Pith Number

pith:XRUAAMWU

pith:2026:XRUAAMWUOR4RBHSLJ73ISN3VOV

not attested not anchored not stored refs pending

Reliability-Aware Hard--Soft Physics-Informed Neural Networks for Robust Learning of Challenging Partial Differential Equations

Dinh Gia Ninh, Duc Tien Nguyen, Hang Tran, Nguyen Duc Manh, Trinh Minh Tuan

arxiv:2607.19377 v1 · 2026-07-01 · math.NA · cs.LG · cs.NA · physics.flu-dyn

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XRUAAMWUOR4RBHSLJ73ISN3VOV}

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	2026-07-23T00:23:46.869289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bc680032d47479109e4b4ff6893775755adcd32a810bcb0179e05f7ae5712fb3

Aliases

arxiv: 2607.19377 · arxiv_version: 2607.19377v1 · doi: 10.48550/arxiv.2607.19377 · pith_short_12: XRUAAMWUOR4R · pith_short_16: XRUAAMWUOR4RBHSL · pith_short_8: XRUAAMWU

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/XRUAAMWUOR4RBHSLJ73ISN3VOV \
  | 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: bc680032d47479109e4b4ff6893775755adcd32a810bcb0179e05f7ae5712fb3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95d137b38cbfed6369a160f80df209a8837de609f99a584e6e9ada6ed9357f20",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-07-01T01:21:04Z",
    "title_canon_sha256": "11f0c13a74ebeb468f67acd05c20c3a1a6225b23d95240a019114aa13eddbbcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.19377",
    "kind": "arxiv",
    "version": 1
  }
}