Pith Number

pith:667CMDK5

pith:2026:667CMDK5PMCT7O5DFSVGNPTUCF

not attested not anchored not stored refs pending

When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning

Hugo Melchers, Michael Abdelmalik, Victorita Dolean

arxiv:2605.19867 v1 · 2026-05-19 · 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{667CMDK5PMCT7O5DFSVGNPTUCF}

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	2026-05-20T01:06:18.288792Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7be260d5d7b053fbba32caa66be74116464f16548f70d2be8778043948b1455

Aliases

arxiv: 2605.19867 · arxiv_version: 2605.19867v1 · doi: 10.48550/arxiv.2605.19867 · pith_short_12: 667CMDK5PMCT · pith_short_16: 667CMDK5PMCT7O5D · pith_short_8: 667CMDK5

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/667CMDK5PMCT7O5DFSVGNPTUCF \
  | 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: f7be260d5d7b053fbba32caa66be74116464f16548f70d2be8778043948b1455

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0d91c096d41f88974e263e4cf3e563bfa0f34e1025726bf1e5853cea25d3265",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-19T13:58:31Z",
    "title_canon_sha256": "129e8d262e3a5eff097fa3f438d90eecf8a25aa8a1fc03ad0e78cd916453481c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.19867",
    "kind": "arxiv",
    "version": 1
  }
}