module module high

`IndisputableMonolith.Papers.DraftV1`

Papers.DraftV1 states the central paper theorem that the induced map from the recognition quotient C_R to the observable space E is injective. Researchers formalizing uniqueness properties in Recognition Science would cite this module for its assembly of the core claim. The module imports Alexander duality to secure D=3, the composition module for the refinement theorem, and the quotient construction, then records the injectivity result without a self-contained proof body.

claimThe induced map $R̄ : C_R → E$ is injective, where $C_R = C/∼$ is the recognition quotient obtained by collapsing configurations indistinguishable under the recognizer and $E$ is the space of observables.

background

The module imports three upstream components to support its statement. Alexander duality supplies the topological foundation that non-trivial circle linking in the D-sphere exists if and only if D = 3, replacing a prior definitional tautology with a proof from reduced cohomology axioms. Recognition Geometry Composition develops composite recognizers and establishes the Refinement Theorem. Recognition Geometry Quotient constructs the recognition quotient C_R = C/~ where ~ is the indistinguishability relation that collapses configurations the recognizer cannot separate.

proof idea

This module imports the topological, compositional, and quotient foundations and states the injectivity claim; it contains no proof bodies or tactic scripts of its own. The argument structure therefore rests entirely on the upstream results: Alexander duality for the dimension constraint, the refinement theorem from composition, and the quotient construction that defines C_R.

why it matters in Recognition Science

The module records the injectivity result that serves as the paper's central uniqueness statement in the Recognition framework. It assembles the T0-T8 forcing chain elements and the recognition composition law into a single declarative claim, though the snapshot lists no direct downstream uses. The statement fills the paper proposition on the induced map R̄ being injective.

scope and limits

Does not contain a self-contained proof of the injectivity claim.
Does not extend the result beyond the assumptions of the three imported modules.
Does not address numerical checks against the alpha band or mass ladder.
Does not derive further consequences such as synchronization or Kepler principles.

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Foundation.AlexanderDuality module_import
IndisputableMonolith.RecogGeom.Composition module_import
IndisputableMonolith.RecogGeom.Quotient module_import

declarations in this module (28)

theorem injectivity_of_observable_map L36
theorem refinement L43
def syncPeriod L55
lemma syncPeriod_def L57
theorem syncPeriod_eq_mul L61
theorem synchronization_selection_principle L71
theorem syncPeriod_3_eq_360 L119
theorem sync_resource_functional_minimized L128
def apsidalAngle L148
theorem kepler_selection_principle L153
def ConstraintS L207
def ConstraintK L211
theorem constraintS_forces_D3 L216
theorem constraintS_iff_D3 L223
def AlexanderDualityForCircleHypothesis L245
def LinkingInvariantHypothesis L250
def RGConditionsForDualityHypothesis L258
theorem rg_conditions_for_duality L260
def CentralPotentialDerivationHypothesis L265
theorem rg_derivation_of_central_potentials L267
def RobustnessHypothesis L272
theorem robustness_of_D3_signature L274
def AlexanderDualityApplies L279
def LinkingSelectionPrincipleHypothesis L286
theorem linking_selection_principle L289
theorem dimensional_rigidity_main L298
theorem dimensional_rigidity_full_forward L309
theorem no_higher_dimensional_alternative L317