Pith Number

pith:GUI372PF

pith:2026:GUI372PFNR7OV5N6YSCO44JFJR

not attested not anchored not stored refs pending

What Makes a Representational Prior Work? Feature Families, Label-Free Invariances, and Critical Windows in Grokking

Gunner Levi Howe

arxiv:2607.12735 v1 · 2026-07-14 · 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{GUI372PFNR7OV5N6YSCO44JFJR}

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	2026-07-15T01:22:14.950274Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3511bfe9e56c7eeaf5bec484ee71254c7800909d6dc8f91918fe0b53c52039cd

Aliases

arxiv: 2607.12735 · arxiv_version: 2607.12735v1 · doi: 10.48550/arxiv.2607.12735 · pith_short_12: GUI372PFNR7O · pith_short_16: GUI372PFNR7OV5N6 · pith_short_8: GUI372PF

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/GUI372PFNR7OV5N6YSCO44JFJR \
  | 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: 3511bfe9e56c7eeaf5bec484ee71254c7800909d6dc8f91918fe0b53c52039cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3849fc2796bd5cb3374cd9ae1d82ce6e06a0181dae58e8a64eb714fe5d92b63",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-14T13:06:44Z",
    "title_canon_sha256": "0583cec37b50fa46f456ae6f202495a7d6b267b3f347c56766f1429516f1e3a6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.12735",
    "kind": "arxiv",
    "version": 1
  }
}