Pith Number

pith:CWRYYA44

pith:2015:CWRYYA44QM4ANTDNZNES4BX5F4

not attested not anchored not stored refs pending

On the critical one-component velocity regularity criteria to 3-D incompressible MHD system

Yanlin Liu

arxiv:1509.05531 v1 · 2015-09-18 · 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{CWRYYA44QM4ANTDNZNES4BX5F4}

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	2026-05-18T01:32:42.917218Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

15a38c039c833806cc6dcb492e06fd2f2062caa9c23a7b3837ee681f724bc1a8

Aliases

arxiv: 1509.05531 · arxiv_version: 1509.05531v1 · doi: 10.48550/arxiv.1509.05531 · pith_short_12: CWRYYA44QM4A · pith_short_16: CWRYYA44QM4ANTDN · pith_short_8: CWRYYA44

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/CWRYYA44QM4ANTDNZNES4BX5F4 \
  | 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: 15a38c039c833806cc6dcb492e06fd2f2062caa9c23a7b3837ee681f724bc1a8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f0936e08b5a14eacc30319980601bba2634136fd0827f671d21812844b10009d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-09-18T07:58:44Z",
    "title_canon_sha256": "37744047866a55598398bc701b9f0e510c5286013b5b6f670f1aa7d1ba87986f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.05531",
    "kind": "arxiv",
    "version": 1
  }
}