Pith Number

pith:FV6QY6YL

pith:2011:FV6QY6YLHBZJOMVQKXADFSFLK5

not attested not anchored not stored refs pending

A proof of the invariant torus theorem of Kolmogorov

Jacques F\'ejoz

arxiv:1102.0923 v2 · 2011-02-04 · math.DS · 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{FV6QY6YLHBZJOMVQKXADFSFLK5}

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	2026-05-18T02:03:16.664919Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d7d0c7b0b38729732b055c032c8ab575a518b3706b3dfb61063b8c8506d907c

Aliases

arxiv: 1102.0923 · arxiv_version: 1102.0923v2 · doi: 10.48550/arxiv.1102.0923 · pith_short_12: FV6QY6YLHBZJ · pith_short_16: FV6QY6YLHBZJOMVQ · pith_short_8: FV6QY6YL

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/FV6QY6YLHBZJOMVQKXADFSFLK5 \
  | 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: 2d7d0c7b0b38729732b055c032c8ab575a518b3706b3dfb61063b8c8506d907c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5375769a130e385aec691f04cd2409928dd5b51a0b5b299587f80d0f9bdaad7",
    "cross_cats_sorted": [
      "math-ph",
      "math.FA",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2011-02-04T14:20:39Z",
    "title_canon_sha256": "23f3240b83f306084dbb5f79eeffb5adfb547f3b0247d9fb452ed8ce445e4656"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1102.0923",
    "kind": "arxiv",
    "version": 2
  }
}