SG5 complete 50-100 page challenge solution - distinct revision 2.0

Gate: Electroweak breaking, the photon, vector masses, and tree-level rho
Document role: worked derivation and adversarial execution
Required terminal: CONDITIONAL ELECTROWEAK CERTIFICATE: PASS; PHYSICAL SG5: OPEN
Architecture rule: BB-DDR-1 dossier/solution separation
Date: 2026-08-03

Solution move 001 - Challenge statement

Solve this bounded question: Given the declared minimal Higgs doublet and neutral VEV, does the zero-mode mass matrix leave exactly one photon and reproduce the tree-level electroweak relations? The solution is restricted to the candidate, inputs, domains, and status grammar frozen by the cumulative building blocks. It is not allowed to fill an absent physical witness with conventional physics or to treat a known target as a prediction.

Move audit tag: SG5-SOLUTION-MOVE-001. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 002 - Permitted inputs

Use only the frozen status record, quantitative certificate, scope reconciliation, session manifests, and validation report named in the input manifest. A solution step may transform those records or derive an exact consequence; it may not edit their authority or import an unlisted repair.

Move audit tag: SG5-SOLUTION-MOVE-002. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 003 - Output contract

The worked result must end at CONDITIONAL ELECTROWEAK CERTIFICATE: PASS; PHYSICAL SG5: OPEN. Intermediate positive legs are reported at their actual scope, negative controls remain negative, and unresolved physical dependencies remain visible. The challenge solution is successful when it derives the scoped result honestly, not when it forces a global PASS.

Move audit tag: SG5-SOLUTION-MOVE-003. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 004 - Notation and ruler

Every symbol is evaluated in the basis, normalization, ordering, energy domain, branch, and representation chart declared by the certificate. Before comparing two quantities, the solution checks that they live on the same ruler. A convention change must be transported explicitly.

Move audit tag: SG5-SOLUTION-MOVE-004. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 005 - No-hidden-dial rule

A coefficient, representation, parity, graph, stabilization term, or measured anchor introduced after seeing the target is labeled as an input or construction anchor. Algebra performed after that input can be exact without making the input itself a derived prediction.

Move audit tag: SG5-SOLUTION-MOVE-005. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 006 - First-failure discipline

For every adversarial candidate, evaluation stops at the earliest violated rule. Later numerical agreement cannot repair a missing object, wrong domain, incomplete ruler, target-loaded input, or absent ownership record.

Move audit tag: SG5-SOLUTION-MOVE-006. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 007 - Freeze the scalar input

Operation 1. Use one complex multiplet with T=1/2 and Y=1/2; this representation is a gate input rather than a derived geometric theorem.

For operation 1, Freeze the scalar input, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-007. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 008 - Choose the neutral component

Operation 2. The lower component has T3=-1/2, so T3+Y=0 and the declared VEV is electrically neutral.

For operation 2, Choose the neutral component, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-008. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 009 - Expand the covariant derivative

Operation 3. Insert the VEV into |Dmu H| squared and keep the quadratic terms in W1, W2, W3, and B.

For operation 3, Expand the covariant derivative, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-009. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 010 - Read charged-vector masses

Operation 4. The W1 and W2 directions combine into W plus/minus with mW squared equal to g squared v squared over four.

For operation 4, Read charged-vector masses, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-010. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 011 - Assemble the neutral matrix

Operation 5. The W3-B block is proportional to v squared times [[g squared,-g gprime],[-g gprime,gprime squared]] over four.

For operation 5, Assemble the neutral matrix, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-011. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 012 - Find the null direction

Operation 6. The neutral matrix determinant is zero and its kernel is the photon direction proportional to (gprime,g).

For operation 6, Find the null direction, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-012. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 013 - Find the massive neutral direction

Operation 7. The orthogonal eigenvector has mZ squared=(g squared+gprime squared)v squared over four.

For operation 7, Find the massive neutral direction, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-013. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 014 - Count massless vectors

Operation 8. Exactly one neutral zero eigenvalue survives; the charged vectors and the orthogonal Z direction are massive.

For operation 8, Count massless vectors, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-014. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 015 - Evaluate rho

Operation 9. With cos squared thetaW=g squared/(g squared+gprime squared), mW squared divided by mZ squared cos squared thetaW is one.

For operation 9, Evaluate rho, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-015. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 016 - Classify vEW

Operation 10. The numerical electroweak scale is a MEASURED-ANCHOR calibration, not a prediction from the internal shape.

For operation 10, Classify vEW, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-016. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 017 - Exclude invented mechanisms

Operation 11. Custodial symmetry, a winding Higgs, loop rho0 agreement, and a geometry head-to-head victory are not claimed.

For operation 11, Exclude invented mechanisms, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-017. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 018 - Reduce readiness

Operation 12. Fourteen inherited and five local dependencies keep physical SG5 OPEN.

For operation 12, Reduce readiness, the move is accepted only on the frozen SG5 object. Its output feeds the next operation but does not widen the terminal. A reviewer should recompute the stated equality, count, spectrum, kernel, or reducer transition from the cited certificate. If the operation depends on a declared input, the output is conditional on that input. If the operation exposes a negative eigenvalue, missing artifact, or open dependency, the failure is retained rather than averaged away.

Move audit tag: SG5-SOLUTION-MOVE-018. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 019 - Execution control 01: Engine and verifier compile

The execution harness evaluates Engine and verifier compile. Its frozen result is PASS with recorded detail {"control":"Engine and verifier compile","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 1, Engine and verifier compile, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-019. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 020 - Execution control 02: Two byte-identical generated runs

The execution harness evaluates Two byte-identical generated runs. Its frozen result is PASS with recorded detail {"artifact_count":22,"control":"Two byte-identical generated runs","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 2, Two byte-identical generated runs, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-020. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 021 - Execution control 03: All generated JSON parses

The execution harness evaluates All generated JSON parses. Its frozen result is PASS with recorded detail {"control":"All generated JSON parses","json_count":21,"result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 3, All generated JSON parses, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-021. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 022 - Execution control 04: Answer-key commitment and escrow

The execution harness evaluates Answer-key commitment and escrow. Its frozen result is PASS with recorded detail {"control":"Answer-key commitment and escrow","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 4, Answer-key commitment and escrow, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-022. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 023 - Execution control 05: Seven blinded sessions and complete manifests

The execution harness evaluates Seven blinded sessions and complete manifests. Its frozen result is PASS with recorded detail {"control":"Seven blinded sessions and complete manifests","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 5, Seven blinded sessions and complete manifests, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-023. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 024 - Execution control 06: Manifest and witness hash escrow

The execution harness evaluates Manifest and witness hash escrow. Its frozen result is PASS with recorded detail {"control":"Manifest and witness hash escrow","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 6, Manifest and witness hash escrow, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-024. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 025 - Execution control 07: All seven verdicts match sealed key

The execution harness evaluates All seven verdicts match sealed key. Its frozen result is PASS with recorded detail {"control":"All seven verdicts match sealed key","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 7, All seven verdicts match sealed key, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-025. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 026 - Execution control 08: Five challenge decoys caught at intended first failures

The execution harness evaluates Five challenge decoys caught at intended first failures. Its frozen result is PASS with recorded detail {"control":"Five challenge decoys caught at intended first failures","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 8, Five challenge decoys caught at intended first failures, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-026. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 027 - Execution control 09: Honest triplet rho=1/2 non-target accepted

The execution harness evaluates Honest triplet rho=1/2 non-target accepted. Its frozen result is PASS with recorded detail {"control":"Honest triplet rho=1/2 non-target accepted","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 9, Honest triplet rho=1/2 non-target accepted, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-027. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 028 - Execution control 10: Frozen SG4 Q=T3+Y table replay

The execution harness evaluates Frozen SG4 Q=T3+Y table replay. Its frozen result is PASS with recorded detail {"control":"Frozen SG4 Q=T3+Y table replay","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 10, Frozen SG4 Q=T3+Y table replay, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-028. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 029 - Execution control 11: Minimal doublet state table and neutral VEV

The execution harness evaluates Minimal doublet state table and neutral VEV. Its frozen result is PASS with recorded detail {"control":"Minimal doublet state table and neutral VEV","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 11, Minimal doublet state table and neutral VEV, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-029. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 030 - Execution control 12: Covariant-derivative mass matrix and one massless photon

The execution harness evaluates Covariant-derivative mass matrix and one massless photon. Its frozen result is PASS with recorded detail {"control":"Covariant-derivative mass matrix and one massless photon","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 12, Covariant-derivative mass matrix and one massless photon, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-030. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 031 - Execution control 13: Exact eigenvalues, weak mixing, and rho_tree=1

The execution harness evaluates Exact eigenvalues, weak mixing, and rho_tree=1. Its frozen result is PASS with recorded detail {"control":"Exact eigenvalues, weak mixing, and rho_tree=1","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 13, Exact eigenvalues, weak mixing, and rho_tree=1, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-031. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 032 - Execution control 14: rho0, custodial, winding, and geometry-test nonclaims

The execution harness evaluates rho0, custodial, winding, and geometry-test nonclaims. Its frozen result is PASS with recorded detail {"control":"rho0, custodial, winding, and geometry-test nonclaims","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 14, rho0, custodial, winding, and geometry-test nonclaims, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-032. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 033 - Execution control 15: Conditional/physical status and measured-anchor firewall

The execution harness evaluates Conditional/physical status and measured-anchor firewall. Its frozen result is PASS with recorded detail {"control":"Conditional/physical status and measured-anchor firewall","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 15, Conditional/physical status and measured-anchor firewall, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-033. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 034 - Execution control 16: Frozen input hashes

The execution harness evaluates Frozen input hashes. Its frozen result is PASS with recorded detail {"control":"Frozen input hashes","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 16, Frozen input hashes, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-034. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 035 - Execution control 17: Frozen SG4 package integrity and extracted manifest replay

The execution harness evaluates Frozen SG4 package integrity and extracted manifest replay. Its frozen result is PASS with recorded detail {"control":"Frozen SG4 package integrity and extracted manifest replay","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 17, Frozen SG4 package integrity and extracted manifest replay, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-035. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 036 - Execution control 18: SG4-to-SG5 cumulative dependency reducer

The execution harness evaluates SG4-to-SG5 cumulative dependency reducer. Its frozen result is PASS with recorded detail {"control":"SG4-to-SG5 cumulative dependency reducer","result":"PASS"}. This challenge page explains how the result constrains the worked solution: the computation must reproduce the same first failure, candidate output, and scope label after the answer key is opened.

A PASS on execution control 18, SG4-to-SG5 cumulative dependency reducer, certifies the named harness behavior only. It cannot supply an absent parent action, independent reviewer packet, full tower, covariance matrix, or nature-selection theorem unless this particular control explicitly owns that evidence. The unique control address prevents a generic validation paragraph from being reused as evidence.

Move audit tag: SG5-SOLUTION-MOVE-036. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 037 - Blind-session replay 01: session-bdb2d5c6c41e801565c6

Session session-bdb2d5c6c41e801565c6 is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 1 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-037. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 038 - Blind-session replay 02: session-d61f1c18a74cc1549c86

Session session-d61f1c18a74cc1549c86 is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 2 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-038. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 039 - Blind-session replay 03: session-4394de2407e67260d2a2

Session session-4394de2407e67260d2a2 is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 3 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-039. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 040 - Blind-session replay 04: session-c248ad12d6102c0dc0ac

Session session-c248ad12d6102c0dc0ac is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 4 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-040. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 041 - Blind-session replay 05: session-c35779b994fc1c059377

Session session-c35779b994fc1c059377 is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 5 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-041. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 042 - Blind-session replay 06: session-d77abfd072df366a38c6

Session session-d77abfd072df366a38c6 is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 6 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-042. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 043 - Blind-session replay 07: session-fb178c195ceae4070ecf

Session session-fb178c195ceae4070ecf is evaluated under the sealed order for SG5. Recompute its manifest from the frozen input hash, apply the rules in order, and compare the actual verdict with escrow only after the witness has been committed. The session contributes to internal reconstructed execution, not to an independent reviewer-issued trial.

The challenge solution records session 7 separately so missing, duplicated, or reordered manifests are detectable. A complete match supports the harness terminal; a mismatch reopens the execution leg while leaving unrelated analytical identities untouched.

Move audit tag: SG5-SOLUTION-MOVE-043. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 044 - Closure boundary 01: SG5-L01

After the scoped calculation finishes, dependency SG5-L01 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 1, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-044. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 045 - Closure boundary 02: SG5-L02

After the scoped calculation finishes, dependency SG5-L02 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 2, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-045. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 046 - Closure boundary 03: SG5-L03

After the scoped calculation finishes, dependency SG5-L03 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 3, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-046. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 047 - Closure boundary 04: SG5-L04

After the scoped calculation finishes, dependency SG5-L04 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 4, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-047. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 048 - Closure boundary 05: SG5-L05

After the scoped calculation finishes, dependency SG5-L05 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 5, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-048. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 049 - Closure boundary 06: SG4-SG5-D01

After the scoped calculation finishes, dependency SG4-SG5-D01 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 6, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-049. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 050 - Closure boundary 07: SG4-SG5-D02

After the scoped calculation finishes, dependency SG4-SG5-D02 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 7, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-050. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 051 - Closure boundary 08: SG4-SG5-D03

After the scoped calculation finishes, dependency SG4-SG5-D03 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 8, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-051. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 052 - Closure boundary 09: SG4-SG5-D04

After the scoped calculation finishes, dependency SG4-SG5-D04 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 9, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-052. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 053 - Closure boundary 10: SG4-SG5-D05

After the scoped calculation finishes, dependency SG4-SG5-D05 remains in the reducer. The worked solution therefore stops before physical closure. This is not an algebraic error: it is the correct propagation of an unpaid evidence interface.

To remove blocker 10, a successor must provide the artifact and validation contract owned by the upstream or local building block, then rerun the cumulative reducer. The present solution does not invent that artifact and does not hide the row in an appendix.

Move audit tag: SG5-SOLUTION-MOVE-053. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 054 - Hostile variant 01: Freeze the scalar input

This hostile variant alters the assumptions surrounding Freeze the scalar input while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Use one complex multiplet with T=1/2 and Y=1/2; this representation is a gate input rather than a derived geometric theorem. Variant 1 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 1 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-054. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 055 - Hostile variant 02: Choose the neutral component

This hostile variant alters the assumptions surrounding Choose the neutral component while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The lower component has T3=-1/2, so T3+Y=0 and the declared VEV is electrically neutral. Variant 2 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 2 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-055. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 056 - Hostile variant 03: Expand the covariant derivative

This hostile variant alters the assumptions surrounding Expand the covariant derivative while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Insert the VEV into |Dmu H| squared and keep the quadratic terms in W1, W2, W3, and B. Variant 3 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 3 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-056. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 057 - Hostile variant 04: Read charged-vector masses

This hostile variant alters the assumptions surrounding Read charged-vector masses while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The W1 and W2 directions combine into W plus/minus with mW squared equal to g squared v squared over four. Variant 4 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 4 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-057. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 058 - Hostile variant 05: Assemble the neutral matrix

This hostile variant alters the assumptions surrounding Assemble the neutral matrix while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The W3-B block is proportional to v squared times [[g squared,-g gprime],[-g gprime,gprime squared]] over four. Variant 5 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 5 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-058. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 059 - Hostile variant 06: Find the null direction

This hostile variant alters the assumptions surrounding Find the null direction while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The neutral matrix determinant is zero and its kernel is the photon direction proportional to (gprime,g). Variant 6 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 6 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-059. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 060 - Hostile variant 07: Find the massive neutral direction

This hostile variant alters the assumptions surrounding Find the massive neutral direction while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The orthogonal eigenvector has mZ squared=(g squared+gprime squared)v squared over four. Variant 7 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 7 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-060. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 061 - Hostile variant 08: Count massless vectors

This hostile variant alters the assumptions surrounding Count massless vectors while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Exactly one neutral zero eigenvalue survives; the charged vectors and the orthogonal Z direction are massive. Variant 8 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 8 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-061. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 062 - Hostile variant 09: Evaluate rho

This hostile variant alters the assumptions surrounding Evaluate rho while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: With cos squared thetaW=g squared/(g squared+gprime squared), mW squared divided by mZ squared cos squared thetaW is one. Variant 9 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 9 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-062. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 063 - Hostile variant 10: Classify vEW

This hostile variant alters the assumptions surrounding Classify vEW while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The numerical electroweak scale is a MEASURED-ANCHOR calibration, not a prediction from the internal shape. Variant 10 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 10 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-063. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 064 - Hostile variant 11: Exclude invented mechanisms

This hostile variant alters the assumptions surrounding Exclude invented mechanisms while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Custodial symmetry, a winding Higgs, loop rho0 agreement, and a geometry head-to-head victory are not claimed. Variant 11 is rejected if it changes the basis, domain, parent, branch, measured-anchor class, or comparison ruler without a new authority record.

The purpose of hostile variant 11 is diagnostic. A robust solution must distinguish a lawful re-expression from a new candidate and must stop at the first unauthorized change. This numbered variant does not modify the controlling SG5 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG5-SOLUTION-MOVE-064. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.

Solution move 065 - Final answer

The bounded challenge has been solved without importing a hidden witness. The exact computations and reconstructed execution retain their certified results, while the cumulative reducer preserves every physical dependency and reviewer boundary. The final answer is CONDITIONAL ELECTROWEAK CERTIFICATE: PASS; PHYSICAL SG5: OPEN. This is the strongest lawful conclusion supported by the frozen package, and no nature-selection claim is added.

Move audit tag: SG5-SOLUTION-MOVE-065. This page is independently addressable in the worked chain. Its premise, operation, output, and failure boundary must be checked before the next numbered move is accepted.