Pith Number

pith:Y4E5K2CB

pith:2011:Y4E5K2CBR3LO2KJI7AGBVIYYFP

not attested not anchored not stored refs pending

The Gardner equation and the stability of multi-kink solutions of the mKdV equation

Claudio Mu\~noz

arxiv:1106.0648 v3 · 2011-06-03 · 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{Y4E5K2CBR3LO2KJI7AGBVIYYFP}

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	2026-05-18T04:15:59.246044Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c709d568418ed6ed2928f80c1aa3182bfb24362807dd808763e02d4648bfd2a9

Aliases

arxiv: 1106.0648 · arxiv_version: 1106.0648v3 · doi: 10.48550/arxiv.1106.0648 · pith_short_12: Y4E5K2CBR3LO · pith_short_16: Y4E5K2CBR3LO2KJI · pith_short_8: Y4E5K2CB

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/Y4E5K2CBR3LO2KJI7AGBVIYYFP \
  | 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: c709d568418ed6ed2928f80c1aa3182bfb24362807dd808763e02d4648bfd2a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4a00e56ff7f32519aa57578dd71816206612e3721dcdcff98ea437c472415d70",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2011-06-03T14:20:40Z",
    "title_canon_sha256": "b9c0373cce2533c25f89ea71043f049803e48fd16ee632a68f337eea8e718178"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.0648",
    "kind": "arxiv",
    "version": 3
  }
}