Pith Number

pith:NGAZOQED

pith:2017:NGAZOQEDZPZHGE2XO4DZHXYTZT

not attested not anchored not stored refs pending

Optimality of integrability estimates for advection-diffusion equations

Gianluca Crippa, Laura V. Spinolo, Maria Colombo, Stefano Bianchini

arxiv:1702.00321 v1 · 2017-02-01 · 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{NGAZOQEDZPZHGE2XO4DZHXYTZT}

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	2026-05-18T00:51:34.653355Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6981974083cbf2731357770793df13ccd6aa733dc5d774ac480265b8496eb416

Aliases

arxiv: 1702.00321 · arxiv_version: 1702.00321v1 · doi: 10.48550/arxiv.1702.00321 · pith_short_12: NGAZOQEDZPZH · pith_short_16: NGAZOQEDZPZHGE2X · pith_short_8: NGAZOQED

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/NGAZOQEDZPZHGE2XO4DZHXYTZT \
  | 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: 6981974083cbf2731357770793df13ccd6aa733dc5d774ac480265b8496eb416

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21566c812858286ef4143845438c17069b0c3a3ba824142e40c75a6de542ea74",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2017-02-01T15:35:39Z",
    "title_canon_sha256": "acf56ebe2d88c45df10a2470afd7abb319fe9c1136f626a684370ff984da90f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.00321",
    "kind": "arxiv",
    "version": 1
  }
}