Pith Number

pith:L4PXRTPX

pith:2015:L4PXRTPXMODWV4T7OG6K5TI3TW

not attested not anchored not stored refs pending

Uniform semigroup spectral analysis of the discrete, fractional \& classical Fokker-Planck equations

Isabelle Tristani (CMLS), St\'ephane Mischler (CEREMADE)

arxiv:1507.04861 v3 · 2015-07-17 · 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{L4PXRTPXMODWV4T7OG6K5TI3TW}

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	2026-05-18T01:19:40.767158Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f1f78cdf763876af27f71bcaecd1b9dbe01bed27d3081033f20e31826893893

Aliases

arxiv: 1507.04861 · arxiv_version: 1507.04861v3 · doi: 10.48550/arxiv.1507.04861 · pith_short_12: L4PXRTPXMODW · pith_short_16: L4PXRTPXMODWV4T7 · pith_short_8: L4PXRTPX

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/L4PXRTPXMODWV4T7OG6K5TI3TW \
  | 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: 5f1f78cdf763876af27f71bcaecd1b9dbe01bed27d3081033f20e31826893893

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b8ed955f6f25541cf91488f22753ebc6ca32c5447900a4029de43f479fa4c425",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2015-07-17T07:44:17Z",
    "title_canon_sha256": "2047a4ecc42a93c16a5fb34f50a8053fd55a72d57e40ed92ab3fa91fccba08be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1507.04861",
    "kind": "arxiv",
    "version": 3
  }
}