Pith Number

pith:ATF6CZJP

pith:2020:ATF6CZJPRY3BKTWZGU57UHXWHP

not attested not anchored not stored refs pending

Two-Layer Neural Networks for Partial Differential Equations: Optimization and Generalization Theory

Haizhao Yang, Tao Luo

arxiv:2006.15733 v2 · 2020-06-28 · math.NA · cs.LG · cs.NA · math.OC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ATF6CZJPRY3BKTWZGU57UHXWHP}

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.

Cited by

1 paper in Pith

Parameterized Representations via Implicit Stochastic Modulation for High-Dimensional and High-Order Neural PDE Solvers

Receipt and verification

First computed	2026-07-05T01:58:41.417036Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

04cbe1652f8e36154ed9353bfa1ef63bd880e9640b06996e74fdd1241fccc0fc

Aliases

arxiv: 2006.15733 · arxiv_version: 2006.15733v2 · doi: 10.48550/arxiv.2006.15733 · pith_short_12: ATF6CZJPRY3B · pith_short_16: ATF6CZJPRY3BKTWZ · pith_short_8: ATF6CZJP

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/ATF6CZJPRY3BKTWZGU57UHXWHP \
  | 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: 04cbe1652f8e36154ed9353bfa1ef63bd880e9640b06996e74fdd1241fccc0fc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "80bcb03b77c82876d082cd302d0e32c863a18d9c426eb4c50e070f54f1fe84c7",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA",
      "math.OC"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2020-06-28T22:24:51Z",
    "title_canon_sha256": "15a106cc7f1881f26aa1fc64bd5f9283c4ff0f08ef63777856a40d5ffac7fcbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.15733",
    "kind": "arxiv",
    "version": 2
  }
}