Abstract
Research question. How can mathematical models of care coordination support the democratization of care without confusing a large space of possible combinations with accessible services, observed demand or economic value? This paper develops a general framework connecting combinatorics, workflow measurement and distributional evaluation. Its primary objective is to make access claims more testable.
Methods. A targeted source audit recalculated the equations in a preliminary 19-page care-flow model, examined two supporting provider-universe tables and checked selected external benchmarks against their primary sources. Integer multiplication, unit analysis and source-to-claim reconciliation were used. No participant-level dataset, platform deployment or empirical treatment effect was evaluated.[1][3][8]
Results. The central expression, 6.5 billion × 800 × 300 million, equals 1.56 × 1021, or 1.56 sextillion, in short-scale English. It does not equal 1.65 sextillion. The result is a count of unconstrained labeled tuples. The current taxonomy file used for comparison contains 883 unique codes; the scenario's 800 is a hypothetical parameter. The 19 visible provider-category ranges sum to 392–632 million, not the reported 392–633 million. Neither correction establishes a valid global provider population.[5][8]
Interpretation. The central arithmetic is reproducible; the empirical population, catalogue and deduplication assumptions are not independently validated. Counts of potential configurations do not measure unmet need, care capacity, completed care, market size or revenue. A more useful evaluation separates raw configurations, feasible pathways, chosen actions, completed care and their distribution across people.
Public-interest contribution. Democratization is operationalized as expanded practical access to appropriate and affordable care, informed choice, and meaningful participation. The proposed measures preserve people who remain offline, lack a feasible option or abandon a journey. The framework permits a finding of no benefit or unequal benefit; it does not assume that technological expansion produces inclusion.
Validated conclusion: 1.56 sextillion is correct for the stated hypothetical inputs. A claim that this number establishes the size or value of a care market is not supported.
Key findings and implications
- The stated inputs produce 1.56 sextillion hypothetical combinations, not 1.65 sextillion or a measured market value.
- The retrieved taxonomy contains 883 unique codes; the provider table’s visible endpoints sum to 392–632 million.
- Correct multiplication does not independently validate the population, catalogue or provider assumptions.
- The useful public-interest measures are feasible choice, timely completion, affordability and who remains excluded.
Why this matters for democratization of care
Democratization of care concerns the distribution of effective opportunities. Let D be the number of people with a defined relevant need during a specified period. Let C be the number who obtain appropriate care within the chosen interval. Then C/D is a completion proportion. The denominator must include eligible people who never start a digital journey when they belong to the target population.
Let C_g/D_g describe a prespecified group g. Report each proportion, its uncertainty and the absolute difference between relevant groups. A system-wide average can rise while the lowest-access group experiences no benefit or deteriorates. Groups should be selected with substantive justification and lawful, proportionate data collection; small samples and missing data must be visible.
| Outcome | Proposed definition | Essential qualification |
|---|---|---|
| Effective option coverage | People with at least one feasible option / people with relevant need | An option must be usable, not merely listed |
| Timely completion | Appropriate completion within interval / eligible need | Define the interval and ascertainment method |
| Affordability | Full patient burden relative to a stated resource measure | Include non-price burdens where measurable |
| Informed agency | Comprehension, meaningful alternatives and supported choice | Respect informed refusal |
| Exclusion gap | Difference in effective access across groups | Report uncertainty and contextual causes |
A simple transition example illustrates the distinction. If 80% find an appropriate option, 75% of those can book and 80% of those attend, overall attendance is 48%. Improving discovery to 90% raises it to 54% if the conditional booking and attendance proportions remain unchanged. This is a hypothetical six-percentage-point gain, not an empirical effect or a relative 6% improvement.
The calculation assumes compatible conditional denominators. Multiplying separately measured marginal rates from different populations is not justified. A real longitudinal dataset should record the same journey cohort through the stages and preserve repeated attempts, changes of preference and missing outcomes.
A public-interest study should also report burden and harm. A completed encounter may still be inappropriate, unaffordable or inconsistent with the person's priorities. Completion is a necessary operational measure for many pathways, but it is not a universal substitute for quality, autonomy or welfare.
Methods and evidence boundaries
The source model is treated as an object of examination, not as independent corroboration of its own assumptions. Its original scope combines health services with personal, family and other care activities. Those domains may share scheduling or communication infrastructure, but they require different definitions of need, appropriateness and outcomes. An expansive care concept cannot justify merging incompatible statistics.
The audit followed four steps. First, each displayed calculation was transcribed with its unit and time basis. Second, arithmetic was independently recalculated. Third, externally attributed numbers were checked against the cited institution's material where accessible. Fourth, conclusions were assessed for whether the arithmetic and sources actually entail them. A correct equation can still support an invalid interpretation.
This is an AI-assisted, targeted research working paper, not an independently peer-reviewed study. Proposed models and interventions are not evidence of deployed capabilities or measured outcomes. The full PDF contains the detailed analysis, assumptions and limitations.
References and source notes
Reference numbers match the PDF. Public sources are linked below; preliminary supplied planning materials are identified as such and do not constitute independent verification.
- User-supplied Careverse™ planning document. Global Interoperability Opportunity by Provider Universe 1(3).pdf. Undated; supplied source reviewed October 2026. Internal seven-page planning source. No supporting citations or reproducible count methodology identified. Quoted ranges are unverified hypotheses, not external evidence.
- CAQH. 2025 CAQH Index Shows U.S. Healthcare Avoided $258 Billion and Accelerated Automation, Interoperability and AI Adoption. February 19, 2026; 2024 underlying period. CAQH-issued release distributed by GlobeNewswire. Summary-level review; underlying Index microdata and full calculation model not independently reanalyzed.Read the source
- Careverse™ internal research revision. The mathematics of a universe of care. September 14, 2026; 19 pages. Retrieved source: Careverse_Care_Flow_Math_Research_Revision(2).pdf. Pages 2 and 16-17 present the 1.56 sextillion scenario. Planning inputs and unconstrained combinations, not validated market demand.
- International Telecommunication Union. Facts and Figures 2025 press release. November 17, 2025. Official estimate of approximately 6.0 billion people using the internet in 2025 and 2.2 billion offline; not a reachable-care population.Read the source
- National Uniform Claim Committee. Health Care Provider Taxonomy Code Set, version 26.1. July 1, 2026; downloaded October 2, 2026. Audit of the downloaded CSV: 883 data rows and 883 unique Code values. Count does not imply independent provider categories or a global care-sector classification.Read the source
- CAQH. 2026 eSolutions Xchange presentation: 2025 CAQH Index Report. 2026; Index edition 2025, underlying period 2024. Primary authored presentation, slides 5, 8 and 10. Slide 10 visually checked: 68.8 billion medical and 5.2 billion dental administrative transactions. Underlying data period cross-checked against the CAQH release.Read the source
- National Bureau of Statistics of China. Statistical Communiqué of the People’s Republic of China on the 2025 National Economic and Social Development. February 28, 2026; 2025 observations. Official HTML retrieved directly. Medical visits: 10.58 billion; see definition in note 81. Visit count is not a count of distinct people.Read the source
- Supplied preliminary provider-universe table. Provider universe stats (1).pdf. Undated; three pages reviewed October 2, 2026. Planning material; no supporting count methodology supplied. Nineteen category endpoints total 392–632 million, compared with a displayed 392–633 million-plus summary. Neither range is empirically validated.
- Google; Sundar Pichai. The AI platform shift and the opportunity ahead for retail. January 11, 2026. Primary corporate statement reporting over 50 billion Shopping Graph product listings. Corporate metric; not independently audited and not a unique-care-product census.Read the source
- World Health Organization. Health workforce: key figures. Accessed October 2, 2026. Official topic page reports an estimated health-worker stock exceeding 70 million. Different unit and scope from mixed adjacent-care provider tables.Read the source