IndisputableMonolith.Astrophysics.AsteroidsFromPhiLadder_v2
Packages asteroid mass and size scales as discrete rungs on the Recognition Science phi-ladder. Astrophysicists citing RS ladder predictions for small-body populations use the domain cost, canonical threshold, and inhabited certificate. Argument is definitional: cost evaluation identities plus a positivity lemma, bundled into a certificate structure.
claimThe module introduces a domain cost on the $\varphi$-ladder, a canonical positive threshold separating asteroid-scale rungs from neighboring regimes, and an inhabited certificate asserting that asteroid scales arise from those discrete ladder rungs under the Recognition cost.
background
Recognition Science places masses and characteristic scales on a geometric ladder with ratio $\varphi$, the self-similar fixed point forced at T6. The mass formula is yardstick times $\varphi$ to a rung offset (rung $-8+$ gap). The Cost import supplies the J-cost $J(x)=(x+x^{-1})/2-1$; Constants fixes the RS time quantum $\tau_0=1$ tick.
This astrophysics module specializes those primitives to small rocky bodies. It defines a domain cost functional for the asteroid regime, a canonical threshold (proved positive), and evaluation identities that pin the cost at ladder points. The local setting is discrete preferred scales rather than continuous collisional cascades.
proof idea
Definition-and-certificate module, not a deep derivation. domainCost and canonicalThreshold are introduced directly; canonicalThreshold_pos is an elementary positivity fact. domainCost_at_eq records evaluation identities at specified ladder points. AsteroidsFromPhiLadder_v2Cert (with cert and cert_inhabited) packages those facts into an inhabited certificate structure. No multi-step tactic chain; the work is naming the threshold and bundling it.
why it matters in Recognition Science
Puts asteroid phenomenology on the same $\varphi$-ladder used for particle masses and other RS scales, so small-body sizes inherit the T6 forcing of $\varphi$ and the eight-tick octave structure upstream. used_by is empty: the module is a leaf packaging the v2 asteroid claim for the broader astrophysics layer. Downstream consumers would cite the certificate when closing observational or catalog comparisons against discrete rung predictions. Touches the mass-ladder formula without reopening J-uniqueness or dimension forcing.
scope and limits
- Does not derive continuous size distributions or collisional evolution models.
- Does not claim observational catalog fits beyond discrete ladder thresholds.
- Does not prove uniqueness of the canonical threshold outside the stated domain cost.
- Does not connect asteroid rungs to planetary or stellar mass formulas here.
- Does not re-derive phi or the J-cost; those are imported.