Pith Number

pith:LT5HK574

pith:2025:LT5HK574FDYZSMHXQVCYXETJGV

not attested not anchored not stored refs pending

Expansive Natural Neural Gradient Flows for Energy Minimization

Wolfgang Dahmen, Wuchen Li, Yuankai Teng, Zhu Wang

arxiv:2507.13475 v1 · 2025-07-17 · math.OC · cs.NA · math.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{LT5HK574FDYZSMHXQVCYXETJGV}

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

2 papers in Pith

Global Convergence and Error Propagation in Neural Gradient Flows: A Riemannian Optimization Framework

A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions

Receipt and verification

First computed	2026-07-05T11:39:18.020054Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cfa7577fc28f19930f785458b9269355993a19b7d461d566c05f47089c5768a

Aliases

arxiv: 2507.13475 · arxiv_version: 2507.13475v1 · doi: 10.48550/arxiv.2507.13475 · pith_short_12: LT5HK574FDYZ · pith_short_16: LT5HK574FDYZSMHX · pith_short_8: LT5HK574

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/LT5HK574FDYZSMHXQVCYXETJGV \
  | 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: 5cfa7577fc28f19930f785458b9269355993a19b7d461d566c05f47089c5768a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e1142dc6b9e325d928dde12b6f6be603319f0f837a14d0b6686ff8d82f6420c",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2025-07-17T18:35:11Z",
    "title_canon_sha256": "04a701a3417a0a88e0bf0cc0d21b4b68453143ff4d3e4504dcb4b8a3f9e96f28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.13475",
    "kind": "arxiv",
    "version": 1
  }
}