Red Team — The Adversarial Audit
Targets A–E: attacking the five load-bearing reductions at their weakest transitions
The deliberately adversarial layer: instead of confirming TFPT, this document attacks the five load-bearing reductions (Targets A–E) at their weakest logical transitions. Each target runs through one fixed protocol — minimal statement, assumptions, logical chain, counterexample search, limiting cases, alternative structures, verdict. A red-team check asserts an adversarial fact (a counterexample really exists, a hidden assumption is really needed, a firewall really holds); the honest outcome lives in the status of each target, never in a green pass. Verdicts: A reduced (one residual), B/D/E survive narrowed, C survives; none broken.
- ›The five load-bearing reductions of the document set, treated as hostile witnesses.
- ›The red-team scripts redteam/rt_A_e8net.py … rt_E_vgeo.py + run_redteam.py.
- ›Target A (seam–Calderón = (E8)₁ net): reduced to ONE residual — boundary-net holomorphy + c = 8 (⇔ the index-4 inclusion); E₈ and bulk uniqueness then follow (v83/v87/v89; Lie-level realisation v143).
- ›Target B (g_car = 5 Pascal selection): survives narrowed — residual = the degree-2 truncation (Quadratic Boundary Locality), since tied to the boundary-net premise (v108–v113).
- ›Target C (k = c₃/2, S = A/4): survives — the only anchor is the UV-sensitive absolute 1/G.
- ›Targets D/E (one scale v_geo): survive narrowed — CP phases and the EW/reheating/leptogenesis scales are explicitly outside v_geo.
- ›No target is closed by this layer; 'survives' means the statement stands as worded, not that its residual is gone.
- ›A fourth verdict, 'broken', is reserved for an actual failure — none occurred, and that is reported as a fact, not a proof.
- ›Each target carries explicit kill tests; the layer is built so it MAY downgrade a claim on re-run when data or counterexamples move.
Key formulas
- Target A residualOne statement; E₈ and the unique 2D bulk then follow. [C/O]
- Same-c rival excludedHolomorphy excludes the only same-c competitor. [E]
Method — three honest verdicts
Each reduction is treated as a hostile witness under one fixed protocol. Allowed outcomes: survives (stands as worded), survives narrowed (stands only after a silent assumption is made explicit), reduced not closed (the conservative wording is correct). A confirmatory script that always passes is worthless here.
Target A — the (E8)₁ boundary-net identification
Level-1 primary counting (det Cartan: D₈ has 4, E₈ has 1) makes holomorphy necessary AND sufficient — a holomorphic c = 8 chiral CFT is the lattice theory of the unique even unimodular rank-8 lattice. Bulk uniqueness is not independent: for a holomorphic net Rep(A) = Vect, so the bulk pairing is unique (machine contrast: SO(16)₁ admits six modular invariants). Target A therefore collapses to one residual statement.
Targets B–E — narrowed, with named residuals
B: the Pascal ladder 2^{g−1} = Σ_{k≤2} C(g,k) is exactly equivalent to the degree-2 truncation; the residual is the QBL premise, since merged with the boundary-net gate. C: the replica chain is derived; the absolute 1/G stays the one anchor. D: the frozen CP phase survives at +0.98σ with a decision threshold σ_γ ≤ 0.96°. E: v_geo carries the dimensionless theory; EW/reheating scales are typed interfaces.
Follow-up rounds — the residual count is monotone
Two machine-checked follow-up rounds (v83–v100, v141–v144) moved Target A from three residuals to one and hardened the firewalls (numerology null test: P ≤ 10⁻³⁰·⁷ conditional on the declared grammar). The front summary table states the final reduction; the historical development is kept below it, honestly dated.