Pith Number

pith:OGCE6MUV

pith:2011:OGCE6MUVTJBCDO3FX5OPQYJRRX

not attested not anchored not stored refs pending

Logarithmic spikes of gradients and uniqueness of weak solutions to a class of active scalar equations

Walter Rusin

arxiv:1106.2778 v1 · 2011-06-14 · 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{OGCE6MUVTJBCDO3FX5OPQYJRRX}

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	2026-05-18T04:20:04.169707Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

71844f32959a4221bb65bf5cf861318dd41ecc34532475bfac0d5a04495a29c9

Aliases

arxiv: 1106.2778 · arxiv_version: 1106.2778v1 · doi: 10.48550/arxiv.1106.2778 · pith_short_12: OGCE6MUVTJBC · pith_short_16: OGCE6MUVTJBCDO3F · pith_short_8: OGCE6MUV

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/OGCE6MUVTJBCDO3FX5OPQYJRRX \
  | 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: 71844f32959a4221bb65bf5cf861318dd41ecc34532475bfac0d5a04495a29c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3fb52267daaa5ecd2bb185cd3a9ef0348dcdda18af8a8a0ac0967f4f61f2ad7d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-06-14T18:19:03Z",
    "title_canon_sha256": "eafb54544e51ad3d059454e894f350e6498008ca91d527b4c3be32795d8ce75c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.2778",
    "kind": "arxiv",
    "version": 1
  }
}