Pith Number

pith:ZWRBBPI5

pith:2024:ZWRBBPI5SYP3GLKKUFCXD3NGEY

not attested not anchored not stored refs pending

The geometry of the deep linear network

Govind Menon

arxiv:2411.09004 v1 · 2024-11-13 · cs.NE · math.DS · math.PR · nlin.AO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ZWRBBPI5SYP3GLKKUFCXD3NGEY}

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

4 papers in Pith

Patnaik-Pearson intrinsic dimension for internal representations of neural networks

Rapid mixing for Gibbs measures in Riemannian manifolds

Geodesics in the Deep Linear Network

Receipt and verification

First computed	2026-07-05T09:35:18.286339Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cda210bd1d961fb32d4aa14571eda62624937786ed4a44dd219cf244319f6fa8

Aliases

arxiv: 2411.09004 · arxiv_version: 2411.09004v1 · doi: 10.48550/arxiv.2411.09004 · pith_short_12: ZWRBBPI5SYP3 · pith_short_16: ZWRBBPI5SYP3GLKK · pith_short_8: ZWRBBPI5

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/ZWRBBPI5SYP3GLKKUFCXD3NGEY \
  | 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: cda210bd1d961fb32d4aa14571eda62624937786ed4a44dd219cf244319f6fa8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "024c77fc59feae948b95812dff65a322dc9059ca228734d2fd26bbbde0f245ad",
    "cross_cats_sorted": [
      "math.DS",
      "math.PR",
      "nlin.AO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.NE",
    "submitted_at": "2024-11-13T20:15:50Z",
    "title_canon_sha256": "fcd9e49d1906576c6fb3d0d175d49650f1c355644c0dafd5f9ffef27fa081484"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.09004",
    "kind": "arxiv",
    "version": 1
  }
}