Controlling terminal and claim firewall

The SG5 conditional candidate certificate passes. Given the minimal complex Higgs doublet (T,Y)=(1/2,1/2), its lower neutral VEV, canonical zero-mode covariant derivative, couplings g,g_prime, and measured calibration v_EW, the generated mass matrix has exactly one massless photon, mW^2=g^2 v^2/4, mZ^2=(g^2+g_prime^2)v^2/4, and rho_tree(d<=4)=1.

The physical SG5 gate remains OPEN. The frozen SG4 terminal contributes fourteen OPEN readiness rows, and SG5 adds five local rows for Higgs derivation, vacuum selection, coupling transport, loop confrontation, and independent review. The conditional result is a construction-anchor; v_EW is a MEASURED-ANCHOR.

No exact tree-level identity is allowed to erase a physical readiness debt or be rewritten as an experimental confirmation.

Authority order and cumulative SG4 lineage

The user-supplied building blocks are the governing source of truth. This build orders authority as the source-of-truth archive, the cumulative SG4 building blocks, the V4.1 execution protocol, the SG2-SG8 challenge specification, the SG4-to-SG5 dependency ledger, and finally the generated candidate witnesses.

The SG4 block archive is frozen at 09588c25b49f7ebb63a65226d870fa22d70dac5aa5fbcf7d0d8ce38041cae9ac. Its exact charge certificate is frozen at 9e832ab23cb6d64e07c701b561d5880deaa5b1985c2cd0f997e9f4c098d2971f. The extracted SG4 package manifest is replayed file by file, including its embedded SG3 lineage.

SG4 conditionally supplies the primitive hypercharge assignment and verified Q_em=T3+Y table. Its physical OPEN status is preserved. SG5 is a cumulative successor overlay, not a reset of earlier gate terminals.

Electroweak conventions and evidence boundary

The covariant derivative convention is D=partial-i g T^a W^a-i g_prime Y B. The scalar expectation value is <H>=v/sqrt(2)|T,m>. Electric charge is Q_em=T3+Y, so a VEV is neutral only when m+Y=0.

Masses are defined from L_mass=(1/2) V^T M^2 V in the real vector basis (W1,W2,W3,B). The physical charged combinations are formed from W1 and W2, which share the same eigenvalue. All coefficients are exact rational numbers; there is no floating-point diagonalization tolerance.

The gate computes only the zero-mode tree-level sector with operators of dimension at most four. v_EW calibrates the magnitude as a measured input. Loop matching, the measured rho0, the scalar vacuum theorem, and physical higher-dimensional normalization are outside the conditional certificate.

Frozen SG4 and Higgs charge-table join

The SG4 certificate supplies ten exact matter-and-Higgs state rows. SG5 replays each Q_em=T3+Y identity before using hypercharge in the mass matrix. It then generates the selected Higgs multiplet table directly from (T,Y).

Upstream charge witness 1: u_L

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 2: d_L

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 3: u_c

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 4: d_c

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 5: nu_L

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 6: e_L

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 7: e_c

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 8: nu_c

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 9: H_plus

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Upstream charge witness 10: H_zero

This row is frozen from SG4 and replayed without reinterpretation. Its exact rational equality verifies the charge generator used by the SG5 photon test. The row is conditionally correct given the representation inventory; physical ownership of that inventory remains one of the cumulative OPEN interfaces.

A Higgs-sector manifest cannot repair or override this charge row. Any mismatch between the frozen charge generator and the claimed unbroken vector fails before the mass spectrum is accepted.

Higgs weight witness 1: T3=1/2

This weight belongs to the generated dimension-two representation. The lower weight is the selected VEV and has zero electric charge; the upper weight has unit charge. Both results use exact fractions and are compared with the candidate manifest under SG5-GNT-01.

The table proves neutrality of the declared component. It does not prove why the scalar exists, why this component condenses, or why the competing vacuum directions are absent; those are local physical readiness rows.

Higgs weight witness 2: T3=-1/2

This weight belongs to the generated dimension-two representation. The lower weight is the selected VEV and has zero electric charge; the upper weight has unit charge. Both results use exact fractions and are compared with the candidate manifest under SG5-GNT-01.

The table proves neutrality of the declared component. It does not prove why the scalar exists, why this component condenses, or why the competing vacuum directions are absent; those are local physical readiness rows.

Generated W1-W2-W3-B mass matrix

The complete coefficient matrix is generated from the declared covariant derivative. For the minimal doublet, the charged coefficient is 1/4 multiplying g^2v^2. The neutral block coefficients are one quarter on both diagonals and minus one quarter on the mixed entries.

M^2 = v^2/4 [[g^2, 0, 0, 0],
             [0, g^2, 0, 0],
             [0, 0, g^2, -g g_prime],
             [0, 0, -g g_prime, g_prime^2]]

The neutral determinant vanishes identically. The full matrix has exactly 1 zero eigenvalue. Matrix construction and diagonalization remain separate gauntlet controls.

Mass-matrix entry M(W1,W1)

The generated coefficient is 1/4 multiplying g^2 v^2. The entry is in row W1 and column W1 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W1,W2)

The generated coefficient is 0 multiplying 1. The entry is in row W1 and column W2 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W1,W3)

The generated coefficient is 0 multiplying 1. The entry is in row W1 and column W3 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W1,B)

The generated coefficient is 0 multiplying 1. The entry is in row W1 and column B of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W2,W1)

The generated coefficient is 0 multiplying 1. The entry is in row W2 and column W1 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W2,W2)

The generated coefficient is 1/4 multiplying g^2 v^2. The entry is in row W2 and column W2 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W2,W3)

The generated coefficient is 0 multiplying 1. The entry is in row W2 and column W3 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W2,B)

The generated coefficient is 0 multiplying 1. The entry is in row W2 and column B of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W3,W1)

The generated coefficient is 0 multiplying 1. The entry is in row W3 and column W1 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W3,W2)

The generated coefficient is 0 multiplying 1. The entry is in row W3 and column W2 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W3,W3)

The generated coefficient is 1/4 multiplying g^2 v^2. The entry is in row W3 and column W3 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(W3,B)

The generated coefficient is -1/4 multiplying g g_prime v^2. The entry is in row W3 and column B of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(B,W1)

The generated coefficient is 0 multiplying 1. The entry is in row B and column W1 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(B,W2)

The generated coefficient is 0 multiplying 1. The entry is in row B and column W2 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(B,W3)

The generated coefficient is -1/4 multiplying g g_prime v^2. The entry is in row B and column W3 of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Mass-matrix entry M(B,B)

The generated coefficient is 1/4 multiplying g_prime^2 v^2. The entry is in row B and column B of the declared real-vector basis. Symmetry with the transposed entry is TRUE.

Zero entries are explicit evidence, not omitted terms. The two charged diagonals follow from [T(T+1)-m^2]/2; the neutral block is the outer product of (g m, g_prime Y) with itself. Therefore every nonzero entry has one covariant-derivative parent and an exact rational coefficient.

The candidate’s published matrix is compared entry by entry. A correct list of eigenvalues cannot compensate for one wrong sign or coefficient here.

Exact vector eigenvalue: W1

Generated eigenvalue: 1/4 g^2 v^2

The first real charged carrier has the common charged eigenvalue. The equality is symbolic in g, g_prime, and v; no measured mass value is inserted. The eigenpair is substituted into the exact matrix and is covered by the manifest and witness hashes.

The eigenvalue statement belongs to the zero-mode tree sector. Canonical higher-dimensional normalization, loop self-energies, thresholds, and the physical spectrum completeness remain outside this conditional row.

Exact vector eigenvalue: W2

Generated eigenvalue: 1/4 g^2 v^2

The second real charged carrier is degenerate with W1 and combines with it into W plus/minus. The equality is symbolic in g, g_prime, and v; no measured mass value is inserted. The eigenpair is substituted into the exact matrix and is covered by the manifest and witness hashes.

The eigenvalue statement belongs to the zero-mode tree sector. Canonical higher-dimensional normalization, loop self-energies, thresholds, and the physical spectrum completeness remain outside this conditional row.

Exact vector eigenvalue: Z

Generated eigenvalue: v^2 (1/4 g^2 + 1/4 g_prime^2)

The orthogonal neutral direction has the trace of the rank-one neutral block as its eigenvalue. The equality is symbolic in g, g_prime, and v; no measured mass value is inserted. The eigenpair is substituted into the exact matrix and is covered by the manifest and witness hashes.

The eigenvalue statement belongs to the zero-mode tree sector. Canonical higher-dimensional normalization, loop self-energies, thresholds, and the physical spectrum completeness remain outside this conditional row.

Exact vector eigenvalue: photon

Generated eigenvalue: 0

The neutral zero mode is the electromagnetic direction because Q_em annihilates the VEV. The equality is symbolic in g, g_prime, and v; no measured mass value is inserted. The eigenpair is substituted into the exact matrix and is covered by the manifest and witness hashes.

The eigenvalue statement belongs to the zero-mode tree sector. Canonical higher-dimensional normalization, loop self-energies, thresholds, and the physical spectrum completeness remain outside this conditional row.

Photon direction

W3/B coefficient pattern [1, 1]

This is proportional to g_prime W3 + g B and has exact zero mass. The claimed vector or mixing relation is substituted back into the neutral mass matrix. The inconsistent-mixing decoy is rejected even though its mass coefficients and scalar representation are otherwise correct.

This test distinguishes an arbitrary surviving U(1) from electromagnetism. A charged VEV still leaves a neutral zero eigenvector, but the standard Q_em direction is massive and therefore fails before being labeled a photon.

Z direction

W3/B coefficient pattern [1, -1]

This is proportional to g W3 - g_prime B and is orthogonal to the photon after canonical normalization. The claimed vector or mixing relation is substituted back into the neutral mass matrix. The inconsistent-mixing decoy is rejected even though its mass coefficients and scalar representation are otherwise correct.

This test distinguishes an arbitrary surviving U(1) from electromagnetism. A charged VEV still leaves a neutral zero eigenvector, but the standard Q_em direction is massive and therefore fails before being labeled a photon.

Weak sine

sin(theta_W) = g_prime/sqrt(g^2+g_prime^2)

The sine is generated from the couplings and is not a separately fitted rotation in this certificate. The claimed vector or mixing relation is substituted back into the neutral mass matrix. The inconsistent-mixing decoy is rejected even though its mass coefficients and scalar representation are otherwise correct.

This test distinguishes an arbitrary surviving U(1) from electromagnetism. A charged VEV still leaves a neutral zero eigenvector, but the standard Q_em direction is massive and therefore fails before being labeled a photon.

Weak cosine

cos(theta_W) = g/sqrt(g^2+g_prime^2)

The cosine gives mZ squared times cos squared theta equal to mW squared for the doublet. The claimed vector or mixing relation is substituted back into the neutral mass matrix. The inconsistent-mixing decoy is rejected even though its mass coefficients and scalar representation are otherwise correct.

This test distinguishes an arbitrary surviving U(1) from electromagnetism. A charged VEV still leaves a neutral zero eigenvector, but the standard Q_em direction is massive and therefore fails before being labeled a photon.

General one-multiplet rho formula

For a neutral complex multiplet, rho_tree=[T(T+1)-Y^2]/[2Y^2]. The result follows from the charged coefficient and the heavy neutral eigenvalue with the generated weak mixing cosine.

The statement is stored in the generated certificate and evaluated under the fixed status grammar. Conditional consistency, target match, measured calibration, loop confrontation, and nature-selection have independent terminals. None can be promoted by rhetorical proximity to another PASS.

This separation directly repairs the historical SG5 weak point: overclaim rather than faulty elementary mass arithmetic.

Minimal-doublet rho witness

Substitution of T=1/2 and Y=1/2 gives rho_tree=1. This is the target structural identity for the dimension-at-most-four zero-mode tree sector.

The statement is stored in the generated certificate and evaluated under the fixed status grammar. Conditional consistency, target match, measured calibration, loop confrontation, and nature-selection have independent terminals. None can be promoted by rhetorical proximity to another PASS.

This separation directly repairs the historical SG5 weak point: overclaim rather than faulty elementary mass arithmetic.

Honest triplet control

A complex T=1,Y=1 triplet with a neutral m=-1 VEV gives rho_tree=1/2. It passes when it claims one half and fails when it claims one. The gate is claim-aware.

The statement is stored in the generated certificate and evaluated under the fixed status grammar. Conditional consistency, target match, measured calibration, loop confrontation, and nature-selection have independent terminals. None can be promoted by rhetorical proximity to another PASS.

This separation directly repairs the historical SG5 weak point: overclaim rather than faulty elementary mass arithmetic.

Measured vEW calibration

The scale v_EW is a MEASURED-ANCHOR. It converts the symbolic mass expressions into calibrated tree-level values but is not predicted by this gate or by the shape.

The statement is stored in the generated certificate and evaluated under the fixed status grammar. Conditional consistency, target match, measured calibration, loop confrontation, and nature-selection have independent terminals. None can be promoted by rhetorical proximity to another PASS.

This separation directly repairs the historical SG5 weak point: overclaim rather than faulty elementary mass arithmetic.

rho0 confrontation boundary

The experimental rho0 comparison is NOT-CLAIMED. The value 1.00038 cannot be called confirmed without loops, matching, the input scheme, thresholds, uncertainties, and a comparison artifact.

The statement is stored in the generated certificate and evaluated under the fixed status grammar. Conditional consistency, target match, measured calibration, loop confrontation, and nature-selection have independent terminals. None can be promoted by rhetorical proximity to another PASS.

This separation directly repairs the historical SG5 weak point: overclaim rather than faulty elementary mass arithmetic.

Retired narrative firewall

Custodial symmetry, a winding-Higgs mechanism, and a geometry head-to-head test are NOT-CLAIMED. The numerical tree identity one does not prove any of those narratives.

The statement is stored in the generated certificate and evaluated under the fixed status grammar. Conditional consistency, target match, measured calibration, loop confrontation, and nature-selection have independent terminals. None can be promoted by rhetorical proximity to another PASS.

This separation directly repairs the historical SG5 weak point: overclaim rather than faulty elementary mass arithmetic.

Gauntlet rule SG5-GNT-01: Charge table and neutral VEV

Recompute Q_em=T3+Y on the frozen matter table and every Higgs weight, then require the declared VEV weight to have Q_em=0.

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Gauntlet rule SG5-GNT-02: Covariant-derivative mass matrix

Generate every entry of the W1,W2,W3,B mass matrix from T, Y, m, g, g_prime, and v; reject hand-authored coefficients.

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Gauntlet rule SG5-GNT-03: Electromagnetic massless vector

Require exactly one zero eigenvalue and require its eigenvector to be the generator of Q_em, not merely some unbroken U(1).

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Gauntlet rule SG5-GNT-04: Exact eigenvalues and mixing

Substitute the claimed photon and Z vectors into the generated neutral block and compare every claimed eigenvalue and mixing relation.

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Gauntlet rule SG5-GNT-05: Representation-aware rho_tree

Compute rho_tree from T and Y; a complex triplet gives one half and cannot claim the doublet value one.

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Gauntlet rule SG5-GNT-06: Calibration and nonclaims firewall

Keep vEW measured and reject rho0, custodial, winding-Higgs, or geometry-test claims that exceed the supplied evidence.

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Gauntlet rule SG5-GNT-07: Claim-aware alternatives

Accept an honest non-target Higgs sector when it reports its actual rho and restricts its scope; separate consistency from target match.

Rules are applied in fixed order and the witness records the first hard failure. The answer key is committed before its roles are opened, while manifest and witness hashes are escrowed for every blinded session.

The supplied sessions are an internal deterministic reconstruction of the reviewer specification. They do not constitute an independent randomized review, so that separate terminal remains NOT-EVALUATED.

Blind session 1: manifest and sealed expectation

Candidate ID: session-4394de2407e67260d2a2
Session role: UNDISCLOSED
Opened role: DECOY
Opened label: inconsistent-mixing-angle
Manifest SHA-256: c9304baa2ff0e5c0db2b01c008a65fb466af6833831b79750e517654283b6d45
Expected verdict: FAIL
Expected first failure: SG5-GNT-04

The manifest claims scope minimal-doublet-electroweak-target, Higgs representation {'T': '1/2', 'Y': '1/2', 'complex': True, 'vev_weight_T3': '-1/2'}, tree rho 1, and rho0 assertion None. No opened role was present when the engine generated its witness.

Blind session 1: generated electroweak witness

Witness SHA-256: d0a1d736162cb35f340d5fb640563ed7abd4063b6c572a67323556270b6f8359
Actual verdict: FAIL
Actual first failure: SG5-GNT-04

The generated representation is {'T': '1/2', 'Y': '1/2', 'dimension': 2, 'vev_weight_T3': '-1/2'} and the VEV record is {'Q_em': '0', 'neutral': True}. The matrix has 1 massless vector(s), with photon pattern [1, 1] and tree rho 1. Target-doublet match is TRUE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

Blind session 2: manifest and sealed expectation

Candidate ID: session-bdb2d5c6c41e801565c6
Session role: UNDISCLOSED
Opened role: DECOY
Opened label: rho0-status-overclaim
Manifest SHA-256: 3d239daa6e2b665af1c93f990eaded010d15909dc7615f027c5f46a2a79d2ca1
Expected verdict: FAIL
Expected first failure: SG5-GNT-06

The manifest claims scope minimal-doublet-electroweak-target, Higgs representation {'T': '1/2', 'Y': '1/2', 'complex': True, 'vev_weight_T3': '-1/2'}, tree rho 1, and rho0 assertion rho0=1.00038 confirmed. No opened role was present when the engine generated its witness.

Blind session 2: generated electroweak witness

Witness SHA-256: cb79e45fffe516f39ecbf2e186f987dce2cd929bf6abfb0aea87f723759a4f80
Actual verdict: FAIL
Actual first failure: SG5-GNT-06

The generated representation is {'T': '1/2', 'Y': '1/2', 'dimension': 2, 'vev_weight_T3': '-1/2'} and the VEV record is {'Q_em': '0', 'neutral': True}. The matrix has 1 massless vector(s), with photon pattern [1, 1] and tree rho 1. Target-doublet match is TRUE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

Blind session 3: manifest and sealed expectation

Candidate ID: session-c248ad12d6102c0dc0ac
Session role: UNDISCLOSED
Opened role: INCUMBENT
Opened label: incumbent
Manifest SHA-256: 8142d5bc36e07236366b012e34ff829551e70e15a79b35ccc21c019239ae757a
Expected verdict: PASS
Expected first failure: None

The manifest claims scope minimal-doublet-electroweak-target, Higgs representation {'T': '1/2', 'Y': '1/2', 'complex': True, 'vev_weight_T3': '-1/2'}, tree rho 1, and rho0 assertion None. No opened role was present when the engine generated its witness.

Blind session 3: generated electroweak witness

Witness SHA-256: a78ea3b8773005226512e7cce0a71a466bd06085eaa95fd5f9216722c9e2af8d
Actual verdict: PASS
Actual first failure: None

The generated representation is {'T': '1/2', 'Y': '1/2', 'dimension': 2, 'vev_weight_T3': '-1/2'} and the VEV record is {'Q_em': '0', 'neutral': True}. The matrix has 1 massless vector(s), with photon pattern [1, 1] and tree rho 1. Target-doublet match is TRUE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

Blind session 4: manifest and sealed expectation

Candidate ID: session-c35779b994fc1c059377
Session role: UNDISCLOSED
Opened role: DECOY
Opened label: wrong-higgs-hypercharge
Manifest SHA-256: d5772f7e6baeba9a07992cd038ffaa43c8402f24dd99de2e2ee84e7fa10e8111
Expected verdict: FAIL
Expected first failure: SG5-GNT-01

The manifest claims scope minimal-doublet-electroweak-target, Higgs representation {'T': '1/2', 'Y': '0', 'complex': True, 'vev_weight_T3': '-1/2'}, tree rho None, and rho0 assertion None. No opened role was present when the engine generated its witness.

Blind session 4: generated electroweak witness

Witness SHA-256: 861547cf7755f0fd9f6e7a81bfec3ac6eeb4391cf2d461ee0484378fbacc86b2
Actual verdict: FAIL
Actual first failure: SG5-GNT-01

The generated representation is {'T': '1/2', 'Y': '0', 'dimension': 2, 'vev_weight_T3': '-1/2'} and the VEV record is {'Q_em': '-1/2', 'neutral': False}. The matrix has 1 massless vector(s), with photon pattern [0, 1] and tree rho None. Target-doublet match is FALSE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

Blind session 5: manifest and sealed expectation

Candidate ID: session-d61f1c18a74cc1549c86
Session role: UNDISCLOSED
Opened role: DECOY
Opened label: triplet-claims-rho-one
Manifest SHA-256: 1a117e02decefbf044a837594fd2a5be1a8d4ae93e729f6d0006d5966578355e
Expected verdict: FAIL
Expected first failure: SG5-GNT-05

The manifest claims scope minimal-doublet-electroweak-target, Higgs representation {'T': '1', 'Y': '1', 'complex': True, 'vev_weight_T3': '-1'}, tree rho 1, and rho0 assertion None. No opened role was present when the engine generated its witness.

Blind session 5: generated electroweak witness

Witness SHA-256: 2f24c47dda30151bf8bd379b9b129be6120ad937a7905324910c6433747ccc13
Actual verdict: FAIL
Actual first failure: SG5-GNT-05

The generated representation is {'T': '1', 'Y': '1', 'dimension': 3, 'vev_weight_T3': '-1'} and the VEV record is {'Q_em': '0', 'neutral': True}. The matrix has 1 massless vector(s), with photon pattern [1, 1] and tree rho 1/2. Target-doublet match is FALSE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

Blind session 6: manifest and sealed expectation

Candidate ID: session-d77abfd072df366a38c6
Session role: UNDISCLOSED
Opened role: DECOY
Opened label: charged-component-vev
Manifest SHA-256: 4289feb5de3f7f578099cd4f8213381e8992147c4f0866b6e7d2ab27bc7f907b
Expected verdict: FAIL
Expected first failure: SG5-GNT-01

The manifest claims scope minimal-doublet-electroweak-target, Higgs representation {'T': '1/2', 'Y': '1/2', 'complex': True, 'vev_weight_T3': '1/2'}, tree rho None, and rho0 assertion None. No opened role was present when the engine generated its witness.

Blind session 6: generated electroweak witness

Witness SHA-256: ebfb2d0670f04d53a65920e7f9a8b7a7c4c7ef0f215dd02fd9c3ff28f8083d42
Actual verdict: FAIL
Actual first failure: SG5-GNT-01

The generated representation is {'T': '1/2', 'Y': '1/2', 'dimension': 2, 'vev_weight_T3': '1/2'} and the VEV record is {'Q_em': '1', 'neutral': False}. The matrix has 1 massless vector(s), with photon pattern [1, -1] and tree rho None. Target-doublet match is FALSE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

Blind session 7: manifest and sealed expectation

Candidate ID: session-fb178c195ceae4070ecf
Session role: UNDISCLOSED
Opened role: INNOCENT-NON-TARGET
Opened label: honest-triplet-rho-half
Manifest SHA-256: 4f0ae8b637128304be18ef6c0ec441b3e05ca39f2e45b155a00ef1f34b13e82e
Expected verdict: PASS
Expected first failure: None

The manifest claims scope honest-alternative-higgs-sector, Higgs representation {'T': '1', 'Y': '1', 'complex': True, 'vev_weight_T3': '-1'}, tree rho 1/2, and rho0 assertion None. No opened role was present when the engine generated its witness.

Blind session 7: generated electroweak witness

Witness SHA-256: 244e4f263f788a71aac3dbc13952ec4374da43ac14cea24924ac4462348b132a
Actual verdict: PASS
Actual first failure: None

The generated representation is {'T': '1', 'Y': '1', 'dimension': 3, 'vev_weight_T3': '-1'} and the VEV record is {'Q_em': '0', 'neutral': True}. The matrix has 1 massless vector(s), with photon pattern [1, 1] and tree rho 1/2. Target-doublet match is FALSE.

The actual result matches the sealed expectation. The honest non-target is accepted, and each decoy stops at its intended first hard failure.

SG4-to-SG5 cumulative dependency reducer

The reducer receives physical SG4 OPEN, fourteen direct upstream OPEN rows, and five SG5-local OPEN rows. It therefore returns physical SG5 OPEN with 19 blockers.

The conditional electroweak tuple is reported alongside, never in place of, the physical terminal. Future promotion must attach evidence to each exact row and replay the entire cumulative package.

Physical readiness row 1: SG4-SG5-D01

Status: OPEN
Requirement: Physical gauge-group realization

The W and B zero modes and their couplings require physically realized SU(2) and U(1) carriers; the cumulative gauge construction remains OPEN.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 2: SG4-SG5-D02

Status: OPEN
Requirement: Faithful global gauge group

The conditional Z6 matter kernel is exact, but the physical global quotient and carrier character ownership remain OPEN.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 3: SG4-SG5-D03

Status: OPEN
Requirement: Admitted one-copy chiral inventory

The charged matter representations remain admitted inputs rather than complete physical kernels of the coupled operator.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 4: SG4-SG5-D04

Status: OPEN
Requirement: Three-family module and mirror completeness

SG3 conditionally supplies three copies and zero mirrors, while its action and spectral ownership remain physically OPEN.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 5: SG4-SG5-D05

Status: OPEN
Requirement: Fermion domain and anomaly completeness

The physical chiral domain, regulated determinant, heavy tower, inflow, and counterterms are not closed.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 6: SG4-SG5-D06

Status: OPEN
Requirement: SG1 geometric realization lineage

The internal shape, admissibility, operator construction, and full reduction inherited from SG1 remain OPEN.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 7: SG4-SG5-D07

Status: OPEN
Requirement: Gauge-carrier action, gauge fixing, and ghosts

The action-level ownership and BRST-complete zero-mode reduction for the electroweak carriers has not reached PASS.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 8: SG4-SG5-D08

Status: OPEN
Requirement: Family Actor action ownership

The family multiplicity module has conditional arithmetic but no closed primitive action parent.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 9: SG4-SG5-D09

Status: OPEN
Requirement: No-excess light-state census

A complete spectrum excluding extra light charged vectors, scalars, and chiral modes has not been supplied.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 10: SG4-SG5-D10

Status: OPEN
Requirement: Interaction graph derived from the physical action

The charge-defining Yukawa and Majorana graph is still a declared construction input rather than a completed geometric consequence.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 11: SG4-SG5-D11

Status: OPEN
Requirement: U(1) generator and coupling normalization

Primitive hypercharge normalization does not close the dynamical normalization of the U(1) kinetic term or coupling.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 12: SG4-SG5-D12

Status: OPEN
Requirement: Regulated anomaly descent

Six zero-mode anomaly sums vanish conditionally, but the higher-dimensional anomaly theorem remains OPEN.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 13: SG4-SG5-D13

Status: OPEN
Requirement: Global Z6 quotient realized by compactification

The 36-element character kernel has not yet been promoted to the physical compactification quotient.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 14: SG4-SG5-D14

Status: OPEN
Requirement: Independent SG4 reviewer gauntlet

The reconstructed SG4 gauntlet passes internally, but its independent reviewer-randomized execution remains NOT-EVALUATED.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 15: SG5-L01

Status: OPEN
Requirement: Minimal equivariant Higgs doublet derived from the action

The T=1/2, Y=1/2 Higgs zero mode is a declared gate input; its unique equivariant origin, action parent, and no-duplication proof are not supplied.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 16: SG5-L02

Status: OPEN
Requirement: Neutral VEV selection and scalar stability

The neutral VEV orientation and nonzero magnitude are assumed; the complete potential, vacuum selection, scalar Hessian, and competing extrema are not executed here.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 17: SG5-L03

Status: OPEN
Requirement: Electroweak kinetic and coupling normalization

The zero-mode mass matrix is exact given g, g-prime, and v, but canonical normalization and coupling transport from the higher-dimensional action remain open.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 18: SG5-L04

Status: OPEN
Requirement: Loop corrections and rho0 confrontation

Only the d<=4 tree-level rho parameter is computed; radiative corrections, matching, uncertainties, and comparison to the measured rho0 are explicitly not claimed.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Physical readiness row 19: SG5-L05

Status: OPEN
Requirement: Independent SG5 reviewer-randomized gauntlet

The internally reconstructed seven-session gauntlet passes; no independently randomized reviewer manifests and opened key were supplied.

This required row contributes one blocker to physical SG5. It is not discharged merely by the exact tree-level mass matrix unless new evidence directly proves the stated action, spectrum, vacuum, loop, calibration, or review requirement.

Building-block exhibit 1: BB_EWC_1_ELECTROWEAK_MASS_AND_RHO_CERTIFICATE

Artifact: BUILDING_BLOCKS/NEW_BLOCKS/BB_EWC_1_ELECTROWEAK_MASS_AND_RHO_CERTIFICATE.md
SHA-256: adc8dd870acbf6d544d685ba2249b1e5ed12456446c09211b2d6b5d121c3329d

block_id: BB-EWC-1 title: Electroweak Mass and Rho Certificate version: 1.0-RC status: conditional-candidate-pass date: 2026-08-02 parent_authority: BB-SOT-2026-07-18-V1 upstream: SG4_UPDATED_BUILDING_BLOCKS_CUMULATIVE_FROM_SG3_2026-08-02

BB-EWC-1 - Electroweak mass and rho certificate

Purpose

This block turns an electroweak-breaking narrative into one exact, representation-aware certificate. It prevents a charged VEV from being called neutral, a triplet result from being reported as doublet rho, a hand-written mass matrix from being paired with an inconsistent mixing angle, or a tree-level calculation from being promoted to a loop-level experimental test.

Typed input contract

The certificate consumes the representation (T,Y), the VEV weight m, the convention <H>=v/sqrt(2)|T,m>, canonical zero-mode covariant derivative D=partial-i g T^a W^a-i g_prime Y B, and the frozen SG4 charge table. The VEV is electromagnetically neutral only if m+Y=0.

For a single complex multiplet, define

c_W = [T(T+1)-m^2]/2.

In the basis (W1,W2,W3,B), the generated mass-squared matrix has diagonal charged entries c_W g^2 v^2 and neutral block

v^2 [[g^2 m^2, g g_prime m Y],
     [g g_prime m Y, g_prime^2 Y^2]].

Every coefficient is exact rational data. The artifact must print the matrix, not only quote eigenvalues.

Eigenvalue and mixing reducer

When m=-Y, the standard electromagnetic direction annihilates the VEV. The neutral block has one exact zero eigenvalue and one heavy eigenvalue. For the minimal doublet (T,Y,m)=(1/2,1/2,-1/2):

m_W^2 = g^2 v^2 / 4
m_A^2 = 0
m_Z^2 = (g^2 + g_prime^2) v^2 / 4
A proportional to g_prime W3 + g B
Z proportional to g W3 - g_prime B
sin theta_W = g_prime / sqrt(g^2+g_prime^2)
cos theta_W = g / sqrt(g^2+g_prime^2)

The certificate substitutes the claimed rotation into the generated matrix. A claimed diagonalization or mixing vector that is not an eigenvector fails.

Tree-level rho and claim-aware alternatives

For a neutral VEV, the one-multiplet result is

rho_tree = [T(T+1)-Y^2] / [2 Y^2].

The doublet gives one; a complex (T,Y)=(1,1) triplet gives one half. An honest triplet claiming one half is an innocent non-target and must pass. A triplet claiming one fails. Consistency, target match, and nature-selection are separate terminals.

Non-claims firewall

The block labels v_EW as a MEASURED-ANCHOR. It forbids any rho0 confrontation without a loop computation, matching prescription, input scheme, and uncertainty ledger. Custodial symmetry, winding-Higgs mechanisms, and a geometry head-to-head test are NOT-CLAIMED unless independently evidenced.

Output tuple

(representation, charge_table, vev_charge, exact_mass_matrix,
 exact_eigenvalues, photon_direction, z_direction, mixing_relations,
 rho_tree, vEW_provenance, forbidden_claim_scan, first_hard_failure)

The current replay returns the minimal neutral doublet, one photon, exact Standard Model tree-level masses, and rho_tree=1 as a construction-anchor conditional PASS. It does not close physical SG5.

Building-block exhibit 2: BB_EWR_1_ELECTROWEAK_READINESS_AND_CUMULATIVE_DEPENDENCY

Artifact: BUILDING_BLOCKS/NEW_BLOCKS/BB_EWR_1_ELECTROWEAK_READINESS_AND_CUMULATIVE_DEPENDENCY.md
SHA-256: a91fb777bd33efc0c55295dda53a653f44ec5e94c983c15478892fd7f1a6d8de

block_id: BB-EWR-1 title: Electroweak Readiness and Cumulative Dependency version: 1.0-RC status: open date: 2026-08-02 parent_authority: BB-SOT-2026-07-18-V1 upstream: SG4_UPDATED_BUILDING_BLOCKS_CUMULATIVE_FROM_SG3_2026-08-02

BB-EWR-1 - Electroweak readiness and cumulative dependency

Purpose

This block joins the exact SG5 zero-mode tree calculation to every inherited physical debt. It prevents a correct doublet mass matrix from being mistaken for a completed derivation of the Higgs, its vacuum, radiative corrections, or the experimentally confronted Standard Model.

Frozen SG4 join

The consumed SG4 block archive has SHA-256 09588c25b49f7ebb63a65226d870fa22d70dac5aa5fbcf7d0d8ce38041cae9ac. Its primitive hypercharge ray, six anomaly sums, Witten parity, and 36-element Z6 kernel pass conditionally. Its physical terminal is OPEN with fourteen readiness rows. SG5 preserves all fourteen.

Local readiness rows

Five SG5 rows are added:

1. derive the unique minimal equivariant Higgs doublet and its action parent;
2. derive neutral VEV selection, scalar stability, and competing extrema;
3. establish electroweak kinetic normalization and coupling transport;
4. compute loops, matching, uncertainties, and the rho0 confrontation;
5. execute an independent reviewer-randomized SG5 gauntlet.

The tree-level mass matrix cannot discharge any row merely by being exact.

Reducer

if a required row is contradictory: physical_SG5 = FAIL
elif a required row is OPEN, NOT-EVALUATED, or CONSTRUCTION-ANCHOR:
    physical_SG5 = OPEN
else: physical_SG5 = PASS

Current result:

conditional_SG5_candidate = PASS
internal_reconstructed_gauntlet = PASS
reviewer_randomized_gauntlet = NOT-EVALUATED
physical_SG5 = OPEN
blocking_dependency_count = 19

Evidence promotion must name the exact readiness row, preserve all frozen hashes, and replay the cumulative package.

Building-block exhibit 3: BB_MAP_1_SG5_VEW_AND_RHO0_SCOPE_AMENDMENT

Artifact: BUILDING_BLOCKS/AMENDMENTS/BB_MAP_1_SG5_VEW_AND_RHO0_SCOPE_AMENDMENT.md
SHA-256: 75ed4408b2af6598bb662e3c4d92fb088a15a83ae9886e51161135c6598636a8

amends: BB-MAP-1 title: SG5 vEW and rho0 Scope Amendment version: 1.3-RC date: 2026-08-02

BB-MAP-1 SG5 amendment - vEW and rho0 scope

The electroweak scale v_EW is a MEASURED-ANCHOR used to calibrate the exact tree-level zero-mode mass matrix. The gate does not derive its numerical value. Any statement that the geometry predicts v_EW requires a separate calibrated observable map, action normalization, and uncertainty ledger.

rho_tree(d<=4)=1 is a conditional structural result of the minimal neutral doublet. It is not the measured rho0. A confrontation with rho0, including the quoted value 1.00038, requires a complete loop computation, renormalized input scheme, threshold matching, theoretical errors, and experimental comparison. Without those artifacts the only lawful terminal is NOT-CLAIMED.

Custodial symmetry, winding-Higgs, and a head-to-head geometry test are independent claims and cannot be inferred retroactively from the value one.

Building-block exhibit 4: BB_AHG_1_SG5_HIGGS_PARENT_AND_VACUUM_AMENDMENT

Artifact: BUILDING_BLOCKS/AMENDMENTS/BB_AHG_1_SG5_HIGGS_PARENT_AND_VACUUM_AMENDMENT.md
SHA-256: 8e0b492a2a961ab4b4bd4a75e3eb025d581339d6536bf8e1ded2b09c878c8eb9

amends: BB-AHG-1 title: SG5 Higgs Parent and Vacuum Amendment version: 1.1-RC date: 2026-08-02

BB-AHG-1 SG5 amendment - Higgs parent and vacuum

An SG5 physical closure claim must register the Higgs doublet, its covariant kinetic term, scalar potential, boundary conditions, and symmetry-breaking VEV with one primitive action parent. A representation label and neutral VEV manifest are conditional inputs until the reduction proves their zero-mode origin, normalizability, uniqueness or declared degeneracy, and non-duplication.

The vacuum witness must include the complete scalar Hessian, gauge-orbit quotient, Goldstone directions, competing extrema, and the absence or census of additional light scalars. Neutrality alone does not prove vacuum selection or stability. This amendment therefore keeps Higgs derivation and VEV selection OPEN even when the generated electroweak mass matrix passes exactly.

Building-block exhibit 5: SG5_BUILDING_BLOCK_FINDINGS

Artifact: BUILDING_BLOCKS/SG5_BUILDING_BLOCK_FINDINGS.md
SHA-256: 770d3241ee7849685aae42e8fa8d9d06d4b916b4f02faaf5d754d7e1d9315560

SG-5 building-block findings

The cumulative SG4 blocks correctly freeze hypercharge and its conditional physical limitations, but SG5 exposed four reusable registry gaps: no mandatory representation-to-mass-matrix generator; no explicit distinction between a neutral massless direction and electromagnetism; no claim-aware rho formula for alternative Higgs representations; and no hard firewall between tree-level rho and the loop-level measured rho0.

BB-EWC-1 supplies the exact representation-aware certificate. BB-EWR-1 joins it to the physical dependency reducer. The MAP amendment makes vEW a MEASURED-ANCHOR and the rho0 comparison NOT-CLAIMED, while the AHG amendment requires an action-owned Higgs and vacuum witness before physical promotion.

The improved blocks catch all five challenge decoys and accept the honest triplet with rho one half. They preserve the SG4 archive, charge certificate, and OPEN terminal byte-for-byte.

Building-block exhibit 6: SG5_SCOPE_RECONCILIATION

Artifact: BUILDING_BLOCKS/SG5_SCOPE_RECONCILIATION.md
SHA-256: d18154e10d6cf245a75da9909d0a86a5771bdfc5e1993fc5e8e231f1f4214965

SG-5 scope reconciliation

Conditional result

Given the minimal complex doublet (T,Y)=(1/2,1/2), the lower neutral VEV, canonical zero-mode kinetic normalization, couplings g,g_prime, and measured calibration v_EW, the generated matrix has exactly one massless photon, mW^2=g^2v^2/4, mZ^2=(g^2+g_prime^2)v^2/4, and rho_tree(d<=4)=1. This conditional certificate is PASS.

Physical result

Physical SG5 is OPEN with fourteen inherited and five local blockers. The Higgs representation and neutral VEV are declared gate inputs; the full scalar potential, vacuum selection, kinetic transport, loop corrections, rho0 confrontation, and independent reviewer execution are not closed.

Explicit non-claims

• No claim that shape uniquely derives the Higgs doublet.
• No claim that geometry predicts the measured value of vEW.
• No loop-level rho0 confrontation.
• No invented custodial symmetry or winding-Higgs mechanism.
• No head-to-head experimental test won by the geometry.
• No reviewer-randomized PASS, nature-selection, or full physical closure.

Execution validation summary

The independent verifier reports 18 controls PASS. It compiles and executes twice, requires byte-identical artifacts, verifies the blind escrow, recomputes the electroweak identities, freezes SG4 inputs, replays the extracted block manifest, and applies the nineteen-row reducer.

Execution validation control 01

Control: Engine and verifier compile
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 02

Control: Two byte-identical generated runs
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 03

Control: All generated JSON parses
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 04

Control: Answer-key commitment and escrow
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 05

Control: Seven blinded sessions and complete manifests
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 06

Control: Manifest and witness hash escrow
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 07

Control: All seven verdicts match sealed key
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 08

Control: Five challenge decoys caught at intended first failures
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 09

Control: Honest triplet rho=1/2 non-target accepted
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 10

Control: Frozen SG4 Q=T3+Y table replay
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 11

Control: Minimal doublet state table and neutral VEV
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 12

Control: Covariant-derivative mass matrix and one massless photon
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 13

Control: Exact eigenvalues, weak mixing, and rho_tree=1
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 14

Control: rho0, custodial, winding, and geometry-test nonclaims
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 15

Control: Conditional/physical status and measured-anchor firewall
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 16

Control: Frozen input hashes
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 17

Control: Frozen SG4 package integrity and extracted manifest replay
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Execution validation control 18

Control: SG4-to-SG5 cumulative dependency reducer
Result: PASS

This PASS belongs to the stated validation boundary. It establishes artifact integrity or a conditional mathematical identity; it never promotes the physical SG5 terminal beyond the evidence class actually tested.

Final controlling statement

The SG5 challenge is solved at the conditional certificate level. The minimal neutral doublet generates the exact zero-mode electroweak mass matrix, exactly one photon, the Standard Model tree-level W and Z eigenvalues, and rho_tree(d<=4)=1. The internal seven-session gauntlet and all eighteen execution controls pass.

Full physical closure is not achieved. Physical SG4 is OPEN, and SG5 adds five local readiness debts. The controlling terminal is SG5 PHYSICAL GATE: OPEN (19 blockers). The measured scale is calibrated, not predicted; rho0 confrontation and the retired custodial, winding, and geometry test narratives are NOT-CLAIMED; reviewer-randomized execution is NOT-EVALUATED; nature-selection is NOT-CLAIMED.

The improved blocks encode these distinctions as reusable registry controls and carry the complete SG4 cumulative archive forward.