Pith Number

pith:GIEBCWGF

pith:2008:GIEBCWGF6XX47DRHA6L6CTZ7LY

not attested not anchored not stored refs pending

Tunnel effect for Kramers-Fokker-Planck type operators: return to equilibrium and applications

Frederic Herau (LM-Reims), Johannes Sjoestrand (CMLS-EcolePolytechnique), Michael Hitrik

arxiv:0801.3615 v1 · 2008-01-23 · math.AP · math.SP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GIEBCWGF6XX47DRHA6L6CTZ7LY}

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	2026-07-04T15:07:01.349358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

32081158c5f5efcf8e270797e14f3f5e005e82ab99fb5dcf86ecf5b95e782e59

Aliases

arxiv: 0801.3615 · arxiv_version: 0801.3615v1 · doi: 10.48550/arxiv.0801.3615 · pith_short_12: GIEBCWGF6XX4 · pith_short_16: GIEBCWGF6XX47DRH · pith_short_8: GIEBCWGF

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/GIEBCWGF6XX47DRHA6L6CTZ7LY \
  | 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: 32081158c5f5efcf8e270797e14f3f5e005e82ab99fb5dcf86ecf5b95e782e59

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "645e2fb98032cbeb900ef3878243d435d72bca3d26626c0ac079bdfcf6c28dd2",
    "cross_cats_sorted": [
      "math.SP"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2008-01-23T16:16:22Z",
    "title_canon_sha256": "b795ddc9e102975798caaddc1ac45ed6c869680465e5f10ea4a698fc4141180b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0801.3615",
    "kind": "arxiv",
    "version": 1
  }
}