Controlling terminal and claim firewall

The SG4 conditional candidate certificate passes. Given the published interaction graph, the all-left-handed field inventory, the conditional SG3 three-family module, and the declared center characters, one executable script derives the primitive charge ray (1,-4,2,-3,6,0,3), reconstructs electric charge, zeros all six local anomaly channels, obtains an even fermionic Witten count, and finds the order-six matter-faithful kernel by complete enumeration.

The physical SG4 gate remains OPEN. The frozen SG3 package is physically OPEN with nine readiness dependencies, and five SG4-local rows are also OPEN. The matrix proves what follows from the declared interaction graph; it does not prove that the internal shape generated that graph. Zero-mode anomaly sums do not replace a regulated higher-dimensional determinant, and the center kernel does not by itself establish the physical compactification quotient.

These terminals are deliberately independent. No exact conditional calculation is allowed to erase an inherited or local physical readiness debt.

Authority order and cumulative lineage

This build uses the user-supplied building blocks as its source of truth. The authority order is: BB-SOT-2026-07-18-V1; the SG3 cumulative building-block archive; the V4.1 constraint-driven gate protocol; the SG2-SG8 reviewer challenge specification; the frozen SG4 dependency ledger; then the generated candidate manifests and witnesses.

The SG3 archive is frozen byte-for-byte at SHA-256 eedd26d63f0097c0d8ece86d95bdf268857290534eb10017bc66c41f31d47085. Its package manifest is replayed file by file. The operation is a cumulative successor overlay, not a silent replacement and not a retrospective claim that earlier physical gates were closed.

The SG3 conditional family certificate supplies three copies per admitted representation and zero vectorlike mirrors. The physical SG3 terminal is OPEN; that status is consumed, preserved, and joined to SG4. Every later equation in this dossier must be read under this cumulative dependency relation.

Field basis, chirality, and normalization conventions

The ordered integer basis is (Q,u_c,d_c,L,e_c,nu_c,H). All fermions are left-handed Weyl fields. Thus u_c, d_c, and e_c carry charges opposite to the conventionally named right-handed particles. The vector records 6Y, so ordinary hypercharge is obtained by division by six.

Q is a color triplet and weak doublet; u_c and d_c are color antitriplet weak singlets; L is a color-singlet weak doublet; e_c and nu_c are singlets; H is a scalar weak doublet. Scalar data are used in the interaction equations and center action but are excluded from all fermionic anomaly and Witten counts.

Primitive gcd normalization chooses the shortest nonzero integer lattice representative. It does not determine the U(1) kinetic normalization or the gauge coupling. The distinction is a mandatory claim firewall.

Published interaction matrix and exact nullspace

Columns are ordered Q,u_c,d_c,L,e_c,nu_c,H. Every row is printed; no Smith normal-form summary is accepted without its matrix.

Exact rational row reduction gives rank 6, nullity 1, and the integer basis [1, -4, 2, -3, 6, 0, 3]. All six products vanish. Therefore the declared graph plus [SU(2)]^2U(1) consistency fixes a one-dimensional ray. The provenance question - whether the graph itself follows from shape - is a separate physical readiness row and remains OPEN.

The conditional result has provenance class construction-anchor: it verifies the declared equations with the target known and does not claim that nature or the shape uniquely selected those equations.

Matrix row 1: QHu_c

Yukawa invariance of Q H u_c gives q_Q+q_u+q_H=0.

The complete coefficient row in the fixed field basis is [1, 1, 0, 0, 0, 0, 1]. Substitution of the primitive candidate gives the exact integer product 0. The row is therefore satisfied without floating-point tolerance, implicit rescaling, or omitted sign conventions.

This row is both evidence and an audit boundary. A candidate claiming only anomaly freedom need not satisfy it. A candidate claiming derivation by this interaction graph must satisfy every row; the first nonzero product is a hard failure under SG4-GNT-01. Publishing rows individually also exposes whether a future model changes an interaction, removes the Majorana edge, or changes the weak representation multiplicity.

Matrix row 2: QHdaggerd_c

Yukawa invariance of Q H^dagger d_c gives q_Q+q_d-q_H=0.

The complete coefficient row in the fixed field basis is [1, 0, 1, 0, 0, 0, -1]. Substitution of the primitive candidate gives the exact integer product 0. The row is therefore satisfied without floating-point tolerance, implicit rescaling, or omitted sign conventions.

This row is both evidence and an audit boundary. A candidate claiming only anomaly freedom need not satisfy it. A candidate claiming derivation by this interaction graph must satisfy every row; the first nonzero product is a hard failure under SG4-GNT-01. Publishing rows individually also exposes whether a future model changes an interaction, removes the Majorana edge, or changes the weak representation multiplicity.

Matrix row 3: LHdaggere_c

Yukawa invariance of L H^dagger e_c gives q_L+q_e-q_H=0.

The complete coefficient row in the fixed field basis is [0, 0, 0, 1, 1, 0, -1]. Substitution of the primitive candidate gives the exact integer product 0. The row is therefore satisfied without floating-point tolerance, implicit rescaling, or omitted sign conventions.

This row is both evidence and an audit boundary. A candidate claiming only anomaly freedom need not satisfy it. A candidate claiming derivation by this interaction graph must satisfy every row; the first nonzero product is a hard failure under SG4-GNT-01. Publishing rows individually also exposes whether a future model changes an interaction, removes the Majorana edge, or changes the weak representation multiplicity.

Matrix row 4: LHnu_c

The Dirac neutrino edge L H nu_c gives q_L+q_n+q_H=0.

The complete coefficient row in the fixed field basis is [0, 0, 0, 1, 0, 1, 1]. Substitution of the primitive candidate gives the exact integer product 0. The row is therefore satisfied without floating-point tolerance, implicit rescaling, or omitted sign conventions.

This row is both evidence and an audit boundary. A candidate claiming only anomaly freedom need not satisfy it. A candidate claiming derivation by this interaction graph must satisfy every row; the first nonzero product is a hard failure under SG4-GNT-01. Publishing rows individually also exposes whether a future model changes an interaction, removes the Majorana edge, or changes the weak representation multiplicity.

Matrix row 5: nu_cnu_c

The Majorana self-edge gives 2 q_n=0 over the continuous U(1) Lie algebra.

The complete coefficient row in the fixed field basis is [0, 0, 0, 0, 0, 2, 0]. Substitution of the primitive candidate gives the exact integer product 0. The row is therefore satisfied without floating-point tolerance, implicit rescaling, or omitted sign conventions.

This row is both evidence and an audit boundary. A candidate claiming only anomaly freedom need not satisfy it. A candidate claiming derivation by this interaction graph must satisfy every row; the first nonzero product is a hard failure under SG4-GNT-01. Publishing rows individually also exposes whether a future model changes an interaction, removes the Majorana edge, or changes the weak representation multiplicity.

Matrix row 6: SU2_squared_U1

Weak consistency gives 3 q_Q+q_L=0, where three is color multiplicity.

The complete coefficient row in the fixed field basis is [3, 0, 0, 1, 0, 0, 0]. Substitution of the primitive candidate gives the exact integer product 0. The row is therefore satisfied without floating-point tolerance, implicit rescaling, or omitted sign conventions.

This row is both evidence and an audit boundary. A candidate claiming only anomaly freedom need not satisfy it. A candidate claiming derivation by this interaction graph must satisfy every row; the first nonzero product is a hard failure under SG4-GNT-01. Publishing rows individually also exposes whether a future model changes an interaction, removes the Majorana edge, or changes the weak representation multiplicity.

Primitive charge lattice and ray normalization

The exact integer nullspace generator is [1, -4, 2, -3, 6, 0, 3]. The gcd of its nonzero entries is 1, so the representative is primitive: TRUE.

Any nonzero integer multiple describes the same rational ray, and can retain the same physical charges after a compensating coupling convention. It does not, however, satisfy a claim that the displayed vector is primitive. This is why the scaled-vector decoy fails SG4-GNT-02 even though it points along the correct ray.

Conversely, gcd one is not a dynamical normalization theorem. The U(1) kinetic term, coupling, and possible mixing require action-level evidence. The conditional certificate closes the arithmetic convention and leaves the physical normalization row OPEN.

Complete electric-charge table

Electric charge is recomputed as Q_em=T3+Y with Y=(6Y)/6. Both components of each weak doublet are shown, together with every singlet. Conjugate fields remain in the all-left-handed basis, so their displayed electromagnetic charges are those of the conjugate Weyl fields.

Electric-charge state 1: u_L

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 2: d_L

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 3: u_c

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 4: d_c

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 5: nu_L

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 6: e_L

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 7: e_c

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 8: nu_c

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 9: H_plus

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Electric-charge state 10: H_zero

This row is generated from the primitive integer vector, not entered as a target charge. The weak weight T3 and hypercharge Y are combined using exact rational arithmetic. The result is stored as an auditable string in the charge certificate and is covered by the execution hash escrow.

The row also tests convention consistency. A sign error for a conjugate singlet or a misplaced Higgs component would be visible here even if aggregate anomaly sums happened to cancel. Passing this row is conditional on the declared representation inventory; physical ownership of that inventory is inherited as OPEN from SG3.

Six local four-dimensional anomaly channels

Every channel is evaluated with integer 6Y charges. Overall positive normalization factors are irrelevant to the vanishing test, while integer arithmetic prevents tolerance-based false positives. Local perturbative and global Witten anomalies are reported separately.

Anomaly channel 1: SU2_cubed_local

The perturbative local cubic SU(2) anomaly vanishes structurally because the doublet is pseudoreal; the separate global Witten test follows later.

For three conditional SG3 families, the exact generated sum is 0. The expected value is zero, and the equality is an integer identity rather than a numerical approximation. The manifest and witness preserve this value for independent replay.

This cancellation is a four-dimensional zero-mode certificate. It does not yet establish completeness of the heavy tower, regulated fermion determinant, boundary inflow, or allowed counterterms. BB-AD-1@1.2-RC therefore marks the channel conditional while keeping physical anomaly descent OPEN.

Anomaly channel 2: SU2_squared_U1

The integer trace is 3 q_Q + q_L per family, including Q color multiplicity.

For three conditional SG3 families, the exact generated sum is 0. The expected value is zero, and the equality is an integer identity rather than a numerical approximation. The manifest and witness preserve this value for independent replay.

This cancellation is a four-dimensional zero-mode certificate. It does not yet establish completeness of the heavy tower, regulated fermion determinant, boundary inflow, or allowed counterterms. BB-AD-1@1.2-RC therefore marks the channel conditional while keeping physical anomaly descent OPEN.

Anomaly channel 3: SU3_cubed

Two fundamental color components from Q cancel the two antitriplet singlets u_c and d_c.

For three conditional SG3 families, the exact generated sum is 0. The expected value is zero, and the equality is an integer identity rather than a numerical approximation. The manifest and witness preserve this value for independent replay.

This cancellation is a four-dimensional zero-mode certificate. It does not yet establish completeness of the heavy tower, regulated fermion determinant, boundary inflow, or allowed counterterms. BB-AD-1@1.2-RC therefore marks the channel conditional while keeping physical anomaly descent OPEN.

Anomaly channel 4: SU3_squared_U1

The integer trace is 2 q_Q + q_u + q_d per family.

For three conditional SG3 families, the exact generated sum is 0. The expected value is zero, and the equality is an integer identity rather than a numerical approximation. The manifest and witness preserve this value for independent replay.

This cancellation is a four-dimensional zero-mode certificate. It does not yet establish completeness of the heavy tower, regulated fermion determinant, boundary inflow, or allowed counterterms. BB-AD-1@1.2-RC therefore marks the channel conditional while keeping physical anomaly descent OPEN.

Anomaly channel 5: U1_cubed

The cubic trace weights q^3 by the full color and weak multiplicities; it is the most nonlinear local test.

For three conditional SG3 families, the exact generated sum is 0. The expected value is zero, and the equality is an integer identity rather than a numerical approximation. The manifest and witness preserve this value for independent replay.

This cancellation is a four-dimensional zero-mode certificate. It does not yet establish completeness of the heavy tower, regulated fermion determinant, boundary inflow, or allowed counterterms. BB-AD-1@1.2-RC therefore marks the channel conditional while keeping physical anomaly descent OPEN.

Anomaly channel 6: gravity_squared_U1

The trace sums hypercharge over all left-handed Weyl components with color and weak multiplicities.

For three conditional SG3 families, the exact generated sum is 0. The expected value is zero, and the equality is an integer identity rather than a numerical approximation. The manifest and witness preserve this value for independent replay.

This cancellation is a four-dimensional zero-mode certificate. It does not yet establish completeness of the heavy tower, regulated fermion determinant, boundary inflow, or allowed counterterms. BB-AD-1@1.2-RC therefore marks the channel conditional while keeping physical anomaly descent OPEN.

Global SU(2) Witten parity

For each family, Q supplies three weak fermion doublets because of color and L supplies one. Thus the fermion-only count is 3+1=4 per family. With 3 conditional families, the total is 12, which is even: TRUE.

The Higgs is a scalar and is excluded: TRUE. Including it would reproduce the retired historical error and manufacture an odd count of thirteen. The execution engine rejects that candidate at SG4-GNT-05 before considering later claims.

This test is global and distinct from the structurally vanishing local SU(2)^3 channel. Keeping separate rows prevents a local trace statement from being misreported as the mod-two global theorem.

Matter-faithful center kernel

The candidate enumerates all 36 triples (a,b,k) in Z3 x Z2 x Z6. A field with triality t, weak-doublet parity s, and integer charge q=6Y is fixed when 2*a*t + 3*b*s + k*q = 0 mod 6.

Exactly 6 elements act trivially on every listed matter field and the Higgs:

They form the cyclic subgroup generated by (1,1,1), so the conditional matter-faithful kernel is Z6. The full physical quotient remains OPEN until the carrier action and compactification realize it globally.

Center enumeration row 01: (0,0,0)

The enumerated center triple is a=0, b=0, k=0. Its per-field phase exponents, expressed modulo six, are:

Classification: KERNEL MEMBER. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 02: (0,0,1)

The enumerated center triple is a=0, b=0, k=1. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 03: (0,0,2)

The enumerated center triple is a=0, b=0, k=2. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 04: (0,0,3)

The enumerated center triple is a=0, b=0, k=3. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 05: (0,0,4)

The enumerated center triple is a=0, b=0, k=4. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 06: (0,0,5)

The enumerated center triple is a=0, b=0, k=5. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 07: (0,1,0)

The enumerated center triple is a=0, b=1, k=0. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 08: (0,1,1)

The enumerated center triple is a=0, b=1, k=1. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 09: (0,1,2)

The enumerated center triple is a=0, b=1, k=2. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 10: (0,1,3)

The enumerated center triple is a=0, b=1, k=3. Its per-field phase exponents, expressed modulo six, are:

Classification: KERNEL MEMBER. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 11: (0,1,4)

The enumerated center triple is a=0, b=1, k=4. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 12: (0,1,5)

The enumerated center triple is a=0, b=1, k=5. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 13: (1,0,0)

The enumerated center triple is a=1, b=0, k=0. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 14: (1,0,1)

The enumerated center triple is a=1, b=0, k=1. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 15: (1,0,2)

The enumerated center triple is a=1, b=0, k=2. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 16: (1,0,3)

The enumerated center triple is a=1, b=0, k=3. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 17: (1,0,4)

The enumerated center triple is a=1, b=0, k=4. Its per-field phase exponents, expressed modulo six, are:

Classification: KERNEL MEMBER. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 18: (1,0,5)

The enumerated center triple is a=1, b=0, k=5. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 19: (1,1,0)

The enumerated center triple is a=1, b=1, k=0. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 20: (1,1,1)

The enumerated center triple is a=1, b=1, k=1. Its per-field phase exponents, expressed modulo six, are:

Classification: KERNEL MEMBER. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 21: (1,1,2)

The enumerated center triple is a=1, b=1, k=2. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 22: (1,1,3)

The enumerated center triple is a=1, b=1, k=3. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 23: (1,1,4)

The enumerated center triple is a=1, b=1, k=4. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 24: (1,1,5)

The enumerated center triple is a=1, b=1, k=5. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 25: (2,0,0)

The enumerated center triple is a=2, b=0, k=0. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 26: (2,0,1)

The enumerated center triple is a=2, b=0, k=1. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 27: (2,0,2)

The enumerated center triple is a=2, b=0, k=2. Its per-field phase exponents, expressed modulo six, are:

Classification: KERNEL MEMBER. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 28: (2,0,3)

The enumerated center triple is a=2, b=0, k=3. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 29: (2,0,4)

The enumerated center triple is a=2, b=0, k=4. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 30: (2,0,5)

The enumerated center triple is a=2, b=0, k=5. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 31: (2,1,0)

The enumerated center triple is a=2, b=1, k=0. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 32: (2,1,1)

The enumerated center triple is a=2, b=1, k=1. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 33: (2,1,2)

The enumerated center triple is a=2, b=1, k=2. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 34: (2,1,3)

The enumerated center triple is a=2, b=1, k=3. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 35: (2,1,4)

The enumerated center triple is a=2, b=1, k=4. Its per-field phase exponents, expressed modulo six, are:

Classification: NOT IN KERNEL. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Center enumeration row 36: (2,1,5)

The enumerated center triple is a=2, b=1, k=5. Its per-field phase exponents, expressed modulo six, are:

Classification: KERNEL MEMBER. The classification is computed only after checking every field. It cannot be supplied by a group label or inferred from a subset of representations. This row is one of 36 exhaustive cases, which is why the final order-six result is an enumeration theorem rather than a quoted Smith-normal-form conclusion.

The center table is conditional on the declared characters. Physical ownership of those characters and realization of the quotient remain governed by the cumulative readiness reducer.

Z6 kernel witness 1: (0,0,0)

The triple (0,0,0) has zero phase residue on every field in the 36-row enumeration. Its k coordinate is 0, and the six accepted triples collectively contain one element for each k in 0,...,5. Projection to the k coordinate is therefore bijective on the kernel.

The generator (1,1,1) has order six. Repeated addition modulo (3,2,6) produces exactly the accepted triples and returns to the identity after the sixth power. Hence the kernel is cyclic, not merely a set of six elements.

This witness certifies the conditional character kernel. It remains distinct from a physical proof that the compactified gauge group is the corresponding quotient.

Z6 kernel witness 2: (1,1,1)

The triple (1,1,1) has zero phase residue on every field in the 36-row enumeration. Its k coordinate is 1, and the six accepted triples collectively contain one element for each k in 0,...,5. Projection to the k coordinate is therefore bijective on the kernel.

The generator (1,1,1) has order six. Repeated addition modulo (3,2,6) produces exactly the accepted triples and returns to the identity after the sixth power. Hence the kernel is cyclic, not merely a set of six elements.

This witness certifies the conditional character kernel. It remains distinct from a physical proof that the compactified gauge group is the corresponding quotient.

Z6 kernel witness 3: (2,0,2)

The triple (2,0,2) has zero phase residue on every field in the 36-row enumeration. Its k coordinate is 2, and the six accepted triples collectively contain one element for each k in 0,...,5. Projection to the k coordinate is therefore bijective on the kernel.

The generator (1,1,1) has order six. Repeated addition modulo (3,2,6) produces exactly the accepted triples and returns to the identity after the sixth power. Hence the kernel is cyclic, not merely a set of six elements.

This witness certifies the conditional character kernel. It remains distinct from a physical proof that the compactified gauge group is the corresponding quotient.

Z6 kernel witness 4: (0,1,3)

The triple (0,1,3) has zero phase residue on every field in the 36-row enumeration. Its k coordinate is 3, and the six accepted triples collectively contain one element for each k in 0,...,5. Projection to the k coordinate is therefore bijective on the kernel.

The generator (1,1,1) has order six. Repeated addition modulo (3,2,6) produces exactly the accepted triples and returns to the identity after the sixth power. Hence the kernel is cyclic, not merely a set of six elements.

This witness certifies the conditional character kernel. It remains distinct from a physical proof that the compactified gauge group is the corresponding quotient.

Z6 kernel witness 5: (1,0,4)

The triple (1,0,4) has zero phase residue on every field in the 36-row enumeration. Its k coordinate is 4, and the six accepted triples collectively contain one element for each k in 0,...,5. Projection to the k coordinate is therefore bijective on the kernel.

The generator (1,1,1) has order six. Repeated addition modulo (3,2,6) produces exactly the accepted triples and returns to the identity after the sixth power. Hence the kernel is cyclic, not merely a set of six elements.

This witness certifies the conditional character kernel. It remains distinct from a physical proof that the compactified gauge group is the corresponding quotient.

Z6 kernel witness 6: (2,1,5)

The triple (2,1,5) has zero phase residue on every field in the 36-row enumeration. Its k coordinate is 5, and the six accepted triples collectively contain one element for each k in 0,...,5. Projection to the k coordinate is therefore bijective on the kernel.

The generator (1,1,1) has order six. Repeated addition modulo (3,2,6) produces exactly the accepted triples and returns to the identity after the sixth power. Hence the kernel is cyclic, not merely a set of six elements.

This witness certifies the conditional character kernel. It remains distinct from a physical proof that the compactified gauge group is the corresponding quotient.

Gauntlet rule SG4-GNT-01: Published matrix and exact ray

Publish the labeled interaction matrix, solve its exact integer nullspace, and require a ray-derivation claimant to lie on that ray.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Gauntlet rule SG4-GNT-02: Primitive lattice normalization

Compute the gcd of all nonzero integer charges; a scaled vector is physically equivalent as a ray but fails a claim of primitive normalization.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Gauntlet rule SG4-GNT-03: Electric-charge reconstruction

Evaluate Q_em=T3+Y for every weak component and every singlet in the all-left-handed convention.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Gauntlet rule SG4-GNT-04: Six local anomaly channels

Recompute all six local four-dimensional channels with exact integer arithmetic and compare every claimed sum.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Gauntlet rule SG4-GNT-05: Fermion-only Witten parity

Count three colored Q doublets plus one lepton doublet per family; exclude the scalar Higgs before testing parity.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Gauntlet rule SG4-GNT-06: Full center kernel

Enumerate all 36 center triples and infer the kernel from their actual action; a quoted group label is not evidence.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Gauntlet rule SG4-GNT-07: Claim-aware alternatives

Accept an anomaly-free off-ray assignment if it claims only anomaly freedom; reject it only when it overclaims derivation by the published graph.

This rule is evaluated in fixed order, so the witness records the first hard failure rather than an unordered list of complaints. First-failure discipline keeps decoys diagnostic: an anomaly miss cannot be hidden by a later quotient claim, and an off-ray candidate is not rejected when its scope is honestly limited to anomaly freedom.

The rule result, manifest hash, and witness hash are escrowed before the answer key is opened. The supplied execution is an internal deterministic reconstruction. Because no independent randomized reviewer manifests were provided, the reviewer-randomized terminal remains NOT-EVALUATED.

Blind session 1: manifest and sealed expectation

Candidate ID: session-381da6e50bf4f391e5fd
Presentation role in session: UNDISCLOSED
Opened role: INNOCENT-NON-TARGET
Opened label: honest-B-minus-L-assignment
Manifest SHA-256: fcd11967324c8e9c42566bc256f2a3a22868579e03696affbb8584ad70de1b47
Expected verdict: PASS
Expected first failure: None

The manifest claims scope anomaly-free-assignment and presents integer charges [1, -1, -1, -3, 3, 3, 0]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is ORDER-3. No role label was present during execution.

Blind session 1: generated witness

Witness SHA-256: 3239d4c4f740baf6c54e22ee6d0661e15fec9b14901ae68fa14c082532b75a6c
Actual verdict: PASS
Actual first failure: None

The exact matrix computation returned nullity 1 and candidate products [0, 0, 0, 0, 6, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 0, 'gravity_squared_U1': 0}. The fermion doublet count was 12, and the center enumeration found kernel order 3.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 2: manifest and sealed expectation

Candidate ID: session-3aa0cbf828a54fcad2a6
Presentation role in session: UNDISCLOSED
Opened role: DECOY
Opened label: false-Z6-kernel
Manifest SHA-256: 35277b2ac16ee2731a21b234bc06ea4759da1cfd3b5e6513ad66515af8fb08cf
Expected verdict: FAIL
Expected first failure: SG4-GNT-06

The manifest claims scope anomaly-free-assignment and presents integer charges [-7, 16, -2, 21, -30, -12, -7]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is Z6. No role label was present during execution.

Blind session 2: generated witness

Witness SHA-256: d3c8a96fe51d842a36777b29529559cac703c6141a59ebc9fbee614d239408fd
Actual verdict: FAIL
Actual first failure: SG4-GNT-06

The exact matrix computation returned nullity 1 and candidate products [2, -2, -2, 2, -24, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 0, 'gravity_squared_U1': 0}. The fermion doublet count was 12, and the center enumeration found kernel order 2.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 3: manifest and sealed expectation

Candidate ID: session-46f8df8088b2bd73affa
Presentation role in session: UNDISCLOSED
Opened role: INCUMBENT
Opened label: incumbent
Manifest SHA-256: f100745cc779e9174aefa5890a013e6e72ed5165d70eec1e12ed231a9146920a
Expected verdict: PASS
Expected first failure: None

The manifest claims scope derived-hypercharge-ray and presents integer charges [1, -4, 2, -3, 6, 0, 3]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is Z6. No role label was present during execution.

Blind session 3: generated witness

Witness SHA-256: e36e519bd5a66da3ffd81d4b617576baeb59c287b754d7028415b92bbeb50e2a
Actual verdict: PASS
Actual first failure: None

The exact matrix computation returned nullity 1 and candidate products [0, 0, 0, 0, 0, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 0, 'gravity_squared_U1': 0}. The fermion doublet count was 12, and the center enumeration found kernel order 6.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 4: manifest and sealed expectation

Candidate ID: session-5d6d450efa38aa3ea9c0
Presentation role in session: UNDISCLOSED
Opened role: DECOY
Opened label: anomaly-free-off-ray-overclaim
Manifest SHA-256: 3320794239b810346b927329d5548de2e13cfc1378279eeb48dd01c9b3dc9455
Expected verdict: FAIL
Expected first failure: SG4-GNT-01

The manifest claims scope derived-hypercharge-ray and presents integer charges [1, -1, -1, -3, 3, 3, 0]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is Z6. No role label was present during execution.

Blind session 4: generated witness

Witness SHA-256: 41072c1a1ef571b227aaa2ab41f9adf08c4d38bc4d6f42c6fec7fc647ef82cb2
Actual verdict: FAIL
Actual first failure: SG4-GNT-01

The exact matrix computation returned nullity 1 and candidate products [0, 0, 0, 0, 6, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 0, 'gravity_squared_U1': 0}. The fermion doublet count was 12, and the center enumeration found kernel order 3.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 5: manifest and sealed expectation

Candidate ID: session-63dd8a8f300198c6f018
Presentation role in session: UNDISCLOSED
Opened role: DECOY
Opened label: wrong-primitive-normalization
Manifest SHA-256: 631fadb4717f88e98aaa8478f16742b6d5a7e5584230429ddc1161412ffc3727
Expected verdict: FAIL
Expected first failure: SG4-GNT-02

The manifest claims scope derived-hypercharge-ray and presents integer charges [2, -8, 4, -6, 12, 0, 6]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is Z6. No role label was present during execution.

Blind session 5: generated witness

Witness SHA-256: ac2c60e2c3c0ed59712656127e5b62b8c27a00b557c82e90513f21110a947633
Actual verdict: FAIL
Actual first failure: SG4-GNT-02

The exact matrix computation returned nullity 1 and candidate products [0, 0, 0, 0, 0, 0]. The primitive gcd was 2. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 0, 'gravity_squared_U1': 0}. The fermion doublet count was 12, and the center enumeration found kernel order 6.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 6: manifest and sealed expectation

Candidate ID: session-9866179cde2ec8fb4630
Presentation role in session: UNDISCLOSED
Opened role: DECOY
Opened label: cubic-anomaly-miss
Manifest SHA-256: 51112ca0ebfcd08d9cd6bdf8d3604106896ddcbbd98a78d164bfd3bb94e05da9
Expected verdict: FAIL
Expected first failure: SG4-GNT-04

The manifest claims scope anomaly-free-assignment and presents integer charges [1, -4, 2, -3, 5, 0, 3]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is Z6. No role label was present during execution.

Blind session 6: generated witness

Witness SHA-256: 803a9e100b45146e6ff0852e8916031977e191fc04a7ed962e0ba1fe84c9f1d1
Actual verdict: FAIL
Actual first failure: SG4-GNT-04

The exact matrix computation returned nullity 1 and candidate products [0, 0, -1, 0, 0, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': -273, 'gravity_squared_U1': -3}. The fermion doublet count was 12, and the center enumeration found kernel order 1.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 7: manifest and sealed expectation

Candidate ID: session-d235c857242e5ead7b65
Presentation role in session: UNDISCLOSED
Opened role: DECOY
Opened label: gravitational-anomaly-miss
Manifest SHA-256: fc558c088fe94e58e86fa9ebc3de190bf5cbf5d36b5343815f9f8e04850d791b
Expected verdict: FAIL
Expected first failure: SG4-GNT-04

The manifest claims scope anomaly-free-assignment and presents integer charges [1, -4, 2, -3, 6, 1, 3]. Its claimed primitive gcd is 1, its Witten count is 12, and its center label is Z6. No role label was present during execution.

Blind session 7: generated witness

Witness SHA-256: a6bef4794c94693cf12897c0e364abac520af22ff7c49cf0751bf8394d587953
Actual verdict: FAIL
Actual first failure: SG4-GNT-04

The exact matrix computation returned nullity 1 and candidate products [0, 0, 0, 1, 2, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 3, 'gravity_squared_U1': 3}. The fermion doublet count was 12, and the center enumeration found kernel order 1.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

Blind session 8: manifest and sealed expectation

Candidate ID: session-f79059150ead9c1b6f1c
Presentation role in session: UNDISCLOSED
Opened role: DECOY
Opened label: scalar-in-witten-count
Manifest SHA-256: 0c21f0a6e51165b83663bc3589b0f743069d6c04d82cfb15046a7d2cb35716ec
Expected verdict: FAIL
Expected first failure: SG4-GNT-05

The manifest claims scope derived-hypercharge-ray and presents integer charges [1, -4, 2, -3, 6, 0, 3]. Its claimed primitive gcd is 1, its Witten count is 13, and its center label is Z6. No role label was present during execution.

Blind session 8: generated witness

Witness SHA-256: 11ea683b57c91c7c2c6a126bfe00ab0474ff5a720e61a4fe5e68d2d29bbab488
Actual verdict: FAIL
Actual first failure: SG4-GNT-05

The exact matrix computation returned nullity 1 and candidate products [0, 0, 0, 0, 0, 0]. The primitive gcd was 1. The six anomaly sums were {'SU2_cubed_local': 0, 'SU2_squared_U1': 0, 'SU3_cubed': 0, 'SU3_squared_U1': 0, 'U1_cubed': 0, 'gravity_squared_U1': 0}. The fermion doublet count was 12, and the center enumeration found kernel order 6.

The actual verdict and first failure match the sealed expectation. Honest non-target consistency is kept separate from matching the Standard Model hypercharge ray.

SG3-to-SG4 dependency reducer

The frozen SG3 physical terminal is OPEN. There are 9 direct upstream and 5 SG4-local OPEN rows, for 14 total blockers. With no contradiction the reducer returns physical SG4 OPEN.

Conditional arithmetic does not mutate any row. A future closure attempt must attach new evidence to the exact row, change its status with justification, and replay the entire cumulative package.

Physical readiness row 1: SG3-SG4-D01

Status: OPEN
Requirement: Physical gauge-group realization

The charge generator and anomaly traces require physically realized SU(3), SU(2), and U(1) carriers; SG2 remains physically OPEN.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 2: SG3-SG4-D02

Status: OPEN
Requirement: Faithful global gauge group

The conditional Z6 kernel must be owned by the physical carrier actions and their complete character table before it is a global gauge-group theorem.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 3: SG3-SG4-D03

Status: OPEN
Requirement: Admitted one-copy chiral representation inventory

Q, u_c, d_c, L, e_c, and nu_c are still admitted one-copy inputs rather than physical kernels derived from the coupled operator.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 4: SG3-SG4-D04

Status: OPEN
Requirement: Three-family module and one-copy kernels

SG3 conditionally returns three copies and zero mirrors, but its family Actor and one-copy kernel ownership remain physically OPEN.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 5: SG3-SG4-D05

Status: OPEN
Requirement: Fermion domain, chirality, and mirror completeness

Anomaly sums are physical only after the self-adjoint chiral domain and the absence of uncounted boundary or mirror modes are executed.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 6: SG3-SG4-D06

Status: OPEN
Requirement: SG1 geometric realization lineage

The physical internal shape, admissibility, and operator construction inherited through SG2 and SG3 remain OPEN.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 7: SG3-SG4-D07

Status: OPEN
Requirement: Gauge-carrier action and ownership

Complete action, boundary, gauge-fixing, and ghost ownership for the gauge carriers has not reached physical PASS.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 8: SG3-SG4-D08

Status: OPEN
Requirement: Family Actor action ownership

The Hodge-singlet multiplicity module has a conditional arithmetic certificate but not a closed primitive action parent.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 9: SG3-SG4-D09

Status: OPEN
Requirement: No-excess state census

A complete physical census excluding extra light charged or chiral states has not been supplied.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 10: SG4-L01

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

The Yukawa and Majorana edges that define the ray are declared challenge inputs; their emergence from the completed action is not yet proved.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 11: SG4-L02

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

Primitive integer normalization fixes a charge lattice convention, not the dynamical normalization of the U(1) kinetic term or coupling.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 12: SG4-L03

Status: OPEN
Requirement: Regulated anomaly descent and heavy-mode completeness

The zero-mode sums vanish, but the regulated higher-dimensional determinant, inflow, counterterms, and heavy tower have not been executed.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 13: SG4-L04

Status: OPEN
Requirement: Global Z6 quotient realized by the compactification

The 36-element matter-kernel enumeration is exact, but the corresponding quotient has not been derived as the physical global gauge group.

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Physical readiness row 14: SG4-L05

Status: OPEN
Requirement: Independent reviewer-randomized gauntlet

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

This row is required by the cumulative physical reducer. It is not discharged by the conditional matrix, anomaly, Witten, or center calculation unless the new evidence directly proves the stated physical requirement. Its current OPEN status therefore contributes one unit to the controlling blocker count.

Building-block exhibit 1: BB_CAC_1_CHARGE_ANOMALY_AND_CENTER_CERTIFICATE

Artifact: BUILDING_BLOCKS/NEW_BLOCKS/BB_CAC_1_CHARGE_ANOMALY_AND_CENTER_CERTIFICATE.md
SHA-256: efce9563f669a03a31c7596bb2339feab159c1c01f753c5a8865d1cff117c2dd

block_id: BB-CAC-1 title: Charge, Anomaly, and Center Certificate version: 1.0-RC status: conditional-candidate-pass date: 2026-08-02 parent_authority: BB-SOT-2026-07-18-V1 upstream: SG3_UPDATED_BUILDING_BLOCKS_CUMULATIVE_FROM_SG2_2026-08-01

BB-CAC-1 — Charge, anomaly, and center certificate

Purpose

This block turns the SG4 charge claim into one replayable certificate. It prevents a document from supplying the charge vector it claims to derive, reporting anomaly cancellation without publishing conventions, including a scalar in the Witten test, or asserting a global quotient without enumerating the matter kernel.

Typed input contract

The certificate consumes:

1. an ordered field basis (Q,u_c,d_c,L,e_c,nu_c,H);
2. a labeled integer interaction matrix whose rows are the four Yukawa edges, the nu_c nu_c Majorana edge, and [SU(2)]^2 U(1) consistency;
3. one-copy chiral representations and family multiplicity from the cumulative SG3 interface;
4. a declared all-left-handed convention, including conjugate fields;
5. center characters for every matter representation and the Higgs doublet.

The matrix, row labels, field basis, and sign conventions are mandatory evidence. A quoted Smith normal form or nullspace dimension without the matrix is not sufficient.

Exact derivation reducer

Let M be the published 6 x 7 matrix and y the integer charge vector. The certificate must compute exact rational row reduction, the rank, and an integer nullspace basis. Conditional ray derivation passes only when

rank(M) = 6
dim ker_Z(M) = 1
ker_Z(M) = Z * (1,-4,2,-3,6,0,3)
M y = 0
gcd(nonzero entries of y) = 1

The gcd fixes a primitive lattice representative. It does not fix the U(1) kinetic-term normalization or the physical coupling.

Charge and anomaly ledger

The block requires Q_em=T3+Y, with Y=(6Y)/6, on every weak component. It then evaluates, using integer arithmetic, the six local four-dimensional channels:

SU(3)^3
SU(2)^3 local
SU(3)^2 U(1)
SU(2)^2 U(1)
gravity^2 U(1)
U(1)^3

Structural zeros must be labeled as such: the SU(2)^3 perturbative anomaly vanishes for pseudoreal doublets. It must not be confused with the global Witten obstruction. The Witten row counts only left-handed fermion doublets, including color copies of Q; scalars such as the Higgs are excluded.

Global quotient enumeration

Enumerate exactly

(a,b,k) in Z3 x Z2 x Z6

for the center element (omega_3^a,(-1)^b,exp(i*pi*k/3)). For a field of color triality t, doublet parity s, and integer charge q=6Y, the action is trivial precisely when

2 a t + 3 b s + k q = 0 mod 6.

All 36 rows and their per-field residues are evidence. The Standard Model assignment passes when the six trivial-action rows form the cyclic subgroup generated by (1,1,1). A claimed Z6 whose own table has another order fails.

Claim-scope firewall

An assignment may be anomaly-free without lying on the derived hypercharge ray. Such a candidate passes only if it claims exactly anomaly freedom. It fails if it claims the interaction graph derived it. Conditional consistency, target match, physical emergence, uniqueness, and nature-selection are separate terminals.

Output tuple

(matrix_hash, rank, integer_nullspace_basis, primitive_gcd,
 electric_charge_table, six_anomaly_sums, fermion_doublet_count,
 36_center_rows, kernel_order, first_hard_failure, claim_scope)

Current SG4 replay

The supplied execution produces the primitive ray (1,-4,2,-3,6,0,3), ten correct electric-charge state rows, six vanishing local channels, twelve fermion doublets for three families, and a cyclic order-six matter kernel. The result is a construction-anchor conditional PASS; physical SG4 remains OPEN.

Building-block exhibit 2: BB_CDR_1_CHARGE_DERIVATION_READINESS_AND_CUMULATIVE_DEPENDENCY

Artifact: BUILDING_BLOCKS/NEW_BLOCKS/BB_CDR_1_CHARGE_DERIVATION_READINESS_AND_CUMULATIVE_DEPENDENCY.md
SHA-256: 88fd81b5889cb34c64bab198b1c83b8f6f60b7371146b5387d07319e91898ddf

block_id: BB-CDR-1 title: Charge Derivation Readiness and Cumulative Dependency version: 1.0-RC status: open date: 2026-08-02 parent_authority: BB-SOT-2026-07-18-V1 upstream: SG3_UPDATED_BUILDING_BLOCKS_CUMULATIVE_FROM_SG2_2026-08-01

BB-CDR-1 — Charge derivation readiness and cumulative dependency

Purpose

This block prevents exact charge arithmetic from being mistaken for physical closure. It joins the frozen SG3 terminal to the local SG4 readiness ledger and returns the controlling physical result by an explicit reducer.

Upstream join

The consumed SG3 package has SHA-256 eedd26d63f0097c0d8ece86d95bdf268857290534eb10017bc66c41f31d47085. Its conditional three-family certificate passes, but its physical terminal is OPEN with nine blocking dependencies. SG4 cannot silently reset those rows.

The direct SG4 upstream interface preserves physical gauge realization, faithful global group, one-copy chiral inventory, three-family and mirror kernels, fermion domain, SG1 geometry, gauge-carrier action, family-Actor ownership, and a no-excess state census as nine OPEN rows.

Local physical readiness

Five additional rows are required:

1. the interaction graph must be derived from the completed physical action;
2. the U(1) generator and kinetic/coupling normalization must be owned;
3. regulated anomaly descent, inflow, counterterms, and the heavy tower must be shown complete;
4. the conditional Z6 matter kernel must be realized as the physical global quotient;
5. an independent reviewer-randomized gauntlet must be executed.

The primitive gcd solves only a lattice normalization. It cannot discharge the second row. Likewise, a vanishing four-dimensional zero-mode sum cannot by itself discharge the third row.

Reducer

if any required row is contradictory:
    physical_SG4 = FAIL
elif any required row is OPEN, NOT-EVALUATED, or CONSTRUCTION-ANCHOR:
    physical_SG4 = OPEN
else:
    physical_SG4 = PASS

Current counts are nine upstream and five local blocking rows. Therefore:

conditional_SG4_candidate = PASS
internal_reconstructed_gauntlet = PASS
reviewer_randomized_gauntlet = NOT-EVALUATED
physical_SG4 = OPEN
blocking_dependency_count = 14

Non-promotion rule

No successful matrix reduction, anomaly sum, parity test, or center enumeration may rewrite an OPEN physical terminal to PASS. Promotion requires new evidence tied to the exact readiness row, an updated dependency ledger, and replay of the cumulative package.

Building-block exhibit 3: BB_AD_1_SG4_EXACT_ANOMALY_LEDGER_AMENDMENT

Artifact: BUILDING_BLOCKS/AMENDMENTS/BB_AD_1_SG4_EXACT_ANOMALY_LEDGER_AMENDMENT.md
SHA-256: c18b73d0c92d2bb6026f75f6576971cc4093636889b8c5d762eead86b4699a45

amends: BB-AD-1 title: SG4 Exact Anomaly Ledger Amendment version: 1.2-RC date: 2026-08-02

BB-AD-1 SG4 amendment — exact anomaly ledger

The anomaly-descent block now requires a field-by-field, all-left-handed trace ledger before a four-dimensional cancellation claim is accepted. At minimum, the artifact publishes multiplicities, color/weak indices, integer 6Y, and the exact contributions to SU(3)^3, SU(2)^3 local, SU(3)^2U(1), SU(2)^2U(1), gravity^2U(1), and U(1)^3.

The global Witten test is a separate row. Its doublet count includes the three color copies of Q and the lepton doublet for each family, but never the Higgs or any scalar. Zero-mode cancellation is labeled conditional until the regulated higher-dimensional determinant, anomaly inflow, boundary terms, counterterms, and heavy-mode completeness have a physical witness.

This amendment preserves the prior SG3 family-kernel interpretation and adds a join key from every anomaly contribution to its representation and family kernel. Unjoined or excess light states keep physical SG4 OPEN.

Building-block exhibit 4: BB_MAP_1_SG4_CHARGE_RAY_PROVENANCE_AMENDMENT

Artifact: BUILDING_BLOCKS/AMENDMENTS/BB_MAP_1_SG4_CHARGE_RAY_PROVENANCE_AMENDMENT.md
SHA-256: 8dcf5465defc0c31257856ba96b585cd99e124ae852d9535474410fb3a7a5aa6

amends: BB-MAP-1 title: SG4 Charge-Ray Provenance Amendment version: 1.2-RC date: 2026-08-02

BB-MAP-1 SG4 amendment — charge-ray provenance

The vector (1,-4,2,-3,6,0,3) is a target-known construction anchor unless the interaction graph, Majorana edge, representation inventory, and [SU(2)]^2U(1) row have independent geometric provenance. Exact nullspace recovery proves that the declared equations determine the ray; it does not prove that shape uniquely generated those equations.

The required reporting split is:

Claim | Current terminal |

||| | Exact nullspace of the published matrix | PASS | | Primitive integer normalization | PASS | | Six local zero-mode anomaly sums | PASS | | Fermion-only Witten parity | PASS | | Conditional 36-element matter kernel | PASS | | Interaction graph derived from physical shape | OPEN | | Physical global quotient | OPEN | | Reviewer-randomized challenge | NOT-EVALUATED | | Nature-selection | NOT-CLAIMED |

An anomaly-free assignment outside the matrix ray is not a decoy merely for being different. It is an innocent control when it claims only anomaly freedom. It becomes a hard failure only when it claims derivation by equations it does not satisfy.

Building-block exhibit 5: SG4_BUILDING_BLOCK_FINDINGS

Artifact: BUILDING_BLOCKS/SG4_BUILDING_BLOCK_FINDINGS.md
SHA-256: eedfe482a6acab144bd201016b9f5dd49b45dc359e9fed3b8ac1be161cf6a129

SG-4 building-block findings

The SG3 cumulative blocks correctly prevent family multiplicity and admitted representation inputs from being silently treated as physical facts. SG4 exposed four additional reusable gaps: the lack of a mandatory published charge matrix, conflation of primitive lattice normalization with dynamical U(1) normalization, omission of a field-by-field center enumeration, and conflation of local anomaly cancellation with global and higher-dimensional anomaly closure.

BB-CAC-1 closes the conditional evidence-format gaps. BB-CDR-1 prevents that conditional result from promoting the physical terminal. The amendments to BB-AD-1 and BB-MAP-1 bind each calculation to exact conventions and to an honest construction-anchor provenance class.

The improved blocks catch the six supplied challenge defect types and accept a genuinely different anomaly-free assignment when it makes no ray-derivation claim. They also freeze the SG3 package and replay its internal manifest, so the cumulative lineage cannot be replaced by a summary sentence.

Building-block exhibit 6: SG4_SCOPE_RECONCILIATION

Artifact: BUILDING_BLOCKS/SG4_SCOPE_RECONCILIATION.md
SHA-256: 74e03d48f56707f96bdd34e14e4e2b15dc9075870e17cc0d5151e9632cc489fe

SG-4 scope reconciliation

Conditional result

Given the declared interaction graph, all-left-handed representation content, three-family multiplicity, and center characters, the executable certificate derives the primitive 6Y ray (1,-4,2,-3,6,0,3), reproduces Q_em=T3+Y, zeros six local anomaly channels, finds twelve fermion doublets, and enumerates a cyclic order-six matter kernel. This terminal is PASS.

Physical result

Physical SG4 is OPEN. Nine inherited readiness rows and five local rows have not passed. In particular, the interaction graph is a challenge input, not yet a consequence of a completed physical action; zero-mode trace cancellation is not the regulated higher-dimensional anomaly theorem; and the conditional matter kernel is not yet a derived global quotient of the compactification.

Explicit non-claims

• No claim that shape alone selected the interaction graph.
• No claim that primitive gcd fixes the U(1) gauge coupling.
• No claim that the reviewer-randomized gauntlet was executed.
• No claim that every possible anomaly-free U(1) assignment is excluded.
• No claim of nature-selection or full physical closure.

Execution validation summary

The independent verifier reports 18 controls PASS. It compiles the engine, executes it twice, requires byte-identical generated artifacts, parses every JSON file, replays the answer-key commitment and escrow, checks every exact physics terminal, freezes input hashes, applies the dependency reducer, and replays the extracted SG3 block manifest.

Execution validation control 01

Control: Engine and verifier compile
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 02

Control: Two byte-identical generated runs
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 03

Control: All generated JSON parses
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 04

Control: Answer-key commitment and escrow
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 05

Control: Eight blinded sessions and complete manifests
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 06

Control: Manifest and witness hash escrow
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 07

Control: All eight verdicts match sealed key
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 08

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

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 09

Control: Honest anomaly-free non-target assignment accepted
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 10

Control: Published matrix, exact nullspace, and primitive gcd
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 11

Control: Q=T3+Y table and all six local anomaly channels
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 12

Control: Fermion-only Witten count
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 13

Control: Full 36-element center enumeration reproduces Z6
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 14

Control: Conditional/physical status and provenance firewall
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 15

Control: Frozen input hashes
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 16

Control: Frozen cumulative SG3 package hash and ZIP integrity
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 17

Control: SG3-to-SG4 cumulative dependency reducer
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Execution validation control 18

Control: Extracted SG3 building-block manifest replay
Result: PASS

This control is part of the executable release boundary. Its PASS result is recorded in EXECUTION/VALIDATION_REPORT.json, whose own hash is incorporated into the final package manifests. Validation of an artifact does not promote the physical gate beyond the claim tested by that artifact.

Final controlling statement

The SG4 challenge is solved at the conditional certificate level. The exact interaction matrix yields the primitive hypercharge ray; Q_em=T3+Y is reconstructed state by state; six local anomaly channels vanish; the Witten fermion count is even with the Higgs excluded; and exhaustive center enumeration gives the cyclic matter kernel Z6. The internally reconstructed eight-session gauntlet passes every sealed comparison.

Full physical closure is not achieved. Physical SG3 is OPEN, and SG4 adds five local readiness debts. The controlling physical terminal is therefore SG4 PHYSICAL GATE: OPEN (14 blockers). The reviewer-randomized gauntlet is NOT-EVALUATED, and nature-selection is NOT-CLAIMED.

The new blocks preserve this distinction and state exactly what evidence would be required for promotion. They are saved as a cumulative successor archive with the upstream SG3 block package embedded and hash-frozen.