Pith Number

pith:MBHLJTO2

pith:2026:MBHLJTO2UBUZ4TAKXGFXKPLOB5

not attested not anchored not stored refs pending

The Navier-Stokes equations with dual-scale hereditary viscosity: supercritical norm inflation and global well-posedness in critical spaces

Bruno de Andrade

arxiv:2607.25009 v1 · 2026-07-27 · 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{MBHLJTO2UBUZ4TAKXGFXKPLOB5}

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	2026-07-29T00:24:57.570658Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

604eb4cddaa0699e4c0ab98b753d6e0f776ff33cd366f813cf2a5a91d02e407b

Aliases

arxiv: 2607.25009 · arxiv_version: 2607.25009v1 · doi: 10.48550/arxiv.2607.25009 · pith_short_12: MBHLJTO2UBUZ · pith_short_16: MBHLJTO2UBUZ4TAK · pith_short_8: MBHLJTO2

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/MBHLJTO2UBUZ4TAKXGFXKPLOB5 \
  | 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: 604eb4cddaa0699e4c0ab98b753d6e0f776ff33cd366f813cf2a5a91d02e407b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "906c06a9f560d2128e474afa5b2974b13d1dc3959673862178138d7003e211d2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-27T19:07:16Z",
    "title_canon_sha256": "8062d7eb3acf1654852f4fb26d74ed511236eb53356fda1de18c1b91d5f74ba5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25009",
    "kind": "arxiv",
    "version": 1
  }
}