Pith Number

pith:ECDEKNCA

pith:2026:ECDEKNCAF7SLLWPOQPGDVMCZWB

not attested not anchored not stored refs pending

High Order Asymptotic Expansion at Infinity for Strong Solutions to Incompressible Navier-Stokes Equations

Shuai Xi, Weiquan Chen, Zhongmin Qian

arxiv:2607.22146 v1 · 2026-07-24 · 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{ECDEKNCAF7SLLWPOQPGDVMCZWB}

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	2026-07-27T01:20:50.490201Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

20864534402fe4b5d9ee83cc3ab059b0420841ff5482dfc21ed10830c4481cbe

Aliases

arxiv: 2607.22146 · arxiv_version: 2607.22146v1 · doi: 10.48550/arxiv.2607.22146 · pith_short_12: ECDEKNCAF7SL · pith_short_16: ECDEKNCAF7SLLWPO · pith_short_8: ECDEKNCA

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/ECDEKNCAF7SLLWPOQPGDVMCZWB \
  | 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: 20864534402fe4b5d9ee83cc3ab059b0420841ff5482dfc21ed10830c4481cbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5adf9b790d55878477008b9ec7ac527c503e52c1ce1c2e177910ddd81e9d452b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-24T09:45:38Z",
    "title_canon_sha256": "57826298dbc07c81035efdffc65093bd427c88081de0452b42c047bc96f437f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.22146",
    "kind": "arxiv",
    "version": 1
  }
}