Pith Number

pith:6DG52VLF

pith:2025:6DG52VLFR4IJEDPTO6RJDDMPS2

not attested not anchored not stored refs pending

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems

Hans De Sterck, Jun Liu, Yun Su

arxiv:2508.21213 v1 · 2025-08-28 · 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{6DG52VLFR4IJEDPTO6RJDDMPS2}

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	2026-07-05T12:01:30.149105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f0cddd55658f10920df377a2918d8f96ae896ba3bd6a8ed41ffb47cd6e974a5b

Aliases

arxiv: 2508.21213 · arxiv_version: 2508.21213v1 · doi: 10.48550/arxiv.2508.21213 · pith_short_12: 6DG52VLFR4IJ · pith_short_16: 6DG52VLFR4IJEDPT · pith_short_8: 6DG52VLF

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/6DG52VLFR4IJEDPTO6RJDDMPS2 \
  | 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: f0cddd55658f10920df377a2918d8f96ae896ba3bd6a8ed41ffb47cd6e974a5b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3dd295f381b52d9383d8b8716f318aecec4d7897521fbebd0bae7f1ef44ef8ab",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-08-28T21:04:35Z",
    "title_canon_sha256": "bc61942b8691b086fdfdc8628ac534cc385cf52d9b00cf2b67a7b31188601228"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.21213",
    "kind": "arxiv",
    "version": 1
  }
}