Pith Number

pith:744N4LUM

pith:2025:744N4LUM3IPDI4EGWQ5BGTVUIY

not attested not anchored not stored refs pending

Prediction error certification for PINNs: Theory, computation, and application to Stokes flow

Benjamin Unger, Birgit Hillebrecht

arxiv:2508.07994 v1 · 2025-08-11 · math.NA · cs.LG · 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{744N4LUM3IPDI4EGWQ5BGTVUIY}

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.

Cited by

1 paper in Pith

Reliable Error Estimation for PINNs: Lower and Upper A Posteriori Bounds

Receipt and verification

First computed	2026-07-05T11:52:06.260446Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ff38de2e8cda1e347086b43a134eb4461e45be7e0fff82cbd558641771531172

Aliases

arxiv: 2508.07994 · arxiv_version: 2508.07994v1 · doi: 10.48550/arxiv.2508.07994 · pith_short_12: 744N4LUM3IPD · pith_short_16: 744N4LUM3IPDI4EG · pith_short_8: 744N4LUM

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/744N4LUM3IPDI4EGWQ5BGTVUIY \
  | 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: ff38de2e8cda1e347086b43a134eb4461e45be7e0fff82cbd558641771531172

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2212800aed5c9c4f6882132a4d10339d0f1153484241b124c05d8cd495ea53d4",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-08-11T13:57:02Z",
    "title_canon_sha256": "a20ed49f5026ef90079106745e7b5f6f42360068465d7f7c72446fc5534371d7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2508.07994",
    "kind": "arxiv",
    "version": 1
  }
}