Pith Number

pith:DIYWAHXR

pith:2024:DIYWAHXRM5CQI67XOXFSVIK26E

not attested not anchored not stored refs pending

Deep Ritz-Finite Element methods: Neural Network Methods trained with Finite Elements

Charalambos G. Makridakis, Georgios Grekas

arxiv:2409.08362 v4 · 2024-09-12 · math.NA · cs.NA · physics.comp-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{DIYWAHXRM5CQI67XOXFSVIK26E}

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	2026-07-05T10:09:47.760831Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1a31601ef16745047bf775cb2aa15af107bfa06ed38924c219182f058410b5e4

Aliases

arxiv: 2409.08362 · arxiv_version: 2409.08362v4 · doi: 10.48550/arxiv.2409.08362 · pith_short_12: DIYWAHXRM5CQ · pith_short_16: DIYWAHXRM5CQI67X · pith_short_8: DIYWAHXR

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/DIYWAHXRM5CQI67XOXFSVIK26E \
  | 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: 1a31601ef16745047bf775cb2aa15af107bfa06ed38924c219182f058410b5e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "de36dbeb601caf026a52f005ec873a1bf069beeaf8469247620551943c38851a",
    "cross_cats_sorted": [
      "cs.NA",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-09-12T18:56:21Z",
    "title_canon_sha256": "6ff77f1b2946f084645e10d49f2dea16e40e346952b1d325da2e5bc58c804b4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2409.08362",
    "kind": "arxiv",
    "version": 4
  }
}