Pith Number

pith:OP4CLOPE

pith:1999:OP4CLOPEM5QT3RGHAFDGMQRTWC

not attested not anchored not stored refs pending

Excitation Thresholds for Nonlinear Localized Modes on Lattices

Michael I. Weinstein

arxiv:patt-sol/9903001 v1 · 1999-03-05 · patt-sol · nlin.PS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OP4CLOPEM5QT3RGHAFDGMQRTWC}

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	2026-07-04T16:15:31.351232Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

73f825b9e467613dc4c70146664233b09004b88f282d6f42e508853b8722d670

Aliases

arxiv: patt-sol/9903001 · arxiv_version: patt-sol/9903001v1 · doi: 10.48550/arxiv.patt-sol/9903001 · pith_short_12: OP4CLOPEM5QT · pith_short_16: OP4CLOPEM5QT3RGH · pith_short_8: OP4CLOPE

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/OP4CLOPEM5QT3RGHAFDGMQRTWC \
  | 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: 73f825b9e467613dc4c70146664233b09004b88f282d6f42e508853b8722d670

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a02edd000dc3ae01f5bb6452a170e8ad7c34f9dc66544eeb5aeb12688bee8a88",
    "cross_cats_sorted": [
      "nlin.PS"
    ],
    "license": "",
    "primary_cat": "patt-sol",
    "submitted_at": "1999-03-05T14:54:18Z",
    "title_canon_sha256": "0316c5a16c3a4d6d87d0d81d98e8a15b53fbb2d934a44b471910f8714c8aae0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "patt-sol/9903001",
    "kind": "arxiv",
    "version": 1
  }
}