Pith Number

pith:DQW43JIJ

pith:2011:DQW43JIJQWYYL6ELBPSRM6ESGD

not attested not anchored not stored refs pending

On the ill-posedness of the compressible Navier-Stokes equations in the critical Besov spaces

Changxing Miao, Qionglei Chen, Zhifei Zhang

arxiv:1109.6092 v2 · 2011-09-28 · 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{DQW43JIJQWYYL6ELBPSRM6ESGD}

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	2026-05-18T01:24:31.073215Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1c2dcda50985b185f88b0be516789230f594cf9a3afcf52a4e9314841f1bf233

Aliases

arxiv: 1109.6092 · arxiv_version: 1109.6092v2 · doi: 10.48550/arxiv.1109.6092 · pith_short_12: DQW43JIJQWYY · pith_short_16: DQW43JIJQWYYL6EL · pith_short_8: DQW43JIJ

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/DQW43JIJQWYYL6ELBPSRM6ESGD \
  | 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: 1c2dcda50985b185f88b0be516789230f594cf9a3afcf52a4e9314841f1bf233

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "89a049f8675d7860bdbffd54e4098ac689b821375ba2263a77d30ed4bf693b3f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-09-28T04:12:54Z",
    "title_canon_sha256": "eca5ef88753e0614aa743076b45401aaa2bb1996cdbe2ca46a0fcab1a9945b40"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.6092",
    "kind": "arxiv",
    "version": 2
  }
}