.16436 v1 · 2025-07-22 · 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{DDL6AORZJLUJGRZJFWAKENEGW2}

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	2026-07-05T11:41:09.361514Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

18d7e03a394ae89347292d80a23486b69231584872a4a71fcfbc36f3b3a1ba92

Aliases

arxiv: 2507.16436 · arxiv_version: 2507.16436v1 · doi: 10.48550/arxiv.2507.16436 · pith_short_12: DDL6AORZJLUJ · pith_short_16: DDL6AORZJLUJGRZJ · pith_short_8: DDL6AORZ

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/DDL6AORZJLUJGRZJFWAKENEGW2 \
  | 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: 18d7e03a394ae89347292d80a23486b69231584872a4a71fcfbc36f3b3a1ba92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2e756128233dd66e1c0c25cc2968dc72d3617f8f6b656684b2e4e96e9aff53b2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2025-07-22T10:31:00Z",
    "title_canon_sha256": "4fda55bdf9b3d3b05ba4d9f631511ef45f450a69210919d766f48c06774c9aea"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.16436",
    "kind": "arxiv",
    "version": 1
  }
}