{ "tool_id": "art-619-ccd2-aprc-annex3-recompute", "note": "Fixture-oracle independence (FORMALVERIF-BUILD-SPEC.md 3d): Annex III itself carries no worked numeric example (unlike Reg Z Appendix J, art-215 source). Golden values derive from CLOSED-FORM ALGEBRA solved forward (given X, solve for flow amounts satisfying Annex III Part I equation by direct substitution) -- a computation direction opposite to this kernel bisection search (given flows, find X). FV 3d preference-3 shape (independently worked, not generated from the same reading that produced the spec, not run through the kernel to produce the target); documented per-vector in fixture_oracle_note. human_sign_off: PENDING.", "vectors": [ { "name": "single-drawdown-single-repayment-10pct-closed-form", "policy_parameters": { "drawdowns": [ { "amount": 1000, "full_periods": 0, "fraction": 0 } ], "repayments": [ { "amount": 1100, "full_periods": 1, "fraction": 0 } ] }, "output_payload": { "aprc_pct": 10, "converged": true, "bracketed": true, "iterations_used": 26, "residual_at_convergence": 4.5454544306267053e-7, "num_drawdowns": 1, "num_repayments": 1, "drawdown_total": 1000, "repayment_total": 1100, "total_charge": 100, "regulatory_basis": "Directive (EU) 2023/2225 (CCD2), Article 30 + Annex III Part I (basic equation).", "note": "APRC solved by bracketed bisection on Annex III Part I's basic equation, real-valued t_k/s_l per the Directive's own text (no integer/fraction split). Rounded per Annex III Part I remark (d): at least one decimal place, half-up on the next digit. A rate is reported only when a sign-change bracket was established and narrowed to tolerance; otherwise aprc_pct is null and APRC_NOT_BRACKETED or APRC_DID_NOT_CONVERGE is raised. Verify-only recompute: does not determine CCD2 applicability, does not submit anything to a regulator, and does not assert compliance." }, "fixture_oracle_note": "closed-form algebra: D/C - 1 = 1100/1000 - 1 = 0.10 exactly, independent of this kernel bisection.", "golden_hash": "f150499b37a191ee44e9a5a88985cdec17c25c87f5e62473eaa2c98499bdae90" }, { "name": "zero-charge-guard-0pct", "policy_parameters": { "drawdowns": [ { "amount": 1000, "full_periods": 0, "fraction": 0 } ], "repayments": [ { "amount": 1000, "full_periods": 1, "fraction": 0 } ] }, "output_payload": { "aprc_pct": 0, "converged": true, "bracketed": true, "iterations_used": 0, "residual_at_convergence": 0, "num_drawdowns": 1, "num_repayments": 1, "drawdown_total": 1000, "repayment_total": 1000, "total_charge": 0, "regulatory_basis": "Directive (EU) 2023/2225 (CCD2), Article 30 + Annex III Part I (basic equation).", "note": "APRC solved by bracketed bisection on Annex III Part I's basic equation, real-valued t_k/s_l per the Directive's own text (no integer/fraction split). Rounded per Annex III Part I remark (d): at least one decimal place, half-up on the next digit. A rate is reported only when a sign-change bracket was established and narrowed to tolerance; otherwise aprc_pct is null and APRC_NOT_BRACKETED or APRC_DID_NOT_CONVERGE is raised. Verify-only recompute: does not determine CCD2 applicability, does not submit anything to a regulator, and does not assert compliance." }, "fixture_oracle_note": "closed-form algebra: D=C -> X=0 exactly.", "golden_hash": "713fca8851d660a9853edee75cf0ad220e06895cb4ae0bc4e7663081a6c96e03" }, { "name": "multi-period-amortizing-unequal-spacing-20pct", "policy_parameters": { "drawdowns": [ { "amount": 1000, "full_periods": 0, "fraction": 0 } ], "repayments": [ { "amount": 300, "full_periods": 0, "fraction": 0.3 }, { "amount": 859.1619068403334, "full_periods": 1, "fraction": 0 } ] }, "output_payload": { "aprc_pct": 20, "converged": true, "bracketed": true, "iterations_used": 27, "residual_at_convergence": -3.338241185701918e-7, "num_drawdowns": 1, "num_repayments": 2, "drawdown_total": 1000, "repayment_total": 1159.1619068403334, "total_charge": 159.16190684033336, "regulatory_basis": "Directive (EU) 2023/2225 (CCD2), Article 30 + Annex III Part I (basic equation).", "note": "APRC solved by bracketed bisection on Annex III Part I's basic equation, real-valued t_k/s_l per the Directive's own text (no integer/fraction split). Rounded per Annex III Part I remark (d): at least one decimal place, half-up on the next digit. A rate is reported only when a sign-change bracket was established and narrowed to tolerance; otherwise aprc_pct is null and APRC_NOT_BRACKETED or APRC_DID_NOT_CONVERGE is raised. Verify-only recompute: does not determine CCD2 applicability, does not submit anything to a regulator, and does not assert compliance." }, "fixture_oracle_note": "forward-substitution: X fixed at 0.20, D1=300 at t=0.3 given, D2 solved algebraically at t=1.0 so C = D1*(1.2)^-0.3 + D2*(1.2)^-1 holds exactly (verified by direct substitution, independent of this kernel bisection search direction).", "golden_hash": "a10045162912063cb89e23840c8359b00c0f5e64451e0ec67ba2676d291411f5" }, { "name": "f2-shaped-non-convergence-negative-charge", "policy_parameters": { "drawdowns": [ { "amount": 1000, "full_periods": 0, "fraction": 0 } ], "repayments": [ { "amount": 900, "full_periods": 1, "fraction": 0 } ] }, "output_payload": { "aprc_pct": null, "converged": false, "bracketed": false, "iterations_used": 0, "residual_at_convergence": null, "num_drawdowns": 1, "num_repayments": 1, "drawdown_total": 1000, "repayment_total": 900, "total_charge": -100, "regulatory_basis": "Directive (EU) 2023/2225 (CCD2), Article 30 + Annex III Part I (basic equation).", "note": "APRC solved by bracketed bisection on Annex III Part I's basic equation, real-valued t_k/s_l per the Directive's own text (no integer/fraction split). Rounded per Annex III Part I remark (d): at least one decimal place, half-up on the next digit. A rate is reported only when a sign-change bracket was established and narrowed to tolerance; otherwise aprc_pct is null and APRC_NOT_BRACKETED or APRC_DID_NOT_CONVERGE is raised. Verify-only recompute: does not determine CCD2 applicability, does not submit anything to a regulator, and does not assert compliance." }, "fixture_oracle_note": "closed-form: D 12.5000%, already exact at 1dp, confirms half_up passthrough on a non-tie case.", "golden_hash": "04a26449f7ad3b10073c1db0ec753f3a676c6cd630e58785d85d26e99441cee8" }, { "name": "empty-schedule-guard", "policy_parameters": { "drawdowns": [], "repayments": [] }, "output_payload": { "aprc_pct": null, "converged": false, "bracketed": false, "iterations_used": 0, "residual_at_convergence": null, "num_drawdowns": 0, "num_repayments": 0, "drawdown_total": 0, "repayment_total": 0, "total_charge": 0, "regulatory_basis": "Directive (EU) 2023/2225 (CCD2), Article 30 + Annex III Part I (basic equation).", "note": "APRC solved by bracketed bisection on Annex III Part I's basic equation, real-valued t_k/s_l per the Directive's own text (no integer/fraction split). Rounded per Annex III Part I remark (d): at least one decimal place, half-up on the next digit. A rate is reported only when a sign-change bracket was established and narrowed to tolerance; otherwise aprc_pct is null and APRC_NOT_BRACKETED or APRC_DID_NOT_CONVERGE is raised. Verify-only recompute: does not determine CCD2 applicability, does not submit anything to a regulator, and does not assert compliance." }, "fixture_oracle_note": "closed-form: empty arrays sum to zero PV on both sides trivially, no rate dependence by construction.", "golden_hash": "2211a82220337dadcd8b31aeeba792c2078da1c572e51e7875c282b067375788" } ] }