id display_name state family parent_model one_sentence_change boolean_backend pruning_directions supported_modes superseded_by algorithm_document branch_n_prune_2 Branch and Prune 2 experimental Dickinson intervals branch_n_prune_1 Branch-local Halfspace-Rays with a 70 percent jump gate and cheap sign-ranked estimated-longest-first traversal. region stack + ceiling antichain upward+interval CP,SCP,both branch_n_prune_2/ALGORITHM.md branch_n_prune_1 Branch and Prune 1 experimental Dickinson intervals sat_b3 Finishes one index region at a time with exact curvature, half-space rays and disjoint interval subtraction. region stack + ceiling antichain upward+interval CP,SCP,both branch_n_prune_1/ALGORITHM.md bundfuss_2008 Bundfuss 2008 baseline simplicial partition Bundfuss-Duer simplicial partition. none n/a CP,SCP 00-baselines/bundfuss_2008/ALGORITHM.md copomatrix_2011 COPOMATRIX 2011 baseline recursive reduction Xu-Yao COPOMATRIX reduction. none n/a CP,SCP 00-baselines/copomatrix_2011/ALGORITHM.md danninger_1990 Danninger 1990 baseline recursive reduction Danninger's dimension-reducing reconstruction. none n/a CP,SCP,both 00-baselines/danninger_1990/ALGORITHM.md dickinson_2019 Dickinson 2019 baseline Dickinson intervals Dickinson finite certificate enumeration. none interval CP,SCP,both 00-baselines/dickinson_2019/ALGORITHM.md dutour_2018 Dutour 2018 baseline polyhedral cone Dutour Sikiric polyhedral-cone implementation. none n/a CP,SCP 00-baselines/dutour_2018/ALGORITHM.md hadeler_1983 Hadeler 1983 baseline principal supports Hadeler principal-submatrix enumeration. none exact support CP,SCP,both 00-baselines/hadeler_1983/ALGORITHM.md safi_2021 Safi 2021 baseline simplicial partition Safi-Nabavi-Caron simplex partition. none n/a CP,SCP 00-baselines/safi_2021/ALGORITHM.md sponsel_2012 Sponsel 2012 baseline simplicial partition Sponsel certificates with Bundfuss refinement. none n/a CP,SCP 00-baselines/sponsel_2012/ALGORITHM.md adaptive_dutour_copomatrix Adaptive Dutour-COPOMATRIX retained hybrid reduction dutour_2018+copomatrix_2011 Adaptive Dutour/COPOMATRIX hybrid. none n/a CP,SCP adaptive_dutour_copomatrix/ALGORITHM.md adaptive_dutour_danninger Adaptive Dutour-Danninger retained hybrid reduction dutour_2018+danninger_1990 Adaptive Dutour/Danninger hybrid. none n/a CP,SCP adaptive_dutour_danninger/ALGORITHM.md adaptive_sponsel_copomatrix Adaptive Sponsel-COPOMATRIX retained hybrid reduction sponsel_2012+copomatrix_2011 Chooses COPOMATRIX when its best pivot has at most two children; otherwise uses Sponsel subdivision. none n/a CP,SCP adaptive_sponsel_copomatrix/ALGORITHM.md adaptive_zischg_sponsel_copomatrix Adaptive Zischg-Sponsel-COPOMATRIX retained hybrid reduction adaptive_sponsel_copomatrix Adaptive projection-component comparison. none n/a CP,SCP adaptive_zischg_sponsel_copomatrix/ALGORITHM.md affine_companion_dickinson Affine-Companion Dickinson retained Dickinson intervals kernel_cone_dickinson Adds exact consistency and affine-family certificates at singular principal supports. none upward CP,SCP,both affine_companion_dickinson/ALGORITHM.md bdd_b3 BDD-B3 retained Dickinson intervals sat_b3 SAT-B3 mathematics with a BDD coverage backend. BDD upward+downward+interval CP,SCP,both bdd_b3/ALGORITHM.md bdd_dickinson BDD Dickinson retained Dickinson intervals dickinson_2019 Represents the Dickinson interval union with an ordinary BDD. BDD interval CP,SCP,both bdd_dickinson/ALGORITHM.md breadth_first_singular_lift_dickinson Breadth-First Singular-Lift Dickinson retained Dickinson intervals layered_singular_lift_dickinson Uses a FIFO frontier that finishes each lifted cardinality before the next. none upward CP,SCP,both breadth_first_singular_lift_dickinson/ALGORITHM.md cadical_x1 CaDiCaL X1 retained Dickinson intervals sat_b3 Expands arbitrary uncovered CaDiCaL seeds through one Schur-guided maximal-chain pass. CaDiCaL upward+downward+interval CP,SCP,both cadical_x1/ALGORITHM.md cardinality_bdd_dickinson Cardinality-BDD Dickinson archived Dickinson intervals bdd_dickinson Archived cardinality-BDD traversal retained for historical comparison. BDD interval CP,SCP,both bdd_dickinson cardinality_bdd_dickinson/ALGORITHM.md cardinality_zdd_dickinson Cardinality-ZDD Dickinson archived Dickinson intervals zdd_dickinson Archived cardinality-ZDD traversal retained for historical comparison. ZDD interval CP,SCP,both zdd_dickinson cardinality_zdd_dickinson/ALGORITHM.md cbdd_dickinson CBDD Dickinson retained Dickinson intervals dickinson_2019 Uses Bryant chain-reduced BDD interval algebra for Dickinson certificates. CBDD interval CP,SCP,both cbdd_dickinson/ALGORITHM.md cbdd_dickinson_improved_1 CBDD Dickinson Improved One retained Dickinson intervals cbdd_dickinson Adds batched affine and homogeneous singular certificates, including the complete nullity-two stacked-line family. CBDD interval CP,SCP,both cbdd_dickinson_improved_1/ALGORITHM.md cbdd_halfspace_dickinson CBDD-Halfspace Dickinson retained Dickinson intervals cbdd_dickinson Adds cumulative exact coordinate search over strictly positive right-hand sides. CBDD interval CP,SCP,both cbdd_halfspace_dickinson/ALGORITHM.md ceiling_pruned_dickinson Ceiling-Pruned Dickinson retained support enumeration dickinson_2019 Retains only Dickinson certificates whose upper endpoint is the full index set. support generator upward CP,SCP,both ceiling_pruned_dickinson/ALGORITHM.md clasp_b3 Clasp-B3 retained Dickinson intervals sat_b3 SAT-B3 mathematics with a clasp coverage backend. clasp upward+downward+interval CP,SCP,both clasp_b3/ALGORITHM.md clingo_dickinson Clingo Dickinson retained Dickinson intervals dickinson_2019 Uses Clingo/clasp backtracking enumeration with native cardinality layers. clingo/clasp interval CP,SCP,both clingo_dickinson/ALGORITHM.md clingo_halfspace_dickinson Clingo-Halfspace Dickinson retained Dickinson intervals clingo_dickinson Adds cumulative exact coordinate search over strictly positive right-hand sides. clingo/clasp interval CP,SCP,both clingo_halfspace_dickinson/ALGORITHM.md czdd_dickinson CZDD Dickinson retained Dickinson intervals dickinson_2019 Uses Bryant chain-reduced ZDD interval algebra for Dickinson certificates. CZDD interval CP,SCP,both czdd_dickinson/ALGORITHM.md dense_bitset_dickinson Dense-Bitset Dickinson retained Dickinson intervals dickinson_2019 Traverses cardinality layers using one literal packed bit per support. none interval CP,SCP,both dense_bitset_dickinson/ALGORITHM.md dual_frontier_nbc Dual-Frontier NBC retained Dickinson intervals improved_nbc_b7 Adds a floating walk toward both curvature frontiers with exact verification of retained candidates. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both dual_frontier_nbc/ALGORITHM.md dual_frontier_nbc_four Dual-Frontier NBC Four retained Dickinson intervals dual_frontier_nbc_three Launches the coverage-aware dual-frontier walk from the exact Dickinson upper endpoint. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both dual_frontier_nbc_four/ALGORITHM.md dual_frontier_nbc_three Dual-Frontier NBC Three retained Dickinson intervals dual_frontier_nbc_two Processes every emitted seed exactly before beginning its coverage-aware frontier walk. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both dual_frontier_nbc_three/ALGORITHM.md dual_frontier_nbc_two Dual-Frontier NBC Two retained Dickinson intervals dual_frontier_nbc Allows a frontier-walk step only when NBC reports that its support remains uncovered. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both dual_frontier_nbc_two/ALGORITHM.md f1 F1: Full-Upward Curvature and Dickinson Search retained support enumeration sat_c3 Uses exact pair and endpoint curvature plus full-ceiling Halfspace-Rays Dickinson roots. support generator upward CP,SCP,both f1/ALGORITHM.md f2 F2 retained support enumeration sat_b3 Preserves SAT-B3 mathematics while splitting support generation from interval filtering. support generator upward+downward+interval CP,SCP,both f2/ALGORITHM.md fracessa FracESSA First-Order Global-Minimum Model retained support enumeration hadeler_1983 Adapts FracESSA to first-order global-simplex-minimum classification. support generator upward CP,SCP,both fracessa/ALGORITHM.md fracessa_circular FracESSA Circular Global-Minimum Model archived support enumeration fracessa Archived adaptation limited to symmetric circulant matrices. support generator upward CP,SCP,both fracessa fracessa_circular/ALGORITHM.md frank_wolfe_dickinson Frank-Wolfe Dickinson retained Dickinson intervals dickinson_2019 Adds bounded Frank-Wolfe witness proposals before Dickinson. none interval CP,SCP,both frank_wolfe_dickinson/ALGORITHM.md frank_wolfe_sponsel Exact One-Step Frank-Wolfe Sponsel retained hybrid reduction sponsel_2012 Adds one exact Frank-Wolfe segment before Sponsel. none n/a CP,SCP frank_wolfe_sponsel/ALGORITHM.md g1 G1: Generator with Bounded Dickinson Guidance retained support enumeration f1 Adds expiring Dickinson guidance and cardinality-boundary root compaction to F1. support generator upward CP,SCP,both g1/ALGORITHM.md improved_nbc_b7 Improved NBC-B7 retained Dickinson intervals nbc_b7 Uses a resumable Improved NBC backend with permanent root-inconsistency detection. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_b7/ALGORITHM.md improved_nbc_b8 Improved NBC-B8 retained Dickinson intervals improved_nbc_b7 Removes the high frontier and downward pruning. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+interval CP,SCP,both improved_nbc_b8/ALGORITHM.md improved_nbc_b9 Improved NBC-B9 retained Dickinson intervals improved_nbc_b7 Adds bounded reproducibly jittered KKT walks with exactly verified no-hiding curvature closures. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_b9/ALGORITHM.md improved_nbc_g2 Improved NBC-G2 retained Dickinson intervals improved_nbc_b7 Adds a bounded closed-cone right-hand-side extension with exact reconstruction and verification. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_g2/ALGORITHM.md improved_nbc_x2 Improved NBC-X2 retained Dickinson intervals improved_nbc_b7 Adds exact greedy reduction of the Dickinson lower endpoint. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x2/ALGORITHM.md improved_nbc_x3 Improved NBC-X3 retained Dickinson intervals improved_nbc_x2 Adds a targeted LP proposal with exact reconstruction and exact dominance selection. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x3/ALGORITHM.md improved_nbc_x4 Improved NBC-X4 retained Dickinson intervals improved_nbc_x3 Runs the ordinary exact shrink first and skips the LP when that interval is already maximal. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x4/ALGORITHM.md improved_nbc_x5 Improved NBC-X5 retained Dickinson intervals improved_nbc_x3 Adds a cheap necessary bound that can skip an unproductive target LP. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x5/ALGORITHM.md improved_nbc_x6 Improved NBC-X6 retained Dickinson intervals improved_nbc_x3 Repeats exactly verified targeted-LP upper-endpoint enlargements before shrinking the lower endpoint once. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x6/ALGORITHM.md improved_nbc_x7 Improved NBC-X7 retained Dickinson intervals improved_nbc_x6 Compares at most two exactly successful LP targets per continuation round. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x7/ALGORITHM.md improved_nbc_x8 Improved NBC-X8 retained Dickinson intervals improved_nbc_x6 Adds curvature-first pruning and a complete local maximum-halfspace MILP. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x8/ALGORITHM.md improved_nbc_x9 Improved NBC-X9 retained Dickinson intervals improved_nbc_x6 Adds floating spectral right-hand-side proposals, exact verification, and one exact Rays cleanup. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x9/ALGORITHM.md improved_nbc_x10 Improved NBC-X10 retained Dickinson intervals improved_nbc_x6 Runs a best-improvement downward Halfspace-Rays search from each unresolved independent high-frontier support, minimizing the lower endpoint while keeping that support inside the interval. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x10/ALGORITHM.md improved_nbc_x11 Improved NBC-X11 retained Dickinson intervals improved_nbc_x10 Traverses only from the high frontier and installs exact curvature downward closures or downward Dickinson intervals, with no upward pruning. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) downward+interval CP,SCP,both improved_nbc_x11/ALGORITHM.md improved_nbc_x12 Improved NBC-X12 retained Dickinson intervals improved_nbc_x10 Uses the cheap first-improvement downward Halfspace-Rays search from historical X10 d356, with one exact high-support factorization and an exact interval for every nonsingular high support. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x12/ALGORITHM.md improved_nbc_x13 Improved NBC-X13 retained Dickinson intervals improved_nbc_x12 Repeatedly takes the first exact one-coordinate Schur step that reduces the lower endpoint, then runs the inherited cheap downward Halfspace-Rays walk from the reduced face. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x13/ALGORITHM.md improved_nbc_x14 Improved NBC-X14 retained curvature frontiers improved_nbc_x13 Exhausts every curvature-preserving branch from each curvature certificate and inserts every distinct minimal upward or maximal downward frontier closure. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x14/ALGORITHM.md improved_nbc_x15 Improved NBC-X15 retained curvature frontiers improved_nbc_x14 Reuses direction-specific curvature-frontier subproblems only after their complete exact traversal, avoiding repeated overlap between later roots. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x15/ALGORITHM.md improved_nbc_x16 Improved NBC-X16 active curvature frontiers improved_nbc_x15 Traverses curvature frontiers directionally, using floating Schur updates on nonsingular interiors and exact singular handling. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x16/ALGORITHM.md improved_nbc_x17 Improved NBC-X17 active curvature frontiers improved_nbc_x16 Replaces only X16's high-frontier Dickinson search with the cheap first-improvement search preserved from historical X10. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x17/ALGORITHM.md improved_nbc_x18 Improved NBC-X18 active Dickinson intervals improved_nbc_x6 Restores historical X10 d356: a floating high-frontier active-face walk, followed by exact replay and verification of its complete zero set. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x18/ALGORITHM.md improved_nbc_x19 Improved NBC-X19 active curvature frontiers improved_nbc_x16 Keeps X16's Schur-updated curvature-frontier traversal and replaces only its unresolved high-frontier Dickinson search with X18's floating active-face proposal and exact replay. Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x19/ALGORITHM.md improved_nbc_x20 Improved NBC-X20 active Dickinson intervals improved_nbc_x19 Ranks Dickinson candidates by volume inside the completed low/high frontiers' remaining band and retains at most two equal-score intervals with a runtime maximum overlap percentage (default 50). Shared upward merging includes the latest finished low layer. Improved NBC (complete high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x20/ALGORITHM.md improved_nbc_x21 Improved NBC-X21 active Dickinson intervals improved_nbc_x6 Retains X6 traversal and ranks Dickinson candidates by open-band volume and retains at most two equal-score intervals with a runtime maximum overlap percentage (default 50). Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x21/ALGORITHM.md improved_nbc_x31 Improved NBC-X31 active Dickinson intervals improved_nbc_x21 X21 search and open-band objective with only the first maximum-volume interval retained; secondary selection, overlap calculations and overlap parameter removed. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x31/ALGORITHM.md improved_nbc_x32 Improved NBC-X32 experimental Dickinson intervals improved_nbc_x31 X31 search with one equal-band-score alternative only when whole intersection is at most 5% of both intervals, using exact bitsets and a five-bit width gap. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x32/ALGORITHM.md improved_nbc_x22 Improved NBC-X22 active Dickinson intervals improved_nbc_x21 Retains X21's traversal, certificate selection, and compaction; creates a fresh SAT instance with permanent exact cardinality whenever a frontier changes layer. Shared upward merging includes the latest finished low layer. Improved NBC (heuristic high; fresh fixed-cardinality SAT per layer) upward+downward+interval CP,SCP,both improved_nbc_x22/ALGORITHM.md improved_nbc_x23 Improved NBC-X23 active Dickinson intervals improved_nbc_x22 Retains X22's fixed-cardinality SAT and certificate algorithms; low queries have no prefix bookkeeping or assumptions and rely on immediate exact certificates. The heuristic high frontier retains its prefix cursor. Improved NBC (prefix-free low; heuristic high; fixed-cardinality SAT) upward+downward+interval CP,SCP,both improved_nbc_x23/ALGORITHM.md ccudd_x24 CCUDD-X24 active Dickinson intervals improved_nbc_x23 Retains X23's matrix tests and open-band certificate optimization; replaces SAT enumeration with native Chain-CUDD interval subtraction and independent low/high layer roots. Unproved high visits remain globally open. Chain-CUDD (fixed-order chained BDD) upward+downward+interval CP,SCP,both ccudd_x24/ALGORITHM.md improved_nbc_x25 Improved NBC-X25 active Dickinson vector combinations improved_nbc_x23 Low-only prefix-free traversal; retains exact traditional vectors even at curvature-pruned roots, searches signed pairs in floating point, and inserts every exactly verified interval without containment filtering. No downward pruning or RHS optimization. Improved NBC (prefix-free low; fixed-cardinality SAT) upward+interval CP,SCP,both improved_nbc_x25/ALGORITHM.md improved_nbc_x26 Improved NBC-X26 active Dickinson vector combinations improved_nbc_x25 Caches original all-ones vectors. Primary support filter and secondary marginal bounds; shared sign scans, breakpoint-mask reuse, flat volume cache and reusable ranking buffers. Source-only bounds once per visit. Exact finalists with retries; curvature roots insert only their closure. Improved NBC (prefix-free low; fixed-cardinality SAT) upward+interval CP,SCP,both improved_nbc_x26/ALGORITHM.md improved_nbc_x27 Improved NBC-X27 active Dickinson vector combinations improved_nbc_x26 One certificate per continuing root: curvature closure or maximum-D root-containing Dickinson interval, then maximum U. Original all-ones cache, floating signed-pair search and exact nominee retries. No secondary search, bounds or overlap scoring. Improved NBC (prefix-free low; fixed-cardinality SAT) upward+interval CP,SCP,both improved_nbc_x27/ALGORITHM.md improved_nbc_x28 Improved NBC-X28 active Dickinson vector combinations improved_nbc_x27 X27 primary-only combination search with X6 alternating heuristic high-frontier PSD screening and exactly verified downward curvature closures. No high Dickinson search or high-vector cache; low queries stay prefix-free. Improved NBC (prefix-free low; heuristic high; fixed-cardinality SAT) upward+downward+interval CP,SCP,both improved_nbc_x28/ALGORITHM.md improved_nbc_x29 Improved NBC-X29 active Dickinson vector combinations improved_nbc_x6 Unchanged X6 search followed by at most four cached traditional partners; signed repair-before-damage proposals, exact interval-containment verification, one final certificate. Bounded per-coordinate cache; no mixed vectors cached. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x29/ALGORITHM.md improved_nbc_x30 Improved NBC-X30 active Dickinson vector combinations improved_nbc_x29 Unchanged X6 search, then two closest-to-zero missing upper targets and two cached parents per target/sign; at most eight direct candidates, one crossing each, first exact enlargement. No partner ranking or cancellation-only search. Improved NBC (heuristic high; persistent SAT; compaction-only rebuild) upward+downward+interval CP,SCP,both improved_nbc_x30/ALGORITHM.md interval_recursive_dickinson Interval-Recursive Dickinson retained Dickinson intervals dickinson_2019 Uses Dickinson intervals to prune a recursive support generator. none interval CP,SCP,both interval_recursive_dickinson/ALGORITHM.md interval_supports_g3 Interval-Supports-G3 retained Dickinson intervals improved_nbc_b7 Replaces Improved NBC with a direct exact interval-support generator. interval generator upward+downward+interval CP,SCP,both interval_supports_g3/ALGORITHM.md kernel_cone_dickinson Kernel-Cone Dickinson retained Dickinson intervals ceiling_pruned_dickinson Adds direct exact cone geometry in every high-nullity root kernel. none upward CP,SCP,both kernel_cone_dickinson/ALGORITHM.md layered_singular_lift_dickinson Layered Singular-Lift Dickinson retained Dickinson intervals affine_companion_dickinson Adds layer-delayed ceiling pruning and depth-first singular-support lifting. none upward CP,SCP,both layered_singular_lift_dickinson/ALGORITHM.md milp_1 MILP 1 retained MILP Exact Gondzio-Yildirim mixed-integer formulation for the global simplex minimum. none n/a CP,SCP,both milp_1/ALGORITHM.md minimal_sat_g4 Minimal SAT-G4 retained Dickinson intervals improved_nbc_b7 Replaces Improved NBC with a minimal non-learning DPLL engine. minimal DPLL upward+downward+interval CP,SCP,both minimal_sat_g4/ALGORITHM.md multithreaded_cbdd_dickinson Multithreaded CBDD Dickinson retained Dickinson intervals cbdd_dickinson Uses bounded parallel exact-support batches with coordinator-owned CBDD updates. CBDD interval CP,SCP,both multithreaded_cbdd_dickinson/ALGORITHM.md nbc_b6 NBC-B6 retained Dickinson intervals sat_b3 Uses NBC MiniSat All to enumerate and compact complete ascending cardinality layers. NBC MiniSat All upward+interval CP,SCP,both nbc_b6/ALGORITHM.md nbc_b7 NBC-B7 retained Dickinson intervals sat_b3 Uses a persistent NBC MiniSat All backend with alternating low/high traversal. NBC MiniSat All upward+downward+interval CP,SCP,both nbc_b7/ALGORITHM.md nullity_support_pruned_dickinson Nullity Support-Pruned Dickinson retained Dickinson intervals support_pruned_dickinson Adds singular-vector selection to support-pruned Dickinson. none interval CP,SCP,both nullity_support_pruned_dickinson/ALGORITHM.md one_step_frank_wolfe_dickinson Exact One-Step Frank-Wolfe Dickinson retained Dickinson intervals frank_wolfe_dickinson Uses one exact Frank-Wolfe segment before Dickinson. none interval CP,SCP,both one_step_frank_wolfe_dickinson/ALGORITHM.md pairwise_frank_wolfe_dickinson Pairwise Frank-Wolfe Dickinson retained Dickinson intervals frank_wolfe_dickinson Uses a pairwise-away proposal path before Dickinson. none interval CP,SCP,both pairwise_frank_wolfe_dickinson/ALGORITHM.md rhs_dickinson RHS Dickinson retained Dickinson intervals nullity_support_pruned_dickinson Searches strictly positive Dickinson right-hand sides. none interval CP,SCP,both rhs_dickinson/ALGORITHM.md sat_a1 SAT-A1 retained Dickinson intervals sat_halfspace_rays_dickinson Retains the inclusion-maximal antichain of upper endpoints encountered by existing exact sweeps. CaDiCaL interval CP,SCP,both sat_a1/ALGORITHM.md sat_a2 SAT-A2 retained Dickinson intervals sat_halfspace_rays_dickinson Adds one bounded maximum-halfspace LP relaxation and one LP-guided monotone extension. CaDiCaL interval CP,SCP,both sat_a2/ALGORITHM.md sat_a3 SAT-A3 retained Dickinson intervals sat_halfspace_rays_dickinson Adds bounded monotone LP-feasibility probes that preserve the Rays endpoint. CaDiCaL interval CP,SCP,both sat_a3/ALGORITHM.md sat_a4 SAT-A4: Monotone-Only Dickinson retained Dickinson intervals sat_dickinson Applies bounded monotone LP-feasibility probes directly without Halfspace-Rays. CaDiCaL interval CP,SCP,both sat_a4/ALGORITHM.md sat_a5 SAT-A5 retained Dickinson intervals sat_a3 Uses best-improvement monotone target selection within a shared deadline. CaDiCaL interval CP,SCP,both sat_a5/ALGORITHM.md sat_b1 SAT-B1 retained Dickinson intervals sat_halfspace_rays_dickinson Adds exact strict-convex-face exclusions before Halfspace-Rays. CaDiCaL upward+interval CP,SCP,both sat_b1/ALGORITHM.md sat_b2 SAT-B2 retained Dickinson intervals sat_b1 Adds alternating low/high traversal and exactly verified high-frontier downward pruning. CaDiCaL upward+downward+interval CP,SCP,both sat_b2/ALGORITHM.md sat_b3 SAT-B3 retained Dickinson intervals sat_b2 Broadens the high-frontier filter and downward pruning to consistent singular PSD supports. CaDiCaL upward+downward+interval CP,SCP,both sat_b3/ALGORITHM.md sat_b4 SAT-B4 retained Dickinson intervals sat_b3 Adds recursive exact Johnson-Reams dimension reduction. CaDiCaL upward+downward+interval CP,SCP,both sat_b4/ALGORITHM.md sat_b5 SAT-B5 retained Dickinson intervals sat_b4 Removes the high-frontier scan while retaining Johnson-Reams reduction. CaDiCaL upward+interval CP,SCP,both sat_b5/ALGORITHM.md sat_c1 SAT-C1 retained Dickinson intervals sat_b3 Adds a heuristic-gated exact Schur-residual search inside Dickinson intervals. CaDiCaL upward+downward+interval CP,SCP,both sat_c1/ALGORITHM.md sat_c2 SAT-C2 retained Dickinson intervals sat_c1 Adds bounded SAT-aware stationary-face walks and buffered curvature closures. CaDiCaL upward+downward+interval CP,SCP,both sat_c2/ALGORITHM.md sat_c3 SAT-C3: Exact Upward-Closure Traversal retained support enumeration ceiling_pruned_dickinson Retains only exact full-upward curvature and full-ceiling Dickinson roots. support generator upward CP,SCP,both sat_c3/ALGORITHM.md sat_c4 SAT-C4 retained Dickinson intervals sat_b3 Checks exact curvature at traditional, Halfspace, and synthesized-ray upper endpoints. CaDiCaL upward+downward+interval CP,SCP,both sat_c4/ALGORITHM.md sat_dickinson SAT Dickinson retained Dickinson intervals dickinson_2019 Uses incremental CaDiCaL with one clause per Dickinson interval. CaDiCaL interval CP,SCP,both sat_dickinson/ALGORITHM.md sat_halfspace_dickinson SAT-Halfspace Dickinson retained Dickinson intervals sat_dickinson Adds cumulative exact coordinate search over strictly positive right-hand sides. CaDiCaL interval CP,SCP,both sat_halfspace_dickinson/ALGORITHM.md sat_halfspace_lp_dickinson SAT-Halfspace-LP Dickinson retained Dickinson intervals sat_halfspace_rays_dickinson Adds a tiny numerical full-ceiling LP with exact candidate verification. CaDiCaL interval CP,SCP,both sat_halfspace_lp_dickinson/ALGORITHM.md sat_halfspace_milp_dickinson SAT-Halfspace-MILP Dickinson retained Dickinson intervals sat_dickinson Adds a bounded local MILP maximizing the upper endpoint with exact candidate verification. CaDiCaL interval CP,SCP,both sat_halfspace_milp_dickinson/ALGORITHM.md sat_halfspace_rays_dickinson SAT-Halfspace-Rays Dickinson retained Dickinson intervals sat_halfspace_dickinson Uses a U-first, width-second Halfspace path plus at most two exact synthesized-ray sweeps. CaDiCaL interval CP,SCP,both sat_halfspace_rays_dickinson/ALGORITHM.md sat_halfspace_rays_lookahead_dickinson SAT-Halfspace-Rays Lookahead Dickinson retained Dickinson intervals sat_halfspace_rays_dickinson Adds one-cardinality child analysis and one-layer exact-result caching. CaDiCaL interval CP,SCP,both sat_halfspace_rays_lookahead_dickinson/ALGORITHM.md sat_halfspace_rays_wide_dickinson SAT-Halfspace-Rays Wide Dickinson retained Dickinson intervals sat_halfspace_rays_dickinson Keeps a full interval only when its width exceeds the configured percentage threshold. CaDiCaL interval CP,SCP,both sat_halfspace_rays_wide_dickinson/ALGORITHM.md support_polished_frank_wolfe_dickinson Support-Polished Frank-Wolfe Dickinson retained Dickinson intervals frank_wolfe_dickinson Adds an exact active-support polish before Dickinson. none interval CP,SCP,both support_polished_frank_wolfe_dickinson/ALGORITHM.md support_pruned_dickinson Support-Pruned Dickinson retained Dickinson intervals dickinson_2019 Adds upward support pruning to Dickinson. none interval CP,SCP,both support_pruned_dickinson/ALGORITHM.md upper_endpoint_cbdd_dickinson Upper-Endpoint CBDD Dickinson retained Dickinson intervals cbdd_dickinson Solves each distinct larger certificate upper endpoint before activation. CBDD interval CP,SCP,both upper_endpoint_cbdd_dickinson/ALGORITHM.md wide_certificate_cbdd_dickinson Wide-Certificate CBDD Dickinson retained Dickinson intervals cbdd_dickinson Keeps a full interval only when its width exceeds the configured percentage threshold. CBDD interval CP,SCP,both wide_certificate_cbdd_dickinson/ALGORITHM.md wide_certificate_sat_dickinson Wide-Certificate SAT Dickinson retained Dickinson intervals sat_dickinson Keeps a full interval only when its width exceeds the configured percentage threshold. CaDiCaL interval CP,SCP,both wide_certificate_sat_dickinson/ALGORITHM.md xxx XXX retained Dickinson intervals sat_halfspace_rays_dickinson Adds exact KKT active-set paths whose interval batches commit only at a terminal point. CaDiCaL interval CP,SCP,both xxx/ALGORITHM.md xxx_two XXX Two retained Dickinson intervals xxx Uses binary64 KKT paths with exact verification, alternative-pivot backtracking, and path avoidance. CaDiCaL interval CP,SCP,both xxx_two/ALGORITHM.md zdd_dickinson ZDD Dickinson retained Dickinson intervals dickinson_2019 Represents the Dickinson interval union with a zero-suppressed decision diagram. ZDD interval CP,SCP,both zdd_dickinson/ALGORITHM.md zischg_dickinson Zischg-Dickinson retained support enumeration dickinson_2019 Applies Zischg Level 2 inside Dickinson supports. none interval CP,SCP,both zischg_dickinson/ALGORITHM.md zischg_fracessa Zischg-FracESSA retained support enumeration fracessa Applies Zischg Level 2 inside FracESSA supports. none upward CP,SCP,both zischg_fracessa/ALGORITHM.md zischg_hadeler Zischg-Hadeler retained support enumeration hadeler_1983 Applies Zischg Level 2 inside Hadeler supports. none upward CP,SCP,both zischg_hadeler/ALGORITHM.md