Pith Number

pith:AU2E7YK6

pith:2026:AU2E7YK6UHB2HTP2SB3CVDKBGT

not attested not anchored not stored refs pending

A Function-Space Dichotomy for Compositional Learning: Exponential Sub-Optimality of the Neural Tangent Kernel

Arkaprabha Ganguli, Emil Constantinescu

arxiv:2607.06382 v1 · 2026-07-07 · stat.ML · cs.LG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AU2E7YK6UHB2HTP2SB3CVDKBGT}

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.

Receipt and verification

First computed	2026-07-08T01:19:23.795752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

05344fe15ea1c3a3cdfa90762a8d4134c42aa0145b700de70fda721f74946031

Aliases

arxiv: 2607.06382 · arxiv_version: 2607.06382v1 · doi: 10.48550/arxiv.2607.06382 · pith_short_12: AU2E7YK6UHB2 · pith_short_16: AU2E7YK6UHB2HTP2 · pith_short_8: AU2E7YK6

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/AU2E7YK6UHB2HTP2SB3CVDKBGT \
  | 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: 05344fe15ea1c3a3cdfa90762a8d4134c42aa0145b700de70fda721f74946031

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "44dac5c8a260e59335d21a2d555fe8b8bf47cb4241ddaf74f146a757e4a493f3",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "stat.ML",
    "submitted_at": "2026-07-07T15:21:20Z",
    "title_canon_sha256": "743f2f9d7a4af86e4c080c18b866cd6e9f056e5ef236642b8290559aa3fe8ce6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.06382",
    "kind": "arxiv",
    "version": 1
  }
}