Robustness of crossing under sequential selection

Project: M1-8
Stage: REPORT_EN
Date: 2026-11-04
Classification: reproductive clock and delaying perimenopause; selection, identifiability, and transport of a menstrual classifier
Modality of the decisive evidence: mathematical and computational; longitudinal human and methodological links; no decisive animal, in-vitro, or ex-vivo evidence for the estimand
Final maturity: provisional H1→H2 computational signal; human occupancy H0; translation H0 and HUMAN_QA_REQUIRED

1. Executive scientific abstract

M1-8 asked whether the transport crossing found in M1-7 survived when a static selector and fractional clock were replaced by a more faithful history: entry, LM12, absence of an open candidate, continuity, and retention applied sequentially; two horizons read from the same discrete calendar; susceptibility-dependent duration and gaps; and two generative families calibrated by observable contrasts. For mark k∈{E,A,N−,N+} and horizon h, the estimand was

T_kh = Φ_source,kh − Φ_selected,kh.

The reported run produced a conditionally affirmative answer. In cell C3_candidate_N, N− and N+ retained a positive sign and simultaneous lower bounds greater than 0.05 across G1/G2 × {12 segments,548 days}. The smallest lower bound was 0.055044 for N+, G1, 548 days. Internal calibration therefore did not restore strict containment across the full eight-cell grid. The reported mechanism was almost entirely compositional: the proportion of the synthetic high-susceptibility stratum fell from approximately 0.50 in source to 0.100–0.109 among selected histories; all five gate-specific contributions for N+ had the same sign; and the within-stratum residual was small (−0.000171 to 0.002399). Duration attenuated and gaps reinforced the calendar contrast, but the crossing persisted when both channels were ablated; the clock modulated magnitude and was not its necessary origin.

Adversarial review prevents this output from becoming “demonstrated robustness.” The program and raw outputs were deleted after a hash was recorded; marks were generated as absorbing causes rather than emerging from complete calendars of lengths, candidates, J, and sign; H_pre was degenerate; and G1/G2 shared a program, architecture, and synthetic targets. C3 combined strong N risk, five concordant gates, and terminal positivity only just above 0.05, whereas C5_lowN, C6_opposing, and C7_truncnorm did not replicate the conjunction. The scientifically defensible result is therefore narrower:

There is a reported, internally coherent computational counterexample compatible with a sequential compositional crossing; there is not yet an auditable reproduction, proof that the mark emerges from the calendar, or evidence that a human population occupies that cell.

The surviving primary hypothesis is M1-8-AR-H1R v4: an independent and preserved reimplementation, with derived marks, nondegenerate H_pre, three families, and final support ≥0.10, will retain the same cell, mark, sign, and band beyond 0.05. Competitor M1-8-AR-H2S v4 holds that C3 is an extreme or non-identifiable region and that humanly estimable cells will remain contained. Translational hypothesis M1-8-AR-HT1 v4 remains parked: a source–selected–observed audit will be valuable only if it reduces false physiological attributions without vetoing true source-level signals by more than five percentage points in an independent bank.

The smallest discriminating experiment is D0R-M1-8-REPRO-CONSTRUCT, not a human cohort or molecular assay. It must preserve code and receipts, derive marks from lengths and dates, use independent implementations, add a third semi-Markov/copula family, introduce realistic pre-LM12 history, and execute a duration×gap factorial with simultaneous bands. Until this gate is passed, the result identifies neither human magnitude, ovarian physiology, fertility, delayed perimenopause, nor a therapeutic opportunity.

2. Scientific question and relevance

The exact question was whether there is one calibrated cell c*, one mark k, and one direction d such that the simultaneous lower bound of d·T_k exceeds 0.05 in both horizons and in G1/G2 after sequential selection and a discrete calendar, or whether composition and specification restore strict containment in every valid cell.

This matters because a cohort may recover risk with high precision among people who complete run-in and follow-up yet fail to transport that risk to the source population. Confusing Φ_obs, Φ_selected, and Φ_source can turn a compositional transformation into a physiological explanation for onset of the menopausal transition. M1-8 does not ask which tissue generates irregularity or whether changing the pattern prolongs fertile years. It first asks whether the contrast that would motivate that search is identifiable and robust.

The 0.05 margin is an inherited methodological rule. It is not a validated clinically important difference, does not represent harm or benefit, and does not measure ovulatory function, oocyte competence, fertility, FMP, healthspan, or longevity.

3. Scope, population, and life stage

The conceptual population is naturally cycling women aged 40.5–45.5 years, with a future-blind reference and a biological possibility of constructing a pre-landmark history. Age must be modeled continuously. CP_σ=42.84 years is a model- and cohort-dependent population estimate, not an individual biological boundary.

The primary objects are:

• Φ_source: incidence of the first mark in all eligible histories before analytical gates;
• Φ_selected: incidence after entry, LM12, no-open, continuity, and retention, before the observation overlay;
• Φ_obs: incidence after omission, date error, and censoring;
• T=Φ_source−Φ_selected: transport;
• M=Φ_obs−Φ_selected: metrology, analyzed separately.

A candidate appears when |L_t−L_(t−1)|≥7 days and is confirmed by the next change of at least seven days within ten segments. The competing and absorbing marks are E (J=1, reversal), A (J=1, no reversal), N− (J≥2, reversal), and N+ (J≥2, no reversal). A candidate whose window cannot close is censored; it is never converted into a negative.

The horizons are the first 12 complete segments and the first 548 days from the same reference. The latter is not approximated by 548/30. Pregnancy/postpartum, gonadal suppression, hormone therapy, hysterectomy, oophorectomy, and gonadotoxic treatment must be recorded as transitions or prespecified exclusions when they preclude interpretation of the natural calendar; histories are not removed merely for being extreme.

No current Lua data, PHI, PII, private genomes, or real participants were used. There is no prescription, diagnosis, or intervention proposal.

4. Background and mechanistic map

4.1 Direct statistical mechanism

For the first-mark indicator Y_kh and final selection S_h, the exact identity is:

T_kh = −Cov(Y_kh,S_h)/E(S_h).

If Z=(U_pre,H_pre) summarizes susceptibility and pre-landmark history:

Cov(Y,S)=Cov{p(Z),s(Z)} + E{Cov(Y,S|Z)}.

The first term is compositional change between strata. The second captures residual within-stratum dependence: even with the same baseline history, the trajectory producing the mark may alter continuity or retention.

For gates G_1,…,G_J, let S_j=S_(j−1)G_j and μ_j=E(Y|S_j=1). The contrast decomposes exactly:

T = μ_0−μ_J = Σ_j Δ_j,

Δ_j = −Cov(Y,G_j|S_(j−1)=1)/E(G_j|S_(j−1)=1).

Thus, equal final retention does not imply equal transport. Containment may arise because every Δ_j is small or because informative gates of opposite sign cancel. A crossing may persist when several contributions share a sign or one dominates without cancellation.

4.2 Multiscale chain

The menstrual calendar integrates the follicular cohort, HPO feedback, ovulation, corpus luteum, endometrium, uterine pathology, and observation. Lifetime memory supplies plausible generators: granulosa-cell inhibin B and early FSH may advance follicular selection; luteal and endometrial function may alter bleeding duration and date; thyroid, metabolism, stress, inflammation, and treatment may affect both trajectory and participation. However, no gene, receptor, cell, or tissue was measured jointly with source, the five gates, and the four marks.

Human evidence supports several baseline links but not localization of U:

• inhibin B and FSH change with reproductive age and may alter follicular timing;
• the right tail of duration widens near the transition;
• entry, treatment, gaps, withdrawal, and censoring alter which histories remain observable;
• biological duration and a recording lapse are conceptually distinguishable, although historically confounded.

Therefore, U_pre is a many-to-one latent construct. It is not a hormone, gene, diagnosis, cell, or tissue. N−/N+ are marks from an operator applied to bleeding, not ovulatory states or functional outcomes. J≥2 removes the exact shared segment from two adjacent differences, but not slow state, drift, gaps, error, or selection.

4.3 Discrete clock

At 12 segments, the nominal number of opportunities is fixed, although duration and gaps may prevent windows from closing or histories from remaining observed. At 548 days,

N_548=max{n: Σ_(t=1)^n D_t≤548},

so susceptibility-dependent duration changes the number of opportunities. Gaps may act before selected, affecting continuity/retention and T, or only in the observational overlay, affecting M. Merging duration and gap prevents attribution of the difference between clocks.

5. Evidence method

The SCOPING, EVIDENCE_MAP, EVIDENCE_VERIFICATION, MECHANISTIC_SYNTHESIS, COMPUTE_DECISION, COMPUTE_OPTIONAL, HYPOTHESIS_GENERATION, ADVERSARIAL_REVIEW, and EXPERIMENT_DESIGN artifacts were integrated. The hierarchy was:

1. mathematical identities and estimand rules;
2. computational results with stored truth, downgraded when an executable receipt was absent;
3. longitudinal human and methodological studies for entry, duration, gaps, loss, and calibration;
4. human physiology for plausibility of generators, without attributing the estimand;
5. explicitly labeled inference.

DOIs/PMIDs and decisive numbers were verified during the evidence stages. Human findings were separated from computational findings. Animal, in-vitro, and ex-vivo evidence was not used to adjudicate T because none resolves the source–selected framework. Adversarial evidence was sought: low-N composition, truncated tails, opposing gates, lack of positivity, related families, mark construction, and code deletion.

A “same cell” was defined by source composition, risk contrasts, probabilities and composition after every gate, susceptibility distribution, duration, and gaps—not by shared nominal coefficients. Calibration using Φ_selected, T, Δ_j, or the future mark among selected histories was prohibited because it would circularly impose the answer.

6. Evidence map

The decisive human numbers were: ReSTAGE harmonized 735 TREMIN participants, 216 Melbourne, 279 Seattle, and 2,270 SWAN; 41–51% had intermittently missing data and the median was two gaps per woman. Huang analyzed 617 women and 95,246 segments; the mean changepoint depended on the distribution (42.84 years log-normal, 42.21 gamma), illustrating specification sensitivity. In SWAN, 963 women/37,288 cycles contributed to the transition-onset analysis and 431/18,305 to the FMP analysis; these were selected, overlapping subsamples, not independent sources. Taffe and Dennerstein followed 372 women for seven years and showed that fieldwork determines whether a blank denotes no bleeding or no recording.

7. Contradictory evidence and null findings

1. M1-7 and C3 refute universal containment within their classes, but most executed cells do not cross.
2. C5_lowN had point estimates ≈0.051–0.054 at H12, but its bands touched 0.05 and H548 fell to ≈0.045–0.049; it did not replicate the conjunction.
3. C6_opposing remained at |T|≤0.01460 and changed signs between clock/family, supporting cancellation or specification dependence.
4. C7_truncnorm remained at ≈0.022–0.027, showing that susceptibility scale and tail matter.
5. C4_candidate_common reached points near 0.04735, without a qualified crossing.
6. Controls C0_null and C1_risk_only had bands including zero. Breaking U→K or U→gates collapsed the C3 crossing.
7. C2_selection_only was not a total null at H548: U→duration→N_548→Y remained open. It is a per-segment risk control, not “selection only” for the calendar outcome.
8. Marginal calibration does not identify a latent copula. Two models may fit the same targets and differ in transport.
9. Austin and Putter 2026 found that DGP discordance may have little effect on AUC/Brier, but they studied prediction/calibration, not T; their result does not validate G1/G2 as replication.
10. Better metrology can recover Φ_selected without transporting to Φ_source. In C3, M was small and negative while T was positive and greater than 0.05.

These contradictions are not smoothed over: structural existence and human occupancy are different claims. “Non-identifiable,” “contained,” and “inconclusive” are separate terminal states.

8. Multiscale mechanistic synthesis

The most parsimonious explanation of the synthetic tables is concordant compositional depletion imposed in C3. The stratum with greater N risk also had lower probability of entry, completing LM12, having no open candidate, preserving continuity, and remaining. For N+, all reported contributions were positive. In G1-H12, for example, entry, LM12, no-open, continuity, and retention contributed 0.026275, 0.019124, 0.010384, 0.011824, and 0.004641, summing to 0.072247. G2 reproduced the pattern within the shared architecture.

That mechanism is statistical, not molecular. Selection does not “repair” or “damage” biology; it changes which histories remain in the denominator. Net containment can coexist with strongly informative gates when their contributions cancel. A net crossing can coexist with nearly correct metrology. The positive C3 sign means selection depleted histories at higher N risk; it has no physiological valence.

The small within-U residual cannot be generalized. With degenerate H_pre and generation that was nearly conditionally independent given U, a small residual was expected. In humans, run-in history, symptoms, treatment, age, gaps, and emerging trajectory may create within-stratum dependence, collider bias, and reverse causation. The defensible claim is only that C3 was coded mainly as binary composition.

At the biological layer, inhibin B–FSH, luteal function, endometrium, and systemic states remain competing generators. The crossing prioritizes none of them. Only a material, replicated human source-level residual would justify comparing follicular, luteal/endometrial, thyroid/metabolic, and technical domains on equal footing.

9. Computational layer

The decision was use: microsimulation was the only instrument capable of retaining source, gates, and selected simultaneously. BioNeMo, sequence embeddings, and public omics were omitted because they do not identify T.

The run documented Python 3.15.0, R 4.6.1, base seed 8108001, 128,000 histories per cell×family, 2,048,000 primary histories, 32 batches, and SHA-256 hash 81fa6b0381661d5133c6c48065159fca2dd27893fb335c1d5a6e09c0232b9a26. It used two-sided Bonferroni correction for 128 contrasts (z=3.546337887364). All eight cells passed the reported internal G1–G2 tolerances.

C3 results:

The receipt is insufficient for reproduction: the temporary code file and raw outputs were deleted. A hash without the object cannot verify identity, inspect leakage, or reconstruct the run. In addition, generating N−/N+ as causes and separately validating the state machine does not show that those marks emerge from the generated lengths. The correct terminal state is reported_local_crossing_pending_reproduction, not established robustness.

10. Primary hypothesis

M1-8-AR-H1R v4 — reproducible structural existence

Falsifiable statement: an independent, preserved implementation blinded to T that derives E/A/N−/N+ from complete calendars will retain in C3 the same mark, positive sign, and simultaneous T>0.05 bound across three families and both horizons, with nondegenerate pre-LM12 history and final selection probability ≥0.10 in every required stratum.

Mechanism: susceptibility/history increases propensity to N and concordantly reduces passage through several gates; the Δ_j contributions do not cancel.

Predictions: the witness and nulls are recovered; the derived mark agrees between two implementations; semi-Markov/copula G3 does not change mark or sign; the crossing survives without retuning C3; the band does not depend on the 0.05–0.075 floor; and the within-stratum residual may change without destroying dominant composition.

Evidence for: eight coherent estimates, directional controls, the sum of Δ_j, two generative links, and two clocks.

Evidence against: deleted code, assigned marks, degenerate H_pre, related families, extreme composition, marginal positivity, and failure of low-N/truncnorm.

Kill criteria: failure to reproduce C3 within MCSE; derived mark not N; sign change; any band touching 0.05; dependence on a single implementation/family; final support below 0.10; or failure of controls/persistence.

Status: proposed_weakened; provisional H1→H2; confidence 0.55. The human extension remains parked, H0, confidence 0.10.

11. Competing hypothesis

M1-8-AR-H2S v4 — containment or non-identifiability in human support

Falsifiable statement: after defining an observable source population, deriving marks from calendars, imposing continuous common support, and calibrating composition/gates to external human targets without selected outcomes, every estimable cell will remain within |T|≤0.05; C3-like cells will fail support or positivity before voting.

Mechanism: human N mass is smaller, the susceptibility gradient is continuous, and real gates do not concordantly deplete the same stratum; low-N composition, tail truncation, and opposing early/late contributions reduce or cancel T.

Predictions: an N risk ratio near 4, five gates in the same direction, and ample positivity will not coexist; H548 will fall first when observed N composition is used; support truncation will reduce extremes; and some frames will be non-identifiable rather than contained.

Evidence for: seven of eight cells do not win; C5/C6/C7 embody composition, cancellation, and tail effects; C3 leaves high:low selection near 0.12; no human source exists.

Evidence against: C3 shows that discreteness, sequence, and two families do not guarantee containment; human selection might be concordant.

Kill criteria: two independent source frames occupy C3-equivalent support and replicate the same mark/sign/band in both horizons; or a third family with external human composition retains the crossing and ample support.

Status: strengthened_narrowed; methodological H1/human H0; confidence 0.72 for the support threat and 0.40 for human containment.

12. Translational hypothesis

M1-8-AR-HT1 v4 — source–selected–observed audit before physiology

Falsifiable statement: in a holdout bank generated by an independent implementation, with observable source and frozen attribution rules, a sequential audit will reduce the false physiological-attribution rate relative to observed-only analysis and will not increase veto of true source-level signals by more than 0.05.

Mechanism: separating T, M, and Δ_j prevents attribution to the ovary or memory of a pattern created by selection, cancellation, or error. The audit must declare non-estimability when support is absent.

Predictions: the largest gain will occur in cancellation cells and when M and T have opposite signs; C3 must be preserved if support passes; the advantage must replicate in DGPs not used to design the rules.

Kill criteria: failure to reduce false attribution; exceeding the +0.05 veto margin; dependence on development DGPs; use of future outcomes in calibration; or collapsing non-estimability into nullity.

Status: weakened_parked; H0; confidence 0.20; HUMAN_QA_REQUIRED. It is not a biomarker, device, or clinical tool.

Secondary mechanistic hypothesis M1-8-AR-H3O v4

In a 2×2 duration×gap factorial, duration will attenuate and gap will reinforce T_548, with an interaction on Δ_clock=T_548−T_12 outside [-0.01,0.01] and a concordant direction in three families. It remains H0 because the prior ablations lack bands and a factorial contrast.

13. Falsifiable predictions and kill criteria

Global kill criteria: code or outputs not preserved; source computed after gates; assigned mark; H_pre containing future information; open candidate converted to negative; duration and gap merged; calibration using T/selected; positivity failure rescued with weights; bands touching the margin overinterpreted; disagreement between implementations averaged away; or a selected cohort called source.

14. Discriminating experiment

D0R-M1-8-REPRO-CONSTRUCT

This is the smallest experiment because it attacks reproducibility, mark validity, omitted history, dependence between families, and support simultaneously, without spending participants or attributing biology.

Design:

1. a sealed, human-readable and canonical JSON manifest containing parameters, targets, seeds, contrast family, tolerances, and stopping rules;
2. independent implementations in Python and R/Julia, with no shared functions;
3. complete calendars with at least 18 pre-reference segments, 12 run-in segments, follow-up for both horizons, and a tail of up to ten segments;
4. blinded derivation of candidate, confirmation, J, sign, mark, censoring, and boundaries;
5. nondegenerate H_pre: age, median/MAD, slope, tail, autocorrelation, gaps, open candidate, and time needed for LM12;
6. multinomial-state G1, cause-specific/cloglog G2, and semi-Markov/copula G3;
7. C3_repro, C5_lowN, C6_opposing, and two holdouts; total-null, risk-only, gate-only, clock-only, static-selector, and observational-error controls;
8. blinded calibration using permitted targets only;
9. final support ≥0.10, equivalent ESS ≥400 per stratum/contrast, and overlap curves;
10. preserved code, lockfile, per-batch outputs, logs, example histories, and checksums.

Coprimary outcomes: same cell/mark/sign and simultaneous lower bound T>0.05 in G1/G2/G3, both horizons, and both implementations; mark agreement; no crossing under the total null; ample support.

Size: 256,000 women per cell×family×implementation in 32 batches; blinded expansion to 512,000 only when prespecified precision is insufficient. If the band touches 0.05 at 512,000, the result is inconclusive; simulating until significance is prohibited.

Conditional factorial: D0R-CLOCK-2×2 manipulates U/H_pre→duration and U/H_pre→gap with common random numbers. The primary interaction on Δ_clock must exclude [-0.01,0.01] and preserve mark and direction across three families and two implementations.

Subsequent human phase: only if D0R passes. D1F-SOURCE-FRAME must enumerate a population aged 40.5–45.5 years independently of recent menstruation and also follow people who fail gates. A wave of 3,000, blindly expandable to 6,000, only qualifies support; it does not adjudicate T≈0.05. Confirmatory estimation may require on the order of tens of thousands of source women plus external replication. If precision or an observable source is absent, report bounds/non-identifiability.

15. Biomarkers and stratification

No biomarker is validated. U_pre must not receive a biological label. A vector or score of H_pre may be called a design stratifier only if it:

• is constructed exclusively before the landmark;
• passes reproducibility and stability testing;
• preserves continuous support after every gate;
• does not use a future mark, STRAW derived from the same outcome, future FMP, AMH, or selected information;
• improves identification or out-of-sample precision without replacing source;
• is not interpreted as ovarian reserve, fertile function, or clinical risk.

Minimum stratification includes continuous age, distribution and variation of lengths, trend, tail, gaps, open candidate, time to LM12, treatment/exit, and center/technical calendar. Thyroid, uterine, metabolic, or symptom variables may enter as pre-event determinants only if measured and prespecified; they do not localize U.

16. Individual variability

Relevant variability operates across at least five layers:

1. source composition of E/A/N−/N+;
2. continuous gradient of history/susceptibility over risk;
3. differential probability of every gate;
4. duration distribution, especially its right tail;
5. gaps, treatment, withdrawal, and metrology.

The form of susceptibility changed the conclusion: strong binary U produced C3; truncated-normal U did not. N mass changed the margin: low-N lost the crossing at H548. Opposing gates canceled. These are not secondary nuisances but the scientific phenomenon itself. Age, stage, BMI, group, uterine pathology, thyroid, metabolism, and participation conditions could generate similar mixtures, but current evidence does not adjudicate which dominates or permit effect-size transport between cohorts.

17. Pharma relevance and maturity

M1-8 does not discover a pharmacological target, molecule, causal pathway, intervention, or clinically validated endpoint. It does not demonstrate delayed perimenopause or extension of fertile years. The only plausible Pharma relevance is methodological: a future audit could quantify how much a menstrual endpoint changes between source, selected population, and observed calendars, preventing mechanistic programs from opening around a selection-produced residual.

Conditional research uses could include qualifying cohort feasibility, comparing transportability between centers, auditing inclusion/retention criteria, and deciding whether a residual justifies hormonal or tissue assays. It is not a companion diagnostic, regulatory biomarker, treatment criterion, or dose selector.

Current maturity: translational H0; research preanalytical method; HUMAN_QA_REQUIRED.

Current no-go: original code absent, mark not derived, human source absent, marginal C3 support, threshold without a functional anchor, no multicenter assay, and no validated relation to reproductive function.

Future exploratory go: reproduced D0R; D1F with observable source; D1-T/D2 with replication or informative bounds; and T0-ATTRIBUTION-BENCH with lower false attribution and non-inferior veto.

18. Limitations

1. The original computational source and raw outputs were not preserved.
2. The recorded hash does not substitute for auditable bytes.
3. Marks were assigned as causes; they did not emerge from complete calendars.
4. H_pre was degenerate and binary U was fully observed by the simulation.
5. G1/G2 shared a program, architecture, and targets; they are not independent reproductions.
6. The eight-cell grid is not a sharp bound.
7. C3 uses strong contrasts and support near the floor.
8. Low-N composition, opposing gates, and truncated U did not replicate.
9. Clock ablations lack a factorial and specific bands.
10. Human benchmarks come from already selected cohorts and heterogeneous windows.
11. A frame observing only those who enter and complete LM12 does not identify source.
12. Two frames may share self-selection or noncommensurable metrology.
13. Duration and recording lapse may remain partially confounded even with adjudication.
14. 0.05, 0.01, and support floors are methodological margins.
15. Monte Carlo bands do not represent human population uncertainty.
16. A future enumerated source will still condition on consent and participation.
17. Bleeding pattern does not measure competent ovulation, fertility, reserve, fertile years, or healthspan.
18. No result localizes the ovary, HPO axis, endometrium, thyroid, metabolism, a gene, or a cell.
19. Benefit, safety, and intervention were not evaluated.
20. No current Lua data were used.

19. Conclusions

The answer to the original question is stratified by level of evidence.

Within the reported run: yes. The same C3 cell, N−/N+ marks, and positive direction retained |Φ_source−Φ_selected|>0.05 in both horizons and G1/G2; internal calibration did not restore strict containment across the full grid. The origin was compositional depletion accumulated through five gates, not the fractional clock or a large within-stratum residual.

As a reproduced computational result: not yet. Missing code and raw outputs, assigned marks, degenerate history, and related families require downgrading the finding to a reported counterexample pending reproduction.

As a human claim: not established. The winning cell is extreme, positivity is marginal, and no frame observes the necessary source. The best-supported explanation for human generalization is that C3 is an extreme or non-identifiable region—not that containment has already been demonstrated.

The cumulative delta of M1-8 is the replacement of a vague disjunction by a falsifiable order: first reconstruct the crossing using derived marks, three families, two implementations, and ample support; then determine whether the duration×gap clock interacts; only then test whether a human source frame occupies the cell. This order prevents menstrual classification from being mistaken for reproductive mechanism and protects the Lua Labs mission by pursuing interventions only after the causal estimand survives selection.

20. References

Human evidence on calendars, transition, and observation

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Human/molecular evidence for mechanistic background

11. Groome NP, et al. Dimeric inhibin B during the human menstrual cycle. PMID: 8636341.
12. Welt CK, et al. Human follicular source of inhibin B. PMID: 11232020.
13. Klein NA, et al. Inhibin/activin feedback and FSH in women aged 40–45 years. PMID: 15181087.
14. Klein NA, et al. FSH timing and follicular selection. PMID: 12466381.
15. van Zonneveld P, et al. Advanced follicular growth in women aged 41–46 years. PMID: 12615813.
16. Brûlé E, et al. TGFBR3L as an inhibin B coreceptor. Science Advances. 2021. DOI: 10.1126/sciadv.abl4391. PMID: 34910520.
17. Vanden Brink H, et al. LPDF and luteal function at advanced reproductive age. PMID: 29112593.

Methodological and calibration evidence

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Claims of REPORT_EN

• M1-8-REPORT-EN-C1: C3 is a reported sequential/discrete crossing for N−/N+ across G1/G2 and both horizons, but not an auditable reproduction.
• M1-8-REPORT-EN-C2: concordant compositional depletion is the dominant explanation of the tables; the small within-stratum residual is conditional on an architecture with degenerate H_pre.
• M1-8-REPORT-EN-C3: universal containment of the executed grid is conditionally refuted, while containment or non-identifiability under human support remains the better-supported rival.
• M1-8-REPORT-EN-C4: duration and gaps are potentially antagonistic modulators; their interaction is not demonstrated without a factorial and bands.
• M1-8-REPORT-EN-C5: D0R-M1-8-REPRO-CONSTRUCT is the smallest discriminant and must precede human validation or physiological localization.
• M1-8-REPORT-EN-C6: current Pharma relevance is only a methodological transportability hypothesis; there is no target, biomarker, intervention, or clinical readiness.