SG-5 — Electroweak embedding Q=T3+Y / EWSB to U(1)_em: full dossier

Audience: the specialist who will close the gaps (and the open-science public). Status (binding, matches the live popup): OPEN (gate roll-up) — with the charge/embedding leg at DERIVED-GIVEN-E and the ρ observable fully computed. Direction: held. STATUS-UPGRADES:0. Frozen branch dcc66f1b2685 / manifest meta a5b1e6f9d951 READ-ONLY. given-E ≠ derivation of E; selection ≠ derivation; dissolved ≠ solved; ANCHORED ≠ DERIVED. Honest ceiling: serious candidate, NOT validated. Voice: lead with what is shown; keep every confident sentence true. The honest edge here is a strength — we built the W/Z mass machinery and read ρ target-blind, so the gate carries a falsifiable FINDING, not a hedge.

§0. Executive summary + honest status

0.1 The headline

We embed electric charge exactly — Q = T₃ + Y on every Standard-Model multiplet — and break the electroweak group with a single geometric (Wilson-line / Hosotani) Higgs. Then we did the thing most unified frameworks skip: we actually built the electroweak gauge-boson mass matrix from the frozen geometry and read the custodial parameter ρ off it, target-blind. The result is sharp and honest: ρ is a real, physical, gauge-invariant observable, and the frozen charge law itself pins where the symmetry-breaking direction sits — which produces a target-blind FINDING that ρ_tree ≠ 1, a live precision-electroweak tension against the measured ρ₀ = 1.00038 ± 0.00020. That is not a value we tuned; ρ₀ was an input to nothing.

0.2 The honest grade (must match the live chip)

The gate is OPEN at the roll-up — and it is governed by its least-closed residual, so it cannot be graded higher while the hierarchy and the ρ-realization map stay open. But the components split cleanly, and several are genuinely strong:

0.3 What this dossier establishes and what it does not

This dossier establishes, with full traceability to the frozen corpus: (i) the exact charge embedding and its ℤ₆ consistency rule; (ii) the single-doublet EWSB mechanism and forced photon masslessness; (iii) the structural avoidance of the Higgs quadratic destabilization; and (iv) the complete construction of the geometric W/Z mass matrix, machine-verified, which converts the previously-asserted custodial relation into a computed, target-blind FINDING that ρ_tree ≠ 1. It does not claim to derive the electroweak hierarchy (that is OPEN/RELOCATION), does not claim the geometry predicts ρ = 1 (the opposite — the bare-commutator readout disfavors it), does not treat v_EW as derived (it is a transparent second anchor), and does not prove the selected geometry unique. Every "not" is stated loudly; none is buried.

A note on an internal reconciliation, carried honestly. An older deploy-doc framing (SG5_ELECTROWEAK_CLOSURE_RESULT.md §8) describes ρ as an undetermined flat modulus over [½, ∞). The owner-binding disposition (files 11_R3_VERDICT_FINDING_STANDS and 12_R3_READOUT_MAP_AUDIT, both marked OWNER VERDICT, readout-map audit COMPLETE) supersedes that: the mounted charge law Q=T₃+Y pins the direction, so h₃ is not a free modulus and ρ_tree ≠ 1 is a standing FINDING, not "neither derived nor falsified." This dossier carries the FINDING as the binding disposition and §3.6 reconciles the two framings in full.

§1. The community gap

1.1 The precise open problem

Any theory that claims to unify the Standard Model interactions inherits four obligations in the electroweak sector:

1. Charge quantization & embedding. Reproduce electric charge Q on every fermion — including the famous −⅓ of the down quark and the part-in-10²¹ neutrality of the hydrogen atom — as Q = T₃ + Y, with the hypercharge assignments not free but forced.
2. Electroweak symmetry breaking. Break SU(2)_L × U(1)_Y → U(1)_em and leave exactly one massless gauge boson (the photon), with the breaking sourced by a definite, ideally not-hand-inserted, scalar.
3. The custodial relation ρ ≈ 1. The tree-level relation ρ = M_W² / (M_Z² cos²θ_W) = 1 is the hallmark of breaking by an SU(2)_L doublet. Experimentally ρ₀ = 1.00038 ± 0.00020 (PDG electroweak fit). In the SM this is protected by an accidental custodial SU(2) and is treated as a structural input, not derived from a deeper geometry.
4. The hierarchy. Explain why the electroweak scale v ≈ 246 GeV is ~16 orders of magnitude below M_Pl — the gauge hierarchy problem — without fine-tuning the Higgs mass against quadratic UV sensitivity.

1.2 State of the art / best bounds across the community

• The hierarchy is unsolved. Across frameworks — technicolor, low-scale SUSY, large/warped extra dimensions, composite Higgs, the Hosotani / gauge-Higgs-unification (GHU) program — the lightness of v is either tuned, relocated to another scale, or pushed beyond reach of current data. No framework derives v/M_Pl ∼ 10⁻¹⁶ from a parameter-free UV input. This is the canonical naturalness problem.
• ρ = 1 is an input, not a derivation. In essentially every model ρ = 1 is a custodial-symmetry assumption or an automatic consequence of choosing a single doublet by hand. The measured deviation ρ₀ − 1 = (3.8 ± 2.0)×10⁻⁴ is fitted by the SM through known loop corrections (dominated by the m_t–m_b splitting); it is not predicted by a geometric first-principle in any unified candidate.
• GHU / Hosotani context. In gauge-Higgs unification the Higgs is the extra-dimensional component of a gauge field (A_y), and its potential V_Hos(θ_H) is finite and calculable (Hosotani mechanism: the Higgs mass is protected by higher-dimensional gauge invariance — no quadratic divergence). This is the good feature our construction inherits. The hard, unsolved part everywhere is (a) why the minimum θ_H* is tiny (the hierarchy), and (b) whether the realized breaking is custodial-symmetric (ρ = 1) or not. Realistic GHU models on S¹/ℤ₂ typically engineer custodial protection by enlarging the bulk gauge group to contain SO(4) ≃ SU(2)_L × SU(2)_R or by using an SO(5)/SO(4) coset (the Agashe–Contino–Pomarol composite-Higgs route). That custodial coset is exactly what our frozen object does not contain — and that is the crux of the SG-5 ρ FINDING below.

1.3 Why prior attempts fall short — and where ours stands relative to them

The community's two standard ρ = 1 mechanisms both insert the custodial structure: either by hand (choose one doublet, declare custodial SU(2)) or by enlarging the bulk group to a custodial coset. Neither is a derivation from a fixed higher-dimensional geometry whose breaking direction is independently pinned. Our construction is different in a way that is both a strength and the source of the FINDING: the breaking direction is not free — the same Q = T₃ + Y charge law that gives us exact charges also pins the electroweak-neutral axis. We do not get to choose the doublet's alignment to make ρ come out right; the geometry chooses it for us. When we do the computation honestly, that pinning forces ρ_tree ≠ 1 at the bare-commutator level. So our gap is not "we assumed ρ = 1 like everyone else" — it is "we computed ρ, found a tension, and named it as a live falsifiable finding." That is a more honest and more attackable position than the field's default.

§2. The construction — rigorous math

Full published derivation: GUT.html §6.3 (charge) + §6.8 (Higgs) + Appendices D / E′ / H, at https://physics.magflowmeters.com/articles/GUT.html. This section reproduces the load-bearing math at working-physicist depth so a reader can both check it and build on it.

2.1 The geometric backbone

The frozen SM-routing geometry is

K_gauge = K₆ × S² × S¹_Y/ℤ₂        (× M₄ spacetime)

with K₆ = SU(3)/T² the colour carrier, S² the weak-isospin carrier, and S¹_Y/ℤ₂ the hypercharge carrier (a folded circle). The isometry group of K_gauge delivers SU(3)_c × SU(2)_L × U(1)_Y (this is the SG-2 result, taken as given here). Electromagnetism is then the unbroken combination after EWSB.

The forward chain SG-5 rides:

isometries(K_gauge) → SU(3)_c × SU(2)_L × U(1)_Y           [SG-2, given]
  --S¹_Y/ℤ₂ + ℤ₆ quotient-->  Q = T₃ + Y on every multiplet  [charge leg]
  --one Wilson-line/Hosotani doublet H (n_H=1)-->  V_Hos(θ_H) minimum θ_H*
  --SU(2)_L×U(1)_Y → U(1)_em-->  v = θ_H*/(2πR_γ),  m_h² = V''_Hos(θ_H*)/(2πR_γ)²
  --same η_BK (finite determinant)-->  { v=246.02, m_h=123.82, |y_t/y_b| }

2.2 The charge embedding Q = T₃ + Y (DERIVED-GIVEN-E)

Hypercharge U(1)_Y is the rotation of the folded circle S¹_Y/ℤ₂. Electromagnetism is the unbroken combination Q = T₃ + Y. The charge claim is two exact predicates holding componentwise on each multiplet:

1. Q = T₃ + Y componentwise; and
2. the ℤ₆ consistency rule t/3 + d/2 + Y ∈ ℤ, with t = +1, −1, 0 for 3, 3̄, 1 of colour and d = 1, 0 for SU(2) doublet / singlet.

The second predicate is what makes the embedding rigid: it expresses that the global quotient is [SU(3) × SU(2) × U(1)_Y]/ℤ₆ (realized by the frozen parity table, hash ac4d2df3e708), so a hypercharge that fails the congruence is inconsistent on the geometry, not merely "not observed."

Hand-checkable worked examples (every number here is arithmetic from the frozen Y table):

A killed counterexample, to show the rule has teeth: Y(Q_L) = ⅕ (instead of +⅙) gives ⅓ + ½ + ⅕ = 31/30 ∉ ℤ — barred. This is the corroborated A4-ℤ₆ "Tong congruence" q = 3z₂ − 2z₃ mod 6, satisfied field-by-field by the SM triples, with the χ = −3 global-index constraint honored. The down quark lands at exactly −⅓, and atomic neutrality to ~1 part in 10²¹ is reproduced structurally (it is forced by the congruence, not fitted).

Honest scope. The parity/center table was selected and frozen, not searched: §5.2 of the manuscript states "searched no manifolds; selected the parity/center assignments on the fold; froze the parity table." So charge is forced given that table — DERIVED-GIVEN-E, with the table's selection (and the =ℤ₆ finest-ness) carried as the residue (R9, §6.9). This is the gate's strongest, most defensible leg.

2.3 The single Wilson-line / Hosotani doublet (DERIVED-GIVEN-E)

The Higgs is identified with the holonomy (Wilson-line) mode of the gauge connection on the SU(2)_L-direction cycle γ ⊂ K_gauge:

W_γ = P exp( i ∮_γ A ),     E_Higgs = L_γ ⊗ V_{SU(2),doublet} ⊗ L_{Y=+½}

(bundle hash 2a0462b8aab9, cycle hash 640e1d7f7773). It is exactly one doublet H ∈ (1, 2, +½), carrying integer winding n_H = 1 (hash f65094fd8fd1), which is topologically protected. The winding is the minimal admissible non-zero integer:

• n_H = 0 ⇒ v = 0 (no breaking) — a clean structural kill;
• n_H ≥ 2 ⇒ v ≈ 492 GeV and breaks the one-input-two-outputs alignment (failure ledger L6368/L7650) — a data-dependent kill.

So n_H = 1 is AXIOM-CLOSED at the minimal-winding axiom (R10, §6.10): the n_H=0 exclusion is target-blind; the n_H≥2 exclusion is a disclosed data check.

2.4 The Hosotani phase, the potential, and the breaking

Writing the Wilson-line connection as A_γ = (θ_H / 2πR_γ) T_H with θ_H ∈ [0, 2π) and T_H ∈ su(2)_L, the VEV is ⟨H⟩ = θ_H / (2πR_γ), so

v_EW = θ_H* / (2π R_γ),      θ_H* = argmin V_Hos(θ_H).

The one-loop Coleman–Weinberg / Hosotani potential is

V_Hos(θ_H) = − (3 / 64π⁶R_γ⁴) Σ_{n=1}^∞ (1/n⁵) [ N_b cos(nθ_H) − N_f cos(nθ_H) ],

which is finite (the n⁻⁵ sum converges absolutely), periodic (so n_H is a topological invariant), and cutoff-independent. The non-zero θ_H* is the EWSB; the unbroken direction is U(1)_em with Q = T₃ + Y. Note the N_b − N_f structure: if N_b = N_f the θ_H-dependence vanishes and there is no breaking (this is residual R8, §6.8 — the imbalance is a structural prerequisite).

2.5 The finite determinant η_BK and the near-hit numbers

The Higgs-mass scale and the between-sector Yukawa ratio are set simultaneously by one frozen finite (Berezin–Kontsevich) determinant η_BK = 0.009721281516312024 (hash 84e94518d3f5), via the structural identity

1/η_BK = e^{2β₁*} = 32π · exp(√3 / 24π) ≈ 102.87 = |y_t/y_b|   (raw determinant;
                                                                 certified M_Z value ≈ 58, App J).

Numerical check (recomputed for this dossier): 32π = 100.531, exp(√3/24π) = 1.023238, product = 102.867, and 1/102.867 = 0.009721281516312 — exact to the frozen value. The post-RG outputs are

v   = 246.02 ± 3.5 GeV   (0.06σ_th vs PDG 246.22)
m_h = 123.82 ± 1.8 GeV   (0.48σ_th vs PDG 125.10 ± 0.14)
m_h² = V''_Hos(θ_H*) / (2πR_γ)²

This is the genuine, non-trivial content: one geometric quantity (η_BK), two SM outputs (v, m_h) plus the Yukawa ratio — a one-input-two-outputs compression. (Whether the form of η_BK is target-blind is residual R5, §6.5; the value reproduces, the provenance is unaudited.)

2.6 The Higgs-mass quadratic destabilization is structurally avoided (banked, one-loop)

The would-be δm_H² ∼ M_*² tree counterterm is topologically forbidden: it would require a non-integer change in n_H, which is impossible for an integer winding. V_Hos is finite, periodic, and cutoff-independent, so there is no quadratic UV sensitivity at one loop. The mass is protected to ∼10¹⁴ GeV (SCALE_HIERARCHY_FINAL_VERDICT "PROVEN sub-result"). This is a proven, banked result — but it is one-loop; all-orders protection is Diagnostic-only (R7, §6.7). And, crucially, protection from quadratic divergence is not the same as delivering the smallness of v — the protection ratio √η_BK/(2π) ∼ 10⁻² is twelve orders of magnitude too large to be v/M_Pl ∼ 10⁻¹⁶. The hierarchy is a separate, open problem (§6.1/§6.2).

2.7 The W/Z mass matrix and ρ — the computation, in full

This is the load-bearing new construction. The frozen Higgs is a non-custodial Hosotani object: A_y = (θ_H/2πR_γ)·T_H with T_H ∈ su(2)_L, the doublet tensored in, and the custodial SO(4) coset eliminated from the frozen construction. Because there is no custodial symmetry tensored in, the gauge-boson mass term does not descend from the textbook linear-representation operator |D_μ H|²; it descends from the commutator operator characteristic of gauge-Higgs unification:

mass term ∝ Tr | [A_μ, A_y] |².

Define the VEV-weighted commutator overlaps, with T_H = Σ_b h_b T_b (and T_a = σ_a/2 the su(2) generators):

O_a = ⟨ Tr |[T^a, T_H]|² ⟩.

A short su(2) computation (using [T_a, T_b] = i ε_{abc} T_c, Tr(T_a T_b) = ½δ_{ab}) gives the exact closed form

O_a = ½ ( |h|² − h_a² ),        |h|² = h₁² + h₂² + h₃².

The charged combinations W^± = (W¹ ∓ iW²)/√2 get mass ∝ O₁ + O₂ (call the coefficient C_W), and the neutral W³ gets mass ∝ O₃ (call it C_3); the photon stays massless (the Q=T₃+Y-preserving VEV gives det of the neutral (W³,B) block = 0, normalization-independent — DERIVED-GIVEN-E). The tree custodial parameter is then

ρ_tree = (O₁ + O₂) / (2 O₃) = ½ + h₃² / (h₁² + h₂²)   ∈  [½, ∞),
ρ_tree = 1  ⟺  2h₃² = h₁² + h₂²    (a 54.74° cone about the 3-axis).

Machine verification (reproducer SG5_R3_RHO_REPRODUCER.py, re-run for this dossier — all checks PASS):

[1] O_a == (1/2)(|h|^2 - h_a^2)            max err 8.9e-16  -> PASS
[2] rho == 1/2 + h3^2/(h1^2+h2^2)          max err 4.5e-13  -> PASS
    rho range over directions: min=0.5000  (>= 0.5), max=3866.8 (-> inf)
[3] doublet holonomy eigs == +-theta/2 (dir-independent) dev 3.9e-16 -> PASS
[4] rho invariant under U(1)_3 (Q-preserving)   max dev 2.2e-16 -> PASS
[5] body-diagonal (1,1,1): rho=1.0000 (cone), angle from 3-axis=54.74 deg

So the algebra is verified to machine precision by two independent routes, and ρ varies over the full [½, ∞) as T_H's direction varies — confirming ρ is a real observable, not a constant tautology.

2.8 The decisive step — the charge law pins the direction, forcing ρ_tree ≠ 1

The remaining question is: what direction is T_H? Two facts settle it, and both are mounted in the frozen corpus:

1. The frozen charge law Q = T₃ + Y with T₃ = J₃/2 requires the unbroken photon to lie along T₃ (the EW-neutral 3-axis is pinned by the ℤ₆ fermion-charge table — it must reproduce the observed charges; check [4] above confirms ρ is invariant under exactly the residual Q-preserving U(1)₃, i.e. the 3-axis is the physical, frame-pinned axis).
2. A Hosotani VEV along T_H leaves unbroken the U(1) along T_H.

For the unbroken U(1) to be the electromagnetic U(1) along T₃, we therefore need T_H ∥ T₃. But then [T₃, T_H] = 0, so

(O₁, O₂, O₃) = (½, ½, 0)   ⇒   C_3 = O₃ = 0   ⇒   ρ_tree = C_W / C_3 = (½)/0 = NOT 1.

The neutral W³ receives zero mass from the bare Hosotani commutator. This is a determinate, target-blind FINDING: ρ_tree ≠ 1 (an ill-defined / ≫1 ratio whose neutral denominator vanishes). The body-diagonal ρ = 1 cone (the (1,1,1)/√3 direction at 54.74° from the 3-axis) is barred: it would put the surviving photon along (1,1,1)/√3 ≠ T₃, contradicting Q = T₃ + Y, and is additionally rejected as target-fitting. The only mechanism that would force ρ = 1 is a custodial SO(4) ≃ SU(2)_L × SU(2)_R (or SO(5)/SO(4)) coset selecting the linear operator |D_μ H|² — and that coset is recorded eliminated in the frozen object (S² and S¹_Y are distinct isometry factors; S³/SO(4) eliminated). The measured ρ₀ = 1.00038 ± 0.00020 is used only as a post-hoc falsifier — an input to nothing in the computation above.

This is the owner-binding disposition (files 11_R3_VERDICT_FINDING_STANDS, 12_R3_READOUT_MAP_AUDIT, readout-map audit COMPLETE): SG-5/R3 is a standing FINDING that ρ_tree ≠ 1, a live precision-electroweak tension — not "undetermined." §3.6 reconciles this with the older "flat modulus" framing.

§3. The insights we used

3.1 The charge law is the lever, not just the result

The deepest insight is that Q = T₃ + Y is doing double duty. It is the deliverable of the charge leg, but it is also the constraint that pins the EWSB direction. Most GHU/composite-Higgs constructions treat the Higgs alignment as engineerable (you enlarge the bulk group, or pick the doublet, to get custodial protection). Here you cannot: the requirement that the fermion charges come out right (via the frozen ℤ₆ table) fixes the unbroken U(1) axis to be T₃, which then forces T_H ∥ T₃ for the photon to be electromagnetic. The ρ FINDING is the price of taking the charge law as load-bearing rather than decorative.

3.2 Non-custodial Hosotani ⇒ commutator, not |D_μ H|²

The second insight is recognizing which operator sources the W/Z masses. Because the frozen object is a non-custodial Wilson-line connection (A_y ∈ su(2)_L, no SO(4) tensored in), the gauge-boson masses come from Tr|[A_μ, A_y]|², not the fundamental-doublet |D_μ H|². Three earlier passes were stuck on a red herring (the S²-vs-S¹_Y kinetic co-normalization, blocker #2). The algebraic insight that ρ_tree = C_W/C_3 exactly, with the off-diagonal co-normalization a_B cancelling out of ρ entirely, dissolved blocker #2 for ρ and located the real load-bearing object: the commutator overlaps O_a. (The co-normalization is still owed for the absolute masses — R-abs, §6.5.)

3.3 The flat-direction observation, and why it does NOT make ρ free

A genuinely surprising computed fact: the one-loop V_Hos is exactly flat in the Wilson-line tilt direction. The doublet holonomy eigenvalues are ±θ_H/2, independent of the direction of T_H (the KK weight-multiset is rotation-invariant; check [3] above, dev 3.9e-16). So V_Hos(θ_H, direction) = V_Hos(θ_H) — the one-loop potential selects no direction, and ρ = 1 is one non-preferred level set, not a minimum. The naive reading is "therefore h₃, hence ρ, is a free modulus, undetermined over [½, ∞)." The owner-binding correction is that this reading is wrong: the direction is not free, because it is fixed not by the potential but by the charge law (§2.8). V_Hos being flat means the potential does not pick the direction — but the photon-along-T₃ requirement does. So h₃ is pinned, ρ_tree ≠ 1, and the honest statement is a FINDING, not an undetermined bet (§3.6).

3.4 ρ is a genuine gauge-invariant observable

It would be a fatal error to dismiss ρ_tree ≠ 1 as a gauge artifact. The reproducer settles this: ρ is invariant under the residual Q-preserving U(1)₃ (check [4], dev 2.2e-16) — exactly the symmetry that survives EWSB — and varies under a generic SU(2)_L rotation (0.500..0.777 over the sampled arc). That is the signature of a physical observable whose value is fixed once the frame (the 3-axis) is pinned. The 3-axis is pinned by the frozen ℤ₆ charge table. So the FINDING is about a real observable, not a coordinate choice.

3.5 Target-blindness as the discipline that makes the FINDING credible

The entire ρ computation was run with ρ₀ = 1.00038 as an input to nothing — no normalization, embedding, overlap, exclusion, or tolerance used it (the reproducer's target-blind audit confirms every such flag is false). This is why the result is a finding and not a fit: we did not arrange for ρ to land anywhere. A theory that tuned to ρ = 1 would be unfalsifiable here; by refusing to, we earn a real falsifier.

3.6 Reconciling the two framings (carried in plain sight)

The two agree on every computed fact (the closed form O_a, the range [½,∞), the flatness of V_Hos, the eliminated custodial coset). They disagree only on disposition: is the breaking direction a free modulus, or is it pinned by the charge law? The owner verdict (and the review audit of the draft popup) resolves this: the direction is pinned, because the photon must lie along T₃ to reproduce the observed charges, and a mounted readout map could overturn the FINDING only by giving a T_H not parallel to T₃ — which would contradict Q = T₃ + Y and is rejected as target-fitting. This dossier carries the FINDING as binding. The §8 "undetermined" language is recorded here as the older, unreconciled framing so the specialist sees both, but it is not the disposition.

§4. Evidence & reproducibility

4.1 Frozen-object hash index (load-bearing; READ-ONLY)

4.2 The witness ledger (what reproduces, and at what grade)

W11 is the upgrade over the prior status: the older popup ("M²_WZ is never built; tree ρ=1 is a rep-algebra tautology") is superseded — the mass matrix was built and ρ computed.

4.3 How to re-run / re-derive

• Charge leg: recompute the §2.2 table by hand from the frozen Y table; verify the ℤ₆ congruence per field. No software needed.
• ρ machinery: run …/PER_GATE_DOSSIERS/SG5_R3_RHO_REPRODUCER.py (NumPy + SciPy). It verifies the closed form O_a, the range [½,∞), the direction-independence of the holonomy eigenvalues (V_Hos flatness), the U(1)₃-invariance of ρ, and the 54.74° cone. (For this dossier the run reproduced all five checks to machine precision.)
• η_BK identity: 1/η_BK = 32π·exp(√3/24π); recomputes to 0.009721281516312. Provenance of the form is the open audit (R5).
• v/m_h: the R0 reproducer is referenced (H.4/A1.10); running it byte-equal end-to-end is the open owner-artifact task (R6).
• Endpoint stack: SG5_complete_endpoint_stack/ (23 files, manifest 22/22 intact) carries validate_endpoint.py → PASS (exit 0, fail-closed), compute_textbook_rho.py → ρ=1 (rep-algebra only, correctly labeled as the textbook label, not the geometric readout), reproduce_eta_BK.py → η_BK = 0.009721281516312024 (exact). verdict.json: status_upgrades:0, target_blind:true, original_SG5_rollup:OPEN, all R3/R5/R6/R8 evidence flags false. The validator PASS is a re-run certificate and passes because nothing is promoted.

§5. Open gaps + closure path — the specialist work plan

This is the most load-bearing section. For each open hole: (a) precise statement, (b) why it's hard + traps to avoid (including the exact target-fittings the verifier caught), (c) exactly what closes it (target-blind, with success and refuting criteria), (d) machinery & inputs (cite paths), (e) leverage. Physics only; the firewall on device engineering is absolute.

Attack order by leverage: R3-realization (the bounded, highest-value physics hole) → R6 (cheap machine-lane win) → R8/R-abs (blocked group-theory inputs) → R4 (the KK Schur correction) → R5 (η_BK provenance) → R1/R2 (the hierarchy — RELOCATION, banked near-no-go) → R7/R9/R10 (axiom floors).

5.1 R3-realization — the ρ FINDING's overturn-or-harden map (HIGHEST physics leverage)

(a) Precise statement. The ρ_tree ≠ 1 FINDING follows from the mounted charge law via T_H ∥ T₃ ⇒ O₃ = 0. It can be overturned only by mounting the real frozen Hosotani readout map and showing the actual overlaps give a charge-law-consistent T_H not parallel to T₃. The four named, currently-unmounted artifacts are: (i) the Wilson-line A_y gauge-scalar zero-mode EW-representation table; (ii) the A₅ holonomy generators (MISSING / not source-hashed); (iii) the γ-cycle Hosotani VEV profile/measure; (iv) the M_{0n} overlap integrals (ℓ=0→1 on S², n=0→1 on S¹_Y).

(b) Why it's hard / traps. The FINDING is strong precisely because it rests on the mounted charge law, not on the missing data — so the specialist cannot overturn it merely by supplying the artifacts; the supplied T_H must come out non-parallel to T₃ while still reproducing Q = T₃ + Y. Traps the verifier caught (do not repeat): (1) Do not reframe ρ as an "undetermined free modulus" — files 11/12 reject this as target-fitting; the charge law pins the direction (the draft popup that called ρ "free, not a value we can fake" was flagged OVERCLAIM). (2) Do not import the custodial SO(4)/SO(5) coset to rescue ρ = 1 — it is recorded eliminated in the frozen object; importing it back is rejected as target-fitting. (3) Do not assert C_W = C_3 from the SM doublet label — for a non-custodial Hosotani object it must be earned from the commutator overlaps (it is not). (4) Do not point R8's missing datum at m₀(p,q) — that table is present and verified; the true missing datum is one layer up at the A₅ holonomy generators (see §5.3).

(c) What closes it (target-blind). Mount the four artifacts and run the one fail-closed decision rule (owner-authorized, one pass — not an open rescue campaign): (1) data exist and change the readout (charge-law-consistent T_H ∦ T₃) → REOPENED_BY_READOUT_MAP_CORRECTION; (2) data exist and confirm O₁/O₃ ≠ 1 → FINDING HARDENS; (3) data do not exist → FINDING STANDS (the current outcome); (4) any rescue via asserted custodial symmetry / ordinary-doublet algebra / minimality → REJECT as target-fitting. Refuting result is a valid close: if the mounted map yields a charge-law-consistent T_H ∦ T₃ and ρ → 1, that overturns the FINDING and earns ρ = 1 = DERIVED-GIVEN-E. Either outcome closes R3.

(d) Machinery & inputs. SG5_R3_RHO_REPRODUCER.py (the verified ρ machinery); files 10_R3_RHO_PASS_2026-06-25.md (artifact ledger), 11_R3_VERDICT_FINDING_STANDS_2026-06-25.md, 12_R3_READOUT_MAP_AUDIT_2026-06-25.md (the owner decision rule); the frozen Higgs bundle 2a0462b8aab9, cycle γ 640e1d7f7773. The A₅ holonomy generator must be computed and source-hashed (it is the literal missing object).

(e) Leverage. Closing R3 settles the gate's signature physics claim either way. It is the one residual that is a genuine missing computation (not a relocation) terminating on a measured invariant (ρ₀). Shared structure with the absolute-mass leg (§5.5) and the KK correction (§5.4).

5.2 The two-loop lift of the flat direction (alternative R3 route)

(a) Precise statement. V_Hos is exactly flat in the tilt direction at one loop. The first term that can break the adjoint isotropy and dynamically select the direction appears beyond one loop — the two-loop potential with y_t ≠ y_b and g' ≠ 0. That lifting term is uncomputed.

(b) Why it's hard / traps. The custodial SU(2) is an accidental symmetry broken by U(1)_Y gauging and by Yukawa splitting (y_t ≠ y_b) — exactly the terms entering at two loops. So the two-loop potential is the natural place the direction gets selected, but the computation is genuinely heavy (two-loop CW on a curved internal manifold). Trap: do not assume the two-loop minimum sits on the ρ = 1 cone — that would be target-fitting; read it blind.

(c) What closes it. Compute the two-loop y_t≠y_b, g'≠0 corrected V_Hos, find the selected direction, read ρ off blind. Success: ρ = 1 → DERIVED-GIVEN-E; ρ ≠ 1 → the FINDING hardens into a dynamically-selected falsifiable prediction vs ρ₀ = 1.00038 ± 0.00020. Both are valid closes.

(d) Machinery & inputs. The one-loop V_Hos (§2.4), the frozen KK spectrum (N_b, N_f), the frozen Yukawa anchors y_t (548d7099ef18); two-loop GHU effective-potential methods.

(e) Leverage. This is the route by which the FINDING could flip to a derivation — it directly tests whether the geometry's own dynamics select a custodial-symmetric direction.

5.3 R8 — no-second-VEV certificate (BLOCKED on the A₅ table)

(a) Precise statement. The claim that the protected zero-mode spectrum carries no second EW-breaking VEV source (extra doublet / triplet / charged scalar) is unproven. Needed both for the absolute W/Z masses and for the ρ assembly to be airtight (a triplet VEV w would give ρ = 1 + 4w²/v²).

(b) Why it's hard / traps. Trap (verifier-caught): the missing datum is not the m₀(p,q) zero-weight table — that is present and verified (Kostant: m₀ = min(p,q)+1 for triality-0, else 0). The true un-generable datum is one layer up: the Wilson-line A_y (A₅) gauge-scalar zero-mode EW-representation table — the broken-generator / coset-scalar SU(2)_L × U(1)_Y content and the Q=0 VEV-capability of every Wilson-line scalar zero mode. The corpus declares only n_H=1; it does not compute the EW-rep spectrum of the A_y sector.

(c) What closes it. Build the A_y/A₅ zero-mode EW-representation table, inventory every Wilson-line scalar zero mode, and certify none can take a Q=0 VEV alongside H₀ (unique_vev_source = H₀). Success → VERIFIED (the ρ assembly is airtight, absolute masses unblocked on this axis). Refuting result → a second VEV source exists → the single-doublet picture is corrected (also a valid, informative close).

(d) Machinery & inputs. The verified m₀(p,q) Kostant table (present); the frozen K_gauge KK spectrum; the A₅ holonomy generator (must be computed + source-hashed); file 10_R3_RHO_PASS artifact-2 ledger; EXTRACT_Q_SHAPE_DOUBLET_2026-06-23.md.

(e) Leverage. Unblocks both R3-realization (airtight ρ) and R-abs (absolute masses). Shared A₅-table dependency with R3-realization (§5.1) — close them together.

5.4 R4 — EW KK gauge-boson mixing / Schur correction to ρ (BLOCKED on γ-profile)

(a) Precise statement. The gauge-Higgs-unification T-parameter — the KK gauge-boson mixing correction δρ_KK — is uncomputed. Via Schur complement, M_eff² = M_00² − M_0n²(M_nn²)⁻¹M_n0² for the ℓ=0→1 (S²) / n=0→1 (S¹_Y) tower. It could shift ρ.

(b) Why it's hard / traps. The KK masses are present (M_nn: weak ℓ=1 = √2/R₀ = 8.88×10¹⁶ GeV; hyper n=1 = 1/R₀ = 6.28×10¹⁶ GeV). The off-diagonal M_0n = g v I_0n needs the γ-cycle overlap I_0n, which is absent: a constant VEV profile gives I_0n = 0 (selection rule), a non-constant profile gives I_0n ≠ 0, and the γ-cycle data deciding which is missing. Trap: do not use the dimensional scale ratio (v/M_KK)² = 1.534×10⁻²⁹ as a Schur certificate — it presumes |I_0n| = O(1) over the full tower and a fixed custodial-cancellation structure, both unshown. It is a hint, not a bound.

(c) What closes it. Supply the γ-cycle Hosotani VEV profile + the concrete T_H direction, compute I_0n and δρ_KK, and show |δρ_KK| ≤ 10⁻⁴ (or carry it as a rigorous bound). Success → the KK channel is bounded (ρ assembly complete to per-mille). Refuting → δρ_KK large → a second contribution to the ρ tension.

(d) Machinery & inputs. M_nn (present, pure-geometry S²/S¹_Y spectra); the γ-cycle profile (absent — the artifact-3 blocker in 10_R3_RHO_PASS); Schur-complement / KK-decoupling methods.

(e) Leverage. Completes the ρ readout (tree FINDING + KK correction → effective ρ). Note: even with δρ_KK bounded, the tree FINDING ρ_tree ≠ 1 already settles ρ_eff ≠ 1 per file 10 — so R4 refines magnitude, it does not rescue ρ = 1.

5.5 R-abs — absolute W/Z masses (S²-vs-S¹_Y co-normalization)

(a) Precise statement. The absolute masses M_W, M_Z (not just ρ) still owe the S²-vs-S¹_Y kinetic co-normalization (overlaps a_W, a_B in a common normalization). The co-normalization cancels in ρ (the banked algebraic advance, §3.2) but not in the absolute masses, because the two gauge factors live on geometrically distinct sub-manifolds.

(b) Why it's hard / traps. Trap: this is the blocker three prior passes mis-cited as the ρ blocker — it is a red herring for ρ, but a real obstruction for absolute masses. Keep the two questions separate.

(c) What closes it. Form the SU(2)_L reduction integral over S² and the U(1)_Y reduction over S¹_Y/ℤ₂ in one common normalization, then assemble ∫|D_μ⟨H⟩|² → {W±; W³,B} with the common v = θ_H*/(2πR_γ). Success → absolute M_W, M_Z from geometry; compare to PDG.

(d) Machinery & inputs. The S² and S¹_Y/ℤ₂ reduction integrals; the frozen gauge couplings g, g' from SG-2/SG-7; v from the Hosotani VEV.

(e) Leverage. Promotes the EW sector from "ρ + near-hit v/m_h" to "absolute gauge-boson masses from geometry."

5.6 R5 — η_BK provenance (the one-input-two-outputs headline)

(a) Precise statement. The headline "one geometric quantity, two SM outputs" rests on 1/η_BK = 32π·e^{√3/24π} ≈ 102.87 = |y_t/y_b| (raw). Is the form 32π·e^{√3/24π} written target-blind from the Wilson-line / Berezin–Kontsevich finite determinant, or reverse-engineered to land on |y_t/y_b|?

(b) Why it's hard / traps. 32π = 100.53 is suspiciously close to 102.87, with the e^{√3/24π} = 1.0233 factor doing the fine-adjust — exactly the pattern a reverse-engineered form would show. Trap (the κ³/π cautionary pattern): a constant reverse-engineered to hit a target makes the headline true-by-construction; the falsification test demands the form was written from geometry before and independently of knowing |y_t/y_b|. Same class as SG-8 Route A.

(c) What closes it. Recompute the Berezin–Kontsevich finite determinant on the active branch from scratch, target-blind, with |y_t/y_b| absent from the inputs, and check whether 1/η_BK falls out as 32π·e^{√3/24π}. Pass → VERIFIED (headline genuine). Fail → RELOCATES (headline true-by-construction; the over-determination claim folds — a valid, informative result).

(d) Machinery & inputs. η_BK 84e94518d3f5; the Gate-8 Wilson-line determinant construction; couple to SG-8 Route A (same constant — close them together). Falsification test discipline: the κ³/π rule.

(e) Leverage. Decides whether the gate's quantitative headline (v, m_h, |y_t/y_b| from one determinant) is genuine compression or construction.

5.7 R6 — v/m_h reproducer (AUDIT/BLOCKED; cheapest win)

(a) Precise statement. "v=246.02, m_h=123.82 regenerate byte-equal from frozen η_BK + geometry via the R0 reproducer" is referenced, not independently re-run.

(b) Why it's hard / traps. Not hard — it is an owner-artifact execution task. Trap: do not let a referenced-but-unrun harness stand in for a machine-checked certificate (same class as SG-7's absent δ-harness, SG-8's J.6/K.5 harness).

(c) What closes it. Run the R0 reproducer target-blind against the frozen inputs (η_BK 84e94518d3f5, n_H=1 f65094fd8fd1, cycle γ, M_Z a6852c7a6b00); confirm v=246.02±3.5, m_h=123.82±1.8 to declared precision; re-hash to a5b1e6f9d951. Pass → VERIFIED. Fail-closed: any value missing → Gate-8 downgrade (a valid refuting close).

(d) Machinery & inputs. The R0 reproducer (referenced in H.4/A1.10); the frozen hash set above; reproduce_eta_BK.py (already verified, η_BK exact).

(e) Leverage. Highest value-per-effort — converts an asserted certificate pass into a machine-real one with zero new physics.

5.8 R1 / R2 — the hierarchy (OPEN / RELOCATION; banked near-no-go)

(a) Precise statement. The lightness of v is UNDELIVERED. θ_H* ≈ 2.46×10⁻¹⁴ (so that v = θ_H*/(2πR_γ) with 1/(2πR_γ) ≈ 10¹⁶ GeV) is read from the one-loop V_Hos minimum, not derived. Equivalently the dimensionless exponent I_EW = ln(M_Pl/v) ≈ 36.83 (reduced-Planck; recomputed for this dossier) is not produced blind. R2 is the SCALE firewall: can the scale cell μ_cell be anchored independently of v?

(b) Why it's hard / traps — and why this is NOT a bounded computation. The SCALE firewall (FIREWALL_MUCELL_INDEPENDENCE) is a 4-part conjunction; gates (2) and (4) FAIL: the only specified anchor ∂_σV = 0 is where v is set, and μ_cell → v is closed-form invertible. The two decisive traps: (i) any "blind I_EW" production currently re-logs the input v — I_Hos − I_obs = ln(v_obs/v_corpus) makes the "exponent PASS" bit-identical to comparing v vs v (auto-FAIL); (ii) θ_H* is a stationary point of a periodic potential, not a running coupling, so there is no transmutation exponent t_⋆ = 2π/(bα) to bound (Path B). A symmetry of the cycle would force θ_H* ∈ {0, π} (giving v=0 or maximal), not 10⁻¹⁴ — so the strong "symmetry-fixed" upgrade is refuted in advance: the hierarchy is the smallness of a non-symmetric minimum. Verifier-caught trap: do not file "derive I_EW ≈ 36.83 blind" as a bounded plug-able hole — the firewall has already shown it is a RELOCATION: introducing a UV-floor axiom (AXIOM-UV-CELL-FLOOR / AXIOM-HIERARCHY-IS-UV-EXPONENT) relocates the entire hierarchy into the log-sensitivity of v to log(μ_cell/M_*) — the κ³/π trap — and was campaign-DEMOTED to OPEN.

(c) What closes it (honestly). The honest endpoint is sharper-OPEN / RELOCATION, not closure: bank the near-no-go that explains why v_EW is irreducible here — a dimensional near-no-go (Path A: a second mass cannot be built from {M_Pl, ℏ, dimensionless geometry} without a σ-carrying length; Buckingham-π) plus the mechanistic near-no-go (Path B: periodic minimum supplies no exponent). A genuine DERIVED close would require a v-independent UV readout for μ_cell surviving all six firewall gates blind — judged unreachable in this geometry. A refuting result (someone exhibits such a blind readout) crosses the firewall — not expected.

(d) Machinery & inputs. FIREWALL_MUCELL_INDEPENDENCE_2026-06-23.md; SCALE_HIERARCHY_FINAL_VERDICT_2026-06-23.md; HANDOFF_T_HIERARCHY_RG_EXPONENT.md; CLOSURE_CAMPAIGN_RESULT_2026-06-24.md (the demotion). v_EW is exported to SG5B_EW_HIERARCHY_EXPORT_LEDGER.md (status OPEN/RELOCATION), shared with SG-6.

(e) Leverage. This is the gate's loudest open problem, but it is relocation, not a missing number. Banking the near-no-go is the real (non-promoting) win: "here is the structural reason the hierarchy cannot be reduced here without relocating it." Shared with SG-6 (R4 below) and the SCALE frontier.

5.9 R4-θ / R7 / R9 / R10 — the axiom-floor residuals

• R4-θ (θ_H* read-from-min, SG-6 inheritance). AXIOM-CLOSED at the weak axiom AXIOM-THETA-FROM-MIN ("θ_H* is the global minimum of the frozen one-loop V_Hos" — true by construction, no target value). The strong upgrade AXIOM-THETA-SYMMETRY is refuted in advance (the minimum is not a symmetric point; §5.8). Close by: the clean group-theory falsification — confirm no symmetry of γ/S¹_Y/ℤ₂ fixes θ_H* ∼ 10⁻¹⁴. Shared with SG-6.
• R7 (higher-loop Higgs protection, Diagnostic-only). One-loop protection is proven (gauge invariance preserves n_H); all-orders is not. AXIOM-CLOSED at AXIOM-WINDING-PROTECTION-ALL-LOOPS ("an integer winding cannot deform continuously under perturbative gauge-invariant corrections"). Close by: a loop-resummation theorem bounding the cross-sector contributions H.9.6/H.10.1 flag as not-provably-zero. Hand to a GHU specialist. Trap: do not claim all-loop protection as proven — it is honestly scoped Diagnostic.
• R9 (parity/ℤ₆ table selected-not-searched). AXIOM-CLOSED at AXIOM-PARITY-Z6; the charge leg is rigid given the table. Honest standing (A4-ℤ₆): the line-operator/maximality posit pins only Γ ≤ ℤ₆ (q | 6), not q = 6; "finest" is pinnable only by already wanting ℤ₆, so =ℤ₆ is OPEN. But the SM triples satisfy the Tong congruence field-by-field and χ=−3 is honored, so the charge assignments are consistent. Close by: force =ℤ₆ from the surviving spectrum + global well-definedness of Q=T₃+Y (expected: ≤ℤ₆ forced, =ℤ₆ selected).
• R10 (n_H=1 minimality). AXIOM-CLOSED at AXIOM-MINIMAL-WINDING. The n_H=0 exclusion is structural/target-blind; the n_H≥2 exclusion leans on v≈492 missing PDG (a disclosed data check). Close by: an a-priori reason to prefer 1 over 2 independent of v — none currently given; absent that, the named minimality axiom is the honest floor.

5.10 Specialist work-plan roll-up

REDUCE-vs-RELOCATE verdict. The plan does not turn one hard problem into many — but it is brutally honest that R1/R2 RELOCATE (the hierarchy is a genuine second dimensionful anchor with a near-no-go, not a missing number). The one place real physics progress is available is R3 (mount the realization map, or compute the two-loop lift), which can either harden the FINDING into a dynamical falsifiable prediction or overturn it into ρ = 1 = DERIVED-GIVEN-E. The cheap machine-lane win is R6. None of this is a promotion: the gate stays OPEN; the wins are honesty, reproducibility, and a computed ρ where the field assumes one.

§6. Honest ceiling & scope

6.1 What is explicitly NOT claimed

• NOT that the geometry predicts/derives ρ = 1. The opposite is the binding disposition: the bare-commutator readout, with the direction pinned by the charge law, gives a FINDING ρ_tree ≠ 1 — a live precision-electroweak tension against ρ₀ = 1.00038 ± 0.00020. We make no claim the model predicts ρ = 1, and introduced no parameter tuned to the measured value.
• NOT that the electroweak hierarchy is solved or that v = 246 "emerges." The lightness of v is OPEN/RELOCATION: θ_H* is read from the one-loop minimum (~85% of the hierarchy undelivered), √η_BK/(2π) ∼ 10⁻² is 12 orders too large, and the SCALE firewall is uncrossed. "v emerges" would be a circular re-log of the standing input.
• NOT that v_EW is derived. It is a transparent measured-but-irreducible second dimensionful anchor (alongside M_Pl), realized by the Wilson-line VEV, not derived. given-E ≠ derivation of E.
• NOT that the selected K₆/parity geometry is the unique structure realizing Q = T₃ + Y. Charge is forced given the frozen, selected parity table; absolute uniqueness over all possible math is a unicorn (§6.2).
• NOT all-orders Higgs protection. One-loop is proven; higher loops are Diagnostic-only.

6.2 Dissolved unicorns — framed as shared ceilings, never as proven, never as open weakness

These are universal negatives over all possible mathematics — unprovable for everyone, not gaps in our work. We dissolve them and state the bounded, plug-able version that remains:

• "ρ = 1 is THE absolutely forced value under any possible completion of the geometry." A universal forcedness claim is unprovable in principle. The bounded, real hole: does the frozen γ-cycle/ℤ₆ embedding pin the 3-axis (it does — that is the FINDING), and does a two-loop term lift the flat direction to the cone (R3 two-loop, §5.2)?
• "No future theory / no alternative geometry could derive the electroweak hierarchy more cheaply." An open-ended universal negative. The honest banked result is the SCALE-firewall near-no-go explaining why the hierarchy cannot be reduced inside this structure without relocating it.
• "The selected geometry is THE unique structure realizing Q = T₃ + Y." Absolute uniqueness over all math is a unicorn; the bounded claim is that charge is forced given the frozen, selected parity table.

6.3 The anchors paid

SG-5 terminates on the two dimensionful anchors M_Pl and v_EW, and on no measured invariant beyond them. The charge leg carries no anchor of its own — it is structural / DERIVED-GIVEN-E once the observed content E (the SM hypercharge triples) is supplied. The breaking and the near-hit numbers ride the existing anchors (η_BK/spectrum-E, y_t, α_i(M_Z)); they are frozen outputs given the anchors, not a derived lightness. The single open dimensionful leg is the hierarchy-lightness of v_EW, which rests on θ_H* read-from-min and terminates on no v-independent invariant — so v_EW stands as a genuine second anchor, OPEN. No scheme-anchor is load-bearing for the gate's target statement.

6.4 The honest one-line

SG-5's charge/embedding leg is DERIVED-GIVEN-E (Q=T₃+Y, EWSB to U(1)_em, single Wilson-line/Hosotani doublet, v_EW a measured anchor), with the Higgs quadratic destabilization structurally avoided at one loop. We built the geometric W/Z mass matrix and read ρ target-blind: the frozen charge law forces T_H ∥ T₃, so the neutral W³ gets zero mass from the bare Hosotani commutator and ρ_tree ≠ 1 — a live, falsifiable precision-electroweak FINDING (the custodial SO(4) rescue is recorded eliminated). The hierarchy is OPEN/RELOCATION (v_EW a second anchor with a near-no-go), η_BK provenance is SUSPECT, the v/m_h harness is AUDIT, and the gate is OPEN by its least-closed residual. NOT a hierarchy derivation; NOT a proof the geometry yields ρ = 1. Serious candidate, NOT validated. STATUS-UPGRADES:0.

References & source map

Website source-of-truth (common material — link, don't duplicate): - Paper I, GUT.html — https://physics.magflowmeters.com/articles/GUT.html — §6.3 charge card; §6.8 Higgs card; §5.2/§5.7 narrative; Appendix D (charge tables); Appendix E′ (chirality/anomaly); Appendix H (H.1–H.11: Wilson-line formula + V_Hos, H.4 outputs, H.9.7 non-claims box, H.10 corrections); Appendices A1/A2/R0 (constants + freeze records). - Paper IV, TOE.html — https://physics.magflowmeters.com/articles/TOE.html — SCALE/hierarchy firewall conclusions; v_EW second-anchor irreducibility. - Gaps & Walls Register — https://physics.magflowmeters.com/articles/GAPS_AND_WALLS_REGISTER.html — disposition vocabulary.

Corpus files synthesized for this dossier (all read directly): - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_ELECTROWEAK_CLOSURE_RESULT.md — §1–§8 closure result; ρ machinery; the §8 "undetermined" framing (superseded). - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_R3_RHO_REPRODUCER.py — the verified ρ machinery (re-run for this dossier: all checks PASS). - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_COMPLETION_HANDOFF/10_R3_RHO_PASS_2026-06-25.md — artifact ledger; FINDING_RHO_NOT_1; m₀(p,q) present, A₅ blocker. - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_COMPLETION_HANDOFF/11_R3_VERDICT_FINDING_STANDS_2026-06-25.md — OWNER VERDICT (binding): ρ_tree ≠ 1 FINDING STANDS. - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_COMPLETION_HANDOFF/12_R3_READOUT_MAP_AUDIT_2026-06-25.md — readout-map audit COMPLETE → FINDING STANDS. - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_ROUTEB_MWZ_HANDOFF/01_DOSSIER_SG5_ELECTROWEAK.md — full attack dossier; residual register R1–R10; firewall tables; anchoring map. - …/rendered/TOE/PER_GATE_DOSSIERS/SG5_COMPLETION_HANDOFF/01_DOSSIER.md — attack dossier (superseded-attack header). - …/rendered/TOE/GATE_REGRADE_BESTCASE_AND_HOLES_2026-06-29.md (SG-5 line) — the binding popup status + review notes (the FINDING-vs-undetermined reconciliation). - …/rendered/TOE/SPECIALIST_HOLE_QUEUE_2026-06-29.md (SG-5, 9 holes) — the specialist hole framing folded into §5.

Frozen hashes (READ-ONLY): branch dcc66f1b2685 · meta a5b1e6f9d951 · parity table ac4d2df3e708 · Higgs bundle 2a0462b8aab9 · cycle γ 640e1d7f7773 · n_H=1 f65094fd8fd1 · η_BK=0.009721281516312024 84e94518d3f5 · y_t 548d7099ef18 · |V_us| a1bc510bc7cd · M_Z a6852c7a6b00 · M_* = 7.467×10¹⁶ GeV.

Dossier built 2026-06-29 from the frozen 13D K₆ branch only. Common material referenced to the published website source-of-truth, not duplicated. STATUS-UPGRADES:0; frozen branch READ-ONLY; given-E ≠ derivation of E; selection ≠ derivation; dissolved ≠ solved; ANCHORED ≠ DERIVED. Serious candidate, NOT validated.