-- Lutar/Gate/InternalFeedback.lean
-- A37 InternalFeedbackIntegrity
-- Citation: Hickok, Houde, Rong (2011). Sensorimotor integration in speech processing:
-- Computational basis and neural organization. Neuron 69, 407-422.
-- DOI: 10.1016/j.neuron.2011.01.019
--
-- Authored by Yachay (CTO), SZL Holdings. Co-Authored-By: Perplexity Computer Agent.
-- Doctrine v11 LOCKED 749/14/163 · Λ Conjecture 1 · SLSA L1 honest · ADDITIVE only
--
-- Interpretation:
--   Hickok's state feedback control architecture requires that an agent's
--   internal feedback loop checks the *predicted* sensory consequence of a planned
--   action against the *sensory target* before the action executes.
--   When this loop is damaged (conduction aphasia), motor plans and outputs can
--   appear intact while the checking mechanism is broken.
--
--   In SZL a11oy: SafeToExecute holds iff the PAC-Bayes Governance Head's
--   predicted sensory consequence is within epsilon of the observed actual consequence.
--   The Conduction-Aphasia Detector (conduction_aphasia.py) provides the LIVE
--   evaluator for this anchor (status: live, severity: enforced).
--
-- Proof status: ts-only (TypeScript + Python evaluator live; Lean proof scheduled
-- for Doctrine v12). The `sorry` is honest: this stub documents the INTENT.

namespace Lutar.Gate

-- Abstract types (concrete implementations live in conduction_aphasia.py)
opaque Sensory : Type
opaque SafeToExecute : Prop
opaque dist : Sensory → Sensory → Float

-- A37 InternalFeedbackIntegrity (live, enforced)
-- An action may execute only when dist(predicted, target) <= epsilon.
theorem internal_feedback_intact
    (predicted target : Sensory) (ε : Float) (h : dist predicted target ≤ ε) :
    SafeToExecute := by
  sorry  -- ts-only; proof scheduled for Doctrine v12

-- A36 DualStreamRoutingAxiom (ts-only, advisory)
-- Every a11oy tick routes through exactly one of {dorsal, ventral}, never both, never neither.
-- Citation: Hickok & Poeppel 2007, Nat Rev Neurosci 8:393-402. DOI 10.1038/nrn2113
inductive Stream : Type where
  | dorsal  : Stream   -- action / repetition / sensorimotor
  | ventral : Stream   -- meaning / comprehension / lexical
  deriving DecidableEq

opaque Tick : Type
opaque stream_of : Tick → Stream

axiom dual_stream_routing : ∀ (t : Tick),
    (stream_of t = Stream.dorsal ∧ ¬(stream_of t = Stream.ventral)) ∨
    (stream_of t = Stream.ventral ∧ ¬(stream_of t = Stream.dorsal))

-- A38 HierarchicalLinearizationRoundTrip (ts-only, advisory)
-- Receipt chain linearization is lossless: recover(linearize(h)) = h
-- Citation: Hickok 2025, Wired for Words (MIT Press); C-STAR lecture 2026
opaque Hierarchy : Type
opaque linearize : Hierarchy → List Hierarchy
opaque recover : List Hierarchy → Hierarchy

theorem hier_linearization_round_trip
    (h : Hierarchy) : recover (linearize h) = h := by
  sorry  -- ts-only; proof scheduled for Doctrine v12

end Lutar.Gate