diff --git a/tooling/web/index.html b/tooling/web/index.html
index 6dfbbe3e..d3409a8d 100644
--- a/tooling/web/index.html
+++ b/tooling/web/index.html
@@ -13,8 +13,8 @@
   <script language="javascript">
     window.onload = function() {
       console.log("onload!");
-      // let fname = "json/fibonacci_witness.json";
-      let fname = "json/lookup_witness.json";
+      let fname = "json/fibonacci_witness.json";
+      // let fname = "json/lookup_witness.json";
       // let fname = "json/outer_witness.json";
       load_witness(fname);
     }
@@ -51,6 +51,7 @@
         <tr>
           <th>index</th>
           <th width="200px">gate type</th>
+          <th>count</th>
         </tr>
       </table>
     </div>
@@ -61,12 +62,12 @@
 
     <div class="horiz">
       <table id="cell-properties">
-        <tr><th>property</th><th width="200px">value (hover!)</th></tr>
-        <tr><td>row     </td><td id="cell-row"   ></td></tr>
-        <tr><td>column  </td><td id="cell-column"></td></tr>
-        <tr><td>value   </td><td id="cell-value" ></td></tr>
-        <tr><td>gate    </td><td id="cell-gate"  ></td></tr>
-        <tr><td>equation</td><td id="cell-equ"   ></td></tr>
+        <tr><th>property </th><th width="200px">value (hover!)</th></tr>
+        <tr><td>gate     </td><td id="cell-gate"  ></td></tr>
+        <tr><td>position </td><td id="cell-pos"   ></td></tr>
+        <tr><td>value    </td><td id="cell-value" ></td></tr>
+        <tr><td>role     </td><td id="cell-role"  ></td></tr>
+        <tr><td>equation </td><td id="cell-equ"   ></td></tr>
       </table>
     </div>  
 
diff --git a/tooling/web/json/fibonacci_witness.json b/tooling/web/json/fibonacci_witness.json
index 2f405ca5..168a8deb 100644
--- a/tooling/web/json/fibonacci_witness.json
+++ b/tooling/web/json/fibonacci_witness.json
@@ -1 +1 @@
-{"gates":["ConstantGate:2","PublicInputGate","ArithmeticGate:20","PoseidonGate:12"],"selector_vector":[2,2,2,2,2,3,1,0],"matrix":[[0,6765,102334155,1548008755920,23416728348467685,0,8416658900775745054,0],[1,1,1,1,1,1,12574228347150446423,1],[1,10946,165580141,2504730781961,37889062373143906,3736710860384812976,9629056739760131473,0],[1,17711,267914296,4052739537881,61305790721611591,0,3119289788404190010,0],[1,10946,165580141,2504730781961,37889062373143906,0,0,0],[1,1,1,1,1,0,0,0],[1,17711,267914296,4052739537881,61305790721611591,0,0,0],[2,28657,433494437,6557470319842,99194853094755497,0,0,0],[1,17711,267914296,4052739537881,61305790721611591,0,0,0],[1,1,1,1,1,0,0,0],[2,28657,433494437,6557470319842,99194853094755497,0,0,0],[3,46368,701408733,10610209857723,160500643816367088,0,0,0],[2,28657,433494437,6557470319842,99194853094755497,8416658900775745054,0,0],[1,1,1,1,1,12574228347150446423,0,0],[3,46368,701408733,10610209857723,160500643816367088,9629056739760131473,0,0],[5,75025,1134903170,17167680177565,259695496911122585,3119289788404190010,0,0],[3,46368,701408733,10610209857723,160500643816367088,14861960955103405647,0,0],[1,1,1,1,1,372802127489869527,0,0],[5,75025,1134903170,17167680177565,259695496911122585,17949976003686161308,0,0],[8,121393,1836311903,27777890035288,420196140727489673,1857324986026215171,0,0],[5,75025,1134903170,17167680177565,259695496911122585,5971167677106193079,0,0],[1,1,1,1,1,11693818845587106938,0,0],[8,121393,1836311903,27777890035288,420196140727489673,2069952246609707872,0,0],[13,196418,2971215073,44945570212853,679891637638612258,217879661521314238,0,0],[8,121393,1836311903,27777890035288,420196140727489673,0,0,0],[1,1,1,1,1,0,0,0],[13,196418,2971215073,44945570212853,679891637638612258,0,0,0],[21,317811,4807526976,72723460248141,1100087778366101931,0,0,0],[13,196418,2971215073,44945570212853,679891637638612258,0,0,0],[1,1,1,1,1,10040222711290671429,0,0],[21,317811,4807526976,72723460248141,1100087778366101931,14620731031104971238,0,0],[34,514229,7778742049,117669030460994,1779979416004714189,17044025898016030703,0,0],[21,317811,4807526976,72723460248141,1100087778366101931,7238567237932994928,0,0],[1,1,1,1,1,15906345692884439372,0,0],[34,514229,7778742049,117669030460994,1779979416004714189,5144700563978952905,0,0],[55,832040,12586269025,190392490709135,2880067194370816120,8166204101423404765,0,0],[34,514229,7778742049,117669030460994,1779979416004714189,477486086501229569,0,0],[1,1,1,1,1,9608939408992013865,0,0],[55,832040,12586269025,190392490709135,2880067194370816120,3967372222851101859,0,0],[89,1346269,20365011074,308061521170129,4660046610375530309,6747904536878816765,0,0],[55,832040,12586269025,190392490709135,2880067194370816120,10676707001551177325,0,0],[1,1,1,1,1,15582639502207228120,0,0],[89,1346269,20365011074,308061521170129,4660046610375530309,13686409820604502173,0,0],[144,2178309,32951280099,498454011879264,7540113804746346429,1567790829695590004,0,0],[89,1346269,20365011074,308061521170129,4660046610375530309,17435189342848201979,0,0],[1,1,1,1,1,6880593622141894941,0,0],[144,2178309,32951280099,498454011879264,7540113804746346429,8426833217377909941,0,0],[233,3524578,53316291173,806515533049393,12200160415121876738,1750952861857697999,0,0],[144,2178309,32951280099,498454011879264,7540113804746346429,7363947565712320428,0,0],[1,1,1,1,1,3124824639148633302,0,0],[233,3524578,53316291173,806515533049393,12200160415121876738,9815057002508797666,0,0],[377,5702887,86267571272,1304969544928657,1293530150453638846,8800225758791566091,0,0],[233,3524578,53316291173,806515533049393,12200160415121876738,15770247867912269728,0,0],[1,1,1,1,1,3135653937829880960,0,0],[377,5702887,86267571272,1304969544928657,1293530150453638846,15779646663237235129,0,0],[610,9227465,139583862445,2111485077978050,13493690565575515584,6797675489104882722,0,0],[377,5702887,86267571272,1304969544928657,1293530150453638846,2449041418020548842,0,0],[1,1,1,1,1,7190423305376289408,0,0],[610,9227465,139583862445,2111485077978050,13493690565575515584,17337800908067952557,0,0],[987,14930352,225851433717,3416454622906707,14787220716029154430,5830228614653198906,0,0],[610,9227465,139583862445,2111485077978050,13493690565575515584,8884464056103704513,0,0],[1,1,1,1,1,5363825021791947577,0,0],[987,14930352,225851433717,3416454622906707,14787220716029154430,15220052284474590997,0,0],[1597,24157817,365435296162,5527939700884757,9834167212190085693,8505277843539538987,0,0],[987,14930352,225851433717,3416454622906707,14787220716029154430,9904213084008489739,0,0],[1,1,1,1,1,16267234471440708648,0,0],[1597,24157817,365435296162,5527939700884757,9834167212190085693,7397784185928096775,0,0],[2584,39088169,591286729879,8944394323791464,6174643858804655802,18428755921504058133,0,0],[1597,24157817,365435296162,5527939700884757,9834167212190085693,3337122630204711140,0,0],[1,1,1,1,1,16198616623652854046,0,0],[2584,39088169,591286729879,8944394323791464,6174643858804655802,15666646868790223685,0,0],[4181,6324598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\ No newline at end of file
+{"gates":["ConstantGate:2","PublicInputGate","ArithmeticGate:20","PoseidonGate:12"],"selector_vector":[2,2,2,2,2,3,1,0],"selector_columns":[[2,2,2,2,2,4294967295,1,0],[4294967295,4294967295,4294967295,4294967295,4294967295,3,4294967295,4294967295]],"constants_columns":[[1,1,1,1,1,0,0,0],[1,1,1,1,1,0,0,1]],"matrix":[[0,6765,102334155,1548008755920,23416728348467685,0,8416658900775745054,0],[1,1,1,1,1,1,12574228347150446423,1],[1,10946,165580141,2504730781961,37889062373143906,3736710860384812976,9629056739760131473,0],[1,17711,267914296,4052739537881,61305790721611591,0,3119289788404190010,0],[1,10946,165580141,2504730781961,37889062373143906,0,0,0],[1,1,1,1,1,0,0,0],[1,17711,267914296,4052739537881,61305790721611591,0,0,0],[2,28657,433494437,6557470319842,99194853094755497,0,0,0],[1,17711,267914296,4052739537881,61305790721611591,0,0,0],[1,1,1,1,1,0,0,0],[2,28657,433494437,6557470319842,99194853094755497,0,0,0],[3,46368,701408733,10610209857723,160500643816367088,0,0,0],[2,28657,433494437,6557470319842,99194853094755497,8416658900775745054,0,0],[1,1,1,1,1,12574228347150446423,0,0],[3,46368,701408733,10610209857723,160500643816367088,9629056739760131473,0,0],[5,75025,1134903170,17167680177565,259695496911122585,3119289788404190010,0,0],[3,46368,701408733,10610209857723,160500643816367088,14861960955103405647,0,0],[1,1,1,1,1,372802127489869527,0,0],[5,75025,1134903170,17167680177565,259695496911122585,17949976003686161308,0,0],[8,121393,1836311903,27777890035288,420196140727489673,1857324986026215171,0,0],[5,75025,1134903170,17167680177565,259695496911122585,5971167677106193079,0,0],[1,1,1,1,1,11693818845587106938,0,0],[8,121393,1836311903,27777890035288,420196140727489673,2069952246609707872,0,0],[13,196418,2971215073,44945570212853,679891637638612258,217879661521314238,0,0],[8,121393,1836311903,27777890035288,420196140727489673,0,0,0],[1,1,1,1,1,0,0,0],[13,196418,2971215073,44945570212853,679891637638612258,0,0,0],[21,317811,4807526976,72723460248141,1100087778366101931,0,0,0],[13,196418,2971215073,44945570212853,679891637638612258,0,0,0],[1,1,1,1,1,10040222711290671429,0,0],[21,317811,4807526976,72723460248141,1100087778366101931,14620731031104971238,0,0],[34,514229,7778742049,117669030460994,1779979416004714189,17044025898016030703,0,0],[21,317811,4807526976,72723460248141,1100087778366101931,7238567237932994928,0,0],[1,1,1,1,1,15906345692884439372,0,0],[34,514229,7778742049,117669030460994,1779979416004714189,5144700563978952905,0,0],[55,832040,12586269025,190392490709135,2880067194370816120,8166204101423404765,0,0],[34,514229,7778742049,117669030460994,1779979416004714189,477486086501229569,0,0],[1,1,1,1,1,9608939408992013865,0,0],[55,832040,12586269025,190392490709135,2880067194370816120,3967372222851101859,0,0],[89,1346269,20365011074,308061521170129,4660046610375530309,6747904536878816765,0,0],[55,832040,12586269025,190392490709135,2880067194370816120,10676707001551177325,0,0],[1,1,1,1,1,15582639502207228120,0,0],[89,1346269,20365011074,308061521170129,4660046610375530309,13686409820604502173,0,0],[144,2178309,32951280099,498454011879264,7540113804746346429,1567790829695590004,0,0],[89,1346269,20365011074,308061521170129,4660046610375530309,17435189342848201979,0,0],[1,1,1,1,1,6880593622141894941,0,0],[144,2178309,32951280099,498454011879264,7540113804746346429,8426833217377909941,0,0],[233,3524578,53316291173,806515533049393,12200160415121876738,1750952861857697999,0,0],[144,2178309,32951280099,498454011879264,7540113804746346429,7363947565712320428,0,0],[1,1,1,1,1,3124824639148633302,0,0],[233,3524578,53316291173,806515533049393,12200160415121876738,9815057002508797666,0,0],[377,5702887,86267571272,1304969544928657,1293530150453638846,8800225758791566091,0,0],[233,3524578,53316291173,806515533049393,12200160415121876738,15770247867912269728,0,0],[1,1,1,1,1,3135653937829880960,0,0],[377,5702887,86267571272,1304969544928657,1293530150453638846,15779646663237235129,0,0],[610,9227465,139583862445,2111485077978050,13493690565575515584,6797675489104882722,0,0],[377,5702887,86267571272,1304969544928657,1293530150453638846,2449041418020548842,0,0],[1,1,1,1,1,7190423305376289408,0,0],[610,9227465,139583862445,2111485077978050,13493690565575515584,17337800908067952557,0,0],[987,14930352,225851433717,3416454622906707,14787220716029154430,5830228614653198906,0,0],[610,9227465,139583862445,2111485077978050,13493690565575515584,8884464056103704513,0,0],[1,1,1,1,1,5363825021791947577,0,0],[987,14930352,225851433717,3416454622906707,14787220716029154430,15220052284474590997,0,0],[1597,24157817,365435296162,5527939700884757,9834167212190085693,8505277843539538987,0,0],[987,14930352,225851433717,3416454622906707,14787220716029154430,9904213084008489739,0,0],[1,1,1,1,1,16267234471440708648,0,0],[1597,24157817,365435296162,5527939700884757,9834167212190085693,7397784185928096775,0,0],[2584,39088169,591286729879,8944394323791464,6174643858804655802,18428755921504058133,0,0],[1597,24157817,365435296162,5527939700884757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\ No newline at end of file
diff --git a/tooling/web/json/lookup_witness.json b/tooling/web/json/lookup_witness.json
index a62b69d1..4b067d64 100644
--- a/tooling/web/json/lookup_witness.json
+++ b/tooling/web/json/lookup_witness.json
@@ -1 +1 @@
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\ No newline at end of file
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314842203320,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[7472,0,7976893166980171693,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,3294414182795338912,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,10629380326888464431,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,10965386824795285604,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,16580269766603961508,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,7081170191930415462,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,381307495885208396,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,11932338890327294610,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,7943922424945436927,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,1356209259737028615,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,9686499502336256849,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,14185401620502514371,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,14525350591386907402,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,16174966815064726157,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,4597294708103049064,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,8140299135400446575,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,13794753086841857347,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,2241041278393919561,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,8289219537838690270,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,823597923857216372,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,8103900730341474847,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,3901225314336218149,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,11961022605790926417,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,6016822306250094533,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,9139298751831861554,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,213400138394106660,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,6259406545409643520,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,14260021141567171556,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,4374816455822456400,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,13966210279958166634,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,1725313968750515219,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,8903494261937866510,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,10831885624052065615,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,9683929612847379814,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,14065908482739460769,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,5569978174269184675,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,8045969578281302085,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,9447216028941965124,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,11883785987246910104,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,4401962237608612124,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,1509999318285604330,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,5980292828683614171,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,17295352549468725573,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,5123326422423265999,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,15728015560999139260,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,4724187432461175180,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,14893952206814687238,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,316456214706582908,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,15342274545351413482,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,13919793037093762578,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,9645801232492508797,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,3563678755708640732,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,10094996241642241518,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,5393738275170507032,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,17493883008068174620,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],[0,0,15756498557682406521,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]}
\ No newline at end of file
diff --git a/tooling/web/witness_view.js b/tooling/web/witness_view.js
index 689ebfcf..c6abe0e9 100644
--- a/tooling/web/witness_view.js
+++ b/tooling/web/witness_view.js
@@ -39,12 +39,142 @@ const the_gate_colors =
   , "#c060c0"     // ReducingExtensionGate       -> medium purple
   ];
 
+function div(a,b) { return Math.floor(a/b); }
+
+function role_Unknown(i,params) { return "n/a"; }
+
+function role_ArithmeticGate(i,params) { 
+  let numops = params[0];
+  if (i>=4*numops) return "unused"; 
+  let k = div(i,4);
+  switch(i%4) { 
+    case 0: return "x" + k;
+    case 1: return "y" + k;
+    case 2: return "z" + k;
+    case 3: return "w" + k;
+  }
+}
+
+function role_ArithmeticExtensionGate(i,params) { 
+  let numops = params[0];
+  if (i>=8*numops) return "unused"; 
+  let k  = div(i,8);
+  let ir = ((i%2) == 0) ? 'r' : 'i';
+  let j  = div(i,2);
+  switch(j%4) { 
+    case 0: return "x" + ir + k;
+    case 1: return "y" + ir + k;
+    case 2: return "z" + ir + k;
+    case 3: return "w" + ir + k;
+  }
+}
+
+function role_LookupGate(i,params) { 
+  let numops = params[0];
+  if (i>=2*numops) return "unused";
+  let k = div(i,2);
+  switch(i%2) { 
+    case 0: return "inp" + k;
+    case 1: return "out" + k;
+  }
+}
+
+function role_LookupTableGate(i,params) {
+  let numops = params[0];
+  if (i>=3*numops) return "unused";
+  let k = div(i,3);
+  switch(i%3) { 
+    case 0: return "inp"  + k;
+    case 1: return "out"  + k;
+    case 2: return "mult" + k;
+  }
+}
+
+function role_NoopGate(i,params) { return "unused"; }
+
+function role_ConstantGate(i,params) { 
+  let nconsts = params[0]
+  if (i>=nconsts) return "unused"
+  return ("x" + i);
+}
+
+function role_PoseidonGate(i,params) {
+  if (i< 12) { return "input"  + (i   ); }
+  if (i< 24) { return "output" + (i-12); }
+  if (i==24) { return "swap_flag";       }
+  if (i< 29) { return "delta" + (i-25);  }
+  if (i< 65) { return "round=" + (div((i-29),12)+1) + " sbox" + ((i-29)%12) + "_in"; }
+  if (i< 87) { return "round=" + (i-65+4) + " sbox_in"; } 
+  return "round=" + (div((i-87),12)+26) + " sbox" + ((i-87)%12) + "_in"; 
+}
+
+function role_BaseSumGate(i,params) {
+  let radix = params[0];
+  if (i>=radix+1) return "unused";
+  if (i==0) return "sum";
+  return ("limb" + (i-1));
+}
+
+function role_MultiplicationExtensionGate(i,params) { 
+  let numops = params[0];
+  if (i>=6*numops) return "unused"; 
+  let k  = div(i,6);
+  let ir = ((i%2) == 0) ? 'r' : 'i';
+  let j  = div(i,2);
+  switch(j%3) { 
+    case 0: return "x" + ir + k;
+    case 1: return "y" + ir + k;
+    case 2: return "z" + ir + k;
+  }
+}
+
+function role_PublicInputGate(i,params) {
+  if (i>=4) return "unused";
+  return ("hash" + i); 
+}
+
+function role_ExponentiationGate(i,params) {
+  let exp_bits = params[0];
+  if (i==0)            return "base";
+  if (i<=exp_bits)     return "expo" + (i-1);
+  if (i==exp_bits+1)   return "output"
+  if (i< 2*exp_bits+2) return "tmp" + (i-exp_bits-2);
+  return "unused";
+}
+
+function role_CosetInterpolationGate      (i,params) { return "dunno"; }
+function role_MultiplicationExtensionGate (i,params) { return "dunno"; }
+function role_PoseidonMdsGate             (i,params) { return "dunno"; }
+function role_RandomAccessGate            (i,params) { return "dunno"; }
+function role_ReducingGate                (i,params) { return "dunno"; }
+function role_ReducingExtensionGate       (i,params) { return "dunno"; }
+
+const the_roles = 
+  [ role_Unknown
+  , role_ArithmeticGate
+  , role_ArithmeticExtensionGate
+  , role_BaseSumGate
+  , role_ConstantGate
+  , role_CosetInterpolationGate
+  , role_ExponentiationGate
+  , role_LookupGate
+  , role_LookupTableGate
+  , role_MultiplicationExtensionGate 
+  , role_NoopGate
+  , role_PoseidonGate
+  , role_PoseidonMdsGate
+  , role_PublicInputGate
+  , role_RandomAccessGate
+  , role_ReducingGate
+  , role_ReducingExtensionGate
+  ];
+
 const the_gate_equations = 
   [ "???"                  // UnknownGate   
   , "w = c0*x*y + c1*z"    // ArithmeticGate
   , "w = c0*x*y + c1*z"    // ArithmeticExtensionGate 
   , "y = sum_i 2^i*b_i"    // BaseSumGate    
-  , "x=c0, y=c1"           // ConstantGate                
+  , "x0=c0, x1=c1"         // ConstantGate                
   , "..."                  // CosetInterpolationGate      
   , "y = x^k"              // ExponentiationGate          
   , "(x,y) in T"           // LookupGate                  
@@ -64,15 +194,17 @@ function findGateIndex(gate) {
   return ((k<0) ? 0 : k);
 } 
 
-function add_table_row(table, idx, text, color) {
+function add_table_row(table, idx, text, count, color) {
   let tr = document.createElement("tr");
   tr.style.background = (color)?color:"#fffff";
 
   let td1 = document.createElement("td"); td1.innerHTML = idx.toString();
   let td2 = document.createElement("td"); td2.innerHTML = text;
+  let td3 = document.createElement("td"); td3.innerHTML = count.toString();
 
   tr.appendChild(td1);
   tr.appendChild(td2);
+  tr.appendChild(td3);
   table.appendChild(tr);
 }
 
@@ -95,22 +227,28 @@ var ncolumns;
 var ncells;
 
 var gates_base   = []; 
+var gates_params = []; 
 var gate_colors  = [];
 var gate_indices = [];       // index into our tables from the selector index
-
+var gate_counts  = [];  
 
 function cell_hover(row,column) {
-  let el_row  = document.getElementById("cell-row"   );
-  let el_col  = document.getElementById("cell-column");
+  let el_pos  = document.getElementById("cell-pos"   );
   let el_val  = document.getElementById("cell-value" );
   let el_gate = document.getElementById("cell-gate"  );
   let el_equ  = document.getElementById("cell-equ"   );
-  let sel = selectors[row];
-  el_row.innerHTML  = row.toString();
-  el_col.innerHTML  = column.toString();
+  let el_role = document.getElementById("cell-role"  );
+  let sel    = selectors[row];
+  let gate   = gate_indices[sel];
+  let params = gates_params[sel];
+  //console.log(gates[sel] + " : " + params);
+  el_pos.innerHTML  = "row=" + row.toString() + " , col=" + column.toString();
   el_val.innerHTML  = matrix[column][row].toString();
   el_gate.innerHTML = gates[sel];
-  el_equ.innerHTML  = the_gate_equations[gate_indices[sel]];
+  el_equ.innerHTML  = the_gate_equations[gate];
+  el_role.innerHTML = the_roles[gate](column,params);
+
+  el_gate.style.background = gate_colors[sel];
 }
 
 function initialize_from_witness(fname,json) {
@@ -133,21 +271,26 @@ function initialize_from_witness(fname,json) {
   el_num_rows.innerHTML = nrows.toString();
   el_num_cols.innerHTML = ncolumns.toString();
 
-
   for(let i=0; i<gates.length; i++) {
-    let full = gates[i];
-    let base = full.split(":")[0];
-    gates_base[i] = base;
-
+    let full  = gates[i];
+    let parts = full.split(":");
+    let base  = parts[0];
+    parts.shift();              // remove the first element
+    gates_base[i]   = base;
+    gates_params[i] = parts.map(parseInt);
     k = findGateIndex(base);
     gate_indices[i] = k;
     gate_colors[i]  = the_gate_colors[k];
+    gate_counts[i]  = 0;
+  }
 
+  for(let i=0; i<nrows; i++) {
+    gate_counts[selectors[i]] ++;
   }
 
   let el_table = document.getElementById("gates");
   for(let i=0; i<ngates; i++) {
-    add_table_row(el_table, i, gates[i], gate_colors[i]);
+    add_table_row(el_table, i, gates[i], gate_counts[i], gate_colors[i]);
   }
 
   let el_svg = document.getElementById("matrix");