Pith Number

pith:WIW2LS2U

pith:2025:WIW2LS2UMP3NGIGXFX5DAVL7FP

not attested not anchored not stored refs pending

PINN-DG: Residual neural network methods trained with Finite Elements

Charalambos G. Makridakis, Georgios Grekas, Tristan Pryer

arxiv:2507.03521 v2 · 2025-07-04 · 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{WIW2LS2UMP3NGIGXFX5DAVL7FP}

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	2026-07-05T11:34:11.310128Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b22da5cb5463f6d320d72dfa30557f2bf2e974f2fe2d0837b91d9f378a9142a4

Aliases

arxiv: 2507.03521 · arxiv_version: 2507.03521v2 · doi: 10.48550/arxiv.2507.03521 · pith_short_12: WIW2LS2UMP3N · pith_short_16: WIW2LS2UMP3NGIGX · pith_short_8: WIW2LS2U

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/WIW2LS2UMP3NGIGXFX5DAVL7FP \
  | 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: b22da5cb5463f6d320d72dfa30557f2bf2e974f2fe2d0837b91d9f378a9142a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26317497aef63ebbe51f6133d949cf5e82fbf8481cbfd923424e0ec90dc792b1",
    "cross_cats_sorted": [
      "cs.NA",
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-04T12:16:57Z",
    "title_canon_sha256": "23138810fad3269a6097e748a0eaf19c1741bc978cec854eb707267063839e8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.03521",
    "kind": "arxiv",
    "version": 2
  }
}