PCM2 Diagnostics And Open Boundaries¶

Regression agreement is only one part of PCM2. Phylogenetic signal tests the response–tree relationship; residual diagnostics test the fitted model; ancestral reconstruction projects a process onto internal nodes; and the intercept-mode sweep remains uncovered. These surfaces answer different questions and retain separate verdicts.

Read Each Surface As A Constraint¶

Surface	Constraint on interpretation	Failure does not automatically invalidate
phylogenetic signal	names the covariance evidence for this response and tree	exact preparation correspondence
residual diagnostics	tests whether fitted-error summaries retain aligned definitions and scales	the coefficient values already recorded under their own contract
ancestral reconstruction	binds internal estimates to clades, mode, and uncertainty	the regression estimand, which is a different question
intercept sweep	identifies a source analysis with no aligned runtime execution	neighboring PGLS or ancestral claims with complete observations

These constraints prevent an omnibus pass or fail. A residual mismatch narrows the residual claim; it also warns readers not to assume identical diagnostic semantics when interpreting the fit. It does not erase an exact input identity or silently become evidence against a different model surface.

Treat Diagnostics As Comparable Scientific Objects¶

A diagnostic scalar is the end of another data pipeline. For residual correlation, both implementations must first agree on the admitted rows, fitted-value scale, residual definition, standardization or whitening, missing-value treatment, and outlier policy. Only then does the correlation coefficient have a shared meaning.

The same applies to ancestral diagnostics: node rows require a common rooted tree, clade key, model, estimate scale, and uncertainty convention before a vector difference is meaningful. Matching row counts or similar plots do not establish this identity.

PCM2 therefore retains diagnostics as governed result objects, not secondary illustrations. Their mismatch can qualify use of an otherwise corresponding coefficient because it reveals that the implementations may be inspecting different error or reconstruction quantities.

Coefficients And Diagnostics Can Disagree Honestly¶

Two implementations can produce nearly identical coefficients and likelihoods while exposing different residual vectors. Raw response-scale residuals, normalized residuals, and phylogenetically transformed residuals are different objects even when they come from the same fitted mean. A diagnostic computed from one cannot be compared directly with a diagnostic computed from another.

PCM2 therefore preserves the favorable coefficient correspondence and the unexplained residual correlation mismatch at the same time. That is not an inconsistent verdict: it localizes agreement at the fit-summary surface and an unresolved definition or construction at the residual surface.

flowchart TB
    fit["Shared fitted model"]
    signal["Signal<br/>tree–trait dependence"]
    residuals["Residuals<br/>remaining model structure"]
    ancestors["Ancestral states<br/>node-level projection"]
    boundary["Intercept sweep<br/>not comparable"]
    conclusion["Bounded scientific conclusion"]

    fit --> signal --> conclusion
    fit --> residuals --> conclusion
    fit --> ancestors --> conclusion
    boundary --> conclusion

Evidence State¶

Bundle	Surface	Manifest verdict
`evidence-004`	phylogenetic signal	`matched_with_tolerance`
`evidence-005`	residual diagnostics	`matched_with_tolerance`
`evidence-009`	Brownian and early-burst ancestral reconstruction	`matched_with_tolerance`
`evidence-010`	intercept-mode likelihood sweep	`not_comparable`; boundary register

The first three manifest verdicts are favorable within their claim contracts. The aggregate scalar ledger nevertheless retains five unresolved observations across residual and ancestral outputs. Cite both levels when describing PCM2.

Phylogenetic Signal¶

The longevity signal fit agrees closely across implementations:

Quantity	R reference	Bijux observation
estimated Pagel λ	0.802734424042	0.802734483419
λ=0 likelihood-ratio statistic	41.030418693040	41.030418692855
likelihood-ratio p-value	1.498782717 × 10⁻¹⁰	1.498782717 × 10⁻¹⁰

Under the registered model, the fitted λ is about 0.803 and the λ=0 comparison is rejected at the recorded p-value. This supports a nonzero-signal conclusion for the governed response, taxa, tree, bounds, and likelihood convention. It does not turn λ into a causal fraction, certify the downstream regression, or imply that every covariance family is adequate.

Residual Diagnostics Use Named Scales¶

The baseline fit agrees on the registered summaries: QQ correlation is about 0.97495, absolute-residual–fitted correlation is about 0.02344, and both implementations identify five outliers under the governed rule.

The estimated-λ diagnostics are not uniformly aligned:

Diagnostic	R reference	Bijux observation	Ledger state
QQ correlation	0.980223544139	0.977685036394	within 0.02 tolerance
absolute residual–fitted correlation	0.205562548326	0.109972233803	`mismatch_unexplained`
outlier count	3	4	within the registered count tolerance

The correlation difference is 0.095590314522858 against a 0.05 tolerance. The underlying residual magnitudes also reveal different scales: the R summary is near unit scale while the Bijux residual standard deviation is near 112. This is consistent with normalized versus response-scale residuals, but the evidence record has not adjudicated that explanation. A reader must not interpret similar QQ correlations as proof of identical residual semantics.

For any diagnostic comparison, preserve residual type, standardization, fitted-value scale, outlier rule, row exclusions, and covariance fit. A plot that looks similar is not a machine-verifiable observation contract.

Resolve A Residual Discrepancy At Its Definition¶

The estimated-λ correlation mismatch must be investigated before changing its tolerance. The shortest defensible resolution path is:

align the fitted observation order and exclusions;
identify raw, normalized, studentized, or phylogenetically transformed residuals in each implementation;
identify the fitted-value scale and any centering or variance transform;
recompute the diagnostic from retained row-level residual and fitted-value vectors;
compare the aligned vectors before comparing their correlation summary;
retain the original mismatch and adjudicate a new observation under a predeclared rule.

If a deterministic scale transform fully explains the difference, the new claim may become mismatch_explained; it does not become exact agreement by renaming the residuals. If the row vectors differ after alignment, resolution must move upstream to the fitted model or residual construction.

Ancestral Reconstruction Is Node-Indexed¶

evidence-009 records 74 internal nodes for both Brownian and early-burst reconstruction. Node count agreement is necessary but insufficient. The aggregate ledger retains four mismatch_unexplained vector observations: Brownian and early-burst values at the first and most recent five node positions.

The Brownian differences appear numerically small, but their registered rule requires exact agreement. The early-burst differences are substantive and track the unresolved mode parameterization seen in the transformed-tree and fit observations. The manifest’s matched_with_tolerance verdict is bounded to its named-node contract; it does not erase those aggregate vector rows.

Node identity must be carried explicitly through comparison. Array position, plotting order, or visual node size is not a stable biological identifier.

Intercept-Sweep Boundary¶

evidence-010 identifies mode-linked-intercept-models, the corBlomberg intercept-mode likelihood sweep from the source material. The current runtime mapping does not supply a comparable execution, so the verdict is not_comparable.

The boundary closes only when the record contains:

a reference and Bijux implementation of the same intercept-mode sweep;
matching taxa, response, tree scaling, parameter direction, and intercept convention;
retained likelihood observations and optimizer outcomes;
an explicit tolerance and adjudicated claim-scoped checks.

Neighboring PGLS or continuous-mode results cannot be borrowed to fill this gap. The boundary register is the evidence: it names what is absent and what would make the comparison reviewable.

This is useful evidence even without a numerical verdict. It prevents a reader from inferring coverage from nearby API capability, preserves the source analysis as a concrete target, and states the minimum outputs needed for a future comparison. Its role is to bound the public claim, not to contribute a favorable row to the parity denominator.

Distinguish The Four Review Outcomes¶

Surface	Present outcome	Why it matters
signal scalar observations	corresponding within registered tolerances	supports only the named λ and λ=0 claim
estimated-λ residual correlation	`mismatch_unexplained` in the aggregate ledger	comparable values exist and violate the registered rule
aggregate ancestral vectors	`mismatch_unexplained` under their exact rule	named-node bundle tolerance does not erase broader vector differences
intercept sweep	`not_comparable`	required aligned execution and observation rows do not exist

The last two states are not synonyms. A mismatch requires comparable observations that disagree; not_comparable records that the comparison cannot yet be made. Their resolution work therefore starts at different owners.

What PCM2 Supports¶

PCM2 supports the baseline and Pagel-λ regression correspondence and the governed phylogenetic-signal observations. It also supplies reviewable diagnostic and ancestral contracts. It does not support uniform parity for early-burst behavior, every residual statistic, every ancestral vector, or the intercept-mode likelihood sweep.

That mixed conclusion is stronger than an unqualified pass: readers can see which scientific statements are reproduced, which depend on tolerance, and which observations still require resolution.

A citable PCM2 statement should therefore name the surface. “The baseline GLS and Pagel-lambda PGLS coefficients correspond under their bundle contracts” is supported. “PCM2 reproduces all comparative methods” is contradicted by the 12 unresolved scalar observations and the non-comparable intercept sweep.