diff --git a/src/sat/smt/polysat_core.cpp b/src/sat/smt/polysat_core.cpp
index d4b62e8b6..be4bb0cf0 100644
--- a/src/sat/smt/polysat_core.cpp
+++ b/src/sat/smt/polysat_core.cpp
@@ -308,4 +308,8 @@ namespace polysat {
         return m_assignment.apply_to(p);
     }
 
+    trail_stack& core::trail() {
+        return s.get_trail_stack();
+    }
+
 }
diff --git a/src/sat/smt/polysat_core.h b/src/sat/smt/polysat_core.h
index 3c8a79bd6..b7c9f9eb8 100644
--- a/src/sat/smt/polysat_core.h
+++ b/src/sat/smt/polysat_core.h
@@ -128,6 +128,7 @@ namespace polysat {
         unsigned size(pvar v) const { return var2pdd(v).power_of_2(); }
 
         constraints& cs() { return m_constraints; }
+        trail_stack& trail();
 
         std::ostream& display(std::ostream& out) const { throw default_exception("nyi"); }
     };
diff --git a/src/sat/smt/polysat_viable.cpp b/src/sat/smt/polysat_viable.cpp
index deb6d415c..d68822563 100644
--- a/src/sat/smt/polysat_viable.cpp
+++ b/src/sat/smt/polysat_viable.cpp
@@ -42,6 +42,32 @@ namespace polysat {
         }
     }
 
+    struct viable::pop_viable_trail : public trail {
+        viable& m_s;
+        entry* e;
+        pvar v;
+        entry_kind k;
+    public:
+        pop_viable_trail(viable& s, entry* e, pvar v, entry_kind k)
+            : m_s(s), e(e), v(v), k(k) {}
+        void undo() override {
+            m_s.pop_viable(e, v, k);
+        }
+    };
+
+    struct viable::push_viable_trail : public trail {
+        viable& m_s;
+        entry* e;
+        pvar v;
+        entry_kind k;
+    public:
+        push_viable_trail(viable& s, entry* e, pvar v, entry_kind k)
+            : m_s(s), e(e), v(v), k(k) {}
+        void undo() override {
+            m_s.push_viable(e, v, k);
+        }
+    };
+
     viable::entry* viable::alloc_entry(pvar var) {
         if (m_alloc.empty())
             return alloc(entry);
@@ -52,7 +78,10 @@ namespace polysat {
         return e;
     }
 
-    find_t viable::find_viable(pvar v, rational& out_val) { throw default_exception("nyi"); }
+    find_t viable::find_viable(pvar v, rational& out_val) { 
+        ensure_var(v);
+        throw default_exception("nyi"); 
+    }
 
     /*
     * Explain why the current variable is not viable or signleton.
@@ -63,6 +92,9 @@ namespace polysat {
     * Register constraint at index 'idx' as unitary in v.
     */
     void viable::add_unitary(pvar v, unsigned idx) {
+
+        ensure_var(v);
+
         if (c.is_assigned(v))
             return;
         auto [sc, d] = c.m_constraint_trail[idx];
@@ -76,7 +108,7 @@ namespace polysat {
         if (ne->interval.is_currently_empty()) {
             m_alloc.push_back(ne);
             return;
-        }
+        }        
 
         if (ne->coeff == 1) {
             intersect(v, ne);
@@ -144,7 +176,7 @@ namespace polysat {
                 ne->bit_width -= k;
                 display_one(std::cerr << "reduced entry:  ", v, ne) << "\n";
                 LOG("reduced entry to unit in bitwidth " << ne->bit_width);
-                return intersect(v, ne);
+                intersect(v, ne);
             }
 
             // TODO: later, can reduce according to shared_parity
@@ -153,12 +185,92 @@ namespace polysat {
             insert(ne, v, m_equal_lin, entry_kind::equal_e);
             return;
         }
-
     }
 
-    void viable::intersect(pvar v, entry* e) {
+    void viable::ensure_var(pvar v) {
+        while (v >= m_units.size()) {
+            m_units.push_back(layers());
+            m_equal_lin.push_back(nullptr);
+            m_diseq_lin.push_back(nullptr);
+        }
+    }
 
-        throw default_exception("nyi");
+    bool viable::intersect(pvar v, entry* ne) {
+        SASSERT(!c.is_assigned(v));
+        SASSERT(!ne->src.empty());
+        entry*& entries = m_units[v].ensure_layer(ne->bit_width).entries;
+        entry* e = entries;
+        if (e && e->interval.is_full()) {
+            m_alloc.push_back(ne);
+            return false;
+        }
+
+        if (ne->interval.is_currently_empty()) {
+            m_alloc.push_back(ne);
+            return false;
+        }
+
+        auto create_entry = [&]() {
+            c.trail().push(pop_viable_trail(*this, ne, v, entry_kind::unit_e));
+            ne->init(ne);
+            return ne;
+            };
+
+        auto remove_entry = [&](entry* e) {
+            c.trail().push(push_viable_trail(*this, e, v, entry_kind::unit_e));
+            e->remove_from(entries, e);
+            e->active = false;
+            };
+
+        if (ne->interval.is_full()) {
+            // for (auto const& l : m_units[v].get_layers())
+            //     while (l.entries)
+            //         remove_entry(l.entries);
+            while (entries)
+                remove_entry(entries);
+            entries = create_entry();
+            return true;
+        }
+
+        if (!e)
+            entries = create_entry();
+        else {
+            entry* first = e;
+            do {
+                if (e->interval.currently_contains(ne->interval)) {
+                    m_alloc.push_back(ne);
+                    return false;
+                }
+                while (ne->interval.currently_contains(e->interval)) {
+                    entry* n = e->next();
+                    remove_entry(e);
+                    if (!entries) {
+                        entries = create_entry();
+                        return true;
+                    }
+                    if (e == first)
+                        first = n;
+                    e = n;
+                }
+                SASSERT(e->interval.lo_val() != ne->interval.lo_val());
+                if (e->interval.lo_val() > ne->interval.lo_val()) {
+                    if (first->prev()->interval.currently_contains(ne->interval)) {
+                        m_alloc.push_back(ne);
+                        return false;
+                    }
+                    e->insert_before(create_entry());
+                    if (e == first)
+                        entries = e->prev();
+                    SASSERT(well_formed(m_units[v]));
+                    return true;
+                }
+                e = e->next();
+            } while (e != first);
+            // otherwise, append to end of list
+            first->insert_before(create_entry());
+        }
+        SASSERT(well_formed(m_units[v]));
+        return true;
     }
 
     void viable::log() {
@@ -170,10 +282,94 @@ namespace polysat {
         throw default_exception("nyi");
     }
 
-    void viable::insert(entry* e, pvar v, ptr_vector<entry>& entries, entry_kind k) {
-        throw default_exception("nyi");
+
+    viable::layer& viable::layers::ensure_layer(unsigned bit_width) {
+        for (unsigned i = 0; i < m_layers.size(); ++i) {
+            layer& l = m_layers[i];
+            if (l.bit_width == bit_width)
+                return l;
+            else if (l.bit_width < bit_width) {
+                m_layers.push_back(layer(0));
+                for (unsigned j = m_layers.size(); --j > i; )
+                    m_layers[j] = m_layers[j - 1];
+                m_layers[i] = layer(bit_width);
+                return m_layers[i];
+            }
+        }
+        m_layers.push_back(layer(bit_width));
+        return m_layers.back();
     }
 
+    viable::layer* viable::layers::get_layer(unsigned bit_width) {
+        return const_cast<layer*>(std::as_const(*this).get_layer(bit_width));
+    }
+
+    viable::layer const* viable::layers::get_layer(unsigned bit_width) const {
+        for (layer const& l : m_layers)
+            if (l.bit_width == bit_width)
+                return &l;
+        return nullptr;
+    }
+
+    void viable::pop_viable(entry* e, pvar v, entry_kind k) {
+        SASSERT(well_formed(m_units[v]));
+        SASSERT(e->active);
+        e->active = false;
+        switch (k) {
+        case entry_kind::unit_e:
+            entry::remove_from(m_units[v].get_layer(e)->entries, e);
+            SASSERT(well_formed(m_units[v]));
+            break;
+        case entry_kind::equal_e:
+            entry::remove_from(m_equal_lin[v], e);
+            break;
+        case entry_kind::diseq_e:
+            entry::remove_from(m_diseq_lin[v], e);
+            break;
+        default:
+            UNREACHABLE();
+            break;
+        }
+        m_alloc.push_back(e);
+    }
+
+    void viable::push_viable(entry* e, pvar v, entry_kind k) {
+        // display_one(verbose_stream() << "Push entry: ", v, e) << "\n";
+        entry*& entries = m_units[v].get_layer(e)->entries;
+        SASSERT(e->prev() != e || !entries);
+        SASSERT(e->prev() != e || e->next() == e);
+        SASSERT(k == entry_kind::unit_e);
+        SASSERT(!e->active);
+        e->active = true;
+        (void)k;
+        SASSERT(well_formed(m_units[v]));
+        if (e->prev() != e) {
+            entry* pos = e->prev();
+            e->init(e);
+            pos->insert_after(e);
+            if (e->interval.lo_val() < entries->interval.lo_val())
+                entries = e;
+        }
+        else
+            entries = e;
+        SASSERT(well_formed(m_units[v]));
+    }
+
+    void viable::insert(entry* e, pvar v, ptr_vector<entry>& entries, entry_kind k) {
+        SASSERT(well_formed(m_units[v]));
+
+        c.trail().push(pop_viable_trail(*this, e, v, k));
+
+        e->init(e);
+        if (!entries[v])
+            entries[v] = e;
+        else
+            e->insert_after(entries[v]);
+        SASSERT(entries[v]->invariant());
+        SASSERT(well_formed(m_units[v]));
+    }
+
+
     std::ostream& viable::display_one(std::ostream& out, pvar v, entry const* e) const {
         auto& m = c.var2pdd(v);
         if (e->coeff == -1) {
@@ -229,4 +425,51 @@ namespace polysat {
         return out;
     }
 
+      /*
+     * Lower bounds are strictly ascending.
+     * Intervals don't contain each-other (since lower bounds are ascending, it suffices to check containment in one direction).
+     */
+    bool viable::well_formed(entry* e) {
+        if (!e)
+            return true;
+        entry* first = e;
+        while (true) {
+            if (!e->active)
+                return false;
+
+            if (e->interval.is_full())
+                return e->next() == e;
+            if (e->interval.is_currently_empty())
+                return false;
+
+            auto* n = e->next();
+            if (n != e && e->interval.currently_contains(n->interval))
+                return false;
+
+            if (n == first)
+                break;
+            if (e->interval.lo_val() >= n->interval.lo_val())
+                return false;
+            e = n;
+        }
+        return true;
+    }
+
+    /*
+     * Layers are ordered in strictly descending bit-width.
+     * Entries in each layer are well-formed.
+     */
+    bool viable::well_formed(layers const& ls) {
+        unsigned prev_width = std::numeric_limits<unsigned>::max();
+        for (layer const& l : ls.get_layers()) {
+            if (!well_formed(l.entries))
+                return false;
+            if (!all_of(dll_elements(l.entries), [&l](entry const& e) { return e.bit_width == l.bit_width; }))
+                return false;
+            if (prev_width <= l.bit_width)
+                return false;
+            prev_width = l.bit_width;
+        }
+        return true;
+    }
 }
diff --git a/src/sat/smt/polysat_viable.h b/src/sat/smt/polysat_viable.h
index 322b30551..f1c826d10 100644
--- a/src/sat/smt/polysat_viable.h
+++ b/src/sat/smt/polysat_viable.h
@@ -86,6 +86,9 @@ namespace polysat {
         ptr_vector<entry>       m_equal_lin;    // entries that have non-unit multipliers, but are equal
         ptr_vector<entry>       m_diseq_lin;    // entries that have distinct non-zero multipliers
 
+        bool well_formed(entry* e);
+        bool well_formed(layers const& ls);
+
         entry* alloc_entry(pvar v);
 
         std::ostream& display_one(std::ostream& out, pvar v, entry const* e) const;
@@ -93,13 +96,20 @@ namespace polysat {
         void log();
         void log(pvar v);
 
+        struct pop_viable_trail;
+        void pop_viable(entry* e, pvar v, entry_kind k);
+        struct push_viable_trail;
+        void push_viable(entry* e, pvar v, entry_kind k);
+
         void insert(entry* e, pvar v, ptr_vector<entry>& entries, entry_kind k);
 
-        void intersect(pvar v, entry* e);
+        bool intersect(pvar v, entry* e);
 
+        void ensure_var(pvar v);
 
     public:
         viable(core& c);
+
         ~viable();
 
         /**