Pith Number

pith:SS7O2NIL

pith:2026:SS7O2NILQ6LHAV4SOVSEFUXMSK

not attested not anchored not stored refs pending

Lyapunov Guidance: A Unified Framework for Stabilizing Generative Flows

Jingdong Zhang, Junhong Liu, Luan Yang, Minkai Xu, Xinze Li, Yize Jiang

arxiv:2607.14272 v1 · 2026-07-15 · cs.LG · math.DS · 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{SS7O2NILQ6LHAV4SOVSEFUXMSK}

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	2026-07-17T00:21:02.661830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

94beed350b8796705792756442d2ec9284f6111d97faf57233526d1a32802643

Aliases

arxiv: 2607.14272 · arxiv_version: 2607.14272v1 · doi: 10.48550/arxiv.2607.14272 · pith_short_12: SS7O2NILQ6LH · pith_short_16: SS7O2NILQ6LHAV4S · pith_short_8: SS7O2NIL

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/SS7O2NILQ6LHAV4SOVSEFUXMSK \
  | 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: 94beed350b8796705792756442d2ec9284f6111d97faf57233526d1a32802643

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d4af0285174fdf3c3e50245220f1d17f7f322dfb371f1b9eddf0871b65c48781",
    "cross_cats_sorted": [
      "math.DS",
      "math.OC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-15T18:28:08Z",
    "title_canon_sha256": "0b2eedd648b1c258d175d0c0c49bdac3c1a1b8a07a5da4874968bf90781c1555"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.14272",
    "kind": "arxiv",
    "version": 1
  }
}