Pith Number

pith:UIY6SKTG

pith:2025:UIY6SKTGPVFM7OYBEEP2A2CS4T

not attested not anchored not stored refs pending

On understanding and overcoming spectral biases of deep neural network learning methods for solving PDEs

Lulu Zhang, Wei Cai, Zhi-Qin John Xu

arxiv:2501.09987 v1 · 2025-01-17 · math.NA · cs.NA

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UIY6SKTGPVFM7OYBEEP2A2CS4T}

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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

2 papers in Pith

A Greedy PDE Router for Blending Neural Operators and Classical Methods

On the Convergence Behavior of Preconditioned Gradient Descent Toward the Rich Learning Regime

Receipt and verification

First computed	2026-07-05T10:02:14.386793Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a231e92a667d4acfbb01211fa06852e4c637561cc62bd475577478e909dea8a1

Aliases

arxiv: 2501.09987 · arxiv_version: 2501.09987v1 · doi: 10.48550/arxiv.2501.09987 · pith_short_12: UIY6SKTGPVFM · pith_short_16: UIY6SKTGPVFM7OYB · pith_short_8: UIY6SKTG

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/UIY6SKTGPVFM7OYBEEP2A2CS4T \
  | 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: a231e92a667d4acfbb01211fa06852e4c637561cc62bd475577478e909dea8a1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d064b0ba09b9d2b69974ab7d538745c0b6adcdbbe08ccd654de9f3486affac1",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-01-17T06:56:51Z",
    "title_canon_sha256": "41b1d213c939a9b5288318ed57ac1babb8f112030cdf7c8a6298f0bc02f814d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.09987",
    "kind": "arxiv",
    "version": 1
  }
}