PCM4 Mixed-Model Evidence Boundary

PCM4 uses a Bayesian mixed-model workflow whose decisive outputs are posterior summaries, convergence diagnostics, and phylogenetic variance estimates. The checked-in dossiers currently govern the claim map and source boundary; they do not retain a completed reference-versus-Bijux comparison.

What PCM4 Is Designed To Establish

PCM4 asks whether a Gaussian trait model can separate its population-level effects from phylogenetic and residual variation while retaining a trustworthy posterior. Its evidence roles are distinct:

Evidence role	Required scientific object
establish the analysis population	reconciled cichlid observations, ordered tree tips, and exclusions
establish posterior usability	identified chains, retained draws, convergence, autocorrelation, and effective sample size
establish fixed-effect correspondence	aligned coefficient parameters under matched design and priors
establish variance correspondence	phylogenetic and residual components on explicitly matched scales
establish a comparator	Brownian PGLS quantities linked to the same population and covariance identity

The current dossiers make these dependencies and absences reviewable. Their evidentiary contribution is a claim-complete closure contract, not a posterior result. Adjacent Bayesian or PGLS capability cannot satisfy a row until the PCM4 population, priors, draws, and parameter identities are governed together.

What Is Known Without A Posterior

The current record identifies the intended cichlid population, source model sequence, formulas, tree-derived covariance role, priors and chain questions, seven claim boundaries, and the primary outputs required to compare them. Those facts make the missing computation precise and reproducible as future work.

It does not establish that a chain mixed, a parameter existed, a coefficient had a particular sign, or phylogeny explained any share of variance. Those statements require governed posterior draws and diagnostics. A complete map of missing evidence is stronger than an ambiguous claim of coverage, but it remains a map rather than a numerical result.

What The First Governed Posterior Must Prove

The first acceptable PCM4 execution cannot be only a posterior summary table. It must join four independently reviewable objects:

1. the exact species-level population and ordered tree covariance;
2. the model identity, including fixed effects, random effects, family, priors, and covariance scaling;
3. every expected chain with terminal state, burn-in, retained draw keys, and parameter-specific diagnostics;
4. primary draws and summaries whose parameter keys and transforms align across the reference and Bijux records.

This packet could close one bounded Gaussian posterior claim while variance or PGLS-comparator claims remain open. Evidence advances by closing a complete dependency slice, not by collecting disconnected favorable means from several claims.

flowchart LR
    source["Lund source, data,<br/>tree and workspace"]
    contract["Claims · manifests<br/>contract wrappers"]
    missing["No governed primary outputs<br/>or comparison observations"]
    execution["Matched reference and<br/>Bijux executions"]
    verdict["Claim-level<br/>adjudication"]

    source --> contract --> missing
    missing -. required closure .-> execution --> verdict

Current Boundary By Record

Record	Current state	Review consequence
source program	preserved Lund PCM4 source with repository-owned provenance	the intended computation can be located and inspected
datasets	cichlid observations, tree, and workspace objects have governed identities	input provenance is available; derived workspace correctness is not implied
claim decomposition	seven claim IDs and evidence IDs are checked in	each analytical question has a stable review address
reference wrapper	writes source locators and the named source script	it records intent but does not invoke the posterior workflow
Python wrapper	BUILD_SCRIPT = None, PRIMARY_OUTPUTS = [], execution mode bundle_contract_only	no Bijux scientific result is produced by the bundle wrapper
results manifest	governed_primary_output_count is zero in all seven bundles	no coefficient, posterior, variance, chain, or PGLS output is governed here
bundle verdict	all seven are not_comparable	numerical correspondence has not been adjudicated

Claim Closure Matrix

Bundle	Missing comparison evidence
evidence-001	aligned species table, tree-tip reconciliation observations, and comparison rule
evidence-002	Gaussian baseline coefficients, uncertainty, fit convention, and adjudication
evidence-003	retained chains, burn-in, autocorrelation, ESS, convergence, and comparable summaries
evidence-004	exact inverse covariance, taxon order, scaling, and structural comparison
evidence-005	aligned fixed-effect posterior draws or declared summaries under matched priors
evidence-006	phylogenetic and residual variance-component posteriors under matching parameterization
evidence-007	Brownian PGLS and posterior-model quantities with an explicit comparison rationale

Closure Dependency Order

The claims do not close independently. Later numerical claims consume the population, chain, and covariance identities established by earlier records:

flowchart LR
    population["evidence-001<br/>analysis population"]
    baseline["evidence-002<br/>Gaussian baseline"]
    chains["evidence-003<br/>chains and diagnostics"]
    inverse["evidence-004<br/>inverse covariance"]
    fixed["evidence-005<br/>fixed-effect posterior"]
    variance["evidence-006<br/>variance posterior"]
    comparator["evidence-007<br/>Brownian comparator"]

    population --> baseline
    population --> chains
    population --> inverse
    chains --> fixed
    inverse --> fixed
    chains --> variance
    inverse --> variance
    baseline --> comparator
    inverse --> comparator
    fixed --> comparator

A later bundle may retain its own verdict, but it cannot silently substitute a different species population, tree order, chain set, or covariance scaling. The dependency must be recorded by immutable artifact identities rather than assumed from execution order.

Comparable Posterior Identity

A comparable run fixes:

• observation unit and species-level aggregation;
• taxon names, order, pruning, rootedness, branch lengths, and inverse covariance scaling;
• response, predictors, fixed and random terms, family, and link;
• fixed-effect and variance-component priors;
• chain count, initialization, seed, iterations, burn-in, thinning, and tuning;
• monitored parameters, transformation rules, and interval definitions;
• failed-chain, excluded-parameter, and missing-output denominators.

If one of these identities differs, the observation must classify the difference before comparing values.

Build The Posterior Denominator Before Comparing Summaries

A posterior mean or interval is a projection of selected draws. The comparable unit is therefore not the printed table row but an identified parameter over an admissible draw population:

model × parameter × chain set × retained states × transform × summary rule

flowchart LR
    expected["Expected chains and states"] --> diagnostics["Chain-level diagnostic gate"]
    diagnostics --> admitted["Explicit admitted-draw ledger"]
    admitted --> parameter["Stable parameter identity"]
    parameter --> summary["Declared summary and interval"]
    summary --> observation["Reference-versus-Bijux observation"]

Denominator defect	Why a similar summary is insufficient
a chain is absent or silently discarded	the retained posterior population differs
burn-in, thinning, or terminal state differs	the draw indices do not represent the same sampling contract
a variance parameter is transformed on one side	labels may match while scale and distribution differ
non-finite or failed draws vanish from one summary	the eligible denominator and failure rate are hidden
intervals use different quantiles or highest-density rules	endpoints answer different summary questions

The denominator ledger must be shared by fixed effects, variance components, and any derived quantity that claims same-draw correspondence. Diagnostics can exclude a declared population under a pre-registered rule; they cannot be used after inspection to select whichever draws make summaries agree.

Posterior Admission Is Parameter-Aware

A run-level “converged” flag is too coarse for PCM4. Fixed effects and variance components can have materially different mixing, boundary behavior, and effective sample sizes within the same chains.

Admission layer	Evidence retained	Unsafe shortcut
chain	initialization, seed, terminal state, iterations, burn-in, thinning, warnings	count only chains that produced a file
parameter	expected key, presence in every chain, finite states, scale, boundary state	infer availability from one summary table
mixing	autocorrelation, effective sample size, between-chain behavior, selected window	apply one global diagnostic result to every parameter
summary	admitted chain/draw keys, statistic, interval rule, transform	compare rounded means from differently admitted draws
claim	complete expected parameter and diagnostic denominator	omit a poorly mixing variance component while matching fixed effects

Admission rules should be declared before comparing posterior summaries. A parameter that fails its diagnostic rule remains present as failed or excluded evidence with its denominator; it must not disappear from the bundle because another parameter mixes well.

Required Observation Ledger

Each claim needs rows that identify the bundle, parameter or structure, reference value or distribution, Bijux value or distribution, comparison rule, tolerance or distributional criterion, outcome, and mismatch reason. Posterior claims additionally need chain-level diagnostics and retained-sample counts.

Missing execution produces not_comparable; it is not a numerical failure. Completed execution with unexplained disagreement may justify mismatch_unexplained. Agreement can justify matched or matched_with_tolerance only after all eligible observations are adjudicated.

Distinguish Structural And Numerical Checks

Check class	Examples	Failure meaning
identity	source revision, dataset digest, tree digest, taxon order, formula, priors	the computations are not yet the same analytical claim
structural	matrix dimensions, parameter keys, chain membership, draw counts, finite-value policy	the comparison population is malformed or incomplete
diagnostic	effective sample size, autocorrelation, between-chain behavior	posterior summaries may not support scientific interpretation
numerical	coefficient difference, interval overlap rule, posterior-distance rule	comparable observations agree or disagree under a declared criterion
completeness	expected versus observed parameters, chains, and claim rows	the verdict denominator is complete or explicitly reduced

Identity and structural failures are not tolerance failures. They keep the affected observation not_comparable until the analytical objects align. Numerical adjudication begins only after those gates pass, and completeness is evaluated before a bundle-level matched verdict is allowed.

Promote Primary Outputs By Provenance

Adding a path to primary_output_paths is the last step of evidence capture, not the act that makes a file primary. Each promoted output must be generated or losslessly normalized by a governed execution and remain linked to the inputs, model, posterior selection, and diagnostics that determine its meaning.

Candidate output	Promotion requirement	Reject promotion when
fixed-effect summary	parameter keys, transforms, retained chains/draws, interval rule, and parent trace resolve	only a copied or manually transcribed table exists
variance-component summary	component parameterization, covariance scale, same-draw denominator, and posterior samples resolve	labels align but scales or random effects do not
chain diagnostic table	chain identities, selected window, estimator, threshold, and failed-chain denominator resolve	diagnostics were recomputed from an unidentified subset
inverse covariance	tree digest, ordered taxa, construction rule, scaling, and numerical representation resolve	dimensions match but taxon order or scaling is unknown
Brownian comparator	fitted population, model and likelihood conventions, outputs, and comparison rationale resolve	a neighboring PGLS run is attached without analytical identity

Promotion also requires inventory and checksum coverage plus an observation ledger that uses the output. A complete unused file is retained supporting material; it does not silently increase the scientific denominator or change the bundle verdict.

Safe Present-Tense Claims

• PCM4 source material, datasets, claim decomposition, and provenance are checked in and reviewable.
• Seven governed bundles declare direct-parity intent and currently record not_comparable.
• Bijux contains adjacent native Gaussian, PGLS, Bayesian, and covariance capabilities, but these bundles do not establish their equivalence to the PCM4 MCMCglmm workflow.
• No PCM4 bundle currently retains a governed primary scientific output.

Do not describe the posterior, coefficient, variance-component, convergence, or Brownian-comparator claims as reproduced until the missing execution and observation ledgers exist.