Pith Number

pith:WRPYFMVY

pith:2012:WRPYFMVYVGZWI5Z4FLHDK5TQUT

not attested not anchored not stored refs pending

A short proof of the existence of disjoint hypercyclic operators

Stanislav Shkarin

arxiv:1209.1212 v1 · 2012-09-06 · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{WRPYFMVYVGZWI5Z4FLHDK5TQUT}

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	2026-05-18T03:46:06.216234Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b45f82b2b8a9b364773c2ace357670a4d0c466c49675fc5964c8d495e6ba682e

Aliases

arxiv: 1209.1212 · arxiv_version: 1209.1212v1 · doi: 10.48550/arxiv.1209.1212 · pith_short_12: WRPYFMVYVGZW · pith_short_16: WRPYFMVYVGZWI5Z4 · pith_short_8: WRPYFMVY

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/WRPYFMVYVGZWI5Z4FLHDK5TQUT \
  | 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: b45f82b2b8a9b364773c2ace357670a4d0c466c49675fc5964c8d495e6ba682e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3809cad5eb72e28ec87f3bc0f06d9914a57151399fa8c8cff6bb2db8f885c90",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2012-09-06T08:06:35Z",
    "title_canon_sha256": "0ebcb6c7c6a2ea13211c1401fc890aaa6215612a13f1f55cb2c77e8f0288e838"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1212",
    "kind": "arxiv",
    "version": 1
  }
}