Pith Number

pith:4OEMXC3D

pith:2011:4OEMXC3DEO33MAYO4DEJQ62TMC

not attested not anchored not stored refs pending

Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases

Benedetta Ferrario, Hakima Bessaih

arxiv:1103.2151 v1 · 2011-03-10 · math-ph · math.MP · 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{4OEMXC3DEO33MAYO4DEJQ62TMC}

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	2026-05-18T02:02:54.857399Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e388cb8b6323b7b6030ee0c8987b53609959d6282734104d43546d05a1f13ee9

Aliases

arxiv: 1103.2151 · arxiv_version: 1103.2151v1 · doi: 10.48550/arxiv.1103.2151 · pith_short_12: 4OEMXC3DEO33 · pith_short_16: 4OEMXC3DEO33MAYO · pith_short_8: 4OEMXC3D

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/4OEMXC3DEO33MAYO4DEJQ62TMC \
  | 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: e388cb8b6323b7b6030ee0c8987b53609959d6282734104d43546d05a1f13ee9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1b91b4dbe8ff1214031281b3221f468359dd2ad2658a77f05414f895b9e63767",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-03-10T22:05:35Z",
    "title_canon_sha256": "4fb1cd5411b5c600c811c534dbb43a7a431441eb17190c0078897a53b4aef5c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.2151",
    "kind": "arxiv",
    "version": 1
  }
}