Pith Number

pith:GN4EIQPD

pith:2026:GN4EIQPDQ5OUFMVAFM3US2WZIJ

not attested not anchored not stored refs pending

The Implicit Bias of Depth: From Neural Collapse to Softmax Codes

Christos Thrampoulidis, Connall Garrod, Jonathan P. Keating

arxiv:2605.23087 v1 · 2026-05-21 · 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{GN4EIQPDQ5OUFMVAFM3US2WZIJ}

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	2026-05-25T02:01:37.767686Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

33784441e3875d42b2a02b37496ad94254e8a6e70554f37b148c6925dbbdeb36

Aliases

arxiv: 2605.23087 · arxiv_version: 2605.23087v1 · doi: 10.48550/arxiv.2605.23087 · pith_short_12: GN4EIQPDQ5OU · pith_short_16: GN4EIQPDQ5OUFMVA · pith_short_8: GN4EIQPD

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/GN4EIQPDQ5OUFMVAFM3US2WZIJ \
  | 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: 33784441e3875d42b2a02b37496ad94254e8a6e70554f37b148c6925dbbdeb36

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4e6ff8e049f6ddb9d20f8310c43b7645cffac51b2209dc608a0cf54ffc30895f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-21T22:37:25Z",
    "title_canon_sha256": "a5e3b25622eea58dfcdf0212fb0bb334519a2a0d3951610dcb0b98a000aa50b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.23087",
    "kind": "arxiv",
    "version": 1
  }
}