Pith Number

pith:I7DZ2VBU

pith:2011:I7DZ2VBUTXPP53JEWGMTZ3IXL3

not attested not anchored not stored refs pending

Sub and supercritical stochastic quasi-geostrophic equation

Michael R\"ockner, Rongchan Zhu, Xiangchan Zhu

arxiv:1110.1984 v5 · 2011-10-10 · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{I7DZ2VBUTXPP53JEWGMTZ3IXL3}

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	2026-05-18T01:57:41.857724Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

47c79d54349ddefeed24b1993ced175efca55f10057d4687ae046d8bcde0bf0c

Aliases

arxiv: 1110.1984 · arxiv_version: 1110.1984v5 · doi: 10.48550/arxiv.1110.1984 · pith_short_12: I7DZ2VBUTXPP · pith_short_16: I7DZ2VBUTXPP53JE · pith_short_8: I7DZ2VBU

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/I7DZ2VBUTXPP53JEWGMTZ3IXL3 \
  | 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: 47c79d54349ddefeed24b1993ced175efca55f10057d4687ae046d8bcde0bf0c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26215a0f19763342a853b824c5c6a27dfd7c2757a5d4f79ea5b7249df6cc197b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2011-10-10T10:03:11Z",
    "title_canon_sha256": "5f958849d958dcf55b3e7ebd9a2c47686db329459ecaede99cac0849d6f220ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.1984",
    "kind": "arxiv",
    "version": 5
  }
}