Pith Number

pith:QM3G56IZ

pith:2019:QM3G56IZRLD33NN34F4EZLI7VS

not attested not anchored not stored refs pending

Bounds on Lyapunov exponents via entropy accumulation

David Sutter, Omar Fawzi, Renato Renner

arxiv:1905.03270 v4 · 2019-05-08 · math-ph · cs.IT · math.DS · math.IT · math.MP · 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{QM3G56IZRLD33NN34F4EZLI7VS}

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	2026-07-05T02:01:27.775663Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

83366ef9198ac7bdb5bbe1784cad1facb120fceef6919baadfe1902d02d69d75

Aliases

arxiv: 1905.03270 · arxiv_version: 1905.03270v4 · doi: 10.48550/arxiv.1905.03270 · pith_short_12: QM3G56IZRLD3 · pith_short_16: QM3G56IZRLD33NN3 · pith_short_8: QM3G56IZ

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/QM3G56IZRLD33NN34F4EZLI7VS \
  | 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: 83366ef9198ac7bdb5bbe1784cad1facb120fceef6919baadfe1902d02d69d75

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "505ec04feb1a9d130d793f61825c2edf4fc965b033adf3a9f7c058da446c3363",
    "cross_cats_sorted": [
      "cs.IT",
      "math.DS",
      "math.IT",
      "math.MP",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2019-05-08T18:00:49Z",
    "title_canon_sha256": "b455d72a4cbf8d6831d526718bca6f6fa89a452ca848dab32919908dfc84adf2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1905.03270",
    "kind": "arxiv",
    "version": 4
  }
}