Pith Number

pith:Y7VCLZUI

pith:2016:Y7VCLZUIZMSS5KNELQLQAPBZOP

not attested not anchored not stored refs pending

Lyapunov small-gain theorems for networks of not necessarily ISS hybrid systems

Andrii Mironchenko, Daniel Liberzon, Guosong Yang

arxiv:1610.01403 v2 · 2016-10-05 · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Y7VCLZUIZMSS5KNELQLQAPBZOP}

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	2026-05-18T00:31:13.819901Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7ea25e688cb252ea9a45c17003c3973e6d75fd014148d166c754cda491a439b

Aliases

arxiv: 1610.01403 · arxiv_version: 1610.01403v2 · doi: 10.48550/arxiv.1610.01403 · pith_short_12: Y7VCLZUIZMSS · pith_short_16: Y7VCLZUIZMSS5KNE · pith_short_8: Y7VCLZUI

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/Y7VCLZUIZMSS5KNELQLQAPBZOP \
  | 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: c7ea25e688cb252ea9a45c17003c3973e6d75fd014148d166c754cda491a439b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1305038d12e75deea6757ece271e9fe53780a55092654f56f590addac1431aa9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2016-10-05T13:16:03Z",
    "title_canon_sha256": "63dfd76963105bbba149794a61b4ea16774ac510d36769251a9f5542dd85efe7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.01403",
    "kind": "arxiv",
    "version": 2
  }
}