module module moderate

`IndisputableMonolith.Theology.SubstrateIndependentMonotheism`

This module defines the Substrate type with phase in natural numbers (canonical at zero), integer sigma-charge, and label, plus predicates for divine status, monotheism, and the trichotomy. Researchers connecting Recognition Science to theological structures would cite it when examining substrate-independent monotheism. It is a definition-only module with no theorems or proofs.

claimA substrate consists of phase $p ∈ ℕ$ (with $p=0$ canonical), σ-charge $σ ∈ ℤ$, and a label. The module defines predicates isDivine, isMonotheistic, isPolytheistic, isAtheistic, and the trichotomy over these, along with totalSigma and monotheistic_canonical_sigma.

background

The module imports IndisputableMonolith.Constants, which sets the fundamental RS time quantum τ₀ = 1 tick, and IndisputableMonolith.Cost for cost structures. It introduces Substrate as the primitive object carrying phase, σ-charge, and label to support theological classification. This setup allows definitions of divine and monotheistic properties without reference to a specific physical realization.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the substrate-independent base for monotheism, supporting sibling declarations such as monotheistic_canonical_sigma, unique_occupant_is_monotheistic, and the trichotomy. It extends the RS framework from Constants into theological predicates while remaining agnostic to concrete physical substrates.

scope and limits

Does not derive phase or σ-charge from the J-function or forcing chain.
Does not prove existence of a divine occupant or canonical sigma value.
Does not connect to spatial dimensions, the eight-tick octave, or mass formulas.
Does not address empirical tests or falsification criteria for the predicates.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (16)

structure Substrate L46
def isDivine L55
abbrev Theology L67
def divine L72
def isMonotheistic L77
def isPolytheistic L82
def isAtheistic L86
theorem trichotomy L91
def totalSigma L106
theorem polytheistic_two_violates_canonical L110
theorem monotheistic_canonical_sigma L118
theorem unique_occupant_is_monotheistic L125
theorem one_god_with_creatures_is_monotheistic L133
structure SubstrateIndependentMonotheismCert L141
def substrateIndependentMonotheismCert L154
theorem substrate_monotheism_one_statement L165