IndisputableMonolith.ClassicalBridge.Fluids.Simulation2D
The module supplies a nontrivial LNAL program that increments nuPhi by +1 at every instruction pointer. Researchers composing the 2D fluid pipeline cite it as the explicit one-step simulation layer (M3). The module consists entirely of supporting definitions for folding, voxel encoding, and coefficient extraction with no theorem proofs.
claimThe central object is the LNAL program $P$ satisfying $P(ip) = +1$ increment on the nuPhi component for every instruction pointer $ip$.
background
The module operates in the setting of Milestone M3, bridging the finite Fourier truncation of 2D incompressible Navier-Stokes on the torus (Galerkin2D, M1) with the spatial LNAL semantics and voxel encoding (LNALSemantics, M2). Galerkin2D supplies a Finset of modes together with the basic algebraic energy identity for the inviscid case. LNALSemantics defines the LNALField as Array (Reg6 × Aux5) and the encoding map from Galerkin states into voxels without neighbor coupling.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module realizes the one-step simulation (M3) required by the top-level composition theorem in Regularity2D (M6), which assembles M1 through M5 into an abstract existence statement for a continuum solution.
scope and limits
- Does not establish any continuum limit.
- Does not introduce neighbor graphs or inter-voxel coupling.
- Does not prove energy identities for the simulated step.
- Does not address higher-dimensional or viscous cases.
used by (1)
depends on (2)
declarations in this module (21)
-
def
foldPlusOneProgram -
lemma
voxelStep_foldPlusOneProgram -
def
foldPlusOneStep -
lemma
floor_abs_intCast -
lemma
cast_lt_zero_iff -
lemma
clampI32_pos_of_ge_one -
lemma
coeffMag_foldPlusOneStep -
lemma
coeffSign_foldPlusOneStep -
lemma
decide_lt_zero_foldPlusOneStep -
lemma
voxelStep_foldPlusOne_encodeIndex -
def
decodeMag -
def
decodeCoeff -
def
decodeGalerkin2D -
structure
SimulationHypothesis -
theorem
simulation_one_step -
structure
DecodedSimulationHypothesis -
theorem
decoded_simulation_one_step -
def
foldMinusOneProgram -
lemma
voxelStep_foldMinusOneProgram -
def
foldMinusOneDecodedStep -
lemma
decodeCoeff_voxelStep_foldMinusOne_encodeIndex