Pith Number

pith:NWA2ZGQ2

pith:2019:NWA2ZGQ2JSWF662ENFZSITWB37

not attested not anchored not stored refs pending

On the Hypercyclicity Criterion for operators of Read's type

Sophie Grivaux

arxiv:1908.06712 v1 · 2019-08-19 · 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{NWA2ZGQ2JSWF662ENFZSITWB37}

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	2026-07-04T23:58:18.765071Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d81ac9a1a4cac5f7b446973244ec1dfd86f5db148e4aa21a3ab301d1bdb9df0

Aliases

arxiv: 1908.06712 · arxiv_version: 1908.06712v1 · doi: 10.48550/arxiv.1908.06712 · pith_short_12: NWA2ZGQ2JSWF · pith_short_16: NWA2ZGQ2JSWF662E · pith_short_8: NWA2ZGQ2

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/NWA2ZGQ2JSWF662ENFZSITWB37 \
  | 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: 6d81ac9a1a4cac5f7b446973244ec1dfd86f5db148e4aa21a3ab301d1bdb9df0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e410c6cfedbebb5612eb6f84ee75e1dfa3ac45c863a365ef0446abb52ea65c16",
    "cross_cats_sorted": [
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2019-08-19T11:49:55Z",
    "title_canon_sha256": "49d6720086c9353584cb0a4291c4132c390b1b76ce2e97cd9be1c915dec796b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1908.06712",
    "kind": "arxiv",
    "version": 1
  }
}