Pith Number

pith:MROJLY7H

pith:2015:MROJLY7H4Y5ZWTTEF342RXTK2Y

not attested not anchored not stored refs pending

Frequency localized regularity criteria for the 3D Navier-Stokes equations

Zachary Bradshaw, Zoran Grujic

arxiv:1501.01043 v2 · 2015-01-05 · 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{MROJLY7H4Y5ZWTTEF342RXTK2Y}

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	2026-05-18T00:57:38.407951Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

645c95e3e7e63b9b4e642ef9a8de6ad63a604dd0a9b6715ab6c2e426315ecf52

Aliases

arxiv: 1501.01043 · arxiv_version: 1501.01043v2 · doi: 10.48550/arxiv.1501.01043 · pith_short_12: MROJLY7H4Y5Z · pith_short_16: MROJLY7H4Y5ZWTTE · pith_short_8: MROJLY7H

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/MROJLY7H4Y5ZWTTEF342RXTK2Y \
  | 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: 645c95e3e7e63b9b4e642ef9a8de6ad63a604dd0a9b6715ab6c2e426315ecf52

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7fcd9183176937116be2d835d4379ff7198f1624aeb38d0ef796821d0fd9c29",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-01-05T23:57:09Z",
    "title_canon_sha256": "8a26cb2fd6dea3fa0fe4698e02e2745de2ccbd2dd71d654ef6c4ff1c1bfebdb1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.01043",
    "kind": "arxiv",
    "version": 2
  }
}