The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-principle-of-compositionality-s-2f06

stable pending witness
2026-05-29 06:33:28 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the principle of compositionality. State any key formula.
83 chars

Generation

The principle of compositionality states that the meaning of a complex expression is determined by the meanings of its constituent parts and the rules used to combine them. This principle, often attributed to Frege, can be formalized as: **meaning(α ∘ β) = f(meaning(α), meaning(β))**, where ∘ represents a syntactic combination operation and f is the corresponding semantic composition function. It underlies most formal approaches to semantics and allows for the systematic interpretation of infinitely many sentences from a finite vocabulary. Compositionality explains how humans can understand novel sentences they've never encountered before.
28 tokens in · 134 tokens out · 4708 ms · $0.0021

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
4714.8 ms
Base LLM
4707.7 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0021

Trail

06:33:28 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
06:33:28 red_gate decision=pass reason=no disqualifying input patterns detected
06:33:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=134 latency_ms=4707.7 cost_usd=0.0021
06:33:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:33:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:33:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:33:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:33:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:33:32 signed hash_algo=sha256 hash=sha256:e606ad8c387f93a363511766096af8d5b9df66f6ea496a4149c90ecb7cf675ae

Content hash

sha256:e606ad8c387f93a363511766096af8d5b9df66f6ea496a4149c90ecb7cf675ae

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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