Pith Number

pith:Y52BTCK4

pith:2006:Y52BTCK4SLSH5YXCXHFN6DA6Q5

not attested not anchored not stored refs pending

Perturbation Expansion and N-th Order Fermi Golden Rule of the Nonlinear Schr\"odinger Equations

Zhou Gang

arxiv:math/0610381 v2 · 2006-10-11 · math.AP · math-ph · 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{Y52BTCK4SLSH5YXCXHFN6DA6Q5}

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	2026-07-04T14:57:07.998487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c77419895c92e47ee2e2b9cadf0c1e875234b203bf72ce6e76af5648d6c79247

Aliases

arxiv: math/0610381 · arxiv_version: math/0610381v2 · doi: 10.48550/arxiv.math/0610381 · pith_short_12: Y52BTCK4SLSH · pith_short_16: Y52BTCK4SLSH5YXC · pith_short_8: Y52BTCK4

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/Y52BTCK4SLSH5YXCXHFN6DA6Q5 \
  | 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: c77419895c92e47ee2e2b9cadf0c1e875234b203bf72ce6e76af5648d6c79247

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0a8b991fc30c94f0dc1c6edb18ead7762d78a6b8547259f9383235c816537d06",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.AP",
    "submitted_at": "2006-10-11T18:58:41Z",
    "title_canon_sha256": "fcc1280924cafaf97f13f9360bbd6f0cb4b883623ee09380dcda1abac3fa50dc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0610381",
    "kind": "arxiv",
    "version": 2
  }
}