IndisputableMonolith.Foundation.NoetherTheoremDeep
The module establishes that Recognition Science produces exactly four canonical Noether charges, equal to D + 1 with D = 3. Researchers deriving conservation laws from the J-cost functional and discrete time would cite it when linking symmetries to the phi-ladder. The module collects sibling declarations for charge counting, four charges, and energy properties without internal proofs.
claimThe number of canonical Noether charges is $D + 1 = 4$.
background
The module sits in the Foundation layer and imports the RS time quantum τ₀ = 1 tick from Constants together with cost definitions from the Cost module. These set the discrete-time setting in which the J-functional generates charges whose count matches the spatial dimensions plus energy. The module then introduces the charge count and related energy statements inside the phi-ladder structure.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
This module supports the deep formulation of Noether's theorem in Recognition Science and feeds certifications such as NoetherTheoremDeepCert. It aligns with forcing-chain steps T7 and T8 that fix the eight-tick octave and D = 3. The declarations enable energy non-negativity and zero-at-equilibrium statements in RS-native units.
scope and limits
- Does not derive Noether charges from continuous symmetries.
- Does not give explicit expressions for the four charges.
- Does not address time-dependent or Berry-threshold effects.
- Does not extend to curved or higher-dimensional analogs.