Pith Number

pith:XHAVVRZW

pith:2025:XHAVVRZW52IAQUACEDIKJNCZDM

not attested not anchored not stored refs pending

Understanding Learning Invariance in Deep Linear Networks

Guido Mont\'ufar, Hao Duan

arxiv:2506.13714 v1 · 2025-06-16 · stat.ML · cs.LG · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XHAVVRZW52IAQUACEDIKJNCZDM}

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

Equivariance and Augmentation for Bayesian Neural Networks

Conservation Laws from Data Symmetry in Neural Networks

Receipt and verification

First computed	2026-07-05T11:22:25.421502Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9c15ac736ee9008500220d0a4b4591b3032d74566cccdd24666588a1a5b18c7

Aliases

arxiv: 2506.13714 · arxiv_version: 2506.13714v1 · doi: 10.48550/arxiv.2506.13714 · pith_short_12: XHAVVRZW52IA · pith_short_16: XHAVVRZW52IAQUAC · pith_short_8: XHAVVRZW

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/XHAVVRZW52IAQUACEDIKJNCZDM \
  | 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: b9c15ac736ee9008500220d0a4b4591b3032d74566cccdd24666588a1a5b18c7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "82d77191cda0a7f97fe2c1048f9cc74f94649f4a6a27f3674e1a7b3c513a3944",
    "cross_cats_sorted": [
      "cs.LG",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2025-06-16T17:24:07Z",
    "title_canon_sha256": "af585bda2ba4a6dbea0feb729a0e16ba4885e342a6465976acfbe88827c57b61"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.13714",
    "kind": "arxiv",
    "version": 1
  }
}