Pith Number

pith:MCZ5HSR4

pith:2015:MCZ5HSR42RK2F5GHF44LKK7VHN

not attested not anchored not stored refs pending

Lower bounds on blowing-up solutions of the 3D Navier--Stokes equations in $\dot H^{3/2}$, $\dot H^{5/2}$, and $\dot B^{5/2}_{2,1}$

Alejandro Vidal-Lopez, David S. McCormick, Eric J. Olson, James C. Robinson, Jose L. Rodrigo, Yi Zhou

arxiv:1503.04323 v1 · 2015-03-14 · 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{MCZ5HSR42RK2F5GHF44LKK7VHN}

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	2026-05-18T02:23:25.424844Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

60b3d3ca3cd455a2f4c72f38b52bf53b7c26009e369277c1a436ff11780f8142

Aliases

arxiv: 1503.04323 · arxiv_version: 1503.04323v1 · doi: 10.48550/arxiv.1503.04323 · pith_short_12: MCZ5HSR42RK2 · pith_short_16: MCZ5HSR42RK2F5GH · pith_short_8: MCZ5HSR4

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/MCZ5HSR42RK2F5GHF44LKK7VHN \
  | 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: 60b3d3ca3cd455a2f4c72f38b52bf53b7c26009e369277c1a436ff11780f8142

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9a2dfcc7195dc38e9786b59815b62b4ed5e97bc655e925f853836da5e72c3006",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-03-14T16:49:28Z",
    "title_canon_sha256": "107e623c1a5e8bcebc86fb8a271295c6c8062be3989baa3e484932e045398bc8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.04323",
    "kind": "arxiv",
    "version": 1
  }
}