Connective grammar · mathematics-knowledge/1.0
The same mathematics, with different evidentiary roles.
This layer defines the geometry, time, numerical methods, statistics, networks, and decision procedures shared across Maha’s knowledge systems. Every bridge says exactly what goes in, what transformation occurs, what comes out, and where the inference must stop.
Shared method
Coordinate transforms, uncertainty propagation, graphs, and scores can serve several domains without making those domains epistemically equivalent.
Typed bridge
Each of the 42 records declares inputs, transformation, outputs, evidence role, destination, and limitations.
No validity transfer
Formalizing an astrological rule can establish consistency and provenance. Only prospective empirical tests can estimate predictive performance.
New connected domain · 12 explicit bridges
See how graphs, uncertainty, formal logic, time series, and causal inference connect to religion and contemplative studies without certifying metaphysical claims. Open the methodology layer →
Cross-domain bridge matrix
Six systems, one inspectable grammar
7 explicit bridges
Semiconductor manufacturing
Measurement, process control, yield, optimization, and dependency graphs.
- Lithography overlay registration
- Yield learning and process control
- Manufacturing dependency graph
- Accumulated thermal exposure
- Tool and lot regime shifts
- Packaging trade-space optimization
- Metrology uncertainty budget
7 explicit bridges
Celestial facts
Coordinates, timescales, numerical precision, and reproducible calculation contracts.
- Canonical celestial longitude
- Ecliptic and equatorial frame conversion
- Civil time to ephemeris time
- Ephemeris state interpolation
- Ingress and station event location
- Calculation conformance and precision
- Reproducibility digest
7 explicit bridges
Astronomy knowledge
Physical models, calibrated observations, inference, and uncertainty.
- Angular separation on the celestial sphere
- Astrometric covariance propagation
- Orbital state evolution
- Time-domain light-curve analysis
- Periodic-signal search
- Observation-to-model provenance graph
- Model-conditioned parameter inference
7 explicit bridges
Astrology traditions
Formal rule structure and comparisons without transferring scientific authority.
- Source-bound interpretation predicates
- Rule conflict and satisfiability audit
- Tradition and source lineage graph
- Tropical and sidereal label comparison
- House and aspect boundary classification
- Incremental rule information audit
- Corporate-report decision boundary
7 explicit bridges
Pañcāṅga and timing
Calendar arithmetic, periodic boundaries, event searches, and declared conventions.
- Pañcāṅga limb indexing
- Limb boundary time search
- Daśā timing under uncertain birth time
- Local sunrise and civil-day mapping
- Muhūrta eligibility compiler
- Transparent candidate-window ranking
- Transit cycle and repeated crossing model
7 explicit bridges
Empirical validation
Pre-registration, baselines, calibration, scoring, and prospective evaluation.
- Pre-outcome forecast commitment
- Prospective forecast scoring
- Probability calibration audit
- Bayesian rule-pruning protocol
- Milestones plus ordinary non-event periods
- Outcome regime-change audit
- Prediction-versus-causation boundary
Geometry and coordinates
3 concepts
Angle normalization
Represent cyclic angles in one declared interval without losing the original frame or direction of travel.
Inspect concept and applications →
Spherical coordinates
Represent directions on a sphere with radius, longitude-like angle, and latitude-like angle under an explicit convention.
Inspect concept and applications →
Reference-frame transformations
Transform the same physical direction between declared origins, axes, epochs, and correction states.
Inspect concept and applications →
Time and periodicity
3 concepts
Modular arithmetic
Reason about equivalence classes and repeating cycles without mistaking a wrapped label for elapsed distance.
Inspect concept and applications →
Periodic functions and phase
Describe repeating variation through period, frequency, amplitude, and phase while testing whether periodicity is actually stable.
Inspect concept and applications →
Calendar and timescale mappings
Map civil labels, atomic scales, rotational time, and ephemeris arguments without treating them as interchangeable.
Inspect concept and applications →
Numerical methods
4 concepts
Interpolation
Estimate values between computed or measured samples under a declared local model and bounded domain.
Inspect concept and applications →
Root finding and event location
Locate times or states where a continuous residual crosses a target, with bracketing and convergence evidence.
Inspect concept and applications →
Numerical integration
Approximate accumulated quantity over an interval with a stated quadrature rule and convergence check.
Inspect concept and applications →
Convergence, precision, and error
Separate approximation error, floating-point behavior, input uncertainty, and model discrepancy.
Inspect concept and applications →
Probability and statistics
4 concepts
Uncertainty propagation
Carry declared input uncertainty and covariance through a measurement or calculation model.
Inspect concept and applications →
Bayesian updating
Update a declared prior distribution with a likelihood generated by observed data.
Inspect concept and applications →
Calibration and reliability
Test whether stated probabilities agree with observed frequencies and remain stable across relevant groups and time.
Inspect concept and applications →
Proper scoring rules and multiplicity
Score probabilistic forecasts honestly while controlling the many-comparisons problem created by large rule libraries.
Inspect concept and applications →
Systems and networks
4 concepts
Graph theory
Represent entities and typed relationships as nodes and edges while keeping topology distinct from causality.
Inspect concept and applications →
Dynamical systems
Model how state evolves under explicit equations, parameters, inputs, and boundary conditions.
Inspect concept and applications →
Time-series models
Model ordered observations while preserving trend, seasonality, dependence, interventions, and forecast origin.
Inspect concept and applications →
Change-point detection
Detect candidate shifts in level, variance, trend, or model parameters with controlled false alarms.
Inspect concept and applications →
Decisions and computation
6 concepts
Optimization
Choose feasible inputs that maximize or minimize a declared objective, with sensitivity to assumptions and constraints.
Inspect concept and applications →
Constraint satisfaction
Find assignments that satisfy explicit hard rules while distinguishing them from preferences and evidence weights.
Inspect concept and applications →
Information theory
Quantify uncertainty, coding cost, and predictive information without confusing compression with understanding.
Inspect concept and applications →
Cryptographic commitments
Commit to canonical inputs, rules, and forecasts before outcomes while making later changes detectable.
Inspect concept and applications →
Formal logic and rule compilation
Translate bounded source statements into typed conditions, conclusions, exceptions, and conflicts that can be audited.
Inspect concept and applications →
Causal inference and counterfactuals
Distinguish prediction and association from claims about what would happen under an intervention.
Inspect concept and applications →