SG2 complete 50-100 page challenge solution - distinct revision 3.0

Gate: Gauge group and massless-vector carrier accounting
Document role: worked derivation and adversarial execution
Required terminal: CONDITIONAL CANDIDATE: PASS; PHYSICAL SG2: OPEN
Architecture rule: BB-DDR-1 dossier/solution separation
Date: 2026-08-03

Solution move 001 - Challenge statement

Solve this bounded question: Does the locked internal carrier reproduce the Standard Model gauge algebra and faithful quotient with every massless vector direction paid for exactly once? 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: SG2-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: SG2-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 CANDIDATE: PASS; PHYSICAL SG2: 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: SG2-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: SG2-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: SG2-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: SG2-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 - Identify the color carrier

Operation 1. Read the K6 connected Killing algebra as su(3), giving dimension eight and rank two under the frozen metric carrier declaration.

For operation 1, Identify the color carrier, the move is accepted only on the frozen SG2 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: SG2-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 - Identify the weak carrier

Operation 2. Use the round S2 connected Killing algebra su(2), contributing three vector directions and rank one.

For operation 2, Identify the weak carrier, the move is accepted only on the frozen SG2 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: SG2-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 - Exclude an interval vector

Operation 3. The connected interval Killing dimension is zero after the boundary/orbifold rulebook is imposed.

For operation 3, Exclude an interval vector, the move is accepted only on the frozen SG2 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: SG2-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 - Admit hypercharge once

Operation 4. The independent principal U(1)Y connection supplies exactly one even vector zero mode and rank one.

For operation 4, Admit hypercharge once, the move is accepted only on the frozen SG2 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: SG2-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 - Add dimensions

Operation 5. The paid vector count is 8+3+0+1=12; no other p-form or boundary vector zero modes are declared.

For operation 5, Add dimensions, the move is accepted only on the frozen SG2 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: SG2-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 - Add ranks

Operation 6. The carrier ranks sum to 2+1+0+1=4, matching the target algebra without a duplicate abelian direction.

For operation 6, Add ranks, the move is accepted only on the frozen SG2 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: SG2-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 - Audit ownership

Operation 7. Color, weak, and hypercharge each have one declared parent, so no direction is counted under two geometric stories.

For operation 7, Audit ownership, the move is accepted only on the frozen SG2 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: SG2-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 center characters

Operation 8. Apply 2 triality a + 3 doublet b + y6 k = 0 mod 6 to the imported matter-character packet.

For operation 8, Evaluate center characters, the move is accepted only on the frozen SG2 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: SG2-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 - Enumerate the kernel

Operation 9. The 36 center tuples contain six kernel elements generated cyclically, establishing the conditional Z6 label.

For operation 9, Enumerate the kernel, the move is accepted only on the frozen SG2 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: SG2-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 Smith form

Operation 10. The lifted relation matrix has invariants (1,1,6), independently confirming a cyclic group of order six.

For operation 10, Check Smith form, the move is accepted only on the frozen SG2 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: SG2-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 - Apply the no-extra test

Operation 11. Missing vectors and extra vectors both evaluate to zero on the frozen manifest.

For operation 11, Apply the no-extra test, the move is accepted only on the frozen SG2 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: SG2-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 dependencies

Operation 12. Nine direct SG1 V3 rows remain OPEN, so the conditional arithmetic cannot promote the physical gate.

For operation 12, Reduce dependencies, the move is accepted only on the frozen SG2 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: SG2-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 compiles

The execution harness evaluates Engine compiles. Its frozen result is PASS with recorded detail null. 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 compiles, 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: SG2-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 {"engine_stdout":"{\"all_matches\": true, \"decoys\": 5, \"dimension\": 12, \"extras\": 0, \"innocents\": 2, \"kernel\": \"Z6\", \"rank\": 4, \"sessions\": 8}","file_count":24}. 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: SG2-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 JSON parses

The execution harness evaluates All JSON parses. Its frozen result is PASS with recorded detail {"errors":[],"json_file_count":23}. 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 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: SG2-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 "af4676da2873f26843918dffd27f028d0062590fde797dd094e13639fd0395c5". 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: SG2-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: All session verdicts match sealed key

The execution harness evaluates All session verdicts match sealed key. Its frozen result is PASS with recorded detail {"decoys":5,"sessions":8}. 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, All session 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: SG2-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: Every planted historical defect caught exactly once

The execution harness evaluates Every planted historical defect caught exactly once. Its frozen result is PASS with recorded detail ["SG2-GNT-01","SG2-GNT-02","SG2-GNT-03","SG2-GNT-04","SG2-GNT-05"]. 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, Every planted historical defect caught exactly once, 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: SG2-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: Honest non-SM candidates fail only SM-match row

The execution harness evaluates Honest non-SM candidates fail only SM-match row. Its frozen result is PASS with recorded detail ["session-37f6ea093d2cac15c5e9","session-fcebce2758592a4bbbbb"]. 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, Honest non-SM candidates fail only SM-match row, 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: SG2-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: Vector-sector terminal reproduces 12, rank 4, Z6, zero extras

The execution harness evaluates Vector-sector terminal reproduces 12, rank 4, Z6, zero extras. Its frozen result is PASS with recorded detail {"dimension":12,"extras":0,"kernel":"Z6","rank":4}. 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, Vector-sector terminal reproduces 12, rank 4, Z6, zero extras, 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: SG2-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: Smith certificate is exact

The execution harness evaluates Smith certificate is exact. Its frozen result is PASS with recorded detail {"basis_convention":"center tuple (a mod 3, b mod 2, k mod 6)","domain_relation_D":[[3,0,0],[0,2,0],[0,0,6]],"kernel_group":"Z6","kernel_lift_basis_B":[[1,3,0],[1,0,2],[1,0,0]],"phase_rule":"2*triality*a + 3*doublet*b + y6*k = 0 mod 6","quotient_relation_M":[[0,0,6],[1,0,-2],[0,1,-3]],"smith_invariants":[1,1,6],"verified_B_times_M_equals_D":true}. 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, Smith certificate is exact, 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: SG2-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: Every incumbent carrier has one declared parent

The execution harness evaluates Every incumbent carrier has one declared parent. Its frozen result is PASS with recorded detail {"color":["metric:K6"],"hypercharge":["independent-principal-U1Y"],"weak":["metric:S2"]}. 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, Every incumbent carrier has one declared parent, 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: SG2-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: Frozen session and witness set is exact

The execution harness evaluates Frozen session and witness set is exact. Its frozen result is PASS with recorded detail {"sessions":8,"witnesses":8}. 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, Frozen session and witness set is exact, 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: SG2-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: Status and scope firewall

The execution harness evaluates Status and scope firewall. Its frozen result is PASS with recorded detail {"blocking_dependencies":["SG1-O01","SG1-O02","SG1-O03","SG1-O05","SG1-O06","SG1-O07","SG1-O09","SG1-O10","SG1-O11"],"candidate_scope":"declared locked massless-vector manifest plus imported matter-character kernel","conditional_candidate_certificate":"PASS","direct_upstream_open_count":9,"internal_reconstructed_gauntlet":"PASS","nature_selection_claimed":false,"physical_gate_status":"OPEN","provenance_class":"con.... 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, Status and scope 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: SG2-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: Frozen SOT22 input hash

The execution harness evaluates Frozen SOT22 input hash. Its frozen result is PASS with recorded detail "78e42a81536b1b1c2af79e63ba291eeea1be8767c7421833f36b96da537a031d". 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, Frozen SOT22 input hash, 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: SG2-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: Frozen SG1 V3 package hash

The execution harness evaluates Frozen SG1 V3 package hash. Its frozen result is PASS with recorded detail "858b08c9186bb8f6ca7010937b7a9d7c61dd51369e27cc844a2536ea3b9cb7bf". 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, Frozen SG1 V3 package hash, 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: SG2-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: SG1-to-SG2 dependency reducer

The execution harness evaluates SG1-to-SG2 dependency reducer. Its frozen result is PASS with recorded detail {"direct_rows":["SG1-O01","SG1-O02","SG1-O03","SG1-O05","SG1-O06","SG1-O07","SG1-O09","SG1-O10","SG1-O11"],"physical_gate":"OPEN"}. 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, SG1-to-SG2 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: SG2-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: SG1 V3 validator replay

The execution harness evaluates SG1 V3 validator replay. Its frozen result is PASS with recorded detail "VALIDATION PASS\nrows=18 open=18 work_packages=8 mutations=10/10\ngate=OPEN\nregistry_canonical_sha256=37ec18346b5b236d8027902d029940e9abfbadc6d6c75e867378956f818e2c8e". 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, SG1 V3 validator 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: SG2-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 - Blind-session replay 01: session-fcebce2758592a4bbbbb

Session session-fcebce2758592a4bbbbb is evaluated under the sealed order for SG2. 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: SG2-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 - Blind-session replay 02: session-590e8c8330106fe8315b

Session session-590e8c8330106fe8315b is evaluated under the sealed order for SG2. 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: SG2-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 03: session-69b5108731469c3ae360

Session session-69b5108731469c3ae360 is evaluated under the sealed order for SG2. 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: SG2-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 04: session-37f6ea093d2cac15c5e9

Session session-37f6ea093d2cac15c5e9 is evaluated under the sealed order for SG2. 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: SG2-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 05: session-447b5b256e606e8b30d5

Session session-447b5b256e606e8b30d5 is evaluated under the sealed order for SG2. 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: SG2-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 06: session-1962e5f81ef9b8287448

Session session-1962e5f81ef9b8287448 is evaluated under the sealed order for SG2. 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: SG2-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 07: session-3d9d0d855e9f3acfbd7b

Session session-3d9d0d855e9f3acfbd7b is evaluated under the sealed order for SG2. 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: SG2-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 08: session-5fa9e02946c18581b740

Session session-5fa9e02946c18581b740 is evaluated under the sealed order for SG2. 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: SG2-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 - Closure boundary 01: SG1-O01

After the scoped calculation finishes, dependency SG1-O01 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: SG2-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 02: SG1-O02

After the scoped calculation finishes, dependency SG1-O02 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: SG2-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 03: SG1-O03

After the scoped calculation finishes, dependency SG1-O03 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: SG2-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 04: SG1-O05

After the scoped calculation finishes, dependency SG1-O05 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: SG2-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 05: SG1-O06

After the scoped calculation finishes, dependency SG1-O06 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: SG2-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 06: SG1-O07

After the scoped calculation finishes, dependency SG1-O07 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: SG2-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 07: SG1-O09

After the scoped calculation finishes, dependency SG1-O09 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: SG2-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 08: SG1-O10

After the scoped calculation finishes, dependency SG1-O10 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: SG2-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 09: SG1-O11

After the scoped calculation finishes, dependency SG1-O11 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: SG2-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 - Hostile variant 01: Identify the color carrier

This hostile variant alters the assumptions surrounding Identify the color carrier while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Read the K6 connected Killing algebra as su(3), giving dimension eight and rank two under the frozen metric carrier declaration. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 - Hostile variant 02: Identify the weak carrier

This hostile variant alters the assumptions surrounding Identify the weak carrier while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Use the round S2 connected Killing algebra su(2), contributing three vector directions and rank one. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 03: Exclude an interval vector

This hostile variant alters the assumptions surrounding Exclude an interval vector while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The connected interval Killing dimension is zero after the boundary/orbifold rulebook is imposed. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 04: Admit hypercharge once

This hostile variant alters the assumptions surrounding Admit hypercharge once while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The independent principal U(1)Y connection supplies exactly one even vector zero mode and rank one. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 05: Add dimensions

This hostile variant alters the assumptions surrounding Add dimensions while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The paid vector count is 8+3+0+1=12; no other p-form or boundary vector zero modes are declared. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 06: Add ranks

This hostile variant alters the assumptions surrounding Add ranks while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The carrier ranks sum to 2+1+0+1=4, matching the target algebra without a duplicate abelian direction. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 07: Audit ownership

This hostile variant alters the assumptions surrounding Audit ownership while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Color, weak, and hypercharge each have one declared parent, so no direction is counted under two geometric stories. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 08: Evaluate center characters

This hostile variant alters the assumptions surrounding Evaluate center characters while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Apply 2 triality a + 3 doublet b + y6 k = 0 mod 6 to the imported matter-character packet. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 09: Enumerate the kernel

This hostile variant alters the assumptions surrounding Enumerate the kernel while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The 36 center tuples contain six kernel elements generated cyclically, establishing the conditional Z6 label. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 10: Check Smith form

This hostile variant alters the assumptions surrounding Check Smith form while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: The lifted relation matrix has invariants (1,1,6), independently confirming a cyclic group of order six. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 11: Apply the no-extra test

This hostile variant alters the assumptions surrounding Apply the no-extra test while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Missing vectors and extra vectors both evaluate to zero on the frozen manifest. 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 12: Reduce dependencies

This hostile variant alters the assumptions surrounding Reduce dependencies while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Nine direct SG1 V3 rows remain OPEN, so the conditional arithmetic cannot promote the physical gate. Variant 12 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 12 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 13: Identify the color carrier

This hostile variant alters the assumptions surrounding Identify the color carrier while leaving the advertised target unchanged. The test asks whether the operation still follows from the frozen inputs: Read the K6 connected Killing algebra as su(3), giving dimension eight and rank two under the frozen metric carrier declaration. Variant 13 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 13 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 SG2 packet; it demonstrates how the gate would fail closed under a specifically indexed pressure test.

Move audit tag: SG2-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 CANDIDATE: PASS; PHYSICAL SG2: OPEN. This is the strongest lawful conclusion supported by the frozen package, and no nature-selection claim is added.

Move audit tag: SG2-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.