Pith Number

pith:7Z2OUXLX

pith:2016:7Z2OUXLXNBDHYCPK76QFCPZMB6

not attested not anchored not stored refs pending

Optimal time-decay estimates for the compressible navier-stokes equations in the critical l p framework

Jiang Xu, Rapha\"el Danchin

arxiv:1605.00893 v1 · 2016-05-03 · 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{7Z2OUXLXNBDHYCPK76QFCPZMB6}

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	2026-05-18T00:54:36.671711Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe74ea5d7768467c09eaffa0513f2c0fac7cea1c1bdac37857a6d18f57f159f1

Aliases

arxiv: 1605.00893 · arxiv_version: 1605.00893v1 · doi: 10.48550/arxiv.1605.00893 · pith_short_12: 7Z2OUXLXNBDH · pith_short_16: 7Z2OUXLXNBDHYCPK · pith_short_8: 7Z2OUXLX

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/7Z2OUXLXNBDHYCPK76QFCPZMB6 \
  | 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: fe74ea5d7768467c09eaffa0513f2c0fac7cea1c1bdac37857a6d18f57f159f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a72986047c85c50df8397eb338ce85bf662907081603dae52b0e5007d227e26f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-05-03T13:12:17Z",
    "title_canon_sha256": "fd6305e3dd772540f24aa120ee08b704ccf020c165b3108aae5db40fe5273b6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00893",
    "kind": "arxiv",
    "version": 1
  }
}