Pith Number

pith:PJFPR5NJ

pith:2017:PJFPR5NJJFCQFJLRU54NVZJNIO

not attested not anchored not stored refs pending

Quantitative Bounds on the Rate of Approach to Equilibrium for some One-Dimensional Stochastic Non-Linear Schr\"odinger Equations

Eric A. Carlen, Joel Lebowitz, J\"urg Fr\"ohlich, Wei-Min Wang

arxiv:1712.09588 v1 · 2017-12-27 · math-ph · math.FA · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PJFPR5NJJFCQFJLRU54NVZJNIO}

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	2026-05-18T00:27:07.918714Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a4af8f5a9494502a571a778dae52d4396c12be9164569db33e0ddbf6ed9fbb3

Aliases

arxiv: 1712.09588 · arxiv_version: 1712.09588v1 · doi: 10.48550/arxiv.1712.09588 · pith_short_12: PJFPR5NJJFCQ · pith_short_16: PJFPR5NJJFCQFJLR · pith_short_8: PJFPR5NJ

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/PJFPR5NJJFCQFJLRU54NVZJNIO \
  | 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: 7a4af8f5a9494502a571a778dae52d4396c12be9164569db33e0ddbf6ed9fbb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a719162a339a689df94da64c3699e51fcb09e2065d1a43d9ffdb7858be806fa0",
    "cross_cats_sorted": [
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2017-12-27T14:26:04Z",
    "title_canon_sha256": "3a52cb8068a620bb25531966966bd3cbdbf077bf00dca33f7df7708891e63584"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1712.09588",
    "kind": "arxiv",
    "version": 1
  }
}