IndisputableMonolith.Skeleton.Quantum

   1import IndisputableMonolith.Quantum.BornRule
   2import IndisputableMonolith.Quantum.PureTwoQubit.EntropyConcurrence
   3import IndisputableMonolith.Quantum.CommutationStructure
   4
   5/-!
   6# Skeleton chapter: Quantum mechanics from recognition
   7
   8What is proved: the Born rule is forced from J-cost (not postulated), and entanglement
   9entropy is positive exactly when concurrence is. What is honestly still a target: the
  10canonical commutator `[x,p]=iℏ`. The recognition root of non-commutativity is the ℤ/8
  11clock-shift Weyl relation (`Quantum.RecognitionFirst.EightTickWeyl`), which is currently
  12SORRY-bearing, the open D3 keystone the recog-physics loop is grinding. The postulated
  13QM bridge objects (`RSHilbertSpace`, `LedgerToHilbert`, `RHatCorrespondence`) are MODELs to
  14be derived, not theorems.
  15-/
  16
  17namespace IndisputableMonolith
  18namespace Skeleton
  19
  20/-- **The Born rule is forced by J-cost.**
  21The DFT-8 sector measure `Σ‖ψ_k‖²` is the unique probability assignment consistent with
  22normalization, phase invariance, additivity, and calibration, derived from recognition cost,
  23not assumed as von Neumann's Axiom 3. Tier: THEOREM. Drill down: `Quantum.BornRule`,
  24`Foundation.BornRuleForcing`. -/
  25alias guidepost_born_rule_forced :=
  26  IndisputableMonolith.Quantum.BornRule.born_rule_from_jcost
  27
  28/-- **Entanglement entropy is positive iff concurrence is.**
  29For pure two-qubit states, Wootters concurrence > 0 implies strictly positive von Neumann
  30entanglement entropy: entanglement is detected by a recognition-cost-compatible invariant.
  31Tier: THEOREM. Drill down: `Quantum.PureTwoQubit.EntropyConcurrence`. -/
  32alias guidepost_entanglement_entropy_positive :=
  33  IndisputableMonolith.Quantum.PureTwoQubit.EntropyConcurrence.pure_two_qubit_entropy_positive_unconditional
  34
  35/-- **Measurement commutation reduces to projector idempotency.**
  36The available commutation content is `P∘P = P` (projector idempotency). This is honest
  37scaffolding: it is NOT yet the canonical commutator `[x,p]=iℏ`, which remains the open D3
  38keystone (the ℤ/8 Weyl relation). Tier: THEOREM (idempotency only). Drill down:
  39`Quantum.CommutationStructure`, `Quantum.RecognitionFirst.EightTickWeyl` (the open target). -/
  40alias guidepost_projector_idempotency :=
  41  IndisputableMonolith.Quantum.CommutationStructure.commutation_structure
  42
  43end Skeleton
  44end IndisputableMonolith
  45