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Cross-Dimensional Leakage

Prime #
766
Origin domain
Statistics & Experimental Design
Subdomain
measurement and construct validity → Statistics & Experimental Design

Core Idea

Cross-dimensional leakage is the structural pattern in which a single shared source of variance — a channel, instrument, rater, batch, common method, or common shock — contaminates multiple supposedly-independent output dimensions, inflating their apparent correlations above the true cross-dimensional signal and biasing any analysis that reads channel-derived covariance as evidence about the underlying sources. The output dimensions appear to measure or generate multiple distinct things, but the measurement or generation channel is silently sharing one source of variance across all of them, so the cross-dimensional correlations are partly an artefact of the channel rather than a property of the underlying sources. Naive analysis treats the inflated correlations as substantive findings; structural analysis treats them as diagnostics for shared-channel variance to be partitioned out.

The pattern admits a factor decomposition: each measured output y_i is generated by a true underlying source t_i plus a shared channel factor c (loading λ_i on each output) plus noise. The naive covariance cov(y_i, y_j) is inflated by λ_i · λ_j · var(c) beyond the true cov(t_i, t_j). The decisive structural fact is that channel-shared variance has the same statistical signature as substantive cross-dimensional covariance: from a single channel's data the two are indistinguishable. Resolution therefore requires either an independent second channel (orthogonal measurement) or a strong prior on the factor structure (explicit modelling) — which is exactly why multi-trait/multi-method designs, factor models, multi-batch designs, and randomisation work where naive correlation analysis fails. The structural commitments are: multiple supposedly-independent output dimensions sharing a channel; a single shared-variance source affecting all of them; inflated apparent cross-dimensional covariance; and a naive analysis that reads the channel-derived covariance as a substantive cross-source relation.

How would you explain it like I'm…

The Same Wobbly Ruler

Imagine you measure several different things, but you use the same wobbly ruler for all of them. When the ruler wobbles, ALL your measurements wobble together, so they look like they go up and down as a team even when the real things don't. A Cross-Dimensional Leakage is when one shared wobble sneaks into many measurements and makes them look more connected than they really are.

Fake Togetherness

Suppose you measure several things that are supposed to be separate, but they all share one common source, like the same machine, the same rater, or the same batch. If that one shared thing changes, it nudges all your measurements at once, so they seem to move together even when the real things underneath don't. That fake togetherness can fool you into thinking you found a real connection. Cross-Dimensional Leakage is when a single shared source of variation contaminates many supposedly-independent measurements and puffs up how correlated they look.

Shared-Channel Contamination

Cross-dimensional leakage is when a single shared source of variation — one instrument, one rater, one batch, one common method — secretly affects several outputs that are supposed to be independent, making them look more correlated than they really are. The catch is that this channel-driven correlation has the exact same statistical fingerprint as a genuine relationship between the underlying things, so from one channel's data alone you literally cannot tell them apart. Imagine measuring several students' heights with a tape measure that's stretched: all the heights come out wrong together, so they seem to move in lockstep even if the true heights don't. Naively you'd report this as a real finding; structurally it's a warning sign of shared-channel contamination. The only fixes are an independent second channel or a strong model of the structure — which is exactly why multi-method designs and randomization work where naive correlation fails.

 

Cross-Dimensional Leakage is the structural pattern in which a single shared source of variance (a channel, instrument, rater, batch, common method, or common shock) contaminates multiple supposedly-independent output dimensions, inflating their apparent correlations above the true cross-dimensional signal and biasing any analysis that reads channel-derived covariance as evidence about the underlying sources. The output dimensions appear to measure or generate multiple distinct things, but the channel is silently sharing one source of variance across all of them, so the cross-dimensional correlations are partly an artifact of the channel rather than a property of the underlying sources. Naive analysis treats the inflated correlations as substantive findings; structural analysis treats them as diagnostics for shared-channel variance to be partitioned out. The pattern admits a factor decomposition: each measured output y_i is generated by a true underlying source t_i plus a shared channel factor c (with loading lambda_i) plus noise, and the naive covariance between y_i and y_j is inflated by lambda_i times lambda_j times the variance of c beyond the true covariance of t_i and t_j. The decisive fact is that channel-shared variance has the same statistical signature as substantive cross-dimensional covariance: from a single channel's data the two are indistinguishable. Resolution therefore requires either an independent second channel (orthogonal measurement) or a strong prior on the factor structure (explicit modeling), which is exactly why multi-trait/multi-method designs, factor models, multi-batch designs, and randomization work where naive correlation analysis fails.

Structural Signature

the multiple supposedly-independent output dimensions — the single shared-variance source (channel) feeding all of them — the per-dimension loading of the channel onto each output — the inflated apparent cross-dimensional covariance — the statistical indistinguishability of channel variance from substantive covariance — the partitioning move requiring an orthogonal channel or a factor prior

A configuration exhibits cross-dimensional leakage when each of the following holds:

  • Multiple output dimensions. Several quantities are measured or generated and treated as if they index distinct underlying sources: traits, survey items, features, genes, economic series, voxels.
  • A shared channel. A single common source of variance — an instrument, rater, batch, method, or common shock — feeds into all of those output dimensions rather than into one in isolation.
  • Per-dimension loadings. The channel couples to each output with its own strength, so each measured output decomposes into a true source term, a channel term scaled by its loading, and noise.
  • Inflated cross-covariance. The apparent covariance between any two outputs is lifted above the true cross-source covariance by the product of their channel loadings times the channel variance — an artefact of the shared channel, not a property of the sources.
  • Statistical indistinguishability. From a single channel's data, channel-injected covariance and substantive cross-source covariance have the same signature and cannot be told apart; the contamination is structural, so it does not average out with more same-channel data.
  • The partitioning requirement. Resolution requires either an independent second channel (orthogonal crossing) or a strong factor prior (explicit modelling), after which the residual cross-dimensional structure reveals whether the pattern was artefact or substance.

The components compose so that a tight cross-dimensional correlation observed through one channel is exactly what shared-channel variance produces, making inflated correlation a trigger for suspicion rather than a finding — and making channel-crossing, not larger samples, the only remedy.

What It Is Not

  • Not escape_and_leakage. That prime is about confined material crossing a boundary out of its region; this is about shared variance contaminating multiple output dimensions through a common measurement channel. The shared "channel" metaphor is coincidental, not the same structure.
  • Not confounding. A confound is a real third cause acting on the constructs themselves; here the shared variance is introduced by how the dimensions are measured (instrument, rater, batch), not by what drives them. They have the same statistical signature but live at different layers.
  • Not correlation. Correlation is the bare statistical relation; this prime is a specific generative story for why an observed correlation is inflated above the true cross-source signal — a diagnosis, not a measure.
  • Not synergy_and_antagonism. That concerns genuine interaction between sources; cross-dimensional leakage produces apparent relations that are channel artefact, vanishing under channel-crossing rather than reflecting any real interaction.
  • Not stochastic noise. Random error averages out with sample size; channel-shared variance is structural, has a mean structure, and does not diminish with more same-channel data — the defining contrast.
  • Common misclassification. Reading a tight cross-dimensional correlation measured through one channel as a substantive finding. The collect-more-data reflex treats it as stochastic; catch it by asking what single channel feeds all the dimensions and whether an orthogonal channel has ever confirmed the relation.

Broad Use

  • Social cognition: the halo effect — a single overall impression of a person contaminates ratings of distinct traits (intelligence, warmth, competence).
  • Measurement and instrumentation: a single instrument's drift, calibration error, or operator effect contaminates multiple measured quantities; multi-trait/multi-method matrix designs were built to separate trait from method variance.
  • Survey methodology: common-method bias — one questionnaire rated at one sitting by one respondent inflates cross-item correlations beyond what the true cross-construct relations imply.
  • Machine learning: a confounding feature correlated with the target inflates the apparent importance of other features that co-vary with it; importance diagnostics partially reveal but cannot fully resolve this without experimental decoupling.
  • Genomics: batch effects — assay-batch variance contaminates apparent biological signal across many genes at once; correction methods were built specifically to partition this leakage.
  • Macroeconometrics: a common shock (oil prices, monetary policy) contaminates apparent cross-sectoral or cross-country relations; factor models partition out the common component.
  • Reputation and neuroimaging: an organisation's reputation halo contaminates ratings of unrelated products; scanner drift and physiological noise inflate apparent functional connectivity across voxel time series.

Clarity

The label distinguishes the channel-level shared-variance contamination from the substrate-level vocabulary — halo, common method, batch effect, common shock — that names each instance separately and so obscures their identity. Naive analyses treat correlations between output dimensions as substantive findings about the underlying constructs; the cross-dimensional-leakage lens reveals an entire layer of shared-channel variance that must be partitioned out before the substantive question can even be posed. The clarifying separation is between covariance that lives in the sources (cov(t_i, t_j)) and covariance injected by the shared channel (λ_i · λ_j · var(c)), two quantities with the same statistical appearance and very different meanings. Naming the pattern makes the diagnostic question routine across substrates — "what is the shared channel here, and how is it contaminating my apparent cross-dimensional pattern?" — and exposes a recurring inferential trap in which inflated correlations are reported as substantive structure precisely because the channel that produced them was never modelled. Once the channel is named as a separable variable, the analyst can suspect it before crediting the cross-dimensional finding.

Manages Complexity

The pattern compresses a heterogeneous set of substrate-specific methodologies — multi-trait/multi-method matrices, batch-correction algorithms, factor models, halo correction, common-method-bias adjustment, scanner-drift regression, feature-importance auditing — into one structural problem with one solution shape: cross the measurement channel with something else, then partition the variance. The intervention catalogue ports across substrates. Cross the channel with an independent second channel: multi-method designs, independent ground truth, repeat measurement with different instrumentation. Model the shared variance explicitly: a factor model, a batch covariate, a common-method-bias factor, a fixed effect on channel identity. Decouple by experimental design: randomise the channel assignment, balance batches across conditions, blind raters. Test the residual cross-dimensional structure: after removing the shared-channel variance, see what survives — if the cross-dimensional pattern collapses, it was channel artefact; if it persists, it is substantive. The compression is that a psychometrician, a genomicist, a macroeconometrician, and an ML practitioner are running the same four-move procedure under different names, so a method mastered in one substrate transfers as a template in the next. Complexity moves from a per-field corrective literature to a single channel-crossing-and-partitioning discipline.

Abstract Reasoning

The prime trains a reasoner to read any matrix of cross-dimensional correlations as potentially carrying two superimposed signals — true cross-source covariance and channel-injected covariance — and to recognise that the two are indistinguishable from within a single channel. The governing move is to treat a single channel's correlations as untrustworthy by construction and to seek a second, independent channel (or a strong factor prior) before crediting any cross-dimensional finding. The non-obvious consequence is that more data through the same channel does not help: the inflation is structural, not stochastic, so it does not average out with sample size; only an orthogonal channel or an explicit model of the shared factor can separate λ_i · λ_j · var(c) from cov(t_i, t_j). The prime also keeps the failure cleanly distinguished from substantive confounding — here the shared variance is introduced by the measurement or generation channel, not by a real third cause acting on the constructs — and from its input-side dual, in which correlated inputs collapse per-input identifiability rather than correlated outputs inflating cross-output relations. Both arise from shared variance at a layer the naive analysis does not model, and the reasoning move in each is the same: find the unmodelled shared layer and partition it before reading the pattern.

Knowledge Transfer

The diagnostic ports across substrates without redesign. A psychometrician who has learned multi-trait/multi-method analysis recognises the identical structural problem in feature-importance auditing, genomics batch effects, and macroeconometric common shocks; a genomicist who has internalised batch correction predicts correctly that survey research will be contaminated by common-method effects and reputation research by halo. The role mappings transfer directly — output dimensions ↔ traits / survey items / features / genes / economic series / voxels; shared channel ↔ overall impression / single questionnaire / confounding feature / assay batch / common shock / scanner; channel factor ↔ halo / method variance / batch variance / common component; partitioning move ↔ MTMM crossing / factor model / batch covariate / motion regression. The intervention catalogue — cross the channel, model the shared factor, decouple by design, test the residual structure — is invariant, and the only substrate-specific work is identifying what counts as the channel and what kinds of independent crossing are feasible. The transferred and non-obvious lesson is that inflated correlations should be the trigger for suspicion rather than for discovery: a tight cross-dimensional pattern measured through one channel is exactly what shared-channel variance produces, so the right response is to cross the channel before publishing the relation, not to interpret it. Because the inflation does not diminish with sample size, the prime also corrects a common instinct — collecting more data through the same instrument — by showing that the only remedies are an orthogonal channel or an explicit shared-factor model, both of which a practitioner can import from whichever substrate first taught them the move.

Examples

Formal/abstract

The multi-trait/multi-method (MTMM) matrix in psychometrics is the prime's purest worked case, because it was engineered specifically to expose and partition the leakage. Suppose a researcher measures three output dimensions — anxiety, depression, hostility — each by two methods (self-report questionnaire and clinician rating). Each measured score decomposes as y_i = t_i + λ_i·c + noise, where t_i is the true construct, c is the shared method channel (the questionnaire's response style, the clinician's halo), and λ_i is the loading. The naive observation is that all three self-report scores correlate tightly — read uncritically, this says the three constructs are nearly the same thing. But the MTMM design crosses the channel: it asks whether anxiety-by-questionnaire correlates more with depression-by-questionnaire (same method, different trait) than with anxiety-by-clinician (same trait, different method). When the same-method correlations dominate, the tight cross-construct pattern is λ_i·λ_j·var(c) — method variance, not substance. The decisive structural fact the prime names is visible here: from the self-report data alone the inflation is indistinguishable from real covariance, and collecting more questionnaires cannot help because the contamination is structural, not stochastic. Only the orthogonal second method (or an explicit method factor in a confirmatory model) separates λ_i·λ_j·var(c) from cov(t_i,t_j). Mapped back: the three symptom scales are the output dimensions, the questionnaire is the shared channel, the same-method correlation block is the inflated cross-covariance, and the clinician rating is the orthogonal crossing that performs the partition — exactly the prime's "cross the channel, then partition" resolution.

Applied/industry

Two industry instances run the identical structure. First, genomics batch effects: a lab profiles gene expression for hundreds of output dimensions (genes) across samples processed in several assay batches. The shared channel is the batch — reagent lot, technician, machine-day — which loads onto every gene at once. Apparent co-expression across many genes can be λ_i·λ_j·var(batch) rather than coordinated biology, and the giveaway is that samples cluster by batch rather than by condition. More samples within the same batch do not fix it; the remedy is to randomise condition across batches (decouple by design) or fit an explicit batch covariate (model the shared factor), then test which co-expression survives. Second, machine-learning feature-importance auditing: a model is trained on many features, and a confounding feature correlated with the target silently inflates the apparent importance of every feature that co-varies with it, so an importance report reads channel-driven covariance as evidence about the underlying drivers. The corrective is experimental decoupling — permutation or interventional importance that breaks the confound — not a larger training set drawn through the same correlated feature distribution. In both cases the prime's counter-instinct is decisive: the practitioner's reflex to "collect more data" is wrong because the inflation does not average out, and the only remedies are an orthogonal channel or an explicit shared-factor model. Mapped back: genes and features are output dimensions; assay batch and the confounding feature are shared channels; batch-driven co-expression and confound-driven importance are the inflated covariances; and batch-randomisation/covariate-modelling and interventional importance are the channel-crossing and explicit-modelling moves the prime prescribes.

Structural Tensions

T1 — Structural Contamination versus Stochastic Noise (measurement). The leakage is shared-channel variance, which has a non-zero mean structure, not random noise that averages out. The tension is between two things that both look like "imperfect measurement." The characteristic failure mode is the collect-more-data reflex: pouring sample size through the same instrument, rater, or batch and expecting the inflated correlations to shrink — but the contamination is structural, so it does not diminish with n. The diagnostic: ask whether the suspected error is random across observations or shared by a common source; if every output through one channel carries the same lift, more same-channel data is wasted effort and only an orthogonal crossing helps.

T2 — Channel Leakage versus Substantive Confounding (scopal). Both inflate cross-dimensional correlations through an unmodelled shared layer, but one lives in the measurement/generation channel and the other in a real third cause acting on the constructs. The tension is that they have the same statistical signature yet demand different remedies. The failure mode is mislocating the layer: regressing out a method factor when the confound is substantive (erasing real signal), or hunting for a real common cause when the artefact is pure instrument. The diagnostic: ask whether the shared variance was introduced by how the dimensions were measured or by what drives them — channel artefacts vanish under channel-crossing; substantive confounds do not.

T3 — Output-Side Inflation versus Input-Side Collapse (sign/direction). This prime concerns correlated outputs whose cross-relations are inflated; its dual concerns correlated inputs whose individual identifiability collapses. The tension is directional and easily conflated because both stem from shared variance at an unmodelled layer. The failure mode is applying the wrong remedy: trying to partition output covariance when the real problem is that correlated predictors make per-input attribution non-identifiable, or vice versa. The diagnostic: locate whether the shared variance sits on the measured outputs (inflating their apparent relations) or on the inputs (destroying which-input-did-it), and choose channel-crossing for the former, decorrelation or design for the latter.

T4 — Single-Channel Indistinguishability versus Orthogonal Resolution (coupling). From one channel, λ_i·λ_j·var(c) and cov(t_i,t_j) are statistically identical; only an independent second channel or a strong factor prior separates them. The tension is between the convenience of one well-instrumented channel and the irreducible ambiguity it leaves. The failure mode is crediting a tight within-channel correlation as a finding because no second channel was available to challenge it. The diagnostic: before interpreting any cross-dimensional relation, ask whether it has been observed through at least two channels that share no common variance source — if not, the relation is suspect by construction, however large the sample.

T5 — Removing Leakage versus Removing Signal (over-correction). Partitioning out the shared channel is the remedy, but an over-aggressive model can absorb genuine cross-source covariance into the channel factor. The tension is between under-correcting (leaving artefact) and over-correcting (deleting substance). The failure mode is a batch covariate or method factor that is confounded with the biological condition or the true construct, so removing "the channel" also removes the effect of interest. The diagnostic: check whether the channel is balanced against the conditions of interest — if batch is nested within treatment, partitioning the batch erases the treatment, and the residual-structure test will wrongly report the real pattern as artefact.

T6 — Per-Pair Inflation versus Whole-Matrix Structure (scalar). Leakage is described pairwise — cov(y_i,y_j) lifted by the loadings — but a single channel loads on many outputs at once, producing a low-rank lift across the entire correlation matrix. The tension is between auditing pairs and recognising the global signature. The failure mode is whack-a-mole: treating each inflated pair as a separate worry and missing that one dominant factor is inflating the whole block, which mis-estimates how much structure is artefact. The diagnostic: inspect the matrix for a single high-variance shared component (samples clustering by batch, items loading on one method factor) rather than evaluating correlations two at a time — the channel's footprint is matrix-wide, not pairwise.

Structural–Framed Character

Cross-dimensional leakage sits at the structural end of the structural–framed spectrum, with an aggregate of 0.0: it is a measurement-architecture pattern — a single shared-variance source loading onto multiple supposedly-independent output dimensions and inflating their apparent cross-covariance — statable as cov(y_i, y_j) = cov(t_i, t_j) + λ_i·λ_j·var(c). The structure lives in the relation between channels and outputs, not in any field's interpretation.

Every diagnostic reads structural. The pattern carries no home vocabulary that must travel: it is told as the halo effect in social cognition, common-method bias in survey work, batch effects in genomics, common shocks in macroeconometrics, and confound-driven feature importance in machine learning, each substrate naming its own channel while the shared-loading factor decomposition stays invariant. It carries no inherent approval or disapproval — channel-injected covariance is neither good nor bad; it is simply a layer to be partitioned out before a substantive claim can be posed. Its origin is formal — a linear factor model with a shared loading vector — and it runs indifferently in an fMRI scanner's voxel time series, a reagent-batch assay, and an instrument's calibration drift, none of which requires a human practice to generate the contamination. And invoking it RECOGNISES a shared-channel signature already present in the covariance matrix rather than IMPORTING a frame: the diagnostic is to find the unmodelled shared layer and cross the channel, not to overlay an interpretive reading. On every diagnostic the prime reads structural, consistent with the 0.0 aggregate.

Substrate Independence

Cross-dimensional leakage is a maximally substrate-independent prime — composite 5 / 5 on the substrate-independence scale. Its domain breadth is total: the shared-channel-variance contamination recurs with identical force as the halo effect in social cognition, common-method bias in survey methodology, batch effects in genomics, common shocks in macroeconometrics, confound-driven feature importance in machine learning, calibration-drift contamination in instrumentation, and scanner-drift inflation of functional connectivity in neuroimaging — psychological, biological, economic, computational, and physical substrates. Its structural abstraction is maximal because the pattern is statable as a bare linear factor model, cov(y_i, y_j) = cov(t_i, t_j) + λ_i·λ_j·var(c), with a shared loading vector and no domain-specific content; it runs indifferently in a reagent-batch assay, an fMRI scanner, and a questionnaire. The transfer evidence is heavy and concrete: each substrate independently engineered the same remedy — multi-trait/multi-method designs, batch-correction algorithms, factor models, common-method-bias factors — so a psychometrician who knows MTMM crossing recognises the genomicist's batch covariate as the identical "cross the channel, then partition" move, not a translation. Maximal breadth, maximal abstraction, and documented cross-domain method transfer all converge on a canonical 5.

  • Composite substrate independence — 5 / 5
  • Domain breadth — 5 / 5
  • Structural abstraction — 5 / 5
  • Transfer evidence — 5 / 5

Relationships to Other Primes

One-hop neighborhood: parents above, mutual partners to the right, children below.Cross-DimensionalLeakagecomposition: CorrelationCorrelation

Parents (1) — more general patterns this builds on

  • Cross-Dimensional Leakage presupposes, typical Correlation

    A specific generative story for WHY an observed cross-output correlation is inflated above the true cross-source signal: a shared channel loads onto multiple outputs (cov(y_i,y_j) = cov(t_i,t_j) + lambda_ilambda_jvar©). A diagnosis built atop correlation, presupposing it.

Path to root: Cross-Dimensional Leakage → Correlation

Neighborhood in Abstraction Space

Cross-Dimensional Leakage sits in a sparse region of abstraction space (63rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely rather than landing on a neighbor.

Family — Stocks, Flows & Buffering (16 primes)

Nearest neighbors

Computed from structural-signature embeddings · 2026-06-14

Not to Be Confused With

The most consequential confusion is with confounding, because the two are statistically indistinguishable from within a single channel and yet demand opposite remedies. A confound is a real third variable that causally influences two or more of the underlying constructs, so the inflated covariance is a fact about the world: smoking raises both lung cancer and yellow fingers, and their correlation is genuine, mediated by a shared cause. Cross-dimensional leakage is a fact about the measurement apparatus: the underlying constructs may be entirely unrelated, but a shared rater, instrument, batch, or method injects covariance that lives in the channel, not the constructs. The invariants differ precisely here. Confounding's invariant is that the spurious relation survives any change of measurement instrument, because it is in the data-generating process; leakage's invariant is that the relation vanishes under channel-crossing, because it was never in the constructs. The practical hazard of conflation is symmetric and severe: regress out a "method factor" when the shared variance is a substantive confound and you erase real signal; hunt for a hidden common cause when the artefact is pure instrument and you chase a ghost. The diagnostic that separates them is the prime's: cross the channel. If the relation holds through an orthogonal second channel, it is confounding (or real); if it collapses, it was leakage.

A second genuine confusion is with correlation itself. A reader can take an observed correlation as the finding and stop. The prime insists that a cross-dimensional correlation observed through a single channel is underdetermined: it is the sum of true cross-source covariance and channel-injected covariance, and from one channel the decomposition is not identifiable. Correlation is the measured quantity; cross-dimensional leakage is one of the two generative stories that could have produced it, and the dangerous one because it masquerades as substance. Where correlation is agnostic about origin, the prime supplies the missing question — through what shared channel was this measured, and has it ever been seen through another? Treating a correlation as self-interpreting is exactly the inferential trap the prime names.

A third confusion, subtler, is with synergy_and_antagonism. Both involve multiple dimensions whose joint behaviour seems to exceed or differ from their separate behaviour, and both can show up as off-diagonal structure in a covariance matrix. But synergy is a real interaction among sources — the combined effect is genuinely non-additive in the world — whereas cross-dimensional leakage produces apparent joint structure that is an additive artefact of a shared loading, with no interaction among the true sources at all. The distinction matters because synergy is a finding to be modelled and exploited, while leakage is an artefact to be partitioned out before any interaction claim can even be posed. An analyst who reads channel-driven covariance as synergy will build a theory of interaction on top of a measurement artefact.

For a practitioner the through-line is a discipline of suspicion calibrated to layer. Before crediting any cross-dimensional relation, locate the shared channel and ask whether the relation has survived an orthogonal crossing; only then decide among confounding (a real common cause, irreducible by channel-crossing), genuine synergy (a real interaction), and leakage (a channel artefact that disappears when the channel changes). The three look alike in a single matrix and diverge completely in what they license.

Solution Archetypes

No catalogued solution archetypes reference this prime yet.