Pith Number

pith:LD45Q32X

pith:2025:LD45Q32XXKEKISXTASJVSEPG46

not attested not anchored not stored refs pending

Probing Spectrum-Like Organization of States of Mind in Transformer Representation Spaces

Sophie Zhao

Transformer embeddings recover annotated cognitive energy scores and seven-tier labels above chance

arxiv:2512.22227 v3 · 2025-12-23 · cs.CL · cs.LG

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LD45Q32XXKEKISXTASJVSEPG46}

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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.

Claims

C1strongest claim

transformer embedding spaces exhibit statistically significant geometric organization aligned with the annotated cognitive structure.

C2weakest assumption

The human annotations of energy scores and seven-tier cognitive progression accurately capture stable, human-interpretable cognitive attributes rather than surface linguistic features or annotator bias.

C3one line summary

Transformer sentence embeddings linearly recover continuous energy scores and seven-tier cognitive labels from 480 annotated sentences, with UMAP showing a coherent low-to-high gradient.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-07-03T01:16:50.632579Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

58f9d86f57ba88a44af304935911e6e7ae738cc43df6ad21c0cae6aa41b4c522

Aliases

arxiv: 2512.22227 · arxiv_version: 2512.22227v3 · doi: 10.48550/arxiv.2512.22227 · pith_short_12: LD45Q32XXKEK · pith_short_16: LD45Q32XXKEKISXT · pith_short_8: LD45Q32X

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/LD45Q32XXKEKISXTASJVSEPG46 \
  | 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: 58f9d86f57ba88a44af304935911e6e7ae738cc43df6ad21c0cae6aa41b4c522

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "267e18b119e299ec4fb1efe73cb2eb66113f8b3bc0bde9176753a603f9dfcf1b",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CL",
    "submitted_at": "2025-12-23T03:37:34Z",
    "title_canon_sha256": "9c950d8e2d49be72b729ee8cd134f92b5189afc75d29d4d6ec6fb09ba2bd8f0f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.22227",
    "kind": "arxiv",
    "version": 3
  }
}