module module moderate

`IndisputableMonolith.Geology.VolcanicForcingAsJCostImpulse`

The module treats volcanic forcing as J-cost impulses over the minimal climate-cascade period at D=3. This period comes from T7's eight-tick octave. Researchers applying Recognition Science to geology or climate cascades would cite the saturation and per-octave impulse quantities. The module supplies definitions plus basic positivity and equality properties.

claimThe minimal climate-cascade period equals eight ticks, with volcanic explosivity index saturation and J-cost impulse per period defined as nonnegative quantities derived from the time quantum $\tau_0$.

background

Recognition Science obtains all physics from one functional equation. T7 forces the eight-tick octave (period $2^3$) as the minimal repeating unit. Constants supplies the RS-native time quantum $\tau_0 = 1$ tick. Cost supplies the J-cost function. Patterns supplies periodic structures. The module applies these to geology by casting volcanic forcing (VEI) as J-cost impulses over that octave period.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the T7-derived period for climate-cascade modeling inside the Recognition Science framework. It places volcanic impulses on the eight-tick structure at D=3 and supplies the saturation and ratio lemmas needed for downstream forcing calculations.

scope and limits

Does not compute numerical values for specific eruptions.
Does not extend the period beyond D=3.
Does not derive the octave from the functional equation (imports T7).
Does not simulate time evolution of impulses.

depends on (3)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import
IndisputableMonolith.Patterns module_import

declarations in this module (23)

def octavePeriod L66
theorem octavePeriod_eq_eight L68
theorem octavePeriod_is_minimal_cover L76
theorem octavePeriod_pos L84
def vei_saturation L93
theorem vei_saturation_pos L95
def veiRatio L100
theorem veiRatio_pos L102
theorem veiRatio_at_saturation L106
def impulse_per_octave L119
theorem impulse_per_octave_nonneg L123
theorem impulse_at_saturation L136
theorem impulse_per_octave_pos_of_ne_sat L143
theorem pinatubo_below_saturation L166
theorem impulse_pinatubo_pos L170
theorem impulse_tambora_eq_zero L181
def impulse_after_octaves L189
theorem impulse_after_octaves_zero L192
theorem impulse_after_octaves_succ L197
theorem impulse_after_octaves_mono_decay L206
structure VolcanicForcingAsJCostImpulseCert L238
def volcanicForcingAsJCostImpulseCert L249
theorem volcanic_forcing_one_statement L269