Pith Number

pith:5XUYLWIX

pith:2026:5XUYLWIXJVOQUG2NQRXU7TK5DK

not attested not anchored not stored refs pending

Adjoint Method versus Physics-Informed Neural Networks in PDE-Constrained Inverse Problems

Alessandro Alla, George Em Karniadakis, Zhen Zhang

arxiv:2606.12337 v1 · 2026-06-10 · 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{5XUYLWIXJVOQUG2NQRXU7TK5DK}

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	2026-06-11T01:11:02.478850Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ede985d9174d5d0a1b4d846f4fcd5d1a9f424fe2583bc238a90ab4d83a8b53ac

Aliases

arxiv: 2606.12337 · arxiv_version: 2606.12337v1 · doi: 10.48550/arxiv.2606.12337 · pith_short_12: 5XUYLWIXJVOQ · pith_short_16: 5XUYLWIXJVOQUG2N · pith_short_8: 5XUYLWIX

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/5XUYLWIXJVOQUG2NQRXU7TK5DK \
  | 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: ede985d9174d5d0a1b4d846f4fcd5d1a9f424fe2583bc238a90ab4d83a8b53ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a3c174b4a31d4c41f463bbfe0c326af1c9b698540c14e9f87755d86ee60effdb",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-06-10T17:07:09Z",
    "title_canon_sha256": "a8fe7abd1d697e98a44158333dcca4e5c8b03b50fc653ce28b19abaaaa6e295a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.12337",
    "kind": "arxiv",
    "version": 1
  }
}