module module moderate

`IndisputableMonolith.Chemistry.CrystalStructure`

CrystalStructure module supplies definitions for crystal lattices, coordination numbers, and packing efficiencies in RS units. Solid-state chemists extending the framework to periodic structures would cite it before symmetry derivations. The module contains only type and function definitions with no theorems or proofs.

claimDefinitions of crystal structure types $Structure$, coordination numbers, packing efficiencies $\eta$ for BCC, FCC, HCP lattices, and related predicates such as $bcc\_is\_8\_tick$ and $hcp\_ratio\_near\_phi$ in three-dimensional space.

background

Recognition Science starts from the Constants module where the fundamental time quantum satisfies $\tau_0 = 1$ tick. The present module introduces crystal structures as periodic fillings of 3D space (D=3) using the phi-ladder and eight-tick octave. Sibling definitions include Structure as a lattice type, coordination as nearest-neighbor count, and packingEfficiency as the occupied volume fraction.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

Supplies the base layer for the downstream CrystalSymmetry module, which derives the 32 point groups and 7 crystal systems from RS constraints on unit-cell filling. It fills the chemistry slot in the T8 spatial-dimension step and connects to the phi-ladder mass and energy formulas.

scope and limits

Does not derive the 32 crystallographic point groups.
Does not prove packing-efficiency inequalities beyond listed approximations.
Does not reference the full UnifiedForcingChain or J-cost function.
Does not compute numerical values for alpha or particle masses.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Chemistry.CrystalSymmetry module_import

depends on (1)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import

declarations in this module (21)

inductive Structure L41
def coordination L48
def packingEfficiency L54
def packingEfficiencyApprox L60
theorem bcc_is_8_tick L66
theorem close_packed_coordination L69
theorem bcc_packing_lt_fcc L73
theorem fcc_hcp_same_packing L78
def idealHCPRatio L83
theorem ideal_hcp_ratio_value L86
theorem hcp_ratio_near_phi L104
def energyScale L124
theorem close_packed_lower_energy L130
def eightTickCoherence L140
theorem bcc_max_8tick_coherence L146
def stabilityScore L153
theorem stability_tradeoff L159
def prefersBCC L174
def prefersFCC L177
def prefersHCP L180
theorem alkali_prefer_bcc L183