module module high

`IndisputableMonolith.Geology.VolcanicForcingAsJCostImpulse`

This module defines the minimal climate-cascade period at D=3 by modeling volcanic forcing as J-cost impulses derived from the eight-tick octave of T7. Climate and geophysics researchers would cite it when connecting volcanic activity to periodic RS forcing. The module supplies definitions for octavePeriod, veiRatio, and impulse_per_octave together with their positivity and saturation lemmas.

claimThe minimal climate-cascade period at $D=3$ equals the eight-tick octave period $P=8$ (in units of the fundamental tick), obtained by applying T7 to volcanic J-cost impulses with VEI saturation.

background

Recognition Science treats volcanic forcing as an impulse delivered through the J-cost function, where J measures deviation from the identity element. The module imports the RS time quantum from Constants, the J-cost apparatus from Cost, and pattern primitives from Patterns. It works inside the geology domain at three spatial dimensions and inherits the eight-tick octave (period $2^3$) directly from T7.

proof idea

This is a definition module, no proofs. It introduces the core objects octavePeriod, vei_saturation, veiRatio, and impulse_per_octave, then records elementary lemmas establishing non-negativity, positivity at saturation, and the equality octavePeriod_eq_eight.

why it matters in Recognition Science

The module supplies the T7-derived period for the geology sector of the Recognition framework, enabling later climate-cascade calculations that treat volcanic events as J-cost impulses. It closes the link between the eight-tick octave and D=3 without introducing new hypotheses.

scope and limits

Does not model individual eruption dynamics or plume rise.
Does not extend beyond the saturation regime of VEI.
Does not incorporate non-volcanic climate forcings.
Does not derive the octave period from axioms beyond T7.

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