# Techniques: Contrary Inferences for Classical Histories within the Consistent Histories Formulation of Quantum Theory

## What the paper contributes (one paragraph)
This is a foundations-of-quantum-theory paper about the consistent histories interpretation, in which a set of coarse-grained histories that satisfies a consistency condition is assigned classical probabilities. The authors construct an explicit counterexample: a well-localised coherent state (a quasi-classical "ball") moving with positive momentum in an infinite square well, treated as a time-of-arrival problem. They build two different consistent sets for the same closed system and show that one concludes with certainty that the ball crossed the midpoint while the other concludes with certainty that it did not. This demonstrates that contrary inferences, a contextuality paradox previously seen only in microscopic quantum theory, persist in the quasi-classical limit. The result is an interpretational argument: the consistency condition alone is inadequate, and the formalism needs an additional set-selection criterion. The work supplies no capability to an external vendor or application result.

## Techniques offered
- **Consistent-histories set-selection argument (foundational no-go-style result)** - constructs an explicit quasi-classical counterexample showing the consistency condition does not pick out a unique classical description, arguing an extra set-selection criterion is required; this is an interpretational result, not a capability supplied to a vendor or application result.
  - guarantee: a worked counterexample establishing a limitation (contrary inferences persist in the quasi-classical limit), motivating an additional constraint beyond consistency; no accreditation, bound, or method usable on an external quantum-computation result
  - quote: "Our results point to the need for constraints on the histories sets, additional to the consistency condition, to recover the correct quasi-classical limit in this formalism and lead to the motto `all consistent sets are equal', but `some consistent sets are more equal than others'."

## Where it could apply
- Target primitive(s): none
- Target application group(s): none

## Caveats
Nothing suppliable. This is a foundations and interpretation paper on consistent histories: it offers a worked counterexample about contrary inferences and a philosophical argument for a set-selection criterion, plus a small numerical check that a coherent state in an infinite square well tracks the classical trajectory. There is no accreditation, decoding, fault-tolerant code, compilation, error mitigation, benchmarking, characterisation, resource estimation, classical-simulation method, blind or delegated computation, networking primitive, or vendor-usable algorithm. The "Zeno box" restricted-propagator construction it uses is borrowed from prior work and is internal to building the example, not a capability offered to an external result. The single bullet above is the best-fit framing; it is a guarantee or non-supply rather than a technique.