Pith Number

pith:KRPIWLB5

pith:2026:KRPIWLB5W3TUNG57DOOOBTPJ46

not attested not anchored not stored refs pending

Neural Collapse Is Forbidden: Information Floors in Language Models

Bruno Abrahao

arxiv:2607.09487 v1 · 2026-07-10 · cs.LG · cs.CL · stat.ML

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KRPIWLB5W3TUNG57DOOOBTPJ46}

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	2026-07-13T01:20:13.358105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

545e8b2c3db6e7469bbf1b9ce0cde9e7b716fce2c7aca74274d945a0c7060e18

Aliases

arxiv: 2607.09487 · arxiv_version: 2607.09487v1 · doi: 10.48550/arxiv.2607.09487 · pith_short_12: KRPIWLB5W3TU · pith_short_16: KRPIWLB5W3TUNG57 · pith_short_8: KRPIWLB5

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/KRPIWLB5W3TUNG57DOOOBTPJ46 \
  | 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: 545e8b2c3db6e7469bbf1b9ce0cde9e7b716fce2c7aca74274d945a0c7060e18

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8bd50ec055c7b7c5ef958c7a742046703a980b277670faa9ce93c22fd8d3f83",
    "cross_cats_sorted": [
      "cs.CL",
      "stat.ML"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-07-10T15:04:02Z",
    "title_canon_sha256": "1ef49a6e5d2e6b18c16bda570e6d4f89645b933695480c0bdccfdd46103fec96"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2607.09487",
    "kind": "arxiv",
    "version": 1
  }
}