Pith Number

pith:BLL4UUBA

pith:2018:BLL4UUBAQBZEDHJNMVMXI6SB2T

not attested not anchored not stored refs pending

An operator-valued Lyapunov theorem

Christopher Ramsey, Sarah Plosker

arxiv:1801.03109 v2 · 2018-01-09 · math.FA · quant-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BLL4UUBAQBZEDHJNMVMXI6SB2T}

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	2026-05-18T00:06:05.341831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0ad7ca50208072419d2d6559747a41d4faf250d5329bff655b4c96759910641c

Aliases

arxiv: 1801.03109 · arxiv_version: 1801.03109v2 · doi: 10.48550/arxiv.1801.03109 · pith_short_12: BLL4UUBAQBZE · pith_short_16: BLL4UUBAQBZEDHJN · pith_short_8: BLL4UUBA

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/BLL4UUBAQBZEDHJNMVMXI6SB2T \
  | 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: 0ad7ca50208072419d2d6559747a41d4faf250d5329bff655b4c96759910641c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a10bc23a7ccff8fe13d50f5b6c4de83db82861efc5adffdc9afca9548d7dd8a",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.FA",
    "submitted_at": "2018-01-09T19:07:11Z",
    "title_canon_sha256": "27eca79762c55b09beff12a5637adc5016b105d3117abdc77feca28888c4f337"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1801.03109",
    "kind": "arxiv",
    "version": 2
  }
}