Pith Number

pith:SCGAG3PD

pith:2026:SCGAG3PDOJ53LU3A2L6OLS6CPK

not attested not anchored not stored refs pending

Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guarantees

Amartya Mukherjee, David C. Del Rey Fernández, Jun Liu, Maxwell Fitzsimmons

arxiv:2603.19165 v1 · 2026-03-19 · cs.LG · math.AP · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{SCGAG3PDOJ53LU3A2L6OLS6CPK}

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	2026-07-02T08:42:25.892927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

908c036de3727bb5d360d2fce5cbc27aa31a12357b4b1956c0cee7541c9cd4f3

Aliases

arxiv: 2603.19165 · arxiv_version: 2603.19165v1 · doi: 10.48550/arxiv.2603.19165 · pith_short_12: SCGAG3PDOJ53 · pith_short_16: SCGAG3PDOJ53LU3A · pith_short_8: SCGAG3PD

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/SCGAG3PDOJ53LU3A2L6OLS6CPK \
  | 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: 908c036de3727bb5d360d2fce5cbc27aa31a12357b4b1956c0cee7541c9cd4f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71142a7dfecad20f7ea8503114dae942801dc8a464bcd3cb413d1f526aa6876d",
    "cross_cats_sorted": [
      "math.AP",
      "math.FA"
    ],
    "license": "",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-03-19T17:19:48Z",
    "title_canon_sha256": "aedf7bff3e5007ccdb082f301b8d33204c564c9e15046daac6aa73dbfce2b06f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.19165",
    "kind": "arxiv",
    "version": 1
  }
}