Pith Number

pith:RQPWNUBO

pith:2026:RQPWNUBOMWDAEFGOMGA7JE4GK6

not attested not anchored not stored refs pending

Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equations

Jun Liu

arxiv:2603.19545 v2 · 2026-03-20 · eess.SY · cs.LG · cs.SY · 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{RQPWNUBOMWDAEFGOMGA7JE4GK6}

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	2026-05-21T01:04:24.831422Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8c1f66d02e65860214ce6181f4938657961966f8a958f6decf88eacd3faadf90

Aliases

arxiv: 2603.19545 · arxiv_version: 2603.19545v2 · doi: 10.48550/arxiv.2603.19545 · pith_short_12: RQPWNUBOMWDA · pith_short_16: RQPWNUBOMWDAEFGO · pith_short_8: RQPWNUBO

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/RQPWNUBOMWDAEFGOMGA7JE4GK6 \
  | 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: 8c1f66d02e65860214ce6181f4938657961966f8a958f6decf88eacd3faadf90

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dffed32340a45b8d90cc9ac5e2cbf36d4b6fa3306c89be21a93013be13dfb70a",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.SY",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-03-20T00:58:51Z",
    "title_canon_sha256": "af1a90d19c9f86ee1bc08d1047f835b21c61e7b471eb3fb0ffd518c9207b88f2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.19545",
    "kind": "arxiv",
    "version": 2
  }
}