high_tc_implies_phi_lt_two
The theorem shows that high-temperature superconductivity from the ledger forces the golden ratio to obey phi < 2. Condensed-matter theorists using Recognition Science to bound material parameters would cite this result when constraining phi in the phi-ladder mass formula. The proof is a direct term projection that extracts the right conjunct of the defining proposition.
claimIf a system satisfies the ledger condition for high-temperature superconductivity, then the golden ratio obeys $phi < 2$.
background
Recognition Science obtains all constants from the J-cost functional equation, with phi fixed as the self-similar solution (T6). The module models high-Tc superconductivity through a ledger whose defining property is the conjunction 1 < phi and phi < 2. This supplies the local setting for structure theorems once the upstream definition high_tc_superconductivity_from_ledger is assumed.
proof idea
The proof is a one-line term that selects the second conjunct of the hypothesis high_tc_superconductivity_from_ledger.
why it matters in Recognition Science
The result supplies the upper bound on phi required by the high-Tc ledger structure and pairs with the sibling lower-bound theorem. It constrains phi within the forcing chain (T5-T8) so that derived constants such as G = phi^5 / pi remain consistent with the observed alpha band. No open scaffolding questions are closed here.
scope and limits
- Does not establish existence of high-Tc materials.
- Does not derive a critical-temperature formula.
- Does not incorporate doping or lattice details.
- Does not connect to specific experimental datasets.
formal statement (Lean)
20theorem high_tc_implies_phi_lt_two (h : high_tc_superconductivity_from_ledger) : phi < 2 :=
proof body
Term-mode proof.
21 h.2
22
23end HighTcSuperconductivityStructure
24end CondensedMatter
25end IndisputableMonolith