N20 gate outcome: no identified physical fraction

The gate was registered in commit 930dff1e before execution. It did not fit a latent-class model, acquire observations or estimate a new Hi-GAL fraction. Its empirical coverage worker terminated with exit code 1 at the frozen identity check; it was not restarted. The separate exact mathematical identifiability test failed the stated identification criterion.

What the existing table reveals

The MALT90 table has 3,556 entries with unique ID and native recno values. The cached maser/ATLASGAL subset has 896 rows, with two repeated Name strings across four rows. They are not identical full rows: each repeated Name/Clump pair has one distance value and one missing distance. The specific rows and unmodified identifiers are retained in the conflict export. No rows were removed or merged, and this audit does not decide whether the repeated names represent one physical source or multiple unresolved entries.

Consequently the complete population support matrix was not produced. Do not quote the planned coverage intersections or treat this as a successful data preparation/model run. A future coverage run would need a separate registration for native observation-row identities and unresolved alias/source associations. This is a failed prerequisite, not permission to repair identities silently.

Why more indicators alone do not identify the fraction

For binary indicator vector X and hidden state Z, the observable distribution is p(x)=(1−π)p0(x)+πp1(x). Without justified restrictions on within-class response distributions, many prevalences give the same observations. Even a known class-1 distribution and correctly oriented informative indicators do not generally remove that ambiguity.

The checked-in rational witness uses three indicators. Both models have the same eight-pattern observable distribution and identical class-1 response, with positive probability 4/5 for each indicator in class 1:

Mathematical witness	Prevalence	Class-0 positive probability	Class-0 pair covariance
Dependence allowed	1/10	1/3	14/225
Product class-0 response	3/10	1/5	0

Every probability is nonnegative, both classes normalize to one, class 1 is strictly more positive for each indicator, and both mixtures agree exactly for all eight patterns. These 10%/30% values are mathematical counterexample parameters, not astrophysical estimates. The example shows why assuming conditional independence can choose a fraction that the observables alone do not identify. It does not assert that every restricted latent-class model is unidentifiable, or that Hi-GAL must have either example prevalence.

The same ambiguity can occur within a fixed covariate stratum. Mass/distance adjustment alone cannot certify independence or response transfer. Even with an assumed transferable known p1=q, nonnegativity of p0 gives only a conditional bound π<=min p(x)/q(x); the witness bound 199/640 is also mathematical, not a Hi-GAL bound. Actual constraints would require scientifically justified class responses, dependence limits, source ownership and treatment of selection and missingness. Agreement with the old 19% figure supplies none of those.

Scientific conclusion and stopping decision

This gate does not establish an identified physical hidden-protostar fraction or lifetime correction. The approximately 9–25% estimator spread and 45–55% corrected-share scenarios remain descriptive sensitivity. The observed E15 counterparts and enrichment support follow-up, while reddening, neighbouring sources, evolutionary tracer windows and uncertain ownership remain competing explanations. Stop before fitting N20 under the current assumptions.

Exact witness, terminal failure, input hashes and identity-conflict exports are in artifacts/n20_prefit_gate_20261006/. The field coverage remains incomplete; no population precision/recall, new star, massive-protostar exclusion or physical birth was established. The external Atlas remains unpublished at this revision, pending the previously requested cancellation approval.