[BFT-A][R8] Collapse CBE curve math to one canonical piecewise-linear engine

[umwelt]

Title

[BFT-A][R8] Collapse CBE curve math to one canonical piecewise-linear engine

Category

• R8 Invariants & Observability

Authoritative Inputs

• CBE Bonding Curve — Complete Formula Reference
• CBE Bonding Curve — Rust Implementation Specification section 4
• Team decision: represent each band with p_start, not signed intercept b

Problem

The current issue incorrectly excluded sell-path math. The new docs require one canonical piecewise-linear engine that supports:

• price_at
• cost_single_band
• multi-band mint traversal
• inverse_mint
• redemption-value computation for SELL_CBE
• flat-band special-case minting

Current Behavior

The branch still carries duplicate curve implementations, approximation paths, and inconsistent band logic across canonical.rs, pricing.rs, and token.rs.

Required Behavior

Create exactly one canonical curve math engine with:

• one band table
• one lookup rule
• one marginal price function using band-local form m_i * (S - S_start_i) + p_start_i
• one exact single-band cost integral using the documented factored form in band-local coordinates
• one exact multi-band traversal algorithm for buys
• one exact multi-band redemption traversal for sells
• one exact inverse mint function
• one flat-band special-case path

The engine must be pure math only. No state access, no transaction parsing, no runtime dependencies.

Safety Impact

Multiple curve engines or mismatched buy/sell math create deterministic replay risk and break solvency/accounting invariants.

Proposed Fix

Replace the current parallel curve math paths with a single pure module built directly from the p_start-based band/cost/inverse formulas.

Dependencies

• Depends on [BFT-A][R8] Establish canonical CBE curve types and fixed-point state model #1923
• Depends on [BFT-A][R9] Replace curve arithmetic with 18-decimal U256 fixed-point math and deterministic integer sqrt #1924

Acceptance Criteria

• Exact piecewise-linear price lookup is implemented in p_start form
• Exact cost_single_band implementation matches the documented order of operations and band-local factored formula
• Exact multi-band mint traversal is implemented
• Exact multi-band redemption-value math for SELL_CBE is implemented
• Flat-band special-case mint logic is implemented
• Duplicate native curve tables and approximation paths are non-authoritative

Test Plan

• Band continuity tests
• Band boundary lookup tests
• Cross-band mint-cost equality tests
• Inverse normalization vectors
• Multi-band sell/redemption vectors
• Flat-band vectors

Cleanup After

• Remove native authority from duplicate curve math in pricing.rs and token.rs
• Remove comments/tests that still describe spot-price minting shortcuts or signed intercept storage

[github-actions]

The GitHub issue outlines the need to simplify and unify the implementation of native Curve-Based Engine (CBE) pricing in the blockchain by collapsing multiple curve implementations into a single, canonical multi-band curve engine. Currently, the system contains duplicate band tables, redundant math approximations, and inconsistent pricing logic across various files, resulting in execution ambiguity and non-deterministic token issuance. The proposed fix involves creating a streamlined curve module using the canonical band table and integer math, with a single price function, cost function, and lookup rule, while removing native sell path logic. This change aims to ensure deterministic and accurate behavior. Dependencies include issues #1923 and #1924, and the resolution requires passing new tests for band continuity, boundary lookups, cost equality, and inverse normalization. Post-cleanup involves removing the authority of legacy curve helpers.

[umwelt]

Implemented on the bonding-curve rollout branch.

Delivered:

• one canonical piecewise-linear curve engine in lib-blockchain/src/contracts/bonding_curve/canonical.rs
• p_start-based pricing model
• exact single-band cost and cross-band traversal
• buy inverse on widened arithmetic
• sell/redemption traversal support
• review fixes for out-of-range supply rejection and continuity testing

Primary foundation commit:

• c8b8a80d Implement canonical bonding curve math foundation
• follow-up fix on current branch history: 59a49b95

This issue is complete for the current curve rollout.