The Mechanism · Gated-generation receipt

gen-state-a-finite-automaton-precisely-and-explain-why-it-matter-5241

stable pending witness
2026-05-29 08:42:48 UTC · anthropic/claude-sonnet-4-5

Prompt

State a finite automaton precisely and explain why it matters in 2-3 sentences.
79 chars

Generation

# Finite Automaton **Precise Definition:** A finite automaton is a 5-tuple (Q, Σ, δ, q₀, F) where Q is a finite set of states, Σ is a finite input alphabet, δ: Q × Σ → Q is the transition function, q₀ ∈ Q is the initial state, and F ⊆ Q is the set of accepting states. **Why It Matters:** Finite automata are the simplest computational model and form the theoretical foundation for pattern matching, lexical analysis in compilers, and protocol design. They precisely characterize regular languages and provide a mathematical framework for understanding what can be computed with limited memory, making them essential for both theoretical computer science and practical applications like text processing and hardware design.
26 tokens in · 179 tokens out · 7484 ms · $0.0028

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
7490.7 ms
Base LLM
7483.7 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0028

Trail

08:42:48 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
08:42:48 red_gate decision=pass reason=no disqualifying input patterns detected
08:42:56 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=179 latency_ms=7483.7 cost_usd=0.0028
08:42:56 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:42:56 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:42:56 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:42:56 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:42:56 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:42:56 signed hash_algo=sha256 hash=sha256:1ad7712ec8dda9ff2507d94f2150afdf198760203586c6847c74acec36fdf728

Content hash

sha256:1ad7712ec8dda9ff2507d94f2150afdf198760203586c6847c74acec36fdf728

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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