Pith Number

pith:CVF7CKU3

pith:2002:CVF7CKU3ZTTGCQJJZWMKHIT5NB

not attested not anchored not stored refs pending

Periodic motions galore: How to modify nonlinear evolution equations so that they feature a lot of periodic solutions

F. Calogero, J-P Francoise

arxiv:math/0210120 v1 · 2002-10-08 · math.DS · 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{CVF7CKU3ZTTGCQJJZWMKHIT5NB}

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	2026-05-18T01:38:29.413498Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

154bf12a9bcce6614129cd98a3a27d686be771453240ffcc7312611ec67977f5

Aliases

arxiv: math/0210120 · arxiv_version: math/0210120v1 · doi: 10.48550/arxiv.math/0210120 · pith_short_12: CVF7CKU3ZTTG · pith_short_16: CVF7CKU3ZTTGCQJJ · pith_short_8: CVF7CKU3

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/CVF7CKU3ZTTGCQJJZWMKHIT5NB \
  | 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: 154bf12a9bcce6614129cd98a3a27d686be771453240ffcc7312611ec67977f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "db8f48fc24c58f977654be4ae4824b02e45dacc3ce273a3db72992d75616c77e",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "",
    "primary_cat": "math.DS",
    "submitted_at": "2002-10-08T15:09:02Z",
    "title_canon_sha256": "0b61bf8cbe801384033d41ec6ceb83f03530f3ff43a4b5d6c1d02f82922fe0d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0210120",
    "kind": "arxiv",
    "version": 1
  }
}