Pith Number

pith:VXQLT3YI

pith:2026:VXQLT3YIXVHC5WPTELFC22AP7V

not attested not anchored not stored refs pending

Beyond Neural Collapse: Task-Intrinsic Geometry Governs Neural Representations in Modular Arithmetic

Hu Tan, Kuo Gai, Shihua Zhang

arxiv:2606.08985 v1 · 2026-06-08 · 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{VXQLT3YIXVHC5WPTELFC22AP7V}

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	2026-06-09T02:07:51.985556Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ade0b9ef08bd4e2ed9f322ca2d680ffd47d7e9e1ddd96e599eae5faf5814e63b

Aliases

arxiv: 2606.08985 · arxiv_version: 2606.08985v1 · doi: 10.48550/arxiv.2606.08985 · pith_short_12: VXQLT3YIXVHC · pith_short_16: VXQLT3YIXVHC5WPT · pith_short_8: VXQLT3YI

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/VXQLT3YIXVHC5WPTELFC22AP7V \
  | 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: ade0b9ef08bd4e2ed9f322ca2d680ffd47d7e9e1ddd96e599eae5faf5814e63b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "635762ce4c629703336658e726d8e3ebc990c3c000c2823089830c52079d6cc5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-06-08T03:30:56Z",
    "title_canon_sha256": "128a758e1e132ac7738bd5deef9bee9e9310797c1b14ff0c3477be524459ff52"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2606.08985",
    "kind": "arxiv",
    "version": 1
  }
}