Pith Number

pith:COUQ6OIQ

pith:2026:COUQ6OIQ2YDCWRXVHSUW35EZKS

not attested not anchored not stored refs pending

Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing

Anxin Guo, Jingwei Li

Even with perfect data and training, limited capacity forces LLMs to assign high confidence to some non-facts

arxiv:2602.00906 v7 · 2026-01-31 · cs.LG · cs.AI · cs.CL · cs.DS · cs.IT · math.IT

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\usepackage{pith}
\pithnumber{COUQ6OIQ2YDCWRXVHSUW35EZKS}

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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

even with optimal training, perfect data, and a simplified closed world setting, the information-theoretically optimal strategy under limited capacity is not to abstain or forget, but to assign high confidence to some non-facts, resulting in hallucination.

C2weakest assumption

The regime in which facts are sparse in the universe of plausible claims, together with the modeling choice that unifies discrete Bloom-filter error with continuous log-loss under a single rate-distortion objective.

C3one line summary

Hallucinations are the space-optimal behavior for limited-capacity models performing membership testing on sparse facts, as shown by a rate-distortion theorem that equates optimal memory use to minimum KL divergence between fact and non-fact score distributions.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-02T01:03:41.727527Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13a90f3910d6062b46f53ca96df49954b8fd9a643c7b6c3a10203f560440d1fd

Aliases

arxiv: 2602.00906 · arxiv_version: 2602.00906v7 · doi: 10.48550/arxiv.2602.00906 · pith_short_12: COUQ6OIQ2YDC · pith_short_16: COUQ6OIQ2YDCWRXV · pith_short_8: COUQ6OIQ

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/COUQ6OIQ2YDCWRXVHSUW35EZKS \
  | 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: 13a90f3910d6062b46f53ca96df49954b8fd9a643c7b6c3a10203f560440d1fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ded0d6a9ce377f077ab0fd83b96766f8267820895964baf8db5a43b51069eaf6",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.CL",
      "cs.DS",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-31T21:18:28Z",
    "title_canon_sha256": "09c1a2f0b896d2323af97c5dfd4a990494b8d768f3a2d1265f5a5f067db8c74b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.00906",
    "kind": "arxiv",
    "version": 7
  }
}