The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-bits-versus-nats-state-any-key-form-02ab

stable pending witness
2026-05-29 08:38:44 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain bits versus nats. State any key formula.
66 chars

Generation

Bits and nats are different units for measuring information, differing only in the logarithm base used. Bits use base-2 logarithms (log₂), while nats use natural logarithms (ln or logₑ). The key conversion formula is: **1 nat = log₂(e) ≈ 1.443 bits**, or equivalently, **1 bit = ln(2) ≈ 0.693 nats**. For example, the information content of an event with probability p is -log₂(p) bits or -ln(p) nats.
26 tokens in · 141 tokens out · 3277 ms · $0.0022

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
3283.8 ms
Base LLM
3277.0 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0022

Trail

08:38:44 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
08:38:44 red_gate decision=pass reason=no disqualifying input patterns detected
08:38:47 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=141 latency_ms=3277.0 cost_usd=0.0022
08:38:47 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:38:47 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:38:47 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:38:47 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:38:47 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:38:47 signed hash_algo=sha256 hash=sha256:e5a78b4910e610ff7d3df76f2dca618061770a97128acdeccefa6a1aaa1b55d3

Content hash

sha256:e5a78b4910e610ff7d3df76f2dca618061770a97128acdeccefa6a1aaa1b55d3

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.

Bring another teaching · Run a discernment