IndisputableMonolith.Physics.Upsilon_Mass3_FromPhiLadder
Module packaging the Recognition Science derivation of the Upsilon (bottomonium) mass scale from the phi-ladder mass formula. It introduces a domain cost, a canonical positive threshold, and an inhabited certificate `UpsilonMass3Cert` that witnesses the mass-3 placement. Particle-physics auditors of RS mass predictions would cite the certificate. The argument is definitional plus nonnegativity and positivity lemmas over the cost, not a deep tactic proof.
claimOn the Recognition Science $\varphi$-ladder, the Upsilon mass-3 sector is witnessed by a domain cost $C$ with $C\ge 0$, a canonical threshold $\theta>0$, and an inhabited certificate that the mass-3 placement meets that threshold in RS-native units (yardstick $\cdot\varphi^{r-8+\mathrm{gap}(Z)}$).
background
Recognition Science places particle masses on a discrete $\varphi$-ladder: mass $\propto$ yardstick $\cdot\varphi^{\mathrm{rung}-8+\mathrm{gap}(Z)}$, with $\varphi$ the self-similar fixed point forced at T6 and the eight-tick octave at T7. Constants and the J-cost infrastructure are imported from Constants and Cost ($\tau_0=1$ tick in RS-native units; $J$ the unique cost from the Recognition Composition Law).
This physics module specializes that ladder to the Upsilon (heavy quarkonium / mass-3) sector. It defines a domain cost on the relevant rung configuration, records that the cost is nonnegative and agrees with its pointwise evaluation, and fixes a canonical positive threshold against which the mass-3 claim is certified.
The certificate type UpsilonMass3Cert is the module's main export: an inhabited Prop-level witness that the ladder placement clears the threshold, suitable for downstream mass-table or spectroscopy audits.
proof idea
Definition-and-certificate module rather than a long derivation. Domain cost is introduced as a def; equality-at-evaluation and nonnegativity are short lemmas. Canonical threshold is a positive real (positivity lemma). The certificate structure bundles those facts; inhabitation is a one-line or short constructive witness that the Upsilon mass-3 rung meets the threshold under the phi-ladder formula. No deep tactic chain: algebraic comparison on the ladder exponent plus cost nonnegativity.
why it matters in Recognition Science
Closes a concrete particle-mass instance of the RS phi-ladder program for the Upsilon sector (mass-3 / bottomonium scale). Feeds any downstream mass-table, spectroscopy, or "all masses from $\varphi$" assembly that expects an inhabited UpsilonMass3Cert. Anchors the general mass formula (yardstick $\cdot\varphi^{r-8+\mathrm{gap}(Z)}$) at a named hadron rather than a free parameter. No further used-by edges are recorded in the mirror graph yet; the module stands as a leaf certificate in the Physics domain. Ties to T6 ($\varphi$ fixed point) and the ladder rung arithmetic used across RS mass claims.
scope and limits
- Does not derive the full PDG Upsilon mass spectrum or decay widths.
- Does not prove uniqueness of the rung assignment among all hadrons.
- Does not re-derive $\varphi$, $J$, or the global mass formula; imports them.
- Does not claim experimental fit bands beyond the certificate threshold.
- Does not address electroweak or QCD running outside the RS ladder.