Pith Number

pith:XHZW6YV7

pith:2026:XHZW6YV7MS5FDDLWL2DEH42PFL

not attested not anchored not stored refs pending

Neural operator preconditioning from mixed dataset for the Helmholtz equations: Application to transcranial ultrasound

Yanfei Xiang

arxiv:2607.16906 v1 · 2026-07-18 · 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{XHZW6YV7MS5FDDLWL2DEH42PFL}

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	2026-07-21T01:21:04.741719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9f36f62bf64ba518d765e8643f34f2af88e272506fc99f8198f7ebc5c6014bf

Aliases

arxiv: 2607.16906 · arxiv_version: 2607.16906v1 · doi: 10.48550/arxiv.2607.16906 · pith_short_12: XHZW6YV7MS5F · pith_short_16: XHZW6YV7MS5FDDLW · pith_short_8: XHZW6YV7

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/XHZW6YV7MS5FDDLWL2DEH42PFL \
  | 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: b9f36f62bf64ba518d765e8643f34f2af88e272506fc99f8198f7ebc5c6014bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "964e550720886ed8f50c282b1e5e0f2ae115b4aa30518e1fc9175e03bbeb855d",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-18T17:48:59Z",
    "title_canon_sha256": "709a2b5cf885ba2b5930bf4a289a02bc2d89c9c187f1e683dafc0ae9ba8cb203"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.16906",
    "kind": "arxiv",
    "version": 1
  }
}