Pith Number

pith:5FI4JKCB

pith:2026:5FI4JKCBUDPXKODJC7GRV3HONL

not attested not anchored not stored refs resolved

Controlling Logical Collapse in LLMs via Algebraic Ontology Projection over F2

Hisashi Miyashita, Mgnite Inc

Projecting LLM hidden states into the F2 field under substitution constraints extracts ontological relations at up to 93 percent zero-shot accuracy.

arxiv:2605.12968 v1 · 2026-05-13 · cs.LG · cs.AI · cs.CL · cs.LO

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\usepackage{pith}
\pithnumber{5FI4JKCBUDPXKODJC7GRV3HONL}

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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

AOP achieves up to 93.33% zero-shot inclusion accuracy on unseen concept pairs (Gemma-2 Instruct with optimized prompt), with consistent 86.67% accuracy observed across multiple model families -- with no model tuning, but through prompt alone.

C2weakest assumption

That projecting hidden states into F2 under Liskov Substitution Principle constraints using only 42 relational pairs captures general ontological relations that transfer across models and tasks without post-hoc selection effects.

C3one line summary

Projecting LLM hidden states onto F2 algebra with 42 pairs yields 93% zero-shot accuracy on logical relations and identifies prompt-preventable late-layer collapse.

References

19 extracted · 19 resolved · 3 Pith anchors

[1] Understanding intermediate layers using linear classifier probes 2016 · arXiv:1610.01644

[2] Burke, Tristan Hume, Shan Carter, Tom Henighan, and Christopher Olah 2023

[3] Discovering latent knowledge in language models without supervision 2023

[4] Neural-Symbolic Cognitive Reasoning 2009

[5] Toy models of superposition 2022

Formal links

2 machine-checked theorem links

Cited by

1 paper in Pith

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Receipt and verification

First computed	2026-05-18T03:09:09.021256Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e951c4a841a0df75386917cd1aecee6ae81693ef8d4e626cc50fbb80a0e75f46

Aliases

arxiv: 2605.12968 · arxiv_version: 2605.12968v1 · doi: 10.48550/arxiv.2605.12968 · pith_short_12: 5FI4JKCBUDPX · pith_short_16: 5FI4JKCBUDPXKODJ · pith_short_8: 5FI4JKCB

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Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/5FI4JKCBUDPXKODJC7GRV3HONL \
  | 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: e951c4a841a0df75386917cd1aecee6ae81693ef8d4e626cc50fbb80a0e75f46

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "64506fa6ccb0e004d9062234e8d96cecc138cf8529c62c6ab6d4d3a450405868",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL",
      "cs.LO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-05-13T04:01:29Z",
    "title_canon_sha256": "0f15d3561f141e36102d714bd512efa5626787ff9d0f562edfdbd1b61df5f568"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12968",
    "kind": "arxiv",
    "version": 1
  }
}