Pith Number

pith:CJ3JWY5X

pith:2012:CJ3JWY5XMBJQEFKKWFSPSGOVQ4

not attested not anchored not stored refs pending

On the spectrum of frequently hypercyclic operators

Stanislav Shkarin

arxiv:1209.1221 v1 · 2012-09-06 · math.FA · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CJ3JWY5XMBJQEFKKWFSPSGOVQ4}

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	2026-05-18T03:46:06.185460Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12769b63b7605302154ab164f919d58701cd35815a898ac26c64fed2f3afd634

Aliases

arxiv: 1209.1221 · arxiv_version: 1209.1221v1 · doi: 10.48550/arxiv.1209.1221 · pith_short_12: CJ3JWY5XMBJQ · pith_short_16: CJ3JWY5XMBJQEFKK · pith_short_8: CJ3JWY5X

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/CJ3JWY5XMBJQEFKKWFSPSGOVQ4 \
  | 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: 12769b63b7605302154ab164f919d58701cd35815a898ac26c64fed2f3afd634

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ab2e68273d1a06b7acdbc670ad9473a3160bb263d68f603848fa8e51c3722b6",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-06T08:27:53Z",
    "title_canon_sha256": "26b0f4c331993860faf6e3d240660f19deb000e3d65fe6423f61adcc6c453417"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1221",
    "kind": "arxiv",
    "version": 1
  }
}