Red Team — The Adversarial Audit
Targets A–E, the QFT round (F) and the seam round (G): attacking the load-bearing reductions at their weakest transitions
The deliberately adversarial layer: instead of confirming TFPT, this document attacks the load-bearing reductions (Targets A–G) 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/F survive narrowed, C survives; none broken on the load-bearing surface. Target F audits the perturbative-QFT + scale round (v269–v275): the two attacks that landed are now resolved — the R²/Weyl² gravity Stelle ghost is a Seeley–DeWitt truncation artefact (the untruncated KMS spectral-action Hessian is entire and zero-free, so resummation decouples it ⇒ perturbative spin-2 graviton unitarity established [C], v304/v370/v380), and the anchor over-determination is conditional on the Λ-branch — both folded back into v269/v274. The ambient QG.AMB.01 measure is itself discharged as a redundancy [C] (v369+v379), a certification object rather than a nonperturbative frontier. The new seam round (Target G) banks the ten-test side-blind scoreboard on the alignment bit (v512 web, v521 eighth, v525 ninth, v529 tenth — the bit is not derivable from any tested class and is now physically defined as the twist-class choice, v528) and reports the layer's first toy-level firing: Kill-Test 2 of the OS twistor contract fires on the interacting Fidkowski–Kitaev seam toy — reflection positivity breaks for every g > 0 following the straddle law (RP fails exactly on quartet-straddled cuts, 24/24) — a fenced honest threat that doubles as the first hard selection principle for the interacting algebra A_hol. WOIT.OS.TWISTOR.01 stays [O]; no marker moves.
- ›The five load-bearing reductions of the document set, treated as hostile witnesses.
- ›The red-team scripts redteam/rt_A_e8net.py … rt_F_qft4d.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). The free-bulk premise is a fixed-point theorem (quasi-free ⇒ κ₂ₙ=0) and the infinite Schwinger cone is eliminated (cone gap = one-particle gap (2/3)⁶), so the reduction adds no new open content. Net existence and full-cone reflection positivity are discharged to [E] (the CAR second-quantisation functor reduces full-cone RP for every mode to the one-particle contraction, verified on the complete 2¹⁶-dim Fock space; v175), and A2 is an assembled, verified (E₈)₁ certificate. The seam realisation is the keystone SEAM.EQUIV.01 — the raw RP seam IS the holomorphic (E₈)₁ net at τ=i — whose MMST route SEAM.EQUIV.MMST.01 is now closed modulo cited theorems: an explicit gapped lattice model (v367/v368) and the S3 closure stack (v376–v379, ground-state witnesses v489/v490) pin the target at every computable level, Lean-pinned (FORM.SEAM.MMST.01) to the published MMST/Adamo theorems, leaving [O] = the cited continuum scaling-limit existence only (v336) — its 128-spinor extension leg now certified at net level by the peer-reviewed crossed-product package (v469: locality integer h_s = 16/16 = 1 ∈ ℤ, Longo–Rehren 1995 / Böckenhauer 1996 / Böckenhauer–Evans 1998 / KLM μ = 4/2² = 1 ⇒ holomorphic; the AGT/AMT lattice-VOA route demoted to an independent second witness), with the realisation input reduced from model fiat to invariant level R1′ (quasi-free + gap + class D + c₋ = 8 from P1; computed FHS Chern |C| = 1, ν = 16); SEAM.EQUIV.01 stays [O]. Its conformal-deck face QGEO.SYM.01 is a corollary (v335). The full sprint-by-sprint reduction (v176 → v302) is recorded on the /changelog page and in the research contracts.
- ›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 narrowed — the replica/EH chain is now exercised numerically at the collar level with the seam's own kernel (v471); the residual is the cited continuum scaling limit (v336) plus the UV-sensitive absolute 1/G anchor; SEAM.THEOREM.01 stays [O].
- ›Targets D/E (one scale v_geo): survive narrowed — CP phases and the EW/reheating/leptogenesis scales are explicitly outside v_geo.
- ›Target F (perturbative 4D-QFT + scale round, v269–v275): survives narrowed — the two attacks that landed are resolved: the R²/Weyl² Stelle ghost is a Seeley–DeWitt truncation artefact (perturbative spin-2 graviton unitarity established [C], v304/v370/v380) and the ambient QG.AMB.01 measure is discharged as a [C] redundancy (v369+v379).
- ›Target G (the alignment bit + the interacting seam): the bit survives ten side-blind derivation attacks (v512/v521/v525/v529) and is physically defined as the twist-class choice with a gauge-robust order parameter (v528, stays formal input); the OS/RP structure survives free and gauge-fixed (v522/v524) while the interacting straddle law (v529) is the named residual risk of the Woit route — Kill-Test 2 fires at toy level under a typed fence, and every candidate A_hol must pass the straddle filter; the filter, since executed as a selector (v534), keeps exactly ONE member alive — reflection positivity dynamically selects the bit δ = π/2 with positive coupling (the first positive selection datum, toy-fenced).
- ›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 on the load-bearing surface; the first toy-level firing (the straddle law, v529) is reported visibly and fenced, not hidden.
- ›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 follow. (A) factors into the A2 net-existence + the keystone SEAM.EQUIV.01, whose MMST route SEAM.EQUIV.MMST.01 is now closed modulo cited theorems (lattice v367/v368 + S3 stack v376–v379, ground-state witnesses v489/v490; parent [O]; residual [O] = cited continuum existence (v336) + crossed-product certified extension leg (v469, LR/Böckenhauer/KLM; AGT/AMT second witness); stays [O]). [C]
- 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 that carries no new open content: the free-bulk premise is a fixed-point theorem (v160), the infinite Schwinger cone is eliminated since the cone gap equals the one-particle gap (2/3)⁶ (v161/v162), and the irreducible core {π, v_geo} is a theorem (v165). Net existence and full-cone reflection positivity are discharged to [E] on the complete 2¹⁶-dim Fock space (the CAR second-quantisation functor reduces full-cone RP for every mode to the one-particle contraction; v175), and A2 is an assembled, verified (E₈)₁ certificate (E₈ Cartan even unimodular, det 1). The seam realisation is the keystone SEAM.EQUIV.01 (the raw RP seam IS the holomorphic (E₈)₁ net at τ=i), whose MMST route SEAM.EQUIV.MMST.01 is now closed modulo cited theorems: an explicit gapped lattice model (v367/v368) and the S3 closure stack (v376–v379, ground-state witnesses v489/v490) pin the target at every computable level, Lean-pinned (FORM.SEAM.MMST.01) to the published MMST/Adamo theorems, leaving [O] = the cited continuum scaling-limit existence only (v336) — its 128-spinor extension leg certified at net level by the peer-reviewed crossed-product package (v469: h_s = 16/16 = 1 ∈ ℤ fulfils the Longo–Rehren locality criterion, KLM μ = 1 ⇒ holomorphic; AGT/AMT demoted to an independent second witness), with the realisation input reduced to invariant level R1′; stays [O]. Its conformal-deck face QGEO.SYM.01 is a corollary (v335). The step-by-step reduction (v160 → v302) lives on the /changelog page, not here.
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 and now exercised numerically on the discretized collar with the seam's own kernel (v471) — the kernel premise is discharged at the finite level; what remains is the continuum leg (MMST class, v336) plus the one dimensionful anchor (v152), gate [O]. 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.
Target F — the perturbative 4D-QFT + scale round (v269–v275)
Target F audits the perturbative-QFT + scale round. The two attacks that landed are now resolved: the R²/Weyl² gravity Stelle ghost is a Seeley–DeWitt truncation artefact (the untruncated KMS spectral-action form factor a(p²)=e^{p²/M²} keeps its only pole at p²=0, the spin-2 sector is ghost-free via the Barnes–Rivers decomposition, and the nearest truncation-zero modulus runs to infinity), so perturbative spin-2 graviton unitarity is established [C] (v304/v370/v380); and the anchor over-determination is conditional on the Λ-branch — both folded back into v269/v274. The ambient QG.AMB.01 measure is itself discharged as a [C] redundancy (v369+v379), a certification object rather than a nonperturbative frontier.
Target G — the alignment bit and the interacting seam (the first shot that lands)
Two red-team questions: can the bit be derived (a hidden redundancy), and can the OS/RP structure be broken? Attack 1 — ten failures, honestly banked: the v512 equivalence web (no local jet sees the side bit), free RP/Θ existence (the eighth side-blind test, v521), every Wick-computable mark-decorated state (the ninth — the free-plus-twist class is exhausted, v525), and the first genuinely interacting, non-Wick-computable dynamics (the tenth: the interaction sees δ massively yet all side data are mirror-equal, v529). Ten tests, ten kills: the bit is not derivable from any tested class and remains genuine discrete input — now physically DEFINED as the twist-class choice (facets #14/#15 extend the web to 15 exact equivalences, flip-axis fraction a gauge-robust order parameter O = 1/2 at m = 4 else 0, η holonomy in principle interferometrically readable; v528, [C] measurement sketch, no marker moves). Attack 2 — where it fires: on the minimal interacting Fidkowski–Kitaev quartic (16-Majorana NS seam circle, 256-dim, exact) Θ exists exactly (Kill-Test 1 does not fire) but reflection positivity breaks in the interacting ground state for every g > 0 — inertia ladder (37,0,0) → (29,8,0), mechanism interference — and the failure pattern is a law: RP fails exactly on quartet-straddled cuts and stays positive definite on quartet-avoiding ones (the STRADDLE LAW, 24/24). The first live ammunition of the layer, fenced (one toy, one interaction class, [C] flat-band parent) — and simultaneously the first hard selection principle: every candidate A_hol must protect RP against exactly this mechanism, a concrete hurdle for the β₃/γ stages. The filter, executed (v534): run as a selector on the full interacting mark family (independent equivariant couplings, both signs, all admissible cuts — including the π/2 straddled clock axes 7/15 the 24-entry law had not covered), reflection positivity survives for exactly ONE member × sign — δ = π/2 with positive coupling, PD on all four cuts over g ∈ {1/32..8} with the minimum eigenvalue lifted AWAY from the RP boundary; every asymmetric member dies. The law refines (asymmetric straddling kills, symmetric straddling protects), the literal leading-order cone formalization is dead (the protection is nonperturbative), and the unique survivor IS the alignment bit — the same member that carries the twist-class order parameter O = 1/2. Toy-level evidence for a dynamical origin, not a derivation. WOIT.OS.TWISTOR.01 stays [O].
Follow-up rounds — the residual count is monotone
Machine-checked follow-up rounds moved Target A from three residuals to the single named keystone SEAM.EQUIV.01 and hardened the firewalls (numerology null test: P ≤ 10⁻³⁰·⁷ conditional on the declared grammar). This document states the current reduction; the dated round-by-round development lives on the /changelog page.