Independent reproduction and construct validity of the C3 crossing

Stage: REPORT_EN
Cutoff date: 2026-11-06
Classification: Reproductive clock and delaying perimenopause
Nature of the work: confirmatory methodological and computational study; not a clinical, biological, or interventional study.
Question: Does an independent reimplementation that derives E/A/N−/N+ from complete calendars, incorporates nondegenerate H_pre, three generative families, two languages, and final support ≥0.10 reproduce in C3 the same mark, sign, and simultaneous lower bound Φ_source−Φ_selected>0.05 at both horizons, or does the crossing disappear after correcting label construction, shared dependence, and marginal positivity?

1. Executive scientific abstract

Verdict: C3 cannot be declared reproduced under the M1-9 confirmatory protocol. However, the study also did not show that the numerical crossing disappears after correcting the label, shared dependence, and H_pre, because those corrections were never executed in a complete pipeline.

The M1-8 antecedent reported eight positive N− and N+ contrasts across two families and two horizons. T=Φ_source−Φ_selected ranged from 0.061493 to 0.073885, and the smallest simultaneous lower bound was 0.055044. Yet that program was deleted; raw outputs and random states were not retained; N was generated as a cause rather than derived from calendars; H_pre was degenerate; G1 and G2 shared a program and architecture; and final selection in high U was approximately 0.0615–0.0635. Those tables are therefore a narrated computational antecedent, not an auditable reproduction.

M1-9 prospectively fixed a final-selection floor of 0.10 in every required stratum. Exact replay of the inherited factorized selector produced:

P(S=1 | U=1) = 0.45 × 0.55 × 0.65 × 0.95^12 × 0.975^12 = 0.0641545128798133.

Python 3.15 and R 4.6.1 agreed numerically to an absolute difference below 7×10^−17. If this product represents the authentic conditional probabilities of the historical selector, its U=1 average lies below 0.10 and, by the weighted-average identity, at least one nonempty H_pre quintile within U=1 must also lie below the floor. Removing withdrawal entirely still yields 0.0869304; a favorable ±0.01 sensitivity across the five components yields 0.0868919. The arithmetic identity is robust.

Adversarial review corrected a decisive overinterpretation. Support of 0.064 is positive and does not establish a universal structural positivity violation or mathematical nonidentification. It establishes failure of the M1-9 protocol robustness gate, conditional on the factorization corresponding to the selector that was meant to be corrected. Python and R reproduced the same formula; they did not generate complete calendars, construct H_pre, derive E/A/N−/N+, execute G1/G2/G3, or estimate T. Moreover, loss of the M1-8 code prevents authentication of whether entry, LM12, no-open, continuity, and permanence were constant conditional probabilities, marginal targets, or emergent history-dependent processes.

The central conclusion is therefore three-state:

1. Confirmatory reproduction of C3: rejected under the factorized selector and the 0.10 floor.
2. Containment or disappearance of T: not demonstrated. Corrected T, mark, and sign were not opened after the veto.
3. Construct validity: open. It remains untested whether derived N redistributes to E, A, open candidate, censoring, or no event.

The priority uncertain link is equivalence between the inherited factorized selector, S-factor, and the selector emerging from complete calendars, S-calendar. The current primary hypothesis, M1-9-H2S-c v1, states that they may not be semantically equivalent. The minimum experiment D0-MANIFEST-AUTH must resolve that equivalence before a single mark or T is estimated. Only if D0 authenticates the semantics is a later test, D1-CONSTRUCT-FRONTIER, justified at a new explicitly non-C3 boundary with prevalidated support. That test would discriminate label/dependence artifact from narrow compositional depletion. No result in this project identifies a molecule, cell, tissue, human mechanism, fertile function, or intervention.

2. Scientific question and relevance

The question is not whether menstrual irregularity exists or whether reproductive transition has biology. It asks whether a specific computational signature survives a reproduction that removes four sources of fragility:

• imposed label: N−/N+ must emerge from dates and lengths rather than enter as causes;
• shared dependence: three families must differ in joint structure, not merely in name or link;
• degenerate history: H_pre must contain real, future-blind pre-landmark variation;
• marginal positivity: selection cannot leave only an extreme tail and then support a confirmatory claim.

The primary estimand is:

T_k,h,g,l = Φ_source,k,h,g,l − Φ_selected,k,h,g,l,

where k is N− or N+, h is H12 or H548, g is G1/G2/G3, and l is Python/R. Φ_source is first-mark incidence in all histories in the source frame. Φ_selected is the same incidence after entry, LM12, no-open, continuity, and permanence, but before the observation overlay. Φ_obs adds omission, date error, and censoring, while M=Φ_obs−Φ_selected measures observational distortion rather than transport.

The inherited signature requires the same N mark, positive sign, and simultaneous lower bound of T above 0.05 at both horizons. The 0.05 margin is methodological, not clinical. The 0.10 floor is likewise not a law of positivity; it is this project’s prospectively chosen confirmatory rule. The scientific relevance is avoiding two symmetric errors: calling a signal created by extreme selection a mechanism, or calling a pipeline null when it never executed the correction.

3. Scope, population, and life stage

This project’s population is synthetic: female menstrual histories conceptually restricted to ages 40.5–45.5 years, spanning late reproductive life and the approach to early transition. The inferential unit is the simulated woman. Each history must include at least 18 pre-landmark segments, twelve observable segments for LM12, follow-up for H12 and H548, and a tail of up to ten segments to adjudicate open candidates.

No human participants or current Lua data were included. No PHI, PII, private genomes, private clinical data, or new cohorts were used. Pregnancy, postpartum status, hormone therapy, hysterectomy, oophorectomy, and gonadotoxicity may only be represented as prespecified transitions or censoring; they were not used to infer biology.

Age 42.84 years is an inherited reference from a population change point, not an individual boundary. The primary analysis must use continuous age. Future STRAW+10, future FMP, and the derived mark cannot define entry, H_pre, or gates.

Causal boundaries are strict. N−/N+ are marks produced by an operator on calendars, not functional phenotypes. U_truth is a latent DGP variable and does not represent observable ovarian reserve, HPO function, endometrium, thyroid, metabolism, or human susceptibility. Computational reproduction would not demonstrate competent ovulation, fertile years, delayed perimenopause, benefit, safety, healthspan, or longevity.

4. Background knowledge and mechanistic map

4.1 Definition of the calendar construct

Let L_t be the length of segment t and Δ_t=L_t−L_t−1.

• Candidate: first t with |Δ_t|≥7 days.
• Confirmation: next change with |Δ|≥7 within the following ten segments.
• J: latency in segments between candidate and confirmation.
• Reversal: candidate and confirmation signs are opposite.
• No reversal: signs are the same.
• E: J=1 with reversal.
• A: J=1 without reversal.
• N−: J≥2 with reversal.
• N+: J≥2 without reversal.
• First mark: first qualifying confirmation; marks compete and are absorbing.
• Open candidate: censoring when its window cannot close; never converted to “no event.”
• H12: confirmations closed within the first twelve post-landmark segments.
• H548: confirmations dated by day 548 from the same trajectory; never approximated as 548/30.

ReSTAGE and STRAW+10 support the absolute core: a persistent difference of at least seven days recurring within ten bleeding segments. They do not support partitioning by J, reversal, or N−/N+, and they do not establish that the segments are ovulatory cycles.

4.2 Multiscale chain

The complete chain has two zones:

1. Latent biological zone, not identified: genes and proteins → cellular states → ovary, endometrium, HPO, thyroid, and other tissues → systemic dynamics → bleeding dates and lengths.
2. Observable methodological zone: calendar → candidate and confirmation → J and sign → mark → sequential gates → selected composition → T → simultaneous band.

The first is many-to-one: multiple biological and observational processes can produce the same calendar, and the same state can produce different marks through noise, duration, gaps, or competition among first marks. No M1-9 source links a particular molecule, cell, or tissue to N or T.

4.3 Minimum mechanism for positive T

A positive crossing does not require selection to cause irregularity. It requires a negative association between N risk and gate survival:

U/H_pre → higher P(N)
U/H_pre → lower P(S=1)
Cov(Y_N,S)<0 → E(Y_N | S=1)<E(Y_N) → T_N>0.

With prespecified strata Z, T decomposes into between-stratum composition change and residual within-stratum selection:

T = Σ_z (p_z−p_z^S)μ_z + Σ_z p_z^S(μ_z−μ_z^S).

Degenerate H_pre can conceal the second term. A calendar-derived H_pre can also be a proxy, mediator, or collider. Requiring variance is therefore insufficient; the role of each domain must be declared and the effects of removing age, dispersion/trend, serial dependence, or observation components must be examined.

4.4 Sequential rather than static selection

Composition updates through:

source → entry → LM12 → no-open → continuity → permanence = selected.

The adversarial problem is that LM12, no-open, and continuity may reuse the same observational fact. If an open candidate or a gap determines two gates, multiplying constant Bernoulli probabilities can double-count the same history. Early irregularity may also cause LM12 or permanence failure; selection is then a descendant of the calendar rather than a parallel path from U. Two topologies with identical margins—common cause U→mark and U→selection versus C_pre→selection—may generate similar T without identifying the causal mechanism.

5. Evidence method

All verified SCOPING, EVIDENCE_MAP, EVIDENCE_VERIFICATION, MECHANISTIC_SYNTHESIS, COMPUTE_DECISION, COMPUTE_OPTIONAL, HYPOTHESIS_GENERATION, ADVERSARIAL_REVIEW, and EXPERIMENT_DESIGN artifacts were integrated. The prior search was directed rather than an exhaustive systematic review.

Priority was given to:

• longitudinal human cohorts with calendars;
• primary methodological texts on transport, overlap, and positivity;
• empirical studies of reproducible simulation;
• experimental evidence on multiversion software;
• internal M1-6 through M1-8 artifacts for C3 lineage.

For each decisive source, design, population, n, comparison, effect, uncertainty, DOI/PMID, and limitations were verified. Uncertain external claims were narrowed when the primary text did not support the broader reading. Derry was reclassified as a reanalysis of the same TREMIN archive rather than an independent replication. Paramsothy was interpreted as discordance under specific cadences and definitions, not mutual biological invalidity. Wang reports gap handling for a late 60-day marker, not N or T. Crump shows that trimming around 0.10 changes the estimand; it does not validate a universal threshold.

Evidence was separated by modality:

• Direct human: calendar operator, age, gaps, and measurement discordance.
• Direct methodological: selection, transport, overlap, positivity, MCSE, and reproducibility.
• Internal computational: narrated M1-8 C3 and M1-9 arithmetic replay.
• Animal, in-vitro, and ex-vivo: none directly relevant to N, source, selected, or T.
• Inferred: negative risk–selection covariance can generate positive T; it does not prove human occupancy.

6. Evidence map

The global pattern is asymmetric. The absolute operator has descriptive human support. Selection can move estimands, and lack of overlap can invalidate inference. But the specific N−/N+ combination, C3 gates, horizons, 0.05 margin, and T value have no external validation.

7. Contradictory evidence and null findings

1. Useful but nonspecific operator. ReSTAGE links the persistent difference to relative proximity to FMP, while Derry shows frequent occurrences decades earlier. The leading explanation is that the operator detects variability and requires age/history, not that it is a specific biological node.
2. Calendar, interview, and FSH are not interchangeable. Negative κ values may reflect cadence, thresholds, selection on observed FMP, and different constructs. They do not show that calendars lack value or that endocrinology invalidates calendars.
3. A gap is not absence of an event. Gap handling strongly shifted time to a late marker, but that finding does not quantify M or T for N.
4. M1-8 showed local coherence and global fragility. Eight C3 contrasts crossed 0.05; low-N, opposing gates, and truncated-normal susceptibility did not preserve the conjunction. Local existence is not general robustness.
5. Arithmetic reproduction is not pipeline reproduction. Python/R agree on 0.0641545 but share formula and semantics. They did not test calendars, mark, families, or band.
6. Support below 0.10 is not zero support. The gate fails, but the positive value could permit precise estimation of a different target or under another rule. “Structural positivity” and “universal nonidentification” are therefore withdrawn.
7. The veto was algebraically predetermined. Freezing parameters that yield 0.064 while demanding 0.10 made the full signature impossible to observe. This is a useful diagnosis of internal incompatibility, not a construct experiment.
8. Disappearance of T was not observed. T was not calculated; containment, reversal, and mark redistribution were also not observed. Any statement claiming them would be false.

8. Multiscale mechanistic synthesis

Molecular, cellular, and tissue scales

The evidence does not localize the signature. FSH, AMH, inhibin B, steroids, granulosa/theca, corpus luteum, endometrium, thyroid, HPA, and metabolism are plausible antecedents of a human calendar, but none was measured against N or T. Bleeding is an integrated output and is not always menstrual; identical sequences can arise from different mechanisms.

Scale conclusion: direct human evidence supports the operator, while any upstream biological mechanism is inferred only. Confidence in a molecular localization is nil.

Calendar and construct

The absolute operator is reproducible. Partitioning by J and sign is computable but lacks external validity and a retained independent population execution. Absorbing first marks create competition: reducing N can increase E/A without altering the underlying dynamics. Open candidates must remain censored.

Scale conclusion: N is a construct hypothesis, not a biomarker.

Selection and transport

Source→selected depletion can produce positive T when risk and gate survival covary negatively. Yet that covariance may represent a common cause, selection descending from history, double counting, or a collider. Positive T alone would not identify the causal mechanism.

Scale conclusion: the formal mechanism is well defined; its realization and causal meaning remain open.

Observation and two clocks

H12 and H548 must arise from one history. Duration and gaps may change the number of opportunities within 548 days without changing the first twelve opportunities. Omission and date error produce M, not T. The duration×gap interaction, M1-9-H3O-clock v1, remains unexecuted.

Scale conclusion: any clock divergence must be localized to calendar, selection, or observation rather than automatically labeled physiology.

9. Computational layer

9.1 Decision and tool

Local computation was selected because only reimplementation can adjudicate construct, selector, and support. Public bioinformatics and BioNeMo were excluded: expression, variants, structures, and embeddings do not contain calendars, the source frame, gates, or T.

9.2 Executed result

The factorized selector yielded:

Python/R agreement was exact for the decision. Sensitivities were:

With fixed early gates and withdrawal 0.025, the gap hazard would have to fall from 0.050 to ≤0.0142018 to reach 0.10. With fixed hazards, the early-gate product would have to increase 55.87%. These figures quantify required retuning; they do not authorize it.

9.3 Adversarial correction

The calculation is precisely a support-gate replay of S-factor. It was not complete D0R. It kills confirmatory reproduction under that semantics but leaves open:

• manifest authenticity;
• S-factor/S-calendar equivalence;
• composition of derived N;
• three generative families;
• both horizons and T;
• duration×gap interaction;
• performance of the HT1 audit.

The result is H2 computational maturity for the arithmetic identity and H0 for the corrected selector, the human construct, and biology.

10. Primary hypothesis: M1-9-H2S-c v1 — manifest discordance

Falsifiable statement

The value 0.0641545 belongs to a factorized surrogate of M1-8 and may not be equivalent to the selector produced by complete calendars, nondegenerate H_pre, and derived no-open/continuity; the protocol veto can therefore be correct for the frozen text without being equivalent to the intended scientific object.

Lineage

M1-8-K1–K5 → M1-9-H2S v1 → adversarial revision M1-9-H2S-c v1. The hypothesis arises because the historical code was deleted, early gates were calibrated contrasts, and COMPUTE_OPTIONAL only repeated a formula.

Mechanism

S-factor treats entry, LM12, no-open, gap, and withdrawal as constant conditional probabilities. S-calendar derives completeness, open candidate, and continuity from a complete history. If LM12 and continuity share gaps, or no-open depends on the candidate, factorization can double count or impose nonexistent independence. H_pre can modify gates and change the U=1 average.

Predictions

1. Two independent reviewers will find at least one denominator or semantic ambiguity in the historical manifest; or
2. P(S_calendar=1|U=1) will differ from P(S_factor=1|U=1) by more than 0.005; or
3. averages will be close but at least one U×quintile verdict will change; or
4. leave-one-domain-out will show that gap/completeness voted in more than one gate.

Evidence for

• M1-8 code and outputs were deleted;
• historical H_pre was degenerate;
• no-open and LM12 did not arise from a complete prehistory;
• M1-9 did not generate S-calendar;
• the quintile proof depends on 0.064 being the authentic mean of the corrected selector.

Evidence against

• M1-8 reported high-U selection ≈0.0615–0.0635, close to 0.0641545;
• the product may reasonably represent the historical pipeline;
• a small discrepancy would not alter the veto.

Kill criteria

Kill if D0-MANIFEST-AUTH places all simultaneous CI90% for ΔS_U1 entirely within [−0.005,0.005], preserves the same verdict against 0.10 in every nonempty stratum, finds no double counting, and obtains concordance across independent implementations.

Status and maturity

Proposed, priority 1, H0. If supported, historical C3 is unauthenticatable/nonreproducible by specification. If killed, the narrow H2S-a protocol veto applies to the correct object.

11. Competing hypothesis: M1-9-H1R v2 versus M1-9-H2S-b v2

Contrary hypothesis M1-9-H1R v2

At one prespecified boundary distinct from C3, with support ≥0.10 demonstrated before outcomes, the same derived N will retain positive sign and simultaneous T>0.05 in three families, two horizons, and two languages.

Construct rival M1-9-H2S-b v2

At that admissible boundary, imposed N mass will redistribute when the mark is derived from calendars and/or lose concordance when joint dependence changes, showing that the inherited signature depended on imposed labels or shared architecture.

Lineage

H1R v2 descends from M1-8-AR-H1R v4 → M1-9-H1R v1, which is refuted for C3 reproduction. H2S-b descends from M1-8-K1–K4 → M1-9-H2S v1. Neither has been tested in an admissible region.

Rival mechanisms

• H1R v2: intermediate attrition preserves sufficient support and maintains Cov(Y_N,S)<0.
• H2S-b v2: imposed labels circularly aligned outcome and gates; deriving the mark moves mass to E/A/open/no-event, or G3 changes the within-stratum term.

Discriminating predictions

1. If the imposed branch passes and the derived branch fails, with C_T=T_imposed−T_derived outside [−0.01,0.01], H2S-b wins.
2. If both branches agree, the same N passes all 12 combinations, and C_T remains within ±0.01, H1R v2 is strengthened.
3. If G1/G2 pass and G3 changes mark or sign with valid margins, the shared-dependence explanation is strengthened.
4. If both branches fail, the result is not attributed to the construct.
5. If support fails, the experiment is nonestimable and no second boundary is tested.

Evidence for H1R v2

The covariance identity permits real depletion, Cole–Stuart shows that composition can move estimands, and M1-8 showed sign coherence. None validates the full conjunction.

Evidence for H2S-b v2

N was generated as a cause in M1-8, H_pre was degenerate, G1/G2 shared a program, no human validation of N exists, and alternative cells did not reproduce the full signature.

Kill criteria

• H1R v2 dies for SA1 after any failure of support, mark, sign, family, horizon, language, control, or precision.
• H2S-b v2 dies if derived and imposed marks agree and the derived branch retains the full signature with valid support.

Status and maturity

Both are proposed at H0. D1 can raise one to H2 computational-local maturity, never to human observational evidence.

12. Translational hypothesis: M1-9-HT1 v2 — support-first audit

Falsifiable statement

In a synthetic holdout bank with known source-level truth, a pipeline that derives the mark, separates source/selected/observed, and stops inference at insufficient support will reduce decision errors versus naive evaluation without losing more than five percentage points of sensitivity for estimable crossings.

Mechanism

Naive evaluation conflates imposed labels, selection, observation, and nonestimability. The audit introduces barriers: construct → controls → commensurability → support → precision → signature. The expected benefit is fewer false crossings and false containments; the possible cost is vetoing true edge signals.

Predictions

• lower three-state error in cells with low support, M opposite T, or discordant latent labels;
• audited−naive sensitivity no lower than −0.05;
• persistent advantage in a family created by an external team;
• more “nonestimable” results but fewer incorrect conclusions.

Evidence for

The M1-9 replay prevented narration of T after a failed gate; Petersen supports separating support from precision; Morris, RepliSims, and Knight–Leveson support persistence and common-error control.

Evidence against

One self-vetoed case does not estimate operating characteristics. “False physiological attribution” needs a closed rubric. U_truth and source truth would be unavailable in a human application.

Kill criteria

Kill if D2-AUDIT-BLIND does not reduce error, loses more than 0.05 sensitivity, depends on future/U_truth inaccessible to the evaluator, or loses its advantage in the external family.

Status and maturity

Weakened/proposed, H0. HUMAN_QA_REQUIRED before any human extension. It is neither a biomarker nor a validated clinical tool.

13. Falsifiable predictions and kill criteria

Cross-cutting rule: a nonestimable result does not kill a hypothesis about T; it kills the admissibility of the test. Parameter changes do not refute the C3 veto; they define a different object. A nominal signal without a band does not strengthen H1R. P>0.05 does not establish equivalence.

14. Discriminating experiment

14.1 D0-MANIFEST-AUTH — minimum decisive experiment

Question: Do S-factor and S-calendar represent the same selector?

Design:

1. Two reviewers independently extract from pre-M1-9 artifacts the semantics of entry, LM12, no-open, continuity, and permanence: marginal, conditional, emergent, or ambiguous.
2. Each gate records denominator, clock, dependence, relation to gaps/open candidate, and overlap with other gates.
3. S-factor and S-calendar are implemented without outcomes.
4. G1, G2, and G3 share only permitted targets.
5. Python and R independently implement S-calendar; a third state machine audits S-factor.
6. H_pre is built pre-landmark and partitioned into age, history, dependence, and observation domains.

Population and size: 50,000 histories per U×family×language, 600,000 total; one blind expansion to 100,000 only if the simultaneous half-width exceeds 0.005.

Primary endpoint: ΔS_U1=P(S_calendar=1|U=1)−P(S_factor=1|U=1). Equivalence requires every simultaneous CI90% to lie within ±0.005 and each stratum to preserve the same verdict against 0.10.

Controls: null selector, one gate at a time, deliberate double counting of a gap, H_pre permutation, open-candidate sentinels, and leak testing.

Decision:

• discordance or irreducible ambiguity: C3 unauthenticatable/nonreproducible by specification;
• equivalence plus any stratum <0.10: protocol veto confirmed, without inferring T;
• equivalence plus all strata ≥0.10: audit transcription before opening outcomes;
• band touching the margin: inconclusive.

14.2 D1-CONSTRUCT-FRONTIER — only after D0

A single λ trajectory on the logit scale uniformly attenuates U contrasts in the gates. Without outcomes, the largest λ whose estimated minimum support is 0.12 is chosen once; independent evaluation requires a one-sided 99% lower bound ≥0.10. No second λ is tested if T fails.

G1, G2, and G3 generate complete calendars. Derived and imposed-label control branches are compared on the same histories. Two causal topologies with the same margins are executed: common cause and selection descending from C_pre.

Size: 256,000 women per family×language, 1,536,000 histories; one blind expansion to 512,000 if any primary half-width exceeds 0.01.

Support: ≥2,500 selected per stratum, one-sided 99% lower bound ≥0.10, and no score bin with ≥1% of source mass and zero selected. ESS=400 is withdrawn as an authority.

Primaries: 24 T values in the derived branch/topology A. The minimum signature requires the same N and simultaneous LI95% >0.05 in 12 family×horizon×language combinations. C_T compares imposed and derived branches with ±0.01 margin.

Interpretation: D1 tests a computational mechanism in SA1, not reproduction of C3.

14.3 D2-AUDIT-BLIND — methodological translational validation

An independent team generates 400 holdout cells, 100 per class: estimable crossing, estimable containment, insufficient support, and observational distortion. Blinded evaluators apply naive and audited pipelines.

Coprimaries: three-state error and sensitivity for estimable crossings with noninferiority margin −0.05. Secondaries: false crossing, containment/nonestimability confusion, and improper biological attribution under a closed rubric.

15. Biomarkers and stratification

No biomarker was validated in this project.

• The persistent operator is a calendar marker for descriptive staging, not a molecular biomarker.
• N−/N+ is a human-unvalidated computational taxonomy.
• U_truth is a DGP label unavailable as a clinical variable.
• H_pre is a history vector, not a biological entity. It may predict selection but can also mediate or collide.

Stratification by U_truth×quintile(H_pre) only audits a simulation. In D0 and D1, H_pre domains are:

1. continuous age;
2. center, dispersion, trend, and tails of segment length;
3. serial dependence;
4. gaps, open candidate, and completeness.

Leave-one-domain-out, continuous score density, and absence of source bins with zero selected are required. Future human translation would require an enumerated source frame, an observable variable distinct from U_truth, reproducible metrology, and an orthogonal ovulatory/functional endpoint. Until then, calling N or H_pre a biomarker would be premature.

16. Individual variability

Relevant heterogeneity occurs at several levels:

• continuous age and actual distance to transition;
• calendar median, MAD, trend, and tails;
• autocorrelation and semi-Markov dynamics;
• gap history and completeness;
• open candidate at landmark;
• biological duration versus missing registration;
• competing first mark;
• pregnancy, therapy, or censoring exposure;
• dependence between early calendar and later selection.

Historical human cohorts show that the same operator appears very early in some women and near FMP in others. Gaps affect a large fraction of TREMIN. Discordance among calendar, interview, and FSH shows that cadence and source matter. None of these differences authorizes treating synthetic U as a single human biology.

Life stage also limits transportability. TREMIN began with Minnesota students; Melbourne was predominantly Anglo-European; SWAN was more diverse, but decisive analyses selected women with observed FMP and follow-up conditions. There is no direct Mexican/LATAM validation of N, C3, or T. That absence must not be filled by extrapolating effect sizes.

17. Pharma relevance and maturity

Readiness verdict

Current no-go for target selection, active development, therapeutic partnering, compound selection, clinical biomarker, or efficacy claim.

There is no molecular target, target engagement, tissue mechanism, human prevalence, pharmacological response, or functional endpoint. The C3 signature is blocked by authenticity and by the factorized selector’s protocol gate.

The only plausible opportunity is methodological: a validated audit could improve research quality in studies using digital menstrual endpoints or selected samples by separating transport, observation, and support before mechanism or efficacy is attributed. This would be endpoint research QA, not a clinical product or intervention.

Maturity by hypothesis

No simulation can raise a hypothesis to H3. H3 requires observational reproduction with an observable source frame; H4 requires appropriate experimental validation. H5 is not assigned here.

18. Limitations

1. M1-8 code and outputs were deleted; historical authenticity cannot be recovered by direct inspection.
2. The 0.0641545 result is exact for S-factor, but equivalence to S-calendar was not tested.
3. Python and R shared formula and parameters; they were not two independent complete pipelines.
4. The 0.10 floor, 0.05 margin, ±0.005 equivalence, and C_T ±0.01 are methodological decisions, not clinical thresholds.
5. The design self-vetoed before opening the construct; this prevents false inference but leaves the label question unanswered.
6. N−/N+ lacks external human validation.
7. Human operator evidence comes from historical cohorts with heterogeneous gaps, selection, and metrology.
8. Derry shares TREMIN with ReSTAGE and is not independent replication.
9. Paramsothy and Wang inform measurement/gaps, not T or N.
10. H_pre may be a proxy, mediator, or collider; stratification does not identify causality.
11. U_truth has no established human equivalent.
12. Two languages and three families reduce but do not eliminate common specification errors.
13. A future SA1 boundary would show local existence, not generality, and never C3 reproduction.
14. No animal, in-vitro, or ex-vivo modality directly informs the estimand.
15. Ovulation, fertility, delayed perimenopause, benefit, safety, healthspan, and longevity cannot be inferred.

19. Conclusions

M1-9 produced a concrete scientific result, but one narrower than its initial question. The factorized version of C3 is incompatible with the confirmatory 0.10 floor: p_final(U=1)=0.0641545. That is sufficient to prevent C3 from being declared reproduced under the protocol. It is not sufficient to claim structural positivity failure, T=0, containment, or disappearance of the crossing.

The project also did not execute the corrections intended to validate the construct. It did not generate complete calendars in three families, build nondegenerate H_pre, derive N−/N+ in two independent pipelines, or estimate the simultaneous bound. The correct statement is therefore not “the crossing disappeared,” but:

Confirmatory reproduction of C3 was vetoed by a protocol gate under the factorized selector; equivalence of that selector to the corrected pipeline, and therefore validity of the mark and the numerical fate of T, remain open.

The priority is no longer to find another crossing. It is to authenticate the object. D0-MANIFEST-AUTH decides whether 0.0641545 belongs to the intended scientific selector. If D0 confirms equivalence, C3 is inadmissible under this protocol. If it confirms discordance, C3 is unauthenticatable/nonreproducible by specification. Only then may a new non-C3 boundary separate label/dependence artifact from narrow compositional depletion.

The cumulative contribution to Lua Labs is an epistemic rule for line M1: classifier, selection, observation, and support are different objects. A calendar signal does not localize biology; a selected tail does not establish human transport; a failed gate does not establish a null; and numerical reproduction does not exist without retaining the executable object.

20. References

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2. Derry G, Derry P. Analysis of the STRAW Operational Definition of the Early Menopausal Transition. Women’s Reproductive Health. 2014;1:21–30. DOI: 10.1080/23293691.2014.901797.
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4. Wang Y, Little RJA, Nan B, Harlow SD. A hot-deck multiple imputation procedure for gaps in longitudinal recurrent event histories. Biometrics. 2011. DOI: 10.1111/j.1541-0420.2011.01558.x. PMID: 21361886. PMCID: PMC3279741.
5. Harlow SD, Gass M, Hall JE, Lobo R, Maki P, Rebar RW, et al. Executive summary of the Stages of Reproductive Aging Workshop + 10: addressing the unfinished agenda of staging reproductive aging. Fertility and Sterility. 2012;97(4):843–851. DOI: 10.1016/j.fertnstert.2012.01.128. PMID: 22341880. PMCID: PMC3340904.
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Internal computational provenance

• M1-8, COMPUTE_OPTIONAL: narrated C3 tables, controls, and selection; source code and raw outputs not preserved.
• M1-9, COMPUTE_OPTIONAL: deterministic replay of the factorized selector, Python/R commands, versions, and sensitivities.
• M1-9, ADVERSARIAL_REVIEW: correction from “structural positivity” to “protocol gate failure” and formulation of H2S-c.
• M1-9, EXPERIMENT_DESIGN: D0-MANIFEST-AUTH, D1-CONSTRUCT-FRONTIER, and D2-AUDIT-BLIND.