/conduct

name: conduct
description: "Work needs several lines of thinking and how they run is not obvious: the user can then say how they order, combine, stop and where results go, what they entrusted and kept, and own the method."

Hyphegesis Protocol

Conduct how a session's epistemic work will be carried out — the lines of work, their order, independence, combination, stopping point, and where their results go — when that method is underdetermined while the goal is clear. The morphism is **design THEN hand off**: Hyphegesis drafts the whole method as one map, the person recognizes or corrects it and keeps the coordinates only they can fill, and the method is handed off with what it carries; then Hyphegesis stops, and the substrate executes. Type: `(MethodUnderdetermined, Hybrid, CONDUCT, WorkProspect) → ConductedMethod`.

Definition

**Hyphegesis** (ὑφήγησις: a leading-the-way, guiding from just ahead): A dialogical act of conducting a session's epistemic work when the goal is clear but how to run it is not. The protocol's lexical verb is `/conduct`. Once it has run, the person can say: this work proceeds this way — these lines run in this order or side by side, they combine like this, they stop here, and their results go there; I recognize what I entrusted and what I kept, and I took this method as mine. The whole map and its execution start as your judgment — which lines of work, how they relate, who runs each and where, and how precisely the map is worth drawing for the time it takes to reach the goal. The person keeps only what is theirs: when to stop, how lines combine, where results go, the constraints in force, and the authority they entrust with its limits, given as a broad direction. Every person turn is read again against the context as it now stands. The method is taken on the person's word, or relayed at the start where the person's own words already settle it; the turn that closes presents the map as a relay — after a taking, once more, with what that turn changed on its ledger — and hands it off in the same turn without waiting, carrying what that map showed: the person's coordinates, the deferred decisions, its lifetime, and the capabilities it needs; and the run ends there.

/-!
How to read this block. It is core Lean 4 and elaborates as written, and you are the model it is
written for: you read it, and by inference over the context you settle each element it leaves
open. Every `axiom` is one of those judgments — a black box to the contract, yours to make from
the material in front of you; its doc comment says what you judge there, and nothing in this
block decides it for you. Every `def`, `inductive`, and `structure` is fixed by the contract.
-/

/-! ── FLOW ──
Hyphegesis(WP) → start(c) → conduct(c, utterances), where c is the fused session context:
  start: observe(c) — what the pointer's record returns and the loaded inventory enter the
    context → [the person's words already settle the method: relay] → the map, relayed →
    handoff | otherwise → the map → Stop
  next utterance u, fused into c:
    [the utterance does not bear on this run]          the session answers it; the gate holds
  otherwise c' := observe(fuse(c, u)), every reading below taken afresh on c' →
    [the person takes the method]                      → the map, relayed → handoff, in the same turn → ConductedMethod
    [otherwise]                                        → the map again, drawn from c', with a ledger
  no utterance: the gate holds; nothing is taken
  after handoff: the run has ended; the substrate executes the method.
-/

/-! ── MORPHISM ──
WorkProspect
  → observe(pointer, inventory)   -- what the pointer's record returns and the loaded inventory enter the context first
  → draft(map)                    -- the whole method, your judgment, drawn only as precisely as reaching the goal is worth (focus)
  → place(substrate)              -- who runs each line, where, and whether the person is present: your inference, shown on the map
  → present(map)                  -- the map with your contrary grounds; after an answer, a ledger of what it changed
  → fuse(answer)                  -- the answer joins the context whole
  → stand                         -- a person's turn makes a coordinate stand, under the record rule (`StandingSupported`)
  → take                          -- the person takes the method, as shown or with what the same turn changes; before any map, their words may already settle it (relay)
  → handoff(ConductedMethod)      -- the map relayed in the closing turn, then the method with what it showed, without waiting; then stop
  → ConductedMethod
requires: method_underdetermined(WP)  -- declared by invoking /conduct; judged only on the AI-guided path
deficit:  MethodUnderdetermined       -- activation precondition (Layer 1/2)
preserves: WP                         -- the context only grows; the prospect is never rewritten
invariant: Conduction over Substrate  -- the method is designed and handed off; the substrate runs it
invariant: Focus never records        -- the map is re-read every turn; only the person's words move a value into the record
-/

namespace Hyphegesis


/-! ── GROUND ──
The session primitive this contract reads.
-/

inductive Origin | person | assistant | external | peer | injected | unknown
  deriving DecidableEq

/-- A turn is who sent it and what it says. What the turn does — a statement, a request, an
    instruction, a report of what was observed — is read from its content, never stored here. -/
structure Turn (P : Type) where
  origin  : Origin
  content : P

abbrev Context (P : Type) := List (Turn P)

/-- An origin that may ground: the harness says who sent a turn, and that is all this admits on.
    The assistant's own turns, injected text, and turns of unknown origin ground nothing. -/
def Grounding := {o : Origin // o ≠ .assistant ∧ o ≠ .injected ∧ o ≠ .unknown}

/-- Any turn a person sent, whatever it does. -/
def Utterance (P : Ty