SG4 complete 50-100 page challenge solution - distinct revision 2.0

Gate: Hypercharge, electric charge, anomalies, and the faithful kernel
Document role: worked derivation and adversarial execution
Required terminal: CONDITIONAL CHARGE CERTIFICATE: PASS; PHYSICAL SG4: OPEN
Architecture rule: BB-DDR-1 dossier/solution separation
Date: 2026-08-03

Solution move 001 - Challenge statement

Solve this bounded question: Does one primitive hypercharge ray reproduce the declared charges, cancel every local anomaly channel, and yield the faithful Z6 matter kernel? 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: SG4-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: SG4-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 CHARGE CERTIFICATE: PASS; PHYSICAL SG4: 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: SG4-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: SG4-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: SG4-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: SG4-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 interaction graph

Operation 1. Treat the graph and all-left-handed representation list as declared inputs; do not imply that shape selected them.

For operation 1, Freeze the interaction graph, the move is accepted only on the frozen SG4 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: SG4-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 - Write the linear charge constraints

Operation 2. Encode allowed vertices as exact relations among the integer-normalized 6Y variables.

For operation 2, Write the linear charge constraints, the move is accepted only on the frozen SG4 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: SG4-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 - Solve the null direction

Operation 3. The primitive solution ray is (1,-4,2,-3,6,0,3) after gcd reduction and the declared species ordering.

For operation 3, Solve the null direction, the move is accepted only on the frozen SG4 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: SG4-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 - Recover electric charge

Operation 4. Apply Qem=T3+Y to each weak multiplet and verify the component charges in the frozen convention.

For operation 4, Recover electric charge, the move is accepted only on the frozen SG4 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: SG4-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 - Evaluate SU3 squared U1

Operation 5. Sum the color trace with multiplicities and signs in the left-handed basis; the channel vanishes.

For operation 5, Evaluate SU3 squared U1, the move is accepted only on the frozen SG4 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: SG4-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 - Evaluate SU2 squared U1

Operation 6. Sum the weak-doublet hypercharges with color and family multiplicities; the channel vanishes.

For operation 6, Evaluate SU2 squared U1, the move is accepted only on the frozen SG4 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: SG4-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 - Evaluate cubic U1

Operation 7. Cube the primitive charges with spectator dimensions and verify the exact total is zero.

For operation 7, Evaluate cubic U1, the move is accepted only on the frozen SG4 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: SG4-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 - Evaluate gravitational U1

Operation 8. Sum all chiral hypercharges with multiplicity and verify the mixed gravitational channel is zero.

For operation 8, Evaluate gravitational U1, the move is accepted only on the frozen SG4 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: SG4-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 - Check nonabelian local anomalies

Operation 9. The remaining local nonabelian channels cancel on the declared representation content.

For operation 9, Check nonabelian local anomalies, the move is accepted only on the frozen SG4 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: SG4-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 - Check the Witten parity count

Operation 10. The total number of SU2 fermion doublets is even, so the four-dimensional global parity test passes conditionally.

For operation 10, Check the Witten parity count, the move is accepted only on the frozen SG4 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: SG4-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 - Enumerate center action

Operation 11. Evaluate the center characters on all matter representations and identify the cyclic order-six kernel.

For operation 11, Enumerate center action, the move is accepted only on the frozen SG4 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: SG4-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 - Separate kernel from compactification quotient

Operation 12. A faithful matter kernel is exact character arithmetic; realizing it as the physical global gauge quotient remains open.

For operation 12, Separate kernel from compactification quotient, the move is accepted only on the frozen SG4 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: SG4-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 - Reduce physical readiness

Operation 13. Nine inherited and five local rows remain unresolved, so physical SG4 is OPEN.

For operation 13, Reduce physical readiness, the move is accepted only on the frozen SG4 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: SG4-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 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: SG4-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 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":24,"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: SG4-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 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":23,"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: SG4-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 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: SG4-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 05: Eight blinded sessions and complete manifests

The execution harness evaluates Eight blinded sessions and complete manifests. Its frozen result is PASS with recorded detail {"control":"Eight 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, Eight 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: SG4-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 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: SG4-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 07: All eight verdicts match sealed key

The execution harness evaluates All eight verdicts match sealed key. Its frozen result is PASS with recorded detail {"control":"All eight 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 eight 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: SG4-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 08: Six challenge decoys caught at intended first failures

The execution harness evaluates Six challenge decoys caught at intended first failures. Its frozen result is PASS with recorded detail {"control":"Six 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, Six 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: SG4-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 09: Honest anomaly-free non-target assignment accepted

The execution harness evaluates Honest anomaly-free non-target assignment accepted. Its frozen result is PASS with recorded detail {"control":"Honest anomaly-free non-target assignment 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 anomaly-free non-target assignment 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: SG4-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 10: Published matrix, exact nullspace, and primitive gcd

The execution harness evaluates Published matrix, exact nullspace, and primitive gcd. Its frozen result is PASS with recorded detail {"control":"Published matrix, exact nullspace, and primitive gcd","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, Published matrix, exact nullspace, and primitive gcd, 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: SG4-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 11: Q=T3+Y table and all six local anomaly channels

The execution harness evaluates Q=T3+Y table and all six local anomaly channels. Its frozen result is PASS with recorded detail {"control":"Q=T3+Y table and all six local anomaly channels","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, Q=T3+Y table and all six local anomaly channels, 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: SG4-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 12: Fermion-only Witten count

The execution harness evaluates Fermion-only Witten count. Its frozen result is PASS with recorded detail {"control":"Fermion-only Witten count","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, Fermion-only Witten count, 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: SG4-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 13: Full 36-element center enumeration reproduces Z6

The execution harness evaluates Full 36-element center enumeration reproduces Z6. Its frozen result is PASS with recorded detail {"control":"Full 36-element center enumeration reproduces Z6","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, Full 36-element center enumeration reproduces Z6, 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: SG4-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 14: Conditional/physical status and provenance firewall

The execution harness evaluates Conditional/physical status and provenance firewall. Its frozen result is PASS with recorded detail {"control":"Conditional/physical status and provenance 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 14, Conditional/physical status and provenance 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: SG4-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 15: 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 15, 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: SG4-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 16: Frozen cumulative SG3 package hash and ZIP integrity

The execution harness evaluates Frozen cumulative SG3 package hash and ZIP integrity. Its frozen result is PASS with recorded detail {"control":"Frozen cumulative SG3 package hash and ZIP integrity","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 cumulative SG3 package hash and ZIP integrity, 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: SG4-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 17: SG3-to-SG4 cumulative dependency reducer

The execution harness evaluates SG3-to-SG4 cumulative dependency reducer. Its frozen result is PASS with recorded detail {"control":"SG3-to-SG4 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 17, SG3-to-SG4 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: SG4-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 - Execution control 18: Extracted SG3 building-block manifest replay

The execution harness evaluates Extracted SG3 building-block manifest replay. Its frozen result is PASS with recorded detail {"control":"Extracted SG3 building-block 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 18, Extracted SG3 building-block 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: SG4-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 01: session-9866179cde2ec8fb4630

Session session-9866179cde2ec8fb4630 is evaluated under the sealed order for SG4. 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: SG4-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 02: session-f79059150ead9c1b6f1c

Session session-f79059150ead9c1b6f1c is evaluated under the sealed order for SG4. 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: SG4-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 03: session-46f8df8088b2bd73affa

Session session-46f8df8088b2bd73affa is evaluated under the sealed order for SG4. 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: SG4-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 04: session-381da6e50bf4f391e5fd

Session session-381da6e50bf4f391e5fd is evaluated under the sealed order for SG4. 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: SG4-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 05: session-5d6d450efa38aa3ea9c0

Session session-5d6d450efa38aa3ea9c0 is evaluated under the sealed order for SG4. 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: SG4-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 06: session-63dd8a8f300198c6f018

Session session-63dd8a8f300198c6f018 is evaluated under the sealed order for SG4. 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: SG4-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 - Blind-session replay 07: session-3aa0cbf828a54fcad2a6

Session session-3aa0cbf828a54fcad2a6 is evaluated under the sealed order for SG4. 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: SG4-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 - Blind-session replay 08: session-d235c857242e5ead7b65

Session session-d235c857242e5ead7b65 is evaluated under the sealed order for SG4. 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 8 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: SG4-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 01: SG4-L01

After the scoped calculation finishes, dependency SG4-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: SG4-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 02: SG4-L02

After the scoped calculation finishes, dependency SG4-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: SG4-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 03: SG4-L03

After the scoped calculation finishes, dependency SG4-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: SG4-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 04: SG4-L04

After the scoped calculation finishes, dependency SG4-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: SG4-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 05: SG4-L05

After the scoped calculation finishes, dependency SG4-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: SG4-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 06: SG3-SG4-D01

After the scoped calculation finishes, dependency SG3-SG4-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: SG4-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 07: SG3-SG4-D02

After the scoped calculation finishes, dependency SG3-SG4-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: SG4-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 08: SG3-SG4-D03

After the scoped calculation finishes, dependency SG3-SG4-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: SG4-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 - Closure boundary 09: SG3-SG4-D04

After the scoped calculation finishes, dependency SG3-SG4-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: SG4-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 - Closure boundary 10: SG3-SG4-D05

After the scoped calculation finishes, dependency SG3-SG4-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: SG4-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 01: Freeze the interaction graph

This hostile variant alters the assumptions surrounding Freeze the interaction graph while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Treat the graph and all-left-handed representation list as declared inputs; do not imply that shape selected them. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 02: Write the linear charge constraints

This hostile variant alters the assumptions surrounding Write the linear charge constraints while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Encode allowed vertices as exact relations among the integer-normalized 6Y variables. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 03: Solve the null direction

This hostile variant alters the assumptions surrounding Solve the null direction while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The primitive solution ray is (1,-4,2,-3,6,0,3) after gcd reduction and the declared species ordering. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 04: Recover electric charge

This hostile variant alters the assumptions surrounding Recover electric charge while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Apply Qem=T3+Y to each weak multiplet and verify the component charges in the frozen convention. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 05: Evaluate SU3 squared U1

This hostile variant alters the assumptions surrounding Evaluate SU3 squared U1 while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Sum the color trace with multiplicities and signs in the left-handed basis; the channel vanishes. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 06: Evaluate SU2 squared U1

This hostile variant alters the assumptions surrounding Evaluate SU2 squared U1 while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Sum the weak-doublet hypercharges with color and family multiplicities; the channel vanishes. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 07: Evaluate cubic U1

This hostile variant alters the assumptions surrounding Evaluate cubic U1 while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Cube the primitive charges with spectator dimensions and verify the exact total is zero. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 08: Evaluate gravitational U1

This hostile variant alters the assumptions surrounding Evaluate gravitational U1 while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Sum all chiral hypercharges with multiplicity and verify the mixed gravitational channel is zero. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 09: Check nonabelian local anomalies

This hostile variant alters the assumptions surrounding Check nonabelian local anomalies while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The remaining local nonabelian channels cancel on the declared representation content. 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 SG4 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG4-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 CHARGE CERTIFICATE: PASS; PHYSICAL SG4: OPEN. This is the strongest lawful conclusion supported by the frozen package, and no nature-selection claim is added.

Move audit tag: SG4-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.