Pith Number

pith:7RHEK5WT

pith:2025:7RHEK5WTQDQRKVQZHBHFVSKUUT

not attested not anchored not stored refs pending

Mixed-precision iterative refinement for low-rank Lyapunov equations

Peter Benner, Xiaobo Liu

arxiv:2510.02126 v2 · 2025-10-02 · math.NA · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7RHEK5WTQDQRKVQZHBHFVSKUUT}

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	2026-05-18T03:10:12.099573Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc4e4576d380e1155619384e5ac954a4e1a432f6eaa88506d53455d8efa05636

Aliases

arxiv: 2510.02126 · arxiv_version: 2510.02126v2 · doi: 10.48550/arxiv.2510.02126 · pith_short_12: 7RHEK5WTQDQR · pith_short_16: 7RHEK5WTQDQRKVQZ · pith_short_8: 7RHEK5WT

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/7RHEK5WTQDQRKVQZHBHFVSKUUT \
  | 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: fc4e4576d380e1155619384e5ac954a4e1a432f6eaa88506d53455d8efa05636

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90adf5df0b37deccc29994043c5c6d29ca6bea2b3a43407584747f87e01e0fa6",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-10-02T15:35:44Z",
    "title_canon_sha256": "352d9ad8b2ceac2b9309fddb8efb3da771fb8cd49a45793ddd9241d67cad1cc1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2510.02126",
    "kind": "arxiv",
    "version": 2
  }
}