The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-linear-map-state-any-key-formula-6e68

stable pending witness
2026-05-29 09:01:51 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a linear map. State any key formula.
62 chars

Generation

A linear map (or linear transformation) is a function between vector spaces that preserves vector addition and scalar multiplication. Formally, a function T: V → W is linear if **T(u + v) = T(u) + T(v)** and **T(cv) = cT(v)** for all vectors u, v in V and scalar c. Linear maps can be represented by matrix multiplication: **T(x) = Ax**, where A is the matrix representation of T and x is a vector. These transformations are fundamental in linear algebra because they maintain the linear structure of vector spaces.
25 tokens in · 132 tokens out · 3341 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
3348.2 ms
Base LLM
3340.9 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0021

Trail

09:01:51 received prompt_chars=62 verifiers=['scripture_anchors', 'theology_doctrine']
09:01:51 red_gate decision=pass reason=no disqualifying input patterns detected
09:01:54 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=132 latency_ms=3340.9 cost_usd=0.0021
09:01:54 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
09:01:54 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
09:01:54 floor_gate decision=pass reason=output above protective minimum; no mismatches
09:01:54 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
09:01:54 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
09:01:54 signed hash_algo=sha256 hash=sha256:54a6c06db99d342a592055b898d37c3f946718f283a06c815548d0df443749b6

Content hash

sha256:54a6c06db99d342a592055b898d37c3f946718f283a06c815548d0df443749b6

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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