Kill Switches and Debts Owed

6.1 — Kill Switches

KS-22 [LIVE — EMPIRICAL] — Anomalous coherence persistence.

If a quantum system is shown to maintain coherence indefinitely in an environment where decoherence theory predicts exponential decay — with all known sources of environmental coupling accounted for, the factorisation assumptions of 3.3 satisfied, and no alternative explanation (such as decoherence-free subspaces or dynamical decoupling) — then the derivation’s claim that environmental record-writing universally and irreversibly suppresses coherence would be falsified.

Observable: coherence persistence (measured via interferometric visibility or off-diagonal density matrix elements) in a controlled environment where the 3.3 assumptions hold.

Note on spin echo and Loschmidt echo: these phenomena achieve partial reversal of dephasing in controlled subsystems.

Under the axioms, this is consistent with Axiom R if the “reversal” is understood as refocusing within a subsystem whose environmental records remain intact — the global monoid has not lost any records, but the accessible observable has been rotated to a basis where the dephasing is invisible.

This interpretation is consistent with current experiments but remains an interpretation, not a derivation.

If a spin echo or Loschmidt echo experiment is shown to genuinely reverse environmental records (not merely refocus subsystem observables), KS-22 fires. Here is the weapon: find the reversal. Status: LIVE.

KS-23 [LIVE — EMPIRICAL] — Quantum eraser record destruction.

Operational definition: in this paper, “record” means information redundantly encoded into many uncontrolled environmental degrees of freedom such that recovery would require an inverse in the record monoid — not a reversible correlation stored in a single controllable quantum degree of freedom (which can be unitarily unmarked without violating Axiom R).

The architecture predicts that in quantum eraser experiments, the which-path information is an irreversible record in this sense, and that “erasure” is basis rotation, not record destruction (4.3).

Operational criterion for falsification: if an experiment demonstrates that the unconditional (non-postselected) interference pattern is fully restored after which-path information has been redundantly encoded into uncontrolled environmental degrees of freedom — not merely that interference reappears in conditioned sub-ensembles, and not merely that a reversible which-path marking in a single controlled degree of freedom has been unitarily undone — then the which-path record has been genuinely destroyed in a way that violates Axiom R, and the architecture’s reading requires revision.

Note: reversible unmarking of a controlled which-path marker (e.g., a single polarisation qubit) does not trigger KS-23, because such a marker is not a “record” in the architecture’s sense.

Current experimental evidence (Scully et al., 1991; Walborn et al., 2002; Kim et al., 2000) is consistent with the basis-rotation interpretation: recovered interference appears only in postselected coincidence counts, not in the unconditional marginal distribution.

Here is the weapon: restore unconditional interference. Status: LIVE.

KS-24 [LIVE — HARD] — Quantum sector completeness.

If any foundational feature of quantum mechanics is identified that cannot be derived from or structurally identified with {S, B, R, C} plus EH and QRA (both proven, AP20), the completeness claim is falsified.

Known candidates for such features that are not yet addressed in the body of work: einselection (environment-induced pointer basis selection), quantum Darwinism (redundant environmental encoding of classical information), decoherence-free subspaces, and quantum error correction thresholds.

These are listed under Debts Owed below. Here is the weapon: find the feature. Status: LIVE.

6.2 — Debts Owed

The following components are used in this paper but not derived from {S, B, R, C}. They are imported from standard physics or assumed as physically motivated conditions.

Each is a debt that either must be discharged in a future AP or acknowledged as a standing limitation.

D1 — Factorisation assumption. 3.3 assumes the environmental Hilbert space decomposes into independent subsystems with factorised initial state and that interactions are sequential and approximately independent.

Standard in collisional decoherence models but not derived from the axioms. The monoid guarantees composition; it does not guarantee factorisation of the resulting overlaps.

D2 — Decoherence timescale. The quantitative expression for τ_D (3.4) is adopted from standard open quantum systems theory.

The axioms provide the structural mechanism (environmental record-writing under Axiom R) and the exponential form from the product of overlaps, but do not predict specific coupling strengths or interaction rates, which depend on microphysical details outside the axioms.

D3 — Quantum eraser interpretation. 4.3’s claim that record-erasure is basis rotation is an architectural prediction consistent with current experiments, not a derived result.

The formal characterisation of basis rotation within the monoid structure — specifically, whether it corresponds to a change of the homomorphism from the monoid to the observable algebra — is a debt owed.

D4 — Einselection (pointer basis selection). This paper derives that coherence is lost but does not address which states survive.

The environment-induced selection of preferred pointer states (Zurek, 2003) is a major component of the decoherence programme that is not yet derived or structurally identified within the record algebra.

The monoid structure may naturally select states that are eigenstates of the record-writing operation — suggestive but unproven.

D5 — Quantum Darwinism. The redundant encoding of classical information across multiple environmental fragments (Zurek, 2009) is not addressed.

The monoid naturally replicates records (composition produces multiple copies of correlated information) — suggestive but not formalised.

D6 — Scope of structural irreversibility. This paper claims decoherence is structurally irreversible (Axiom R: monoid has no inverse), upgrading the standard “practically irreversible” framing.

The bridge from “monoid has no inverse” to “no physical process can reverse the coherence loss” requires specifying the allowed dynamical class within which the no-reversal claim holds.

This paper asserts the bridge but does not provide a formal no-go theorem. The claim is: within any dynamics compatible with the record algebra, coherence loss from environmental record-writing is irreversible.

A formal proof would strengthen the paper; its absence is a debt.

Load-bearing status: 1 is structural (three regimes). 2 is the core identification (environment = accumulated record; structural identification, not derivation). 3 is the core argument (standard decoherence mechanism from AP09 + Axiom R for irreversibility, under stated assumptions). 4 is the consequence (classicality as saturated decoherence). 5 is the synthesis.