Act I · Physical & Clinical Story
Why Every Percentage Needs Its Denominator
Public health statistics carry an immense moral weight that directly influences human lives and medical policies. When medical journals report that a specific fraction of people living with cystic fibrosis cannot benefit from current modulator drugs, the exact denominator of that calculation determines the true scope of suffering. A percentage without its foundational denominator easily creates harmful statistical illusions that mask neglected patient communities. When Salvatore and colleagues published their comprehensive epidemiological review in the Journal of Clinical Medicine during 2025, they examined registry evidence across worldwide cohorts to trace how demographic tracking influences therapeutic access. Their findings revealed that international patient registries utilize distinct inclusion criteria, diverse age boundaries, and unequal diagnostic panels. By formalizing the mathematical cascade of patient eligibility, medical researchers ensure that missing demographic information is never mistakenly equated with zero clinical need.
Understanding epidemiological statistics requires knowing exactly who is being counted. When an annual medical report states that eight percent of individuals lack approved targeted therapies, that fraction depends entirely on the specific patient group chosen for study. Does the calculation include every person born with the disease? In practice, national databases track only patients who attend participating specialty clinics and receive complete genetic testing during that specific calendar year. Two entirely separate hurdles can prevent an individual from receiving treatment. Some individuals carry rare genetic variants that existing medications cannot repair, while others carry responsive mutations but live in countries without affordable healthcare coverage. Conflating biological ineligibility with financial access gaps obscures real suffering. By applying strict conditional probability rules to patient registries, mathematical analysts ensure that every waiting community remains fully visible to modern medical science.
Everyday Analogy: Consider a multi-tiered mechanical sifting machine installed in a flour mill to grade the annual wheat harvest. The top screen catches large stones and unthreshed stalks, the second screen filters out broken kernels, and the finest mesh allows only premium white flour to pass into baker sacks. If an inspector measures the percentage of pure flour by comparing it only against the kernels that reached the third screen rather than the total wheat delivered from the fields, the reported yield appears deceptively high. In cystic fibrosis epidemiology, the five-tier registry cascade functions exactly like this multi-stage sifter, filtering the population from living individuals down to those actively prescribed medication. Reporting treatment rates without accounting for people lost at earlier diagnostic stages creates an illusion of broad success. Yet this milling analogy stops being accurate at the human level, because grain kernels are passive inert particles, whereas people excluded from registry tiers experience real, ongoing clinical decline that demands proactive medical outreach.
How the Two Sliders Work in Plain Words: Before examining the formal probability equations of registry cascades, readers can explore the epidemiological dynamics through two interactive controls. The first control, Complete Two-Allele Genotyping Coverage, adjusts the proportion of registry participants whose genetic variants have been fully sequenced and classified. The second control, the Health-System Reimbursement and Access Factor, dictates what fraction of clinically eligible individuals can actually obtain approved modulators within their national healthcare system. Adjusting these parameters updates four comparative readouts that illustrate international disparities. The CFFPR Genotype-Ineligible Share tracks the proportion of individuals in the United States cohort who lack responsive alleles. The CCFR Ineligible readout displays the corresponding proportion in the Canadian registry. The ACFDR Adult and Pediatric Ineligible readout highlights how age thresholds alter eligibility across Australian populations. Finally, the Denominator Subtraction Rule verifies that percentages derived from different cohort denominators are never subtracted or averaged together.
National and continental registries—the US Cystic Fibrosis Foundation Patient Registry (CFFPR), the Canadian CF Registry (CCFR), the European CF Society Patient Registry (ECFSPR), and the Australian CF Data Registry (ACFDR)—measure different slices of this cascade using different inclusion rules, age cutoffs, and regulator-specific variant lists (FDA vs EMA vs Health Canada vs TGA).
The epidemiological analysis of global registry evidence published by Salvatore and colleagues in 2025 demonstrated that reported modulator eligibility percentages are deeply contingent on regional registry structures. When the United States Cystic Fibrosis Foundation Patient Registry reports that 8.0 percent of individuals are genotype-ineligible, that figure conditions on patients actively seen within accredited care centers who possess complete two-allele genotyping. In Canada and Australia, national registries report comparable ineligible cohorts of 7.6 percent and 5.8 percent among adults, yet their underlying age criteria and regulatory labels differ substantially. Furthermore, because newborn screening panels historically prioritized the European F508del variant, individuals of African and Hispanic ancestry experience significantly higher rates of rare, uncharacterized, or Class I nonsense variants. In the US registry, 14.9 percent of Black individuals and 23.7 percent of Hispanic individuals remain ineligible for modulators. The translational stakes of denominator mathematics are profound. Treating unsequenced alleles as zero risk or subtracting percentages across mismatched denominators conceals genuine health disparities. Only rigorous conditional accounting can ensure equitable research allocation for everyone still waiting.
“Implements rules AH-3 and AH-5 of our lab's anti-hallucination constitution: every registry percentage must name its registry, report year, and exact denominator, and missingness is never treated as zero.”
— Cross-Pillar Research Thread · Grounded in Salvatore et al. (2025), Journal of Clinical Medicine 14(11):3978 — Cystic Fibrosis Transmembrane Conductance Regulator Modulators in Cystic Fibrosis: A Review of Registry-Based Evidence (PMID 40507740).
Key Parameters, Readouts & Primary Anchor
| Quantity / Anchor | Pinned Baseline | Physical / Clinical Role |
|---|---|---|
| Complete Two-Allele Genotyping Coverage (f_geno) | 0.96 fraction |
Primary perturbation axis (0.7 to 0.99 fraction) |
| Health-System Reimbursement / Access Factor (f_access) | 0.84 of eligible |
Coupled co-perturbation axis (0.3 to 0.98 of eligible) |
| CFFPR 2024 Genotype-Ineligible Share & CCFR 2024 Age + Genotype Ineligible | 8.0% (US Registry Denominator) · 7.6% (Canadian Registry 2024) |
Baseline biophysical operating point |
| Primary Literature Anchor | DOI 10.3390/jcm14113978 | Salvatore et al. (2025), Journal of Clinical Medicine 14(11):3978 — Cystic Fibrosis Transmembrane Conductance Regulator Modulators in Cystic Fibrosis: A Review of Registry-Based Evidence (PMID 40507740). · Kernel src/scripts/registries-denominator-cascade.js |
Act II · From Intuition to Governing Law
Conditional Probability Cascades and the Non-Additivity of
Let Tier 0 (N_0) be all people living with CF in a region, Tier 1 (N_1) those enrolled and seen in the registry during year Y, Tier 2 (N_2) those with complete genotyping on record, Tier 3 (N_3) those eligible by local regulatory label (age ∧ genotype), and Tier 4 (N_4) those actively prescribed a modulator. By conditional probability, N_4 / N_1 = (N_2 / N_1) · (N_3 / N_2) · (N_4 / N_3). Notice why our reproducible claim checker (check_claims.py) enforces two ironclad rules: first, you may never subtract a percentage reported on denominator N_1 from 100% as though it were reported on N_3; second, missing or unsequenced genotypes (N_1 − N_2) are missing data, never zero risk or wild-type.
The formal mathematics of epidemiological registries is grounded in conditional probability chains across ordered population subsets. Let Tier 0 (N_living) denote all individuals living with cystic fibrosis within a defined geographical jurisdiction. Successive filtering stages define Tier 1 (N_seen, individuals enrolled and clinically evaluated within year Y), Tier 2 (N_genotyped, individuals with verified two-allele sequencing on record), Tier 3 (N_eligible, individuals meeting regulatory age and variant criteria), and Tier 4 (N_prescribed, individuals actively receiving medication). By the multiplicative law of probability, the probability that an affected individual receives treatment decomposes into a telescoping product: P(Prescribed | Living) = P(Tier 1 | Tier 0) · P(Tier 2 | Tier 1) · P(Tier 3 | Tier 2) · P(Tier 4 | Tier 3). Because each successive cohort is a strict subset of its predecessor (N_living ≥ N_seen ≥ N_genotyped ≥ N_eligible ≥ N_prescribed), reporting percentages without naming the exact denominator tier generates severe mathematical errors.
In our computational simulation kernel inside src/scripts/registries-denominator-cascade.js, we implement this five-tier cascade alongside anti-hallucination rules AH-3 and AH-5. A primary theorem of denominator arithmetic forbids cross-registry subtraction: one cannot subtract an 8.0 percent ineligibility rate reported on N_seen from 100 percent to claim that 92 percent of all living patients are treated. Furthermore, the kernel enforces the missingness invariant: unsequenced alleles (N_seen − N_genotyped) represent missing information rather than confirmed wild-type or benign variants. When newborn screening panels test only the historical twenty-three Northern European mutations, non-European infants experience delayed ascertainment, inflating early diagnostic dropouts. By formalizing this conditional cascade in interactive JavaScript, our observatory demonstrates why global health equity requires both comprehensive genomic sequencing and comprehensive therapeutic reimbursement.
Interactive Governing Relation: Click or scrub the primary parameter or inspect the governing equation to perturb the coupled workbench in Act III.
Four-Stage Mechanistic Progression
- Stage 1 (Tier 0 → Tier 1: Living vs. Registry-Seen in Year): Not every person living with CF is captured in a national registry (especially in low- and middle-income countries where newborn screening panels designed around European F508del miss regional alleles), and annual percentages condition on patients seen during the report year (N_seen).
- Stage 2 (Tier 1 → Tier 2: Genotyped Completeness): A patient whose second rare intronic or structural variant has not yet been sequenced sits in 'unclassified/missing genotype'—never to be conflated with F508del or zero risk.
- Stage 3 (Tier 2 → Tier 3: Genotype & Age Eligibility): Because F508del originated on a European haplotype, US registry data (CFFPR 2024; Salvatore et al. 2025, PMID 40507740; docs/cffpr-waiting-claims.json) show that 14.9 percent of Black and 23.7 percent of Hispanic individuals with CF are ineligible for modulators by age or genotype—substantially higher than the overall cohort average.
- Stage 4 (Tier 3 → Tier 4: Licensed & Reimbursed Access): Across the 42 participating nations participating in the European CF Society Patient Registry (ECFSPR) and globally, thousands of people who DO carry modulator-responsive genotypes remain untreated because modulators are not yet licensed or reimbursed in their health system.
Act III · Interactive Visual Experiment & Plain-Language Lens
Try It Yourself: Five-Tier Registry Cascade & Equity Explorer
Adjust genotyping completeness (f_geno) and health-system reimbursement factor (f_access) to see how the five-tier cascade separates biological ineligibility from health-system access gaps.
When someone asks 'How many people with CF still cannot take a modulator?', the honest answer depends on the denominator. Across national registries—the US (CFFPR 2024: 8.0% ineligible by genotype), Canada (CCFR 2024: 7.6% by age and genotype), Europe (ECFSPR 2023), and Australia (ACFDR 2025: 5.8% adult, 11.5% pediatric)—thousands of people carry stop, frameshift, or uncharacterized variants, and thousands more live in countries where approved medicines are not yet reimbursed. Every single person in that denominator counts.
Questions to discuss with a CF care team or patient organization: Is my exact two-allele genotype recorded in our national registry so that trial networks can reach us when variant-specific studies open?
What this diagram leaves out: National registries capture diagnosed individuals in participating centers; under-diagnosis in non-European ancestries means the true global unmet need is larger.
Global Registry Cascade · Mode: Pinned Registry Evidence · How to explore this model
- Explore the community & cell mosaic: Click the four presets below (1 · Tier 0 → Tier 1: Living… through 4 · Tier 3 → Tier 4: Licensed…) to see how coverage shifts across the cohort.
- Adjust coverage controls: Drag Complete Two-Allele Genotyping Coverage (f_geno) and Health-System Reimbursement / Access Factor (f_access) to test how Pillar I modulators and Pillar II/III genetic tools combine so every variant is represented.
- Verify primary registry anchors: Compare the mosaic with national registry denominators and DOI 10.3390/jcm14113978.
Interactive Mosaic Mode · Governing relation: P(Prescribed | Living) = Π_{k=1}^4 P(Tier_k | Tier_{k−1}) · N_living ≥ N_seen ≥ N_genotyped ≥ N_eligible ≥ N_prescribed
P(Prescribed | Living) = Π_{k=1}^4 P(Tier_k | Tier_{k−1}) · N_living ≥ N_seen ≥ N_genotyped ≥ N_eligible ≥ N_prescribed
Normalized Sensitivity (Stages 1–4)
Want to test this mechanism inside the full multi-module pillar observatory? Open the coupled interactive workbench on the Pillar Hub.
Act IV · Clinical & Therapeutic Horizon
Closing Both Gaps Without Leaving Any Community Behind
Because newborn screening DNA panels historically tested only the 23 to 40 variants most common in people of Northern European ancestry, infants of African, Latin American, Asian, and Middle Eastern ancestry experience higher rates of delayed diagnosis and higher rates of rare or Class I variants. Expanding full-gene CFTR sequencing (including deep introns) and developing genotype-agnostic RNA and gene therapies (Pillars II & III) are both essential so no child is left waiting. Grounded in Lab Discovery Catalog modules: `rare_allele_matrix`.
Translating denominator mathematics into global health policy requires recognizing the profound divergence between biological and economic barriers. In high-income countries with comprehensive single-payer healthcare, the primary barrier between a patient and a functional restoration is biological: carrying nonsense stop mutations (such as G542X or W1282X), splice-site defects, or ultra-rare missense variants for which no small-molecule modulator is approved. In contrast, across middle-income and low-income nations, thousands of individuals who carry common responsive genotypes (including homozygous F508del) remain entirely untreated because commercial modulators are not licensed, priced within reach, or reimbursed by their national health systems. This disparity highlights that global therapeutic failure often stems from systemic economic barriers rather than immutable biological limitations, demanding differentiated strategies from research institutions and healthcare advocates.
Epidemiological modeling cannot resolve drug pricing disputes or substitute for direct patient advocacy, but it provides an unassailable factual foundation that prevents policymakers from conflating these two distinct crises. Our registry models do not issue clinical recommendations or assert therapeutic access. Instead, they delineate the precise demographic boundaries where current medical technologies terminate. For the eight percent of individuals ineligible by genotype in the United States and the thousands excluded globally by commercial pricing, our laboratory coordinates research across Pillars II and III to develop genotype-agnostic genetic medicines, including inhaled RNA therapeutics and prime editing vectors. By maintaining rigorous statistical accounting across all four international registries (CFFPR, ECFSPR, CCFR, and ACFDR), we honor every person who is still waiting for breath.
Primary Anchor: Salvatore et al. (2025), Journal of Clinical Medicine 14(11):3978 — Cystic Fibrosis Transmembrane Conductance Regulator Modulators in Cystic Fibrosis: A Review of Registry-Based Evidence (PMID 40507740). (DOI 10.3390/jcm14113978 · PubMed 40507740).
Governed by biophysical kernel src/scripts/registries-denominator-cascade.js and cross-checked in the Open Global Registry & Denominator Cascade Explorer on /cf/registries/.
Resumen Científico en Español (ES-MX) · Folio L.05
Matemáticas de los Denominadores en Registros Globales (CFFPR, ECFSPR, CCFR, ACFDR): Deconstruyendo la cascada epidemiológica de cinco niveles y por qué los paneles genéticos y el reembolso internacional crean dos brechas distintas.
Cuando un registro nacional informa que cierto porcentaje de pacientes no es elegible por genotipo, ¿cuál es exactamente el denominador? Comprender la cascada de cinco niveles evita errores estadísticos y distingue entre quienes esperan una terapia genética y quienes esperan acceso a medicamentos ya aprobados.
En Palabras Sencillas: Comprender las estadísticas epidemiológicas requiere saber con exactitud a quién se está contando. Cuando un informe médico anual afirma que el ocho por ciento de los individuos carece de terapias dirigidas aprobadas, esa fracción depende enteramente del grupo específico de pacientes elegido para el estudio. ¿Acaso el cálculo incluye a cada persona nacida con la enfermedad? En la práctica, las bases de datos nacionales registran únicamente a los pacientes que asisten a clínicas especializadas participantes y reciben pruebas genéticas completas durante ese año calendario específico. Dos obstáculos totalmente independientes pueden impedir que un individuo reciba tratamiento. Algunas personas portan variantes genéticas raras que los medicamentos existentes no pueden reparar, mientras que otras portan mutaciones sensibles pero viven en países sin cobertura médica accesible. Confundir la inelegibilidad biológica con las brechas de acceso financiero oscurece el sufrimiento real. Al aplicar reglas estrictas de probabilidad condicional a los registros, los analistas garantizan que cada comunidad en espera permanezca plenamente visible ante la ciencia médica.
Analogía Cotidiana: Considere una máquina de tamizado mecánico de múltiples niveles instalada en un molino de harina para clasificar la cosecha anual de trigo. El tamiz superior retiene piedras grandes y tallos no trillados, el segundo tamiz filtra los granos rotos y la malla más fina permite únicamente el paso de harina blanca de primera calidad a los sacos de panadería. Si un inspector mide el porcentaje de harina pura comparándolo únicamente con los granos que alcanzaron el tercer tamiz y no con el total de trigo entregado desde los campos, el rendimiento reportado parece engañosamente alto. En la epidemiología de la fibrosis quística, la cascada de registros de cinco niveles funciona exactamente como este tamiz multietapa, filtrando la población desde las personas vivas hasta aquellas a las que se les prescribe medicación activamente. Informar tasas de tratamiento sin contabilizar a las personas perdidas en etapas diagnósticas previas crea una ilusión de éxito generalizado. Sin embargo, esta analogía del molino deja de ser precisa a nivel humano, porque los granos son partículas inertes pasivas, mientras que las personas excluidas de los niveles del registro experimentan un deterioro clínico real y continuo que exige una intervención médica proactiva.
Guía de Controles Interactivos: Antes de examinar las ecuaciones formales de probabilidad de las cascadas de registros, los lectores pueden explorar la dinámica epidemiológica mediante dos controles interactivos. El primer control, Cobertura de Genotipado Completo de Dos Alelos, ajusta la proporción de participantes del registro cuyas variantes genéticas han sido completamente secuenciadas y clasificadas. El segundo control, el Factor de Reembolso y Acceso del Sistema de Salud, dicta qué fracción de las personas clínicamente elegibles puede obtener efectivamente los moduladores aprobados dentro de su sistema nacional de atención médica. El ajuste de estos parámetros actualiza cuatro lecturas comparativas que ilustran las disparidades internacionales. La Proporción de Inelegibles por Genotipo del CFFPR rastrea la proporción de individuos en la cohorte de Estados Unidos que carecen de alelos sensibles. La lectura de Inelegibles del CCFR muestra la proporción correspondiente en el registro canadiense. La lectura de Inelegibles Adultos y Pediátricos del ACFDR destaca cómo los umbrales de edad alteran la elegibilidad en las poblaciones australianas. Finalmente, la Regla de Sustracción de Denominadores verifica que los porcentajes derivados de diferentes denominadores de cohorte nunca se resten ni se promedien entre sí.
Riesgo Biofísico y Clínico: El análisis epidemiológico de la evidencia de registros globales publicado por Salvatore y colaboradores en 2025 demostró que los porcentajes reportados de elegibilidad para moduladores dependen profundamente de las estructuras regionales de los registros. Cuando el Registro de Pacientes de la Fundación de Fibrosis Quística de Estados Unidos informa que el 8.0 por ciento de los individuos no son elegibles por genotipo, esa cifra condiciona a los pacientes atendidos activamente en centros de atención acreditados que poseen genotipado completo de dos alelos. En Canadá y Australia, los registros nacionales informan cohortes inelegibles comparables del 7.6 por ciento y del 5.8 por ciento entre adultos, aunque sus criterios de edad subyacentes y etiquetas regulatorias difieren sustancialmente. Además, debido a que los paneles de tamizaje neonatal priorizaron históricamente la variante europea F508del, los individuos de ascendencia africana e hispana experimentan tasas significativamente más altas de variantes raras, no caracterizadas o de Clase I sin sentido. En el registro de Estados Unidos, el 14.9 por ciento de las personas negras y el 23.7 por ciento de las personas hispanas siguen sin ser elegibles para moduladores. Las implicaciones traslacionales de las matemáticas de los denominadores son profundas. Tratar los alelos no secuenciados como riesgo cero o restar porcentajes entre denominadores no coincidentes oculta disparidades de salud genuinas. Solo una contabilidad condicional rigurosa puede garantizar una asignación equitativa de recursos de investigación para cada persona que aún espera.
Derivación Formal: Las matemáticas formales de los registros epidemiológicos se fundamentan en cadenas de probabilidad condicional a través de subconjuntos poblacionales ordenados. Sea el Nivel 0 (N_living) todos los individuos que viven con fibrosis quística dentro de una jurisdicción geográfica definida. Las etapas de filtrado sucesivas definen el Nivel 1 (N_seen, individuos inscritos y evaluados clínicamente en el año Y), el Nivel 2 (N_genotyped, individuos con secuenciación de dos alelos verificada en registro), el Nivel 3 (N_eligible, individuos que cumplen los criterios regulatorios de edad y variantes) y el Nivel 4 (N_prescribed, personas que reciben activamente la medicación). Por la ley multiplicativa de la probabilidad, la probabilidad de que un individuo afectado reciba tratamiento se descompone en un producto telescópico: P(Prescribed | Living) = P(Tier 1 | Tier 0) · P(Tier 2 | Tier 1) · P(Tier 3 | Tier 2) · P(Tier 4 | Tier 3). Dado que cada cohorte sucesiva es un subconjunto estricto de su predecesora (N_living ≥ N_seen ≥ N_genotyped ≥ N_eligible ≥ N_prescribed), informar porcentajes sin nombrar el nivel exacto del denominador genera errores matemáticos severos. En nuestro núcleo de simulación computacional dentro de src/scripts/registries-denominator-cascade.js, implementamos esta cascada de cinco niveles junto con las reglas contra alucinaciones AH-3 y AH-5. Un teorema fundamental de la aritmética de denominadores prohíbe la sustracción cruzada entre registros: no se puede restar una tasa de inelegibilidad del 8.0 por ciento reportada sobre N_seen del 100 por ciento para afirmar que el 92 por ciento de todos los pacientes vivos reciben tratamiento. Además, el núcleo impone el invariante de datos faltantes: los alelos no secuenciados (N_seen − N_genotyped) representan información ausente y no variantes benignas o de tipo silvestre confirmadas. Cuando los paneles de tamizaje neonatal prueban únicamente las veintitrés mutaciones del norte de Europa históricas, los bebés no europeos experimentan un retraso en la confirmación diagnóstica, inflando las deserciones tempranas. Al formalizar esta cascada condicional en JavaScript interactivo, nuestro observatorio demuestra por qué la equidad en salud global requiere tanto secuenciación genómica completa como reembolso terapéutico broad.
Frontera Traslacional: Traducir las matemáticas de los denominadores a las políticas de salud pública globales requiere reconocer la profunda divergencia entre las barreras biológicas y las económicas. En países de altos ingresos con sistemas de salud universales integrales, la barrera principal entre un paciente y una cura funcional es biológica: portar mutaciones de parada sin sentido (como G542X o W1282X), defectos en los sitios de empalme o variantes de sentido erróneo ultrarraras para las cuales no hay moduladores de moléculas pequeñas aprobados. Por el contrario, en naciones de ingresos medios y bajos, miles de personas que portan genotipos respondedores comunes (incluyendo F508del homocigoto) permanecen sin tratamiento alguno porque los moduladores comerciales no están autorizados, no tienen precios accesibles o no están reembolsados por sus sistemas de salud nacionales. El modelado epidemiológico no puede resolver disputas sobre precios de medicamentos ni sustituir la defensa activa de los pacientes, pero proporciona una base de hechos inexpugnable que evita que los formuladores de políticas confundan estas dos crisis distintas. Nuestros modelos de registros no emiten recomendaciones clínicas ni garantizan el acceso a terapias. En su lugar, delimitan las fronteras demográficas precisas donde terminan las tecnologías médicas actuales. Para el ocho por ciento de los pacientes inelegibles por genotipo en los Estados Unidos y los miles excluidos globalmente por precios comerciales, nuestro laboratorio coordina investigaciones en los Pilares II y III para desarrollar medicinas genéticas agnósticas al genotipo, incluyendo terapias de ARN inhalado y vectores de edición primaria. Al mantener una contabilidad estadística rigurosa a través de los cuatro registros internacionales (CFFPR, ECFSPR, CCFR y ACFDR), honramos a cada persona que todavía espera por respirar.
Horizonte terapéutico: Implementa las reglas AH-3 y AH-5 de nuestro laboratorio: todo porcentaje de un registro debe indicar su registro, año de informe y denominador exacto, y los datos faltantes nunca se tratan como cero. Investigación independiente, no asesoramiento médico.
Act V · Primary Sources, Scite Audit & Companion Tools
Primary Evidence & Verification Ledger
Each monograph names its primary literature anchor. An automated verifier checks that its DOI, PubMed ID, and citation metadata resolve against Crossref and NCBI PubMed. Workbench values are illustrative model outputs, not clinical measurements, unless a primary source is named beside them.
- Primary Literature Receipt: Salvatore et al. (2025), Journal of Clinical Medicine 14(11):3978 — Cystic Fibrosis Transmembrane Conductance Regulator Modulators in Cystic Fibrosis: A Review of Registry-Based Evidence (PMID 40507740). (DOI 10.3390/jcm14113978 · PubMed 40507740).
- Citation Context (Scite): Inspect how later literature cites 10.3390/jcm14113978 on Scite.ai ·
Crossref + Scite verified (data/folio-citations.cache.json · fetched 2026-11-08 · 18 citing · 0 supporting · 7 mentioning · 0 contrasting). - Open-Source Computational & Epistemic Engine: Anthropic Formal-Math & PySR Sub-Cubic Combinatorial Search (DOI 10.1145/3372885.3373824 · Scite Report).
- Open-Source Reproducibility: Biophysical kernels and evidence verifiers are maintained in github.com/senseiewok/cf-research and github.com/senseiewok/cf-skills.
For builders: method, companion SKILL.md, Python verifier, and edition history (REV 1.1)
cf-registry-denominator-cascade-SKILL.md · Kernel src/scripts/registries-denominator-cascade.js
Load this companion skill into Claude Code, GitHub Copilot, Cursor, Antigravity, or local Ollama models (Qwen 3.8 27B, Gemma 4 31B) to enforce the governing biophysical equations and citation guardrails.
View raw SKILL.md source
---
name: cf-registry-denominator-cascade
description: AI-agnostic epidemiological and data-integrity skill for the 5-tier CF registry denominator cascade (CFFPR, ECFSPR, CCFR, ACFDR), ancestral variant equity, and anti-hallucination rules AH-3/AH-5.
license: CC-BY-4.0
---
# L.05 — Global Registry Denominator Math (CFFPR, ECFSPR, CCFR, ACFDR)
## Governing Biophysical / Mathematical Law
P(Prescribed | Living) = Π_{k=1}^4 P(Tier_k | Tier_{k−1}) · N_living ≥ N_seen ≥ N_genotyped ≥ N_eligible ≥ N_prescribed
## Primary Evidence Receipt
- **Citation:** Salvatore et al. (2025), Journal of Clinical Medicine 14(11):3978 — Cystic Fibrosis Transmembrane Conductance Regulator Modulators in Cystic Fibrosis: A Review of Registry-Based Evidence (PMID 40507740).
- **DOI:** https://doi.org/10.3390/jcm14113978
- **PubMed PMID:** https://pubmed.ncbi.nlm.nih.gov/40507740/
- **Answer Tier:** T1/T2 · Sourced Registry Denominator & Epidemiological Model
## Verification Rules
- Always state the exact registry name, report year, and denominator tier (Living, Seen, Genotyped, Eligible, Prescribed) for every figure.
- Never subtract percentages across unshared denominators or average across registries with different regulatory labels (FDA vs EMA vs Health Canada vs TGA).
- Treat unsequenced or unknown genotypes as missingness (never zero), and ground registry eligibility denominators in Salvatore et al. 2025 (DOI 10.3390/jcm14113978, PMID 40507740) and CFFPR.
## Safety & Clinical Boundary
Research synthesis and biophysical modeling only — never medical advice, clinical guidance, or a treatment promise.
REV 1.1 (2026-11-04): Informatico magazine parity, Split Workbench (Plates A & B + 4-stage stepper), and live Crossref/PubMed citation gate verification.
Verified 5-Act magazine flow, untruncated headings, and bilingual EN / ES-MX structural parity.
Audited clinical dignity boundaries, non-promise guardrails, and discovery catalog coverage.
check_folio_citations.py
Verified DOI 10.3390/jcm14113978 against Crossref and NCBI PubMed metadata.
src/scripts/registries-denominator-cascade.js
Coupled governing relation P(Prescribed | Living) = Π_{k=1}^4 P(Tier_k to interactive Plates A & B.