Evaluate an explicit experimental opening API for families of XOR-related claims using one case-weighted forest per weight chunk and a shared PCS closure. This extends structured batching in #130; it is not a mandated production path or a generic-ring optimization.
Sources
BitZ integer/field reduction contract and final opening orchestration is normative for the target contract. PoC RLC statement and transcript and lazy case dispatch is implementation reference only; preserve target field, layout, transcript and security requirements unless this issue explicitly introduces a versioned protocol.
Relation and field profile
For j committed bit columns m1…mj (initial scope j≤4), each public claim uses a nonzero XOR mask L_i, canonical mod-q row weights and a claimed value; claims share the required column point. The reference uses q=2^100−15, not arbitrary rings. Select and document the target-supported prime profile explicitly and derive unbiased/target-approved q challenges, canonical lifting, chunk widths and integer exponent bounds. Reject unsupported or wrapping profiles rather than reinterpret q residues as K elements.
Proposed normative flow
Bind the version, root, geometry, field/profile, ordered family columns, masks, weights and claims; retain required OOD from PR #76. Draw γ_i in Fq and derive case weights W_b(m)=Σ_i γ_i w_i,b L_i(m) mod q. Per chunk, send bounded integer column folds, bind their K exponent images, run the merged case-leaf forest and the active monomial-channel residual sumchecks. Check the recombined integer evaluation against Σ_i γ_i claimed_i in Fq. After binding channel claims, draw discharge batching challenges; prove nonlinear monomials by the specified product/discharge cascade until only original committed-column openings remain. Absorb all ordered residual/ring messages, then draw closure challenges and make one Ligerito opening carrying every residual and OOD term.
Ordered verifier and acceptance
Validate profile, masks, common point, plan and counts; replay OOD/γ; reconstruct case/chunk weights; enforce canonical/range/no-wrap checks and evaluation recombination; verify every forest and channel sumcheck; replay discharge challenges and verify every intermediate AND/product obligation; verify ring switching and final authenticated PCS closure; reject malformed, extra or missing data. No derived monomial opening is trusted without discharge to committed columns.
Scope, impact and validation
Begin with j=2's four-case lazy leaves. j=3/4 Dense-JIT remains an opt-in time/memory experiment; dedicated lazy 8/16-case leaf-round kernels are not claimed as existing. Include degree/union-bound accounting and a versioned codec; reference code is experimental and not wired into its general codec. Benchmark complete independent-proof versus family-proof boundaries. Require positive heterogeneous-row-weight families, eager/lazy parity, negative mask/order/field/chunk/monomial/discharge/OOD/root tests and golden vectors. No default promotion or claimed measured target speedup is required.
Dependencies and coordination
Requires #130. Coordinate with #76.
Evaluate an explicit experimental opening API for families of XOR-related claims using one case-weighted forest per weight chunk and a shared PCS closure. This extends structured batching in #130; it is not a mandated production path or a generic-ring optimization.
Sources
BitZ integer/field reduction contract and final opening orchestration is normative for the target contract. PoC RLC statement and transcript and lazy case dispatch is implementation reference only; preserve target field, layout, transcript and security requirements unless this issue explicitly introduces a versioned protocol.
Relation and field profile
For j committed bit columns m1…mj (initial scope j≤4), each public claim uses a nonzero XOR mask L_i, canonical mod-q row weights and a claimed value; claims share the required column point. The reference uses q=2^100−15, not arbitrary rings. Select and document the target-supported prime profile explicitly and derive unbiased/target-approved q challenges, canonical lifting, chunk widths and integer exponent bounds. Reject unsupported or wrapping profiles rather than reinterpret q residues as K elements.
Proposed normative flow
Bind the version, root, geometry, field/profile, ordered family columns, masks, weights and claims; retain required OOD from PR #76. Draw γ_i in Fq and derive case weights
W_b(m)=Σ_i γ_i w_i,b L_i(m) mod q. Per chunk, send bounded integer column folds, bind their K exponent images, run the merged case-leaf forest and the active monomial-channel residual sumchecks. Check the recombined integer evaluation againstΣ_i γ_i claimed_iin Fq. After binding channel claims, draw discharge batching challenges; prove nonlinear monomials by the specified product/discharge cascade until only original committed-column openings remain. Absorb all ordered residual/ring messages, then draw closure challenges and make one Ligerito opening carrying every residual and OOD term.Ordered verifier and acceptance
Validate profile, masks, common point, plan and counts; replay OOD/γ; reconstruct case/chunk weights; enforce canonical/range/no-wrap checks and evaluation recombination; verify every forest and channel sumcheck; replay discharge challenges and verify every intermediate AND/product obligation; verify ring switching and final authenticated PCS closure; reject malformed, extra or missing data. No derived monomial opening is trusted without discharge to committed columns.
Scope, impact and validation
Begin with j=2's four-case lazy leaves. j=3/4 Dense-JIT remains an opt-in time/memory experiment; dedicated lazy 8/16-case leaf-round kernels are not claimed as existing. Include degree/union-bound accounting and a versioned codec; reference code is experimental and not wired into its general codec. Benchmark complete independent-proof versus family-proof boundaries. Require positive heterogeneous-row-weight families, eager/lazy parity, negative mask/order/field/chunk/monomial/discharge/OOD/root tests and golden vectors. No default promotion or claimed measured target speedup is required.
Dependencies and coordination
Requires #130. Coordinate with #76.