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PCM1 Signal And Ancestral Results

PCM1 compares Pagel-λ fits and continuous ancestral reconstruction between the governed R reference and Bijux on fixed, reconciled inputs. The aggregate evidence-001 bundle is matched_with_tolerance: 31 scalar observations contain 16 exact matched rows and 15 matched_with_tolerance rows. Visual and artifact-governance claims remain not_comparable by design.

Know Exactly What Corresponded

PCM1 tests a defined numerical surface, not every possible reading of the study:

Evaluated here Not established here
fitted λ and log likelihood under aligned covariance and likelihood conventions that λ is a causal fraction of longevity variation
registered λ=0 contrast and selected covariance entries that the Brownian/λ model is biologically adequate or uniquely preferred
74 clade-keyed ancestral point and interval rows that ancestral longevity was observed or historically certain
one MRCA extraction and two branch-summary counts that each inferred branch difference is an independently observed event
R–Bijux numerical correspondence under predeclared tolerances equivalence of plots, every software default, unrelated datasets, or unregistered estimators

This table is the citation boundary. A downstream statement may be narrower than an evaluated row, but it must not be broader than the population, model, quantity, and comparison rule that own that row.

Three Questions, Three Evidence Roles

PCM1 is not one omnibus “phylogenetics parity” test. Its numerical ledger answers three connected but distinct questions:

Question Evidence role Conclusion at the current boundary
Do R and Bijux fit the same lambda-defined covariance problem on the governed population? compare lambda, log likelihood, lambda-zero contrast, and selected covariance entries the registered scalar surfaces correspond within their declared tolerances
Do both implementations reconstruct the same conditional values at the same internal clades? align 74 nodes by descendant taxa and compare point and interval estimates the registered ancestral surfaces correspond to floating-point scale
Do derived summaries preserve those reconstructed states? compare one clade-keyed MRCA estimate and two branch-change counts the named summaries correspond, conditional on the same reconstruction

Each question consumes the accepted 75-taxon preparation state. None answers whether the biological model is true, whether the reconstructed values are historical observations, or whether the result generalizes beyond the governed data and configuration.

Read The Scientific Result In Layers

The fitted λ summarizes how the declared covariance model weights shared ancestry among the observed tips. The likelihood-ratio result compares that fit with the registered λ=0 boundary. Ancestral reconstruction then projects the accepted tip values through a declared model onto internal clades, and the branch counts summarize differences between those conditional projections.

These are dependent layers, not progressively more direct observations. The ancestral values inherit the tree, branch lengths, trait preparation, and model; branch counts inherit the ancestral values and threshold. Cross-runtime agreement establishes reproducibility of that chain while leaving biological model criticism and historical interpretation open.

Connected Results Are Not Independent Replications

The lambda fit, likelihood-ratio contrast, covariance entries, ancestral values, MRCA spot check, and branch-change counts share inputs and model components. Their agreement tests different projections of one analytical chain; it must not be counted as multiple independent confirmations of the biological conclusion.

Surface Depends on Additional contract it tests
fitted λ and log likelihood prepared trait vector, tree, covariance, bounds, likelihood optimization and objective correspondence
λ=0 contrast fitted-model likelihood plus the registered null nested-model calculation and p-value convention
covariance entries tree, order, branch lengths, and λ transform matrix parameterization and indexing
ancestral node rows prepared state plus reconstruction convention clade correspondence, estimates, and intervals
MRCA spot check one ancestral row stable descendant-taxon identity and extraction
branch-change counts complete parent/child ancestral rows branch mapping, direction, units, and threshold rule

Agreement at a child surface can localize an implementation comparison. It cannot compensate for a broken parent dependency, and it cannot be multiplied into a stronger causal or generalization claim.

flowchart TD
    inputs["75-tip rooted ultrametric tree<br/>75 aligned longevity values"]
    random["Five seeded 30-tip<br/>random-trait λ fits"]
    observed["Primate longevity<br/>λ and λ=0 comparison"]
    ancestral["74 shared internal nodes<br/>point and 95% interval comparison"]
    spot["MRCA estimate and<br/>branch-change counts"]
    scalar["31-row scalar parity ledger"]
    verdict["Claim-scoped verdicts"]

    inputs --> random --> scalar
    inputs --> observed --> scalar
    inputs --> ancestral --> scalar
    ancestral --> spot --> scalar --> verdict

Model Identity

Pagel's λ transforms the off-diagonal elements of the Brownian phylogenetic covariance while retaining the diagonal. Under this parameterization:

  • λ = 0 removes shared off-diagonal phylogenetic covariance;
  • λ = 1 retains the Brownian shared-path covariance;
  • intermediate λ values scale that shared covariance.

The estimate is conditional on tree, branch lengths, taxon order, trait scale, likelihood definition, bounds, and optimizer behavior. It is not a universal property of “primates” or “longevity.”

For a Brownian covariance matrix V, the compared parameterization can be read conceptually as:

V(lambda)[i, i] = V[i, i]
V(lambda)[i, j] = lambda * V[i, j]    for i != j

This makes the estimand concrete. λ changes modeled cross-species covariance; it does not rescale the longevity observations and does not represent the fraction of longevity “caused by phylogeny.” Agreement on λ therefore requires agreement on the untransformed covariance, diagonal convention, bounds, likelihood, and taxon order before the scalar values are compared.

Governed Lambda Observations

The five seeded random datasets are parity fixtures, not evidence that random traits must yield low λ. In this exact roster, every fitted λ is at or extremely near the upper boundary:

Case R λ Bijux λ absolute difference λ verdict
random_data 0.9999681477851246 1.0 0.00003185221487544965 matched_with_tolerance
random_data2 1.0 1.0 0 matched
random_data3 1.0 1.0 0 matched
random_data4 1.0 1.0 0 matched
random_data5 1.0 1.0 0 matched

The λ tolerance is 0.001. Log-likelihood differences for the same five cases also remain within 0.001; the largest is approximately 0.0009008053 for random_data.

These observations establish cross-implementation agreement for the seeded fixtures. They do not establish the sampling distribution of λ under a no-signal null. A boundary estimate also deserves optimizer and profile review; agreement between implementations does not remove that diagnostic obligation.

Primate Longevity Lambda

Quantity R Bijux absolute difference tolerance
λ 0.8027301202530401 0.803 0.00026987974695991124 0.001
log likelihood -446.94323405402366 -446.94323951456334 0.000005460539682644594 0.001

Both rows are matched_with_tolerance. The separate λ-versus-zero block also records:

  • likelihood-ratio absolute difference 0.00001092107925160235 against a 0.0001 tolerance;
  • p-value absolute difference 8.374938977420018e-16 against a 1e-12 tolerance;
  • λ=0 covariance top-three maximum absolute difference 9.99999993922529e-9 against a 1e-8 tolerance;
  • observed-λ covariance top-three maximum absolute difference 0.

This supports numerical correspondence of the declared fitted and λ=0 comparison surfaces. It does not by itself establish that Brownian covariance with transformed λ is the best biological model.

Match Ancestral Nodes By Clade

The ancestral comparison uses 74 shared internal nodes. Rows are matched by descendant-taxon signature rather than plotting order or an unqualified node number.

Surface maximum absolute R–Bijux difference tolerance verdict
point estimates 5.115907697472721e-13 1e-9 matched_with_tolerance
lower 95% limits 5.684341886080801e-13 1e-9 matched_with_tolerance
upper 95% limits 5.115907697472721e-13 1e-9 matched_with_tolerance

The observed differences are floating-point scale. The claim is numerical parity under the same Brownian/PIC convention; it is not proof that the ancestral states are observed historical facts.

Bonobo–Gibbon MRCA Spot Check

The governed MRCA clade contains:

  • Hylobates_lar;
  • Hylobates_pileatus;
  • Nomascus_concolor;
  • Pan_paniscus;
  • Symphalangus_syndactylus.

The R estimate is 520.0784230077601; the Bijux estimate is 520.07842300776. Their absolute difference is 1.1368683772161603e-13, within the 1e-9 near-exact tolerance. The R record also identifies local node 107, species label Node32, and a 95% interval of [518.7152277621561, 521.441618253364].

The clade signature is the cross-runtime identity. Node 107 is useful within this retained tree but should not be carried into a differently pruned or ordered topology without remapping.

Branch-Wise Increase Counts

R and Bijux both record:

Count Value Verdict
branches with an inferred increase 72 matched
branches with an inferred increase greater than 12 units 55 matched

These are deterministic summaries of inferred parent/child states on this tree. They are not 72 or 55 independently observed evolutionary events. The counts inherit the ancestral model, branch mapping, trait units, and threshold definition.

Claim And Observation Status

The bundle contains three different record grains:

Grain Current state Meaning
bundle manifest matched_with_tolerance aggregate PCM1 analytical and structural contract
analytical claims preparation/tree/join matched; λ and ancestral claims matched_with_tolerance bounded claim-level adjudication
visual/provenance claims not_comparable tracked without a numerical equivalence target

The block registry is more detailed: 10 verified, 6 verified_with_tolerance, 10 plot_only, 2 artifact_only, 1 seeded_input_only, and 1 workflow_only. The scalar ledger contains the 31 numerically adjudicated rows. Do not mix block status counts with claim verdicts or the bundle verdict.

The bundle verdict is driven by the complete required scalar population, not by the most favorable row. Because 15 required rows use tolerance-based agreement, the aggregate numerical claim cannot be called exact even though 16 rows match exactly. Plot-only and artifact-only blocks remain visible as tracked surfaces, but they do not enter the 31-row numerical denominator.

Separate Statistical Evidence From Historical Interpretation

Observation Statistical conclusion available Historical conclusion unavailable
fitted λ near 0.803 the registered model estimates λ near 0.803 on this population a causal fraction of longevity explained by ancestry
λ=0 likelihood-ratio result the registered zero-signal model fits materially worse under the compared likelihood contract proof that every lineage evolved longevity through one process
clade-keyed ancestral estimate R and Bijux produce corresponding conditional node estimates under the declared reconstruction direct observation of an ancestor's longevity
branch increase count the inferred parent/child state difference exceeds the declared threshold on named branches independently observed evolutionary events or rates

These interpretation limits are part of the result, not optional caveats added after the comparison.

What The Evidence Supports

The current record supports these precise statements:

  • fixed PCM1 input preparation and tree/trait alignment match their governed reference contracts;
  • five seeded λ fits agree within the declared scalar tolerances;
  • the primate λ, log likelihood, λ=0 likelihood-ratio comparison, and sampled covariance entries agree within their declared tolerances;
  • 74 clade-aligned ancestral point and interval rows agree to floating-point scale;
  • the MRCA estimate and branch-wise increase counts agree.

It does not support:

  • causal interpretation of phylogenetic signal;
  • a general null distribution from the five random fixtures;
  • proof that λ-transformed Brownian covariance is the best trait model;
  • historical certainty of reconstructed ancestors or inferred increases;
  • pixel-identical plot parity;
  • generalization to other trees, traits, parameterizations, or optimizers.

Follow The Authoritative Record

Begin with the evidence-001 manifest, then read claims.json, checks.json, inputs.manifest.json, results/scalar-parity-table.json, the relevant block payloads, and provenance.json. The scalar ledger owns numerical tolerance decisions; the plots are interpretation surfaces, not substitute data.