Reference-Frame Sweep¶
Test or assessment — instantiates Representation-Invariant Reasoning
Repeats analysis across selected frames or gauges to expose arbitrary-choice dependence.
A Reference-Frame Sweep deliberately recomputes an analysis across a range of arbitrary frame or gauge choices to see whether the conclusion moves. Its defining idea is sensitivity, not certification: rather than asserting that one transformation preserves an output, it varies the choice across many admissible frames and watches for drift, surfacing any hidden dependence on a convention that was supposed not to matter. Where a single check answers "is this output invariant under this transformation?", the sweep answers "does my conclusion secretly depend on a choice I made?" — and if the answer moves as the frame moves, it has found residual freedom leaking into the result. It owns two things: the enumerated family of frames it sweeps, and the register of how much the output varies across them.
Example¶
A quantitative analyst ranks three portfolios by risk-adjusted return and reports that Portfolio A is best. Before publishing, they run a reference-frame sweep on an arbitrary choice buried in the method: the base currency against which everything is valued. They recompute the entire ranking in USD, then EUR, then JPY, then a basket numéraire — the underlying holdings never change, only the currency the figures are quoted in. In USD and EUR, A wins. In JPY, B edges ahead. The conclusion depends on the base currency, which is supposed to be a mere unit of account, not a driver of the ranking.[n1] The sweep has exposed that the "risk-adjusted return" measure is not numéraire-invariant, so the recommendation rests on an arbitrary choice. The analyst now knows the ranking is not trustworthy as stated, and must either find a genuinely invariant measure or disclose the dependence — a flaw a single-frame computation would never have revealed.
How it works¶
- Identify the arbitrary choice to sweep. Name the convention that should not matter — base currency, coordinate origin, phase reference, gauge — and confirm the task treats it as free.
- Enumerate a representative family of frames. Choose a spread of admissible values wide enough to expose dependence, not just two nearby ones that might happen to agree.
- Recompute the whole conclusion in each. Run the analysis end-to-end in every frame, using a transformation law to move between them, and record the output each time.
- Register the variation. Summarize how much the conclusion moves across the sweep — stable, drifting, or flipping — and flag any dependence as residual freedom that has leaked into the result.
Tuning parameters¶
- Sweep breadth — how many frames and how far apart. A wide, coarse sweep exposes gross dependence cheaply; a dense sweep near a suspected boundary characterizes it precisely but costs more runs.
- Which choice to vary — one convention at a time isolates its effect; sweeping several together is efficient but muddies which one the conclusion depends on.
- Sensitivity threshold — how much output movement counts as "dependence." Too lax and a real leak reads as stable; too strict and benign numerical wobble looks like a flaw.
- Conclusion granularity — whether you watch a headline decision (which portfolio wins) or a full output vector; coarse watching catches decision flips, fine watching catches partial drift.
When it helps, and when it misleads¶
Its strength is discovery: it finds dependence you did not know to look for, because it varies the choice rather than asserting a property, and a conclusion that flips as an arbitrary convention changes is caught before it ships.
Its failure mode is a too-narrow sweep giving false confidence — testing two nearby frames that happen to agree and concluding invariance, when a wider spread would have exposed the leak. The mirror misuse is over-reading benign variation: treating last-digit numerical wobble as substantive dependence and discarding a conclusion that was actually sound. The guarding discipline is to choose frames that genuinely stress the suspected dependence, sweep wide before sweeping deep, and separate movement that crosses a decision boundary from movement that merely jitters within tolerance.
How it implements the components¶
admissible_transformation_system— it enumerates and applies the family of admissible frames it sweeps, defining the space of arbitrary choices under test.residual_freedom_register— its output is the record of how much the conclusion varies across that family, exposing residual dependence on a choice that should have been free.
It does not implement gauge_independence_test — the single declared-transformation pass/fail assertion is Invariance Property Test; the sweep varies the choice across a range rather than certifying one. Nor does it implement invariant_output_contract or invariance_failure_gate — the standing, over-time comparison and classification battery is Cross-Representation Regression Suite.
Related¶
- Instantiates: Representation-Invariant Reasoning — provides the archetype's sensitivity probe for hidden choice-dependence.
- Consumes: Coordinate or Basis Transformation — the transformation law used to move the analysis into each swept frame.
- Sibling mechanisms: Canonical Representative Selection · Coordinate or Basis Transformation · Cross-Representation Regression Suite · Gauge-Fixing Condition · Invariance Property Test · Invariant Observable Report · Patchwise Atlas and Transition Map · Quotient-Space Construction · Redundant-Variable Elimination
Editorial Notes¶
Form Classification¶
Form family: Analysis, Modeling & Optimization
Rationale: Reference-Frame Sweep operates as an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution because it repeats analysis across selected frames or gauges to expose arbitrary-choice dependence.
Independent corroboration: The frozen evidence defines Reference-Frame Sweep as 'Repeats analysis across selected frames or gauges to expose arbitrary-choice dependence', so its operative form is Analysis, Modeling & Optimization.
Nearest alternative: Experiment, Test & Rehearsal — Reference-Frame Sweep includes features of an active test, trial, simulation, drill, or rehearsal that generates evidence through a deliberate attempt or perturbation, but its defining operation is an analytical, modeling, inference, comparison, or optimization procedure that derives insight or a solution.
Review outcome: Independent reviewer agreement; medium confidence.
Origin Attribution¶
Primary origin: Physics
Origin pattern: Cross-disciplinary synthesis
Present-day reach: Multi-domain
Rationale: Repeating analysis across frames and gauges is canonical physical invariance testing.
Related originating lineages:
- Mathematics — Transformation groups materially formalize arbitrary-representation dependence.
Review resolution: Both blind reviewers agree that physics is the primary origin. Explicit reconciliation of domain reach disagreement adopts reviewer_a's classification because repeating analysis across frames and gauges is canonical physical invariance testing. The resulting lineage records alternates=mathematics, origin_mode=cross_disciplinary_synthesis, and domain_reach=multi_domain; these describe formative provenance separately from later applicability.
Review outcome: Reconciled after independent review; high confidence.
Notes¶
A sweep is a discovery instrument and an Invariance Property Test is a certification instrument, and they pair naturally: sweep first to find whether any dependence exists, then, once you believe an output is invariant, write a property test to lock that belief against regression. Using a sweep as if it certified invariance is the common error — a passing sweep only means none of the frames you happened to try moved the answer.
[n1] A numéraire is the unit of account against which other values are measured — a base currency or reference asset. A well-posed financial conclusion should be numéraire-invariant: changing the arbitrary base should not change which portfolio is judged better. Dependence on the numéraire signals the measure is conflating value with the unit it is quoted in. ↩