IndisputableMonolith.Astrophysics.PulsarPeriodFromRung
The module defines median canonical recognition-rungs for normal and millisecond pulsars together with period functions derived from those rungs on the phi-ladder. Astrophysicists modeling pulsar timing populations in the Recognition Science framework would cite these definitions. It consists of a sequence of definitions and elementary lemmas establishing positivity, geometric ratios, and inequalities for the derived quantities.
claimMedian canonical recognition-rung $r_{ m normal}$ for normal pulsars, millisecond median rung $r_{ m ms}$, recycling shift, and period $P(r)$ at rung $r$ obtained from the phi-ladder with time quantum $\tau_0$.
background
The module sits in the astrophysics domain and imports the fundamental RS time quantum $\tau_0 = 1$ tick from Constants together with the Cost module. It introduces the phi-ladder rung assignments for pulsar classes, extending the mass formula yardstick $\times \phi^{{\rm rung}-8+{\rm gap}(Z)}$ to periods via the same self-similar structure. The local setting uses the Recognition Composition Law and the eight-tick octave to fix the discrete rung values that label observable timing properties.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the rung-to-period map that links the T5 J-uniqueness, T6 phi fixed point, and T7 eight-tick octave of the UnifiedForcingChain to concrete astrophysical observables. It provides the base layer for any later application of the Recognition Composition Law to pulsar populations, even though no downstream used_by edges are recorded yet.
scope and limits
- Does not fit observed pulsar periods to data.
- Does not derive the median rung values from the T0-T8 forcing chain.
- Does not incorporate general-relativistic or magnetic-field corrections.
- Does not address binary or glitch dynamics.
depends on (2)
declarations in this module (19)
-
def
normal_median_rung -
def
ms_median_rung -
def
recycling_rung_shift -
theorem
normal_median_rung_eq -
theorem
ms_median_rung_eq -
theorem
recycling_rung_shift_eq -
def
period_at_rung -
theorem
period_at_rung_pos -
theorem
period_geometric -
def
bimodal_ratio -
theorem
bimodal_ratio_pos -
theorem
bimodal_ratio_gt_thirty -
theorem
bimodal_ratio_lt_phi_nine -
def
gap_size -
theorem
gap_size_eq -
theorem
gap_size_pos -
structure
PulsarPeriodFromRungCert -
def
pulsarPeriodFromRungCert -
theorem
pulsar_period_one_statement