Pith Number

pith:OZ2TXWJN

pith:2023:OZ2TXWJNI5TCWCG7FV4MOUE2QD

not attested not anchored not stored refs pending

A Mathematical Guide to Operator Learning

Alex Townsend, Nicolas Boull\'e

arxiv:2312.14688 v1 · 2023-12-22 · math.NA · cs.AI · cs.LG · cs.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{OZ2TXWJNI5TCWCG7FV4MOUE2QD}

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

6 papers in Pith

Patnaik-Pearson intrinsic dimension for internal representations of neural networks

Operator learning for the 2D incompressible Navier-Stokes equations: a conformal prediction approach in the data-scarce regime

Is Zero-Shot Super-Resolution Possible in Operator Learning?

Scalable Mechanistic Neural Networks for Differential Equations and Machine Learning

Receipt and verification

First computed	2026-07-05T10:55:17.838716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76753bd92d47662b08df2d78c7509a80e87c96b02df67ca949aaeb4525832b07

Aliases

arxiv: 2312.14688 · arxiv_version: 2312.14688v1 · doi: 10.48550/arxiv.2312.14688 · pith_short_12: OZ2TXWJNI5TC · pith_short_16: OZ2TXWJNI5TCWCG7 · pith_short_8: OZ2TXWJN

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/OZ2TXWJNI5TCWCG7FV4MOUE2QD \
  | 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: 76753bd92d47662b08df2d78c7509a80e87c96b02df67ca949aaeb4525832b07

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "485d420532827b0a0ff31bbbd702195d5de7672a77f7a65a7cb80f3b06c8d177",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2023-12-22T13:43:57Z",
    "title_canon_sha256": "e6b4ba0bb98a35a1000c8928bac951ad9ffb0a605bd4277539d45ea780a6c5ec"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2312.14688",
    "kind": "arxiv",
    "version": 1
  }
}