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 46 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 →
New connected technical domain · 14 explicit bridges
See how dynamics, information, uncertainty, graphs, time series, calibration, constraints, and scoring connect models, silicon, living substrates, and hybrid systems without making them equivalent. Open the substrate-aware layer →
Verification guides
Turn a definition into a checkable implementation boundary.
These method guides specify fixtures, assumptions, uncertainty, and refusal conditions. They do not claim a new theorem proof or numerical result.
Bounded method
Angle normalization: implementation verification
How can an implementation be verified for angle normalization?
Bounded method
Angle normalization: uncertainty
How should uncertainty be represented in angle normalization?
Bounded method
Spherical coordinates: implementation verification
How can an implementation be verified for spherical coordinates?
Bounded method
Bayesian updating: implementation verification
How can an implementation be verified for Bayesian updating?
Bounded method
Graph theory: implementation verification
How can an implementation be verified for graph theory?
Bounded method
Uncertainty propagation: implementation verification
How can an implementation be verified for uncertainty propagation?
Cross-domain bridge matrix
Core 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
8 explicit bridges
Celestial facts
Coordinates, timescales, numerical precision, and reproducible calculation contracts.
- What a calendar chooses to track
- 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
8 explicit bridges
Astronomy knowledge
Physical models, calibrated observations, inference, and uncertainty.
- Residual of the Metonic relation
- 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
8 explicit bridges
Astrology traditions
Formal rule structure and comparisons without transferring scientific authority.
- Seasonal drift of a lunar year
- 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
8 explicit bridges
Pañcāṅga and timing
Calendar arithmetic, periodic boundaries, event searches, and declared conventions.
- Lunisolar intercalation
- 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.
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Spherical coordinates
Represent directions on a sphere with radius, longitude-like angle, and latitude-like angle under an explicit convention.
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Reference-frame transformations
Transform the same physical direction between declared origins, axes, epochs, and correction states.
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Time and periodicity
4 concepts
Calendrical reconciliation
Two astronomical periods that do not divide each other, and the three families of arithmetic built to live with that.
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Modular arithmetic
Reason about equivalence classes and repeating cycles without mistaking a wrapped label for elapsed distance.
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Periodic functions and phase
Describe repeating variation through period, frequency, amplitude, and phase while testing whether periodicity is actually stable.
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Calendar and timescale mappings
Map civil labels, atomic scales, rotational time, and ephemeris arguments without treating them as interchangeable.
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Numerical methods
20 concepts
Jacobian elliptic functions
Doubly periodic functions built on the complete elliptic integral, and the third kind of analytic behaviour in this corpus.
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Exponential and logarithmic integrals
Integrals of a decaying exponential over its argument, and the entire companion that carries the singularity away.
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Confluent hypergeometric functions
One equation that Bessel and Airy are cases of, and the exceptional parameters an alternative form exists to remove.
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Legendre functions
The equation behind spherical harmonics, its three singular points, and a solution pair chosen per interval.
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Number-theoretic functions
Unique factorisation, the functions built on it, and one statement about primes that is asymptotic rather than exact.
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Airy functions
The simplest equation whose behaviour changes character across a point, and the pair chosen to describe it.
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Elliptic integrals
Three Legendre integrals, the conditions that keep them defined, and the one that needs a principal value.
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Incomplete gamma functions
Split the gamma integral at a point, and keep the two halves and their asymmetry straight.
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Riemann zeta function
A series that converges in a half-plane, a product over primes that matches it there, and a function defined everywhere else by continuation.
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Hypergeometric function
One series that many named functions are special cases of, with the parameter values where it stops making sense.
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Asymptotic approximations
Say precisely what an approximation claims in a limit, and what it still leaves undetermined.
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Orthogonal polynomials
Orthogonality is a relation to a declared weight, not a property a family owns, and a recurrence carries it.
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Bessel functions
Solve the equation that appears whenever a problem is posed on a disk or a cylinder, and pick a solution pair that behaves.
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Bernoulli and Euler numbers
Define the coefficients that keep appearing in expansions, and note where their generating series stop converging.
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Gamma function
Extend the factorial to complex arguments, and carry the identities that make it computable.
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Error function and related integrals
Name the integrals of the Gaussian and Fresnel kernels, and keep their definitions exact.
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Interpolation
Estimate values between computed or measured samples under a declared local model and bounded domain.
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Root finding and event location
Locate times or states where a continuous residual crosses a target, with bracketing and convergence evidence.
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Numerical integration
Approximate accumulated quantity over an interval with a stated quadrature rule and convergence check.
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Convergence, precision, and error
Separate approximation error, floating-point behavior, input uncertainty, and model discrepancy.
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Probability and statistics
4 concepts
Uncertainty propagation
Carry declared input uncertainty and covariance through a measurement or calculation model.
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Bayesian updating
Update a declared prior distribution with a likelihood generated by observed data.
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Calibration and reliability
Test whether stated probabilities agree with observed frequencies and remain stable across relevant groups and time.
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Proper scoring rules and multiplicity
Score probabilistic forecasts honestly while controlling the many-comparisons problem created by large rule libraries.
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Systems and networks
4 concepts
Graph theory
Represent entities and typed relationships as nodes and edges while keeping topology distinct from causality.
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Dynamical systems
Model how state evolves under explicit equations, parameters, inputs, and boundary conditions.
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Time-series models
Model ordered observations while preserving trend, seasonality, dependence, interventions, and forecast origin.
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Change-point detection
Detect candidate shifts in level, variance, trend, or model parameters with controlled false alarms.
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Decisions and computation
6 concepts
Optimization
Choose feasible inputs that maximize or minimize a declared objective, with sensitivity to assumptions and constraints.
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Constraint satisfaction
Find assignments that satisfy explicit hard rules while distinguishing them from preferences and evidence weights.
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Information theory
Quantify uncertainty, coding cost, and predictive information without confusing compression with understanding.
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Cryptographic commitments
Commit to canonical inputs, rules, and forecasts before outcomes while making later changes detectable.
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Formal logic and rule compilation
Translate bounded source statements into typed conditions, conclusions, exceptions, and conflicts that can be audited.
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Causal inference and counterfactuals
Distinguish prediction and association from claims about what would happen under an intervention.
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