Pith Number

pith:MRBACWSP

pith:2016:MRBACWSPCD5EJQCFI3BF5GOPYP

not attested not anchored not stored refs pending

On the box-counting dimension of potential singular set for suitable weak solutions to the 3D Navier-Stokes equations

Gang Wu, Yanqing Wang

arxiv:1604.05032 v2 · 2016-04-18 · 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{MRBACWSPCD5EJQCFI3BF5GOPYP}

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	2026-05-18T00:47:21.048724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6442015a4f10fa44c04546c25e99cfc3d385fa9967377aa3d113dda737d91fbd

Aliases

arxiv: 1604.05032 · arxiv_version: 1604.05032v2 · doi: 10.48550/arxiv.1604.05032 · pith_short_12: MRBACWSPCD5E · pith_short_16: MRBACWSPCD5EJQCF · pith_short_8: MRBACWSP

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/MRBACWSPCD5EJQCFI3BF5GOPYP \
  | 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: 6442015a4f10fa44c04546c25e99cfc3d385fa9967377aa3d113dda737d91fbd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ed6dfd79707810c8b4dbce21c2a7cfdedad3bf8ba99b7ac2a494bfeec432e284",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-04-18T08:34:54Z",
    "title_canon_sha256": "dc96dae555a62803cfe93d656b34d86e729b5a64425e0fa05803c532db55857e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.05032",
    "kind": "arxiv",
    "version": 2
  }
}