Pith Number

pith:K4KXYQM3

pith:2025:K4KXYQM3SSL6OR22ZX7RQUUA2F

not attested not anchored not stored refs pending

An entropy formula for the Deep Linear Network

Govind Menon, Tianmin Yu

arxiv:2509.09088 v3 · 2025-09-11 · cs.LG · math.DG · math.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{K4KXYQM3SSL6OR22ZX7RQUUA2F}

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

Geometric and Spectral Alignment for Deep Neural Network I

Receipt and verification

First computed	2026-05-22T01:03:15.471375Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

57157c419b9497e7475acdff185280d15a0bf1475ea7467ac6043158a92f2762

Aliases

arxiv: 2509.09088 · arxiv_version: 2509.09088v3 · doi: 10.48550/arxiv.2509.09088 · pith_short_12: K4KXYQM3SSL6 · pith_short_16: K4KXYQM3SSL6OR22 · pith_short_8: K4KXYQM3

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/K4KXYQM3SSL6OR22ZX7RQUUA2F \
  | 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: 57157c419b9497e7475acdff185280d15a0bf1475ea7467ac6043158a92f2762

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0c43c607c44a215cd75bcada54f2f08d67bb8631d7fc08f8c61f4e011e1c3e27",
    "cross_cats_sorted": [
      "math.DG",
      "math.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2025-09-11T01:40:46Z",
    "title_canon_sha256": "56ef74985779b9345f8e247ab89dec7df6d35634b672842a22ceb67ca0402bda"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.09088",
    "kind": "arxiv",
    "version": 3
  }
}