Foundation Maximal Forcing Reality Closure Session Update Protocol

The session protocol

A session update protocol is a formal checklist for how work on a research program may advance. In the Recognition Science framework, the program is called Maximal Forcing Closure: the attempt to show that every claim in a given universe is either forced by the framework's principles, independent of them, or selected by a named principle. The protocol does not assert that this program has succeeded. It states, as a machine-checked structure, that any legitimate session must land at least one of four kinds of progress: a new forced invariant, a new independence witness, a tightening of admissibility, or an updated execution plan naming the exact remaining blocker.

The point of the protocol is to make the research process itself a formal object. Instead of a vague promise to work on the problem, each session must produce a concrete, checkable artifact. A forced invariant is a claim shown to follow necessarily from the framework's principles. An independence witness is an explicit countermodel showing a claim is not forced. Tightening admissibility means narrowing the class of claims under consideration. Updating the execution plan means stating precisely what remains to be done. The protocol requires that any session do at least one of these four things, so progress is always measurable.

The protocol is deliberately conditional about the program's ultimate goal. The crown theorem, which would assert that every claim in the closure is forced, independent, or selected, is not proved. Instead, the framework states the exact certificate whose construction would prove it: a function that classifies every claim in the closure. The session protocol is the interface for building that certificate step by step. It concedes no contingency lazily: even the classification of a claim as independent or selected carries a proof obligation, not an excuse.

What the protocol does not claim is as important as what it claims. It does not assert that the Maximal Forcing Closure program has been completed, nor that any particular claim has been classified. It does not claim that the framework's principles are consistent, nor that the certificate exists. It does not even claim that a session which lands progress has produced a correct classification; it only guarantees that the session has produced some form of progress. The protocol is a discipline, not a result.

/-- Session protocol: closing a session on this program means either adding a
new forced invariant, adding an independence witness, tightening admissibility,
or updating the execution plan with the exact remaining blocker. -/
structure SessionUpdateProtocol where
  landed_forced_invariant : Prop
  landed_independence_witness : Prop
  tightened_admissibility : Prop
  updated_execution_plan : Prop
  nonempty_progress :
    landed_forced_invariant ∨
    landed_independence_witness ∨
    tightened_admissibility ∨
    updated_execution_plan

/-- Crown theorem in the exact disjunction form: given a classifier certificate,
every claim in the forcing closure is `Forced`, `Independent`, or `Selected`.
This is the literal "as forced as possible" statement; it concedes no contingency
lazily, because `Independent` and `Selected` are themselves proof obligations
(an explicit countermodel witness and a named selection principle, respectively).
-/
theorem maximal_forcing_closure_trichotomy
    {P : Primitive} {U : ClaimUniverse.{u}} (cert : MaximalClosureCert P U)
    (C : RealityClaim U.Realization) (hC : InClosure P U C) :
    Forced U.admissibility.admissible C ∨
    Independent U.admissibility.admissible C ∨
    Selected U.admissibility.admissible C := by
  rcases cert.classifies C hC with h | hw | hs
  · exact Or.inl h
  · exact Or.inr (Or.inl (independent_of_witness hw))
  · exact Or.inr (Or.inr hs)

/-- A maximal closure certificate for a primitive and claim universe. -/
structure MaximalClosureCert (P : Primitive) (U : ClaimUniverse.{u}) where
  classifies :
    forall C : RealityClaim U.Realization,
      InClosure P U C -> ClaimClassification U C

What this page does not claim

The Maximal Forcing Closure program has been completed. Any particular claim has been classified as forced, independent, or selected. The framework's principles are consistent.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Foundation/MaximalForcing/RealityClosure.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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