Pith Number

pith:AA6EMSXM

pith:2010:AA6EMSXMZY3CKC5PMATYUIFJKH

not attested not anchored not stored refs pending

A profile decomposition approach to the $L^\infty_t(L^3_x)$ Navier-Stokes regularity criterion

Fabrice Planchon, Gabriel S. Koch, Isabelle Gallagher

arxiv:1012.0145 v3 · 2010-12-01 · math.AP · math.FA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AA6EMSXMZY3CKC5PMATYUIFJKH}

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	2026-05-18T01:17:26.387256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

003c464aecce36250baf60278a20a951ebba634a8479f63c95d14f1ed700710a

Aliases

arxiv: 1012.0145 · arxiv_version: 1012.0145v3 · doi: 10.48550/arxiv.1012.0145 · pith_short_12: AA6EMSXMZY3C · pith_short_16: AA6EMSXMZY3CKC5P · pith_short_8: AA6EMSXM

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/AA6EMSXMZY3CKC5PMATYUIFJKH \
  | 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: 003c464aecce36250baf60278a20a951ebba634a8479f63c95d14f1ed700710a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0223274b6bd96ab95e54a82ce90acd88ed647d38fa410488857ded5bb4c4395e",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2010-12-01T10:18:52Z",
    "title_canon_sha256": "361adcc84d1d18d1df5a2de9f1f7990b47d5ea2c75193a5a882690e1d22c2fd2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.0145",
    "kind": "arxiv",
    "version": 3
  }
}