Pith Number

pith:VZXOLTMW

pith:2026:VZXOLTMW27YMODBF5FRR35GQXR

not attested not anchored not stored refs pending

Elliptic Regularity Theory in Barron Spaces and Applications to the Deep Ritz Method

Stephan Wojtowytsch

arxiv:2607.25100 v1 · 2026-07-27 · math.AP · cs.NA · math.NA · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VZXOLTMW27YMODBF5FRR35GQXR}

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	2026-07-29T00:25:02.663616Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ae6ee5cd96d7f0c70c25e9631df4d0bc4e42d72eb3b24c44843f1193b7d2ee37

Aliases

arxiv: 2607.25100 · arxiv_version: 2607.25100v1 · doi: 10.48550/arxiv.2607.25100 · pith_short_12: VZXOLTMW27YM · pith_short_16: VZXOLTMW27YMODBF · pith_short_8: VZXOLTMW

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/VZXOLTMW27YMODBF5FRR35GQXR \
  | 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: ae6ee5cd96d7f0c70c25e9631df4d0bc4e42d72eb3b24c44843f1193b7d2ee37

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "faf69945dc73c40922e10207a5997f56ad5d1bdd7b4002fd086ffb2004418d80",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2026-07-27T21:58:13Z",
    "title_canon_sha256": "c781efcb6b9a4113782fbb43a46b0a928c568f961af9fc7bfd3dafea64252e67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.25100",
    "kind": "arxiv",
    "version": 1
  }
}