IndisputableMonolith.Verification.YardstickAssignmentPrinciple
Records the four sector candidate values of the yardstick power offset B_pow and the related r0 offsets used in RS mass anchoring. Supplies algebraic identities (sums, complements, sign relations) that pin those candidates before any assignment is chosen. Downstream choice-set enumeration imports this module as the fixed value pool. Content is mostly closed-form equalities and small finite checks, not a deep existence proof.
claimFor the four mass sectors, the module fixes candidate yardstick power offsets $B_{\mathrm{pow}}$ and companion offsets $r_0$, together with identities such as $\sum B_{\mathrm{pow}} = A$ and $\sum r_0 = VW + E_{\mathrm{passive}}$, plus lepton/EW complement and sign relations used when assigning sectors to values.
background
Recognition Science mass formulas place each species on a $\varphi$-ladder: mass $\propto$ yardstick $\times \varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$. The yardstick itself is fixed only after sector-level power offsets are chosen. This verification module sits in that assignment layer: it does not derive $\alpha$ or the experimental masses, but freezes the discrete candidate numbers that later combinatorial filters will permute.
Upstream, Constants supplies the RS-native time quantum and related units; AlphaDerivation records the cubic-ledger seed assembly (exact infrared $\alpha^{-1}(0)$ remains open); Masses.Anchor centralises the parameter-free mass constants in the Model layer. Against that backdrop the module names the four-sector $B_{\mathrm{pow}}$ pool and the four-sector $r_0$ pool, plus elementary sum and complement identities that any admissible assignment must respect.
proof idea
Definition-and-identity module rather than a single theorem. It introduces the concrete $B_{\mathrm{pow}}$ and $r_0$ value lists, then proves small algebraic facts: formula rewrites, sector sums equaling named anchors ($A$, $VW+E_{\mathrm{passive}}$), lepton/EW magnitude complements, and sign patterns (e.g. up-type negative vs EW positive). Proofs are direct evaluation and ring/arithmetic simplification on fixed integers or $\varphi$-expressions; no analytic estimates.
why it matters in Recognition Science
Feeds Verification.YardstickAssignmentChoiceSet, which treats O1 as a finite search: start from these four $B_{\mathrm{pow}}$ and four $r_0$ candidates, enumerate sector-to-value permutations, and filter by structural yardstick constraints. Without a frozen candidate pool the choice-set module has nothing to permute. In the broader RS chain this is bookkeeping on the mass-ladder yardstick step (primer mass formula), not a T0–T8 forcing result; it keeps the assignment discussion auditable and finite before any claim of uniqueness or data fit.
scope and limits
- Does not prove which sector receives which $B_{\mathrm{pow}}$ or $r_0$ value.
- Does not derive experimental masses or claim agreement with PDG data.
- Does not close the open infrared $\alpha^{-1}(0)$ boundary condition.
- Does not force $D=3$, $\varphi$, or the eight-tick octave; those live upstream.
- Does not enumerate or filter full assignment permutations; that is the downstream choice-set module.
used by (1)
depends on (3)
declarations in this module (23)
-
theorem
B_pow_values -
theorem
B_pow_formula_identities -
theorem
B_pow_sum -
theorem
B_pow_sum_eq_A -
theorem
lepton_ew_complement_down -
theorem
lepton_ew_natAbs_complement_down -
theorem
up_ew_same_magnitude -
theorem
up_negative_and_ew_positive -
theorem
r0_values -
theorem
r0_formula_identities -
theorem
r0_sum -
theorem
r0_sum_eq_V_mul_W_add_Epassive -
theorem
r0_lepton_ew_depth_gap -
theorem
r0_sum_decomposition -
theorem
W_multipliers_sum_to_V -
theorem
additive_corrections_sum_to_Ep -
theorem
r0_sum_from_cube -
theorem
up_ew_sign_duality -
theorem
depths_exhaust_vertices -
theorem
r0_order_constraints -
theorem
cube_partition_budget -
structure
AssignmentConstraints -
def
assignment_valid