diff --git a/.gitignore b/.gitignore
index 0fda7a0..9f11b75 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,2 +1 @@
 .idea/
-**/README.md
diff --git a/quadratic_vote/README.md b/quadratic_vote/README.md
new file mode 100644
index 0000000..b243274
--- /dev/null
+++ b/quadratic_vote/README.md
@@ -0,0 +1,243 @@
+# Quadratic Vote
+
+## Summary
+
+`quadratic_vote` is a governance example that demonstrates Leo **library packages**.
+
+Two reusable libraries handle all the math:
+
+| Package | Kind | What it provides |
+|---------|------|-----------------|
+| `sqrt_math` | library | `isqrt` — integer square root via Newton's method |
+| `vote_math` | library | QV weights, credit costs, voter profiles (depends on `sqrt_math`) |
+| `governance.aleo` | program | Private vote records, proposal outcome checks |
+
+Under **Quadratic Voting (QV)**, a participant's vote weight equals ⌊√(token\_balance)⌋ and
+casting *k* votes costs *k²* credits.  This makes influence grow with the square root of
+wealth rather than linearly — fairer to smaller holders.
+
+| Token balance | Vote weight |
+|---------------|-------------|
+| 1             | 1           |
+| 100           | 10          |
+| 225           | 15          |
+| 1 000         | 31          |
+| 10 000        | 100 (cap)   |
+
+This example is inspired by the [Quadratic Voting](https://en.wikipedia.org/wiki/Quadratic_voting)
+mechanism used in decentralised governance systems such as Gitcoin Grants.
+
+## Noteworthy Features
+
+**Library packages** — `sqrt_math` and `vote_math` are pure libraries: they have no
+`.aleo` program name, are never deployed on their own, and only take effect when included
+by a program package.
+
+**Library submodules** — each extra `.leo` file under `src/` becomes a named module.  No
+declaration is needed; the filename is the module name.  Items are accessed as
+`lib_name::module_name::item`.
+
+**Cross-submodule calls within a library** — `vote_math::cost::build_profile` calls
+`vote_math::weight::compute` internally; `sqrt_math::checks::is_perfect_square` calls
+`sqrt_math::newton::isqrt`.
+
+**Cross-library submodule calls** — `vote_math::weight::compute` reaches directly into
+`sqrt_math::newton::isqrt`, demonstrating the full dependency chain
+(`governance → vote_math::cost → vote_math::weight → sqrt_math::newton`).
+
+**Top-level library constants** — `vote_math::MAX_WEIGHT`, `vote_math::MIN_BALANCE`, and
+`sqrt_math::ISQRT_MAX` are defined in each library's `lib.leo` and referenced by name from
+within submodules.
+
+**Library struct export** — `vote_math::cost::VoterProfile` is defined in a submodule (field:
+`weight: u32`) and used directly as a variable type inside `governance.aleo`.
+
+**Private vote receipt** — the `Vote` record is private; the token balance that drove the
+weight computation is never revealed on-chain.
+
+## How to Build
+
+### Option A — clone this repo and build in place
+
+```bash
+cd quadratic_vote
+
+cd sqrt_math  && leo build && cd ..
+cd vote_math  && leo build && cd ..
+cd governance && leo build && cd ..
+```
+
+### Option B — create from scratch with the Leo CLI
+
+```bash
+# Create the two libraries and the program.
+leo new --library sqrt_math
+leo new --library vote_math
+leo new governance
+
+# Wire up dependencies.
+cd vote_math  && leo add sqrt_math --local ../sqrt_math && cd ..
+cd governance && leo add sqrt_math --local ../sqrt_math && cd ..
+cd governance && leo add vote_math  --local ../vote_math  && cd ..
+
+# Copy source files, then build.
+cd sqrt_math  && leo build && cd ..
+cd vote_math  && leo build && cd ..
+cd governance && leo build && cd ..
+```
+
+`leo new --library` creates a library package — `program.json` has no `.aleo` suffix and the
+source lives in `src/lib.leo` instead of `src/main.leo`.  `leo add --local` records the
+dependency in `program.json` and lets the compiler resolve cross-package symbols.
+
+## How to Run
+
+All `leo run` commands are issued from inside the `governance/` directory.
+
+### Cast a vote
+
+A participant's token balance is kept private.  The program derives their QV weight and
+returns a private `Vote` receipt.
+
+```
+leo run cast_vote <proposal_id: field> <token_balance: u32> <approve: bool>
+```
+
+**Alice (1 000 tokens, approval):**
+```bash
+leo run cast_vote 1field 1000u32 true
+```
+
+Output:
+```
+{
+  owner: aleo1...private,
+  proposal_id: 1field.private,
+  weight: 31u32.private,
+  approve: true.private,
+  _nonce: ...group.public,
+  _version: 1u8.public
+}
+```
+
+**Bob (225 tokens, rejection):**
+```bash
+leo run cast_vote 1field 225u32 false
+```
+
+**Carol (10 000 tokens — hits the `MAX_WEIGHT` cap of 100):**
+```bash
+leo run cast_vote 1field 10000u32 true
+```
+
+### Query the credit cost of casting votes
+
+```
+leo run qv_cost <votes: u32>
+```
+
+How much does it cost to cast 5 votes?
+
+```bash
+leo run qv_cost 5u32
+# Output: 25u32  (= 5²)
+```
+
+### Check whether a number is a perfect square
+
+```
+leo run has_perfect_sqrt <token_balance: u32>
+```
+
+This function bypasses `vote_math` entirely and calls `sqrt_math::checks::is_perfect_square`
+directly, illustrating that a program can reach any library submodule independently.
+
+```bash
+leo run has_perfect_sqrt 1024u32   # 1024 = 32²  → true
+leo run has_perfect_sqrt 1000u32   # 31² = 961, 32² = 1024  → false
+```
+
+### Check whether a proposal is passing
+
+```
+leo run is_passing <approvals: u32> <rejections: u32>
+```
+
+After tallying Alice (31) + Carol (100) = 131 approvals vs Bob's 15 rejections:
+
+```bash
+leo run is_passing 131u32 15u32
+# Output: true
+```
+
+## Run the unit tests
+
+From inside `governance/`:
+
+```bash
+leo test
+```
+
+18 tests covering `cast_vote`, `qv_cost`, `has_perfect_sqrt`, and `is_passing`.
+
+## Run the full demo
+
+```bash
+bash run.sh
+```
+
+## Project structure
+
+Each library is split into **submodules** — separate `.leo` files under `src/` that are
+automatically discovered by the compiler.  No explicit `module` keyword is needed; the
+filename becomes the module name.
+
+```
+quadratic_vote/
+├── sqrt_math/                   # Library: integer square root
+│   ├── program.json             #   "program": "sqrt_math"  (no .aleo suffix)
+│   └── src/
+│       ├── lib.leo              #   const ISQRT_MAX
+│       ├── newton.leo           #   fn isqrt(n) — Newton's method              [module: newton]
+│       └── checks.leo          #   fn is_perfect_square(n)                    [module: checks]
+│
+├── vote_math/                   # Library: QV weight & cost formulas
+│   ├── program.json             #   depends on sqrt_math
+│   └── src/
+│       ├── lib.leo              #   const MAX_WEIGHT, MIN_BALANCE
+│       ├── weight.leo           #   fn compute(balance), fn is_eligible(balance) [module: weight]
+│       └── cost.leo             #   struct VoterProfile { weight },            [module: cost]
+│                                #   fn credits_for_votes, fn build_profile(balance)
+│
+├── governance/                  # Program: private vote receipts
+│   ├── program.json             #   depends on sqrt_math + vote_math
+│   ├── inputs/governance.in
+│   ├── src/main.leo             #   record Vote
+│   │                            #   fn cast_vote       — uses vote_math::weight + vote_math::cost
+│   │                            #   fn qv_cost         — uses vote_math::cost
+│   │                            #   fn has_perfect_sqrt — uses sqrt_math::checks directly
+│   │                            #   fn is_passing
+│   └── tests/
+│       └── test_governance.leo  #   @test fns covering cast_vote, qv_cost, has_perfect_sqrt,
+│                                #   is_passing (18 test cases)
+│
+├── run.sh
+└── README.md
+```
+
+### Call graph
+
+```
+governance.aleo
+├── vote_math::weight::is_eligible(token_balance)
+│     └── vote_math::MIN_BALANCE                  (top-level lib constant)
+├── vote_math::cost::build_profile(token_balance)
+│     └── vote_math::weight::compute(balance)     (cross-submodule call within vote_math)
+│           ├── sqrt_math::newton::isqrt(n)       (cross-library submodule call)
+│           │     └── sqrt_math::ISQRT_MAX         (top-level lib constant, safety assert)
+│           └── vote_math::MAX_WEIGHT              (top-level lib constant)
+├── vote_math::cost::credits_for_votes(votes)
+└── sqrt_math::checks::is_perfect_square(n)       (direct cross-library submodule call)
+      └── sqrt_math::newton::isqrt(n)              (cross-submodule call within sqrt_math)
+            └── sqrt_math::ISQRT_MAX               (top-level lib constant, safety assert)
+```
diff --git a/quadratic_vote/governance/build/abi.json b/quadratic_vote/governance/build/abi.json
new file mode 100644
index 0000000..07b3dc3
--- /dev/null
+++ b/quadratic_vote/governance/build/abi.json
@@ -0,0 +1,189 @@
+{
+  "program": "governance.aleo",
+  "structs": [],
+  "records": [
+    {
+      "path": [
+        "Vote"
+      ],
+      "fields": [
+        {
+          "name": "owner",
+          "ty": {
+            "Primitive": "Address"
+          },
+          "mode": "None"
+        },
+        {
+          "name": "proposal_id",
+          "ty": {
+            "Primitive": "Field"
+          },
+          "mode": "None"
+        },
+        {
+          "name": "weight",
+          "ty": {
+            "Primitive": {
+              "UInt": "U32"
+            }
+          },
+          "mode": "None"
+        },
+        {
+          "name": "approve",
+          "ty": {
+            "Primitive": "Boolean"
+          },
+          "mode": "None"
+        }
+      ]
+    }
+  ],
+  "mappings": [],
+  "storage_variables": [],
+  "functions": [
+    {
+      "name": "cast_vote",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "proposal_id",
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Field"
+            }
+          },
+          "mode": "Public"
+        },
+        {
+          "name": "token_balance",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        },
+        {
+          "name": "approve",
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Boolean"
+            }
+          },
+          "mode": "None"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Record": {
+              "path": [
+                "Vote"
+              ],
+              "program": "governance.aleo"
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    },
+    {
+      "name": "qv_cost",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "votes",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    },
+    {
+      "name": "has_perfect_sqrt",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "token_balance",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Boolean"
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    },
+    {
+      "name": "is_passing",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "approvals",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "Public"
+        },
+        {
+          "name": "rejections",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "Public"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Boolean"
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    }
+  ]
+}
\ No newline at end of file
diff --git a/quadratic_vote/governance/build/imports/governance.aleo b/quadratic_vote/governance/build/imports/governance.aleo
new file mode 100644
index 0000000..91fe277
--- /dev/null
+++ b/quadratic_vote/governance/build/imports/governance.aleo
@@ -0,0 +1,332 @@
+program governance.aleo;
+
+record Vote:
+    owner as address.private;
+    proposal_id as field.private;
+    weight as u32.private;
+    approve as boolean.private;
+
+struct VoterProfile__BuQNrNoHlO8:
+    weight as u32;
+
+function cast_vote:
+    input r0 as field.public;
+    input r1 as u32.private;
+    input r2 as boolean.private;
+    gte r1 1u32 into r3;
+    assert.eq r3 true;
+    div r1 2u32 into r4;
+    add r4 1u32 into r5;
+    is.eq r5 0u32 into r6;
+    ternary r6 1u32 r5 into r7;
+    div r1 r7 into r8;
+    add r5 r8 into r9;
+    div r9 2u32 into r10;
+    lt r10 r5 into r11;
+    ternary r11 r10 r5 into r12;
+    is.eq r12 0u32 into r13;
+    ternary r13 1u32 r12 into r14;
+    div r1 r14 into r15;
+    add r12 r15 into r16;
+    div r16 2u32 into r17;
+    lt r17 r12 into r18;
+    ternary r18 r17 r12 into r19;
+    is.eq r19 0u32 into r20;
+    ternary r20 1u32 r19 into r21;
+    div r1 r21 into r22;
+    add r19 r22 into r23;
+    div r23 2u32 into r24;
+    lt r24 r19 into r25;
+    ternary r25 r24 r19 into r26;
+    is.eq r26 0u32 into r27;
+    ternary r27 1u32 r26 into r28;
+    div r1 r28 into r29;
+    add r26 r29 into r30;
+    div r30 2u32 into r31;
+    lt r31 r26 into r32;
+    ternary r32 r31 r26 into r33;
+    is.eq r33 0u32 into r34;
+    ternary r34 1u32 r33 into r35;
+    div r1 r35 into r36;
+    add r33 r36 into r37;
+    div r37 2u32 into r38;
+    lt r38 r33 into r39;
+    ternary r39 r38 r33 into r40;
+    is.eq r40 0u32 into r41;
+    ternary r41 1u32 r40 into r42;
+    div r1 r42 into r43;
+    add r40 r43 into r44;
+    div r44 2u32 into r45;
+    lt r45 r40 into r46;
+    ternary r46 r45 r40 into r47;
+    is.eq r47 0u32 into r48;
+    ternary r48 1u32 r47 into r49;
+    div r1 r49 into r50;
+    add r47 r50 into r51;
+    div r51 2u32 into r52;
+    lt r52 r47 into r53;
+    ternary r53 r52 r47 into r54;
+    is.eq r54 0u32 into r55;
+    ternary r55 1u32 r54 into r56;
+    div r1 r56 into r57;
+    add r54 r57 into r58;
+    div r58 2u32 into r59;
+    lt r59 r54 into r60;
+    ternary r60 r59 r54 into r61;
+    is.eq r61 0u32 into r62;
+    ternary r62 1u32 r61 into r63;
+    div r1 r63 into r64;
+    add r61 r64 into r65;
+    div r65 2u32 into r66;
+    lt r66 r61 into r67;
+    ternary r67 r66 r61 into r68;
+    is.eq r68 0u32 into r69;
+    ternary r69 1u32 r68 into r70;
+    div r1 r70 into r71;
+    add r68 r71 into r72;
+    div r72 2u32 into r73;
+    lt r73 r68 into r74;
+    ternary r74 r73 r68 into r75;
+    is.eq r75 0u32 into r76;
+    ternary r76 1u32 r75 into r77;
+    div r1 r77 into r78;
+    add r75 r78 into r79;
+    div r79 2u32 into r80;
+    lt r80 r75 into r81;
+    ternary r81 r80 r75 into r82;
+    is.eq r82 0u32 into r83;
+    ternary r83 1u32 r82 into r84;
+    div r1 r84 into r85;
+    add r82 r85 into r86;
+    div r86 2u32 into r87;
+    lt r87 r82 into r88;
+    ternary r88 r87 r82 into r89;
+    is.eq r89 0u32 into r90;
+    ternary r90 1u32 r89 into r91;
+    div r1 r91 into r92;
+    add r89 r92 into r93;
+    div r93 2u32 into r94;
+    lt r94 r89 into r95;
+    ternary r95 r94 r89 into r96;
+    is.eq r96 0u32 into r97;
+    ternary r97 1u32 r96 into r98;
+    div r1 r98 into r99;
+    add r96 r99 into r100;
+    div r100 2u32 into r101;
+    lt r101 r96 into r102;
+    ternary r102 r101 r96 into r103;
+    is.eq r103 0u32 into r104;
+    ternary r104 1u32 r103 into r105;
+    div r1 r105 into r106;
+    add r103 r106 into r107;
+    div r107 2u32 into r108;
+    lt r108 r103 into r109;
+    ternary r109 r108 r103 into r110;
+    is.eq r110 0u32 into r111;
+    ternary r111 1u32 r110 into r112;
+    div r1 r112 into r113;
+    add r110 r113 into r114;
+    div r114 2u32 into r115;
+    lt r115 r110 into r116;
+    ternary r116 r115 r110 into r117;
+    is.eq r117 0u32 into r118;
+    ternary r118 1u32 r117 into r119;
+    div r1 r119 into r120;
+    add r117 r120 into r121;
+    div r121 2u32 into r122;
+    lt r122 r117 into r123;
+    ternary r123 r122 r117 into r124;
+    is.eq r124 0u32 into r125;
+    ternary r125 1u32 r124 into r126;
+    div r1 r126 into r127;
+    add r124 r127 into r128;
+    div r128 2u32 into r129;
+    lt r129 r124 into r130;
+    ternary r130 r129 r124 into r131;
+    is.eq r131 0u32 into r132;
+    ternary r132 1u32 r131 into r133;
+    div r1 r133 into r134;
+    add r131 r134 into r135;
+    div r135 2u32 into r136;
+    lt r136 r131 into r137;
+    ternary r137 r136 r131 into r138;
+    is.eq r138 0u32 into r139;
+    ternary r139 1u32 r138 into r140;
+    div r1 r140 into r141;
+    add r138 r141 into r142;
+    div r142 2u32 into r143;
+    lt r143 r138 into r144;
+    ternary r144 r143 r138 into r145;
+    lte r145 65535u32 into r146;
+    assert.eq r146 true;
+    lt r145 100u32 into r147;
+    ternary r147 r145 100u32 into r148;
+    cast r148 into r149 as VoterProfile__BuQNrNoHlO8;
+    cast self.signer r0 r149.weight r2 into r150 as Vote.record;
+    output r150 as Vote.record;
+
+function qv_cost:
+    input r0 as u32.private;
+    lte r0 65535u32 into r1;
+    assert.eq r1 true;
+    mul r0 r0 into r2;
+    output r2 as u32.private;
+
+function has_perfect_sqrt:
+    input r0 as u32.private;
+    div r0 2u32 into r1;
+    add r1 1u32 into r2;
+    is.eq r2 0u32 into r3;
+    ternary r3 1u32 r2 into r4;
+    div r0 r4 into r5;
+    add r2 r5 into r6;
+    div r6 2u32 into r7;
+    lt r7 r2 into r8;
+    ternary r8 r7 r2 into r9;
+    is.eq r9 0u32 into r10;
+    ternary r10 1u32 r9 into r11;
+    div r0 r11 into r12;
+    add r9 r12 into r13;
+    div r13 2u32 into r14;
+    lt r14 r9 into r15;
+    ternary r15 r14 r9 into r16;
+    is.eq r16 0u32 into r17;
+    ternary r17 1u32 r16 into r18;
+    div r0 r18 into r19;
+    add r16 r19 into r20;
+    div r20 2u32 into r21;
+    lt r21 r16 into r22;
+    ternary r22 r21 r16 into r23;
+    is.eq r23 0u32 into r24;
+    ternary r24 1u32 r23 into r25;
+    div r0 r25 into r26;
+    add r23 r26 into r27;
+    div r27 2u32 into r28;
+    lt r28 r23 into r29;
+    ternary r29 r28 r23 into r30;
+    is.eq r30 0u32 into r31;
+    ternary r31 1u32 r30 into r32;
+    div r0 r32 into r33;
+    add r30 r33 into r34;
+    div r34 2u32 into r35;
+    lt r35 r30 into r36;
+    ternary r36 r35 r30 into r37;
+    is.eq r37 0u32 into r38;
+    ternary r38 1u32 r37 into r39;
+    div r0 r39 into r40;
+    add r37 r40 into r41;
+    div r41 2u32 into r42;
+    lt r42 r37 into r43;
+    ternary r43 r42 r37 into r44;
+    is.eq r44 0u32 into r45;
+    ternary r45 1u32 r44 into r46;
+    div r0 r46 into r47;
+    add r44 r47 into r48;
+    div r48 2u32 into r49;
+    lt r49 r44 into r50;
+    ternary r50 r49 r44 into r51;
+    is.eq r51 0u32 into r52;
+    ternary r52 1u32 r51 into r53;
+    div r0 r53 into r54;
+    add r51 r54 into r55;
+    div r55 2u32 into r56;
+    lt r56 r51 into r57;
+    ternary r57 r56 r51 into r58;
+    is.eq r58 0u32 into r59;
+    ternary r59 1u32 r58 into r60;
+    div r0 r60 into r61;
+    add r58 r61 into r62;
+    div r62 2u32 into r63;
+    lt r63 r58 into r64;
+    ternary r64 r63 r58 into r65;
+    is.eq r65 0u32 into r66;
+    ternary r66 1u32 r65 into r67;
+    div r0 r67 into r68;
+    add r65 r68 into r69;
+    div r69 2u32 into r70;
+    lt r70 r65 into r71;
+    ternary r71 r70 r65 into r72;
+    is.eq r72 0u32 into r73;
+    ternary r73 1u32 r72 into r74;
+    div r0 r74 into r75;
+    add r72 r75 into r76;
+    div r76 2u32 into r77;
+    lt r77 r72 into r78;
+    ternary r78 r77 r72 into r79;
+    is.eq r79 0u32 into r80;
+    ternary r80 1u32 r79 into r81;
+    div r0 r81 into r82;
+    add r79 r82 into r83;
+    div r83 2u32 into r84;
+    lt r84 r79 into r85;
+    ternary r85 r84 r79 into r86;
+    is.eq r86 0u32 into r87;
+    ternary r87 1u32 r86 into r88;
+    div r0 r88 into r89;
+    add r86 r89 into r90;
+    div r90 2u32 into r91;
+    lt r91 r86 into r92;
+    ternary r92 r91 r86 into r93;
+    is.eq r93 0u32 into r94;
+    ternary r94 1u32 r93 into r95;
+    div r0 r95 into r96;
+    add r93 r96 into r97;
+    div r97 2u32 into r98;
+    lt r98 r93 into r99;
+    ternary r99 r98 r93 into r100;
+    is.eq r100 0u32 into r101;
+    ternary r101 1u32 r100 into r102;
+    div r0 r102 into r103;
+    add r100 r103 into r104;
+    div r104 2u32 into r105;
+    lt r105 r100 into r106;
+    ternary r106 r105 r100 into r107;
+    is.eq r107 0u32 into r108;
+    ternary r108 1u32 r107 into r109;
+    div r0 r109 into r110;
+    add r107 r110 into r111;
+    div r111 2u32 into r112;
+    lt r112 r107 into r113;
+    ternary r113 r112 r107 into r114;
+    is.eq r114 0u32 into r115;
+    ternary r115 1u32 r114 into r116;
+    div r0 r116 into r117;
+    add r114 r117 into r118;
+    div r118 2u32 into r119;
+    lt r119 r114 into r120;
+    ternary r120 r119 r114 into r121;
+    is.eq r121 0u32 into r122;
+    ternary r122 1u32 r121 into r123;
+    div r0 r123 into r124;
+    add r121 r124 into r125;
+    div r125 2u32 into r126;
+    lt r126 r121 into r127;
+    ternary r127 r126 r121 into r128;
+    is.eq r128 0u32 into r129;
+    ternary r129 1u32 r128 into r130;
+    div r0 r130 into r131;
+    add r128 r131 into r132;
+    div r132 2u32 into r133;
+    lt r133 r128 into r134;
+    ternary r134 r133 r128 into r135;
+    is.eq r135 0u32 into r136;
+    ternary r136 1u32 r135 into r137;
+    div r0 r137 into r138;
+    add r135 r138 into r139;
+    div r139 2u32 into r140;
+    lt r140 r135 into r141;
+    ternary r141 r140 r135 into r142;
+    lte r142 65535u32 into r143;
+    assert.eq r143 true;
+    mul r142 r142 into r144;
+    is.eq r144 r0 into r145;
+    output r145 as boolean.private;
+
+function is_passing:
+    input r0 as u32.public;
+    input r1 as u32.public;
+    gt r0 r1 into r2;
+    output r2 as boolean.private;
+
+constructor:
+    assert.eq edition 0u16;
diff --git a/quadratic_vote/governance/build/imports/governance.aleo.abi.json b/quadratic_vote/governance/build/imports/governance.aleo.abi.json
new file mode 100644
index 0000000..07b3dc3
--- /dev/null
+++ b/quadratic_vote/governance/build/imports/governance.aleo.abi.json
@@ -0,0 +1,189 @@
+{
+  "program": "governance.aleo",
+  "structs": [],
+  "records": [
+    {
+      "path": [
+        "Vote"
+      ],
+      "fields": [
+        {
+          "name": "owner",
+          "ty": {
+            "Primitive": "Address"
+          },
+          "mode": "None"
+        },
+        {
+          "name": "proposal_id",
+          "ty": {
+            "Primitive": "Field"
+          },
+          "mode": "None"
+        },
+        {
+          "name": "weight",
+          "ty": {
+            "Primitive": {
+              "UInt": "U32"
+            }
+          },
+          "mode": "None"
+        },
+        {
+          "name": "approve",
+          "ty": {
+            "Primitive": "Boolean"
+          },
+          "mode": "None"
+        }
+      ]
+    }
+  ],
+  "mappings": [],
+  "storage_variables": [],
+  "functions": [
+    {
+      "name": "cast_vote",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "proposal_id",
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Field"
+            }
+          },
+          "mode": "Public"
+        },
+        {
+          "name": "token_balance",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        },
+        {
+          "name": "approve",
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Boolean"
+            }
+          },
+          "mode": "None"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Record": {
+              "path": [
+                "Vote"
+              ],
+              "program": "governance.aleo"
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    },
+    {
+      "name": "qv_cost",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "votes",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    },
+    {
+      "name": "has_perfect_sqrt",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "token_balance",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "None"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Boolean"
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    },
+    {
+      "name": "is_passing",
+      "is_final": false,
+      "inputs": [
+        {
+          "name": "approvals",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "Public"
+        },
+        {
+          "name": "rejections",
+          "ty": {
+            "Plaintext": {
+              "Primitive": {
+                "UInt": "U32"
+              }
+            }
+          },
+          "mode": "Public"
+        }
+      ],
+      "outputs": [
+        {
+          "ty": {
+            "Plaintext": {
+              "Primitive": "Boolean"
+            }
+          },
+          "mode": "None"
+        }
+      ]
+    }
+  ]
+}
\ No newline at end of file
diff --git a/quadratic_vote/governance/build/imports/test_governance.aleo b/quadratic_vote/governance/build/imports/test_governance.aleo
new file mode 100644
index 0000000..f33eeda
--- /dev/null
+++ b/quadratic_vote/governance/build/imports/test_governance.aleo
@@ -0,0 +1,86 @@
+import governance.aleo;
+program test_governance.aleo;
+
+struct VoterProfile__BuQNrNoHlO8:
+    weight as u32;
+
+function test_cast_vote_weight_10:
+    call governance.aleo/cast_vote 1field 100u32 true into r0;
+    assert.eq r0.weight 10u32;
+    assert.eq r0.approve true;
+
+function test_cast_vote_weight_31:
+    call governance.aleo/cast_vote 1field 1000u32 false into r0;
+    assert.eq r0.weight 31u32;
+    assert.eq r0.approve false;
+
+function test_cast_vote_cap:
+    call governance.aleo/cast_vote 1field 10000u32 true into r0;
+    assert.eq r0.weight 100u32;
+
+function test_cast_vote_min_balance:
+    call governance.aleo/cast_vote 2field 1u32 true into r0;
+    assert.eq r0.weight 1u32;
+
+function test_cast_vote_ineligible:
+    call governance.aleo/cast_vote 1field 0u32 true into r0;
+
+function test_qv_cost_5:
+    call governance.aleo/qv_cost 5u32 into r0;
+    assert.eq r0 25u32;
+
+function test_qv_cost_1:
+    call governance.aleo/qv_cost 1u32 into r0;
+    assert.eq r0 1u32;
+
+function test_qv_cost_10:
+    call governance.aleo/qv_cost 10u32 into r0;
+    assert.eq r0 100u32;
+
+function test_perfect_square_1024:
+    call governance.aleo/has_perfect_sqrt 1024u32 into r0;
+    assert.eq r0 true;
+
+function test_perfect_square_0:
+    call governance.aleo/has_perfect_sqrt 0u32 into r0;
+    assert.eq r0 true;
+
+function test_not_perfect_square_1000:
+    call governance.aleo/has_perfect_sqrt 1000u32 into r0;
+    not r0 into r1;
+    assert.eq r1 true;
+
+function test_not_perfect_square_2:
+    call governance.aleo/has_perfect_sqrt 2u32 into r0;
+    not r0 into r1;
+    assert.eq r1 true;
+
+function test_perfect_square_40000:
+    call governance.aleo/has_perfect_sqrt 40000u32 into r0;
+    assert.eq r0 true;
+
+function test_perfect_square_65536:
+    call governance.aleo/has_perfect_sqrt 65536u32 into r0;
+    assert.eq r0 true;
+
+function test_not_perfect_square_40001:
+    call governance.aleo/has_perfect_sqrt 40001u32 into r0;
+    not r0 into r1;
+    assert.eq r1 true;
+
+function test_is_passing_true:
+    call governance.aleo/is_passing 131u32 15u32 into r0;
+    assert.eq r0 true;
+
+function test_is_passing_tie:
+    call governance.aleo/is_passing 15u32 15u32 into r0;
+    not r0 into r1;
+    assert.eq r1 true;
+
+function test_is_passing_false:
+    call governance.aleo/is_passing 10u32 20u32 into r0;
+    not r0 into r1;
+    assert.eq r1 true;
+
+constructor:
+    assert.eq edition 0u16;
diff --git a/quadratic_vote/governance/build/main.aleo b/quadratic_vote/governance/build/main.aleo
new file mode 100644
index 0000000..91fe277
--- /dev/null
+++ b/quadratic_vote/governance/build/main.aleo
@@ -0,0 +1,332 @@
+program governance.aleo;
+
+record Vote:
+    owner as address.private;
+    proposal_id as field.private;
+    weight as u32.private;
+    approve as boolean.private;
+
+struct VoterProfile__BuQNrNoHlO8:
+    weight as u32;
+
+function cast_vote:
+    input r0 as field.public;
+    input r1 as u32.private;
+    input r2 as boolean.private;
+    gte r1 1u32 into r3;
+    assert.eq r3 true;
+    div r1 2u32 into r4;
+    add r4 1u32 into r5;
+    is.eq r5 0u32 into r6;
+    ternary r6 1u32 r5 into r7;
+    div r1 r7 into r8;
+    add r5 r8 into r9;
+    div r9 2u32 into r10;
+    lt r10 r5 into r11;
+    ternary r11 r10 r5 into r12;
+    is.eq r12 0u32 into r13;
+    ternary r13 1u32 r12 into r14;
+    div r1 r14 into r15;
+    add r12 r15 into r16;
+    div r16 2u32 into r17;
+    lt r17 r12 into r18;
+    ternary r18 r17 r12 into r19;
+    is.eq r19 0u32 into r20;
+    ternary r20 1u32 r19 into r21;
+    div r1 r21 into r22;
+    add r19 r22 into r23;
+    div r23 2u32 into r24;
+    lt r24 r19 into r25;
+    ternary r25 r24 r19 into r26;
+    is.eq r26 0u32 into r27;
+    ternary r27 1u32 r26 into r28;
+    div r1 r28 into r29;
+    add r26 r29 into r30;
+    div r30 2u32 into r31;
+    lt r31 r26 into r32;
+    ternary r32 r31 r26 into r33;
+    is.eq r33 0u32 into r34;
+    ternary r34 1u32 r33 into r35;
+    div r1 r35 into r36;
+    add r33 r36 into r37;
+    div r37 2u32 into r38;
+    lt r38 r33 into r39;
+    ternary r39 r38 r33 into r40;
+    is.eq r40 0u32 into r41;
+    ternary r41 1u32 r40 into r42;
+    div r1 r42 into r43;
+    add r40 r43 into r44;
+    div r44 2u32 into r45;
+    lt r45 r40 into r46;
+    ternary r46 r45 r40 into r47;
+    is.eq r47 0u32 into r48;
+    ternary r48 1u32 r47 into r49;
+    div r1 r49 into r50;
+    add r47 r50 into r51;
+    div r51 2u32 into r52;
+    lt r52 r47 into r53;
+    ternary r53 r52 r47 into r54;
+    is.eq r54 0u32 into r55;
+    ternary r55 1u32 r54 into r56;
+    div r1 r56 into r57;
+    add r54 r57 into r58;
+    div r58 2u32 into r59;
+    lt r59 r54 into r60;
+    ternary r60 r59 r54 into r61;
+    is.eq r61 0u32 into r62;
+    ternary r62 1u32 r61 into r63;
+    div r1 r63 into r64;
+    add r61 r64 into r65;
+    div r65 2u32 into r66;
+    lt r66 r61 into r67;
+    ternary r67 r66 r61 into r68;
+    is.eq r68 0u32 into r69;
+    ternary r69 1u32 r68 into r70;
+    div r1 r70 into r71;
+    add r68 r71 into r72;
+    div r72 2u32 into r73;
+    lt r73 r68 into r74;
+    ternary r74 r73 r68 into r75;
+    is.eq r75 0u32 into r76;
+    ternary r76 1u32 r75 into r77;
+    div r1 r77 into r78;
+    add r75 r78 into r79;
+    div r79 2u32 into r80;
+    lt r80 r75 into r81;
+    ternary r81 r80 r75 into r82;
+    is.eq r82 0u32 into r83;
+    ternary r83 1u32 r82 into r84;
+    div r1 r84 into r85;
+    add r82 r85 into r86;
+    div r86 2u32 into r87;
+    lt r87 r82 into r88;
+    ternary r88 r87 r82 into r89;
+    is.eq r89 0u32 into r90;
+    ternary r90 1u32 r89 into r91;
+    div r1 r91 into r92;
+    add r89 r92 into r93;
+    div r93 2u32 into r94;
+    lt r94 r89 into r95;
+    ternary r95 r94 r89 into r96;
+    is.eq r96 0u32 into r97;
+    ternary r97 1u32 r96 into r98;
+    div r1 r98 into r99;
+    add r96 r99 into r100;
+    div r100 2u32 into r101;
+    lt r101 r96 into r102;
+    ternary r102 r101 r96 into r103;
+    is.eq r103 0u32 into r104;
+    ternary r104 1u32 r103 into r105;
+    div r1 r105 into r106;
+    add r103 r106 into r107;
+    div r107 2u32 into r108;
+    lt r108 r103 into r109;
+    ternary r109 r108 r103 into r110;
+    is.eq r110 0u32 into r111;
+    ternary r111 1u32 r110 into r112;
+    div r1 r112 into r113;
+    add r110 r113 into r114;
+    div r114 2u32 into r115;
+    lt r115 r110 into r116;
+    ternary r116 r115 r110 into r117;
+    is.eq r117 0u32 into r118;
+    ternary r118 1u32 r117 into r119;
+    div r1 r119 into r120;
+    add r117 r120 into r121;
+    div r121 2u32 into r122;
+    lt r122 r117 into r123;
+    ternary r123 r122 r117 into r124;
+    is.eq r124 0u32 into r125;
+    ternary r125 1u32 r124 into r126;
+    div r1 r126 into r127;
+    add r124 r127 into r128;
+    div r128 2u32 into r129;
+    lt r129 r124 into r130;
+    ternary r130 r129 r124 into r131;
+    is.eq r131 0u32 into r132;
+    ternary r132 1u32 r131 into r133;
+    div r1 r133 into r134;
+    add r131 r134 into r135;
+    div r135 2u32 into r136;
+    lt r136 r131 into r137;
+    ternary r137 r136 r131 into r138;
+    is.eq r138 0u32 into r139;
+    ternary r139 1u32 r138 into r140;
+    div r1 r140 into r141;
+    add r138 r141 into r142;
+    div r142 2u32 into r143;
+    lt r143 r138 into r144;
+    ternary r144 r143 r138 into r145;
+    lte r145 65535u32 into r146;
+    assert.eq r146 true;
+    lt r145 100u32 into r147;
+    ternary r147 r145 100u32 into r148;
+    cast r148 into r149 as VoterProfile__BuQNrNoHlO8;
+    cast self.signer r0 r149.weight r2 into r150 as Vote.record;
+    output r150 as Vote.record;
+
+function qv_cost:
+    input r0 as u32.private;
+    lte r0 65535u32 into r1;
+    assert.eq r1 true;
+    mul r0 r0 into r2;
+    output r2 as u32.private;
+
+function has_perfect_sqrt:
+    input r0 as u32.private;
+    div r0 2u32 into r1;
+    add r1 1u32 into r2;
+    is.eq r2 0u32 into r3;
+    ternary r3 1u32 r2 into r4;
+    div r0 r4 into r5;
+    add r2 r5 into r6;
+    div r6 2u32 into r7;
+    lt r7 r2 into r8;
+    ternary r8 r7 r2 into r9;
+    is.eq r9 0u32 into r10;
+    ternary r10 1u32 r9 into r11;
+    div r0 r11 into r12;
+    add r9 r12 into r13;
+    div r13 2u32 into r14;
+    lt r14 r9 into r15;
+    ternary r15 r14 r9 into r16;
+    is.eq r16 0u32 into r17;
+    ternary r17 1u32 r16 into r18;
+    div r0 r18 into r19;
+    add r16 r19 into r20;
+    div r20 2u32 into r21;
+    lt r21 r16 into r22;
+    ternary r22 r21 r16 into r23;
+    is.eq r23 0u32 into r24;
+    ternary r24 1u32 r23 into r25;
+    div r0 r25 into r26;
+    add r23 r26 into r27;
+    div r27 2u32 into r28;
+    lt r28 r23 into r29;
+    ternary r29 r28 r23 into r30;
+    is.eq r30 0u32 into r31;
+    ternary r31 1u32 r30 into r32;
+    div r0 r32 into r33;
+    add r30 r33 into r34;
+    div r34 2u32 into r35;
+    lt r35 r30 into r36;
+    ternary r36 r35 r30 into r37;
+    is.eq r37 0u32 into r38;
+    ternary r38 1u32 r37 into r39;
+    div r0 r39 into r40;
+    add r37 r40 into r41;
+    div r41 2u32 into r42;
+    lt r42 r37 into r43;
+    ternary r43 r42 r37 into r44;
+    is.eq r44 0u32 into r45;
+    ternary r45 1u32 r44 into r46;
+    div r0 r46 into r47;
+    add r44 r47 into r48;
+    div r48 2u32 into r49;
+    lt r49 r44 into r50;
+    ternary r50 r49 r44 into r51;
+    is.eq r51 0u32 into r52;
+    ternary r52 1u32 r51 into r53;
+    div r0 r53 into r54;
+    add r51 r54 into r55;
+    div r55 2u32 into r56;
+    lt r56 r51 into r57;
+    ternary r57 r56 r51 into r58;
+    is.eq r58 0u32 into r59;
+    ternary r59 1u32 r58 into r60;
+    div r0 r60 into r61;
+    add r58 r61 into r62;
+    div r62 2u32 into r63;
+    lt r63 r58 into r64;
+    ternary r64 r63 r58 into r65;
+    is.eq r65 0u32 into r66;
+    ternary r66 1u32 r65 into r67;
+    div r0 r67 into r68;
+    add r65 r68 into r69;
+    div r69 2u32 into r70;
+    lt r70 r65 into r71;
+    ternary r71 r70 r65 into r72;
+    is.eq r72 0u32 into r73;
+    ternary r73 1u32 r72 into r74;
+    div r0 r74 into r75;
+    add r72 r75 into r76;
+    div r76 2u32 into r77;
+    lt r77 r72 into r78;
+    ternary r78 r77 r72 into r79;
+    is.eq r79 0u32 into r80;
+    ternary r80 1u32 r79 into r81;
+    div r0 r81 into r82;
+    add r79 r82 into r83;
+    div r83 2u32 into r84;
+    lt r84 r79 into r85;
+    ternary r85 r84 r79 into r86;
+    is.eq r86 0u32 into r87;
+    ternary r87 1u32 r86 into r88;
+    div r0 r88 into r89;
+    add r86 r89 into r90;
+    div r90 2u32 into r91;
+    lt r91 r86 into r92;
+    ternary r92 r91 r86 into r93;
+    is.eq r93 0u32 into r94;
+    ternary r94 1u32 r93 into r95;
+    div r0 r95 into r96;
+    add r93 r96 into r97;
+    div r97 2u32 into r98;
+    lt r98 r93 into r99;
+    ternary r99 r98 r93 into r100;
+    is.eq r100 0u32 into r101;
+    ternary r101 1u32 r100 into r102;
+    div r0 r102 into r103;
+    add r100 r103 into r104;
+    div r104 2u32 into r105;
+    lt r105 r100 into r106;
+    ternary r106 r105 r100 into r107;
+    is.eq r107 0u32 into r108;
+    ternary r108 1u32 r107 into r109;
+    div r0 r109 into r110;
+    add r107 r110 into r111;
+    div r111 2u32 into r112;
+    lt r112 r107 into r113;
+    ternary r113 r112 r107 into r114;
+    is.eq r114 0u32 into r115;
+    ternary r115 1u32 r114 into r116;
+    div r0 r116 into r117;
+    add r114 r117 into r118;
+    div r118 2u32 into r119;
+    lt r119 r114 into r120;
+    ternary r120 r119 r114 into r121;
+    is.eq r121 0u32 into r122;
+    ternary r122 1u32 r121 into r123;
+    div r0 r123 into r124;
+    add r121 r124 into r125;
+    div r125 2u32 into r126;
+    lt r126 r121 into r127;
+    ternary r127 r126 r121 into r128;
+    is.eq r128 0u32 into r129;
+    ternary r129 1u32 r128 into r130;
+    div r0 r130 into r131;
+    add r128 r131 into r132;
+    div r132 2u32 into r133;
+    lt r133 r128 into r134;
+    ternary r134 r133 r128 into r135;
+    is.eq r135 0u32 into r136;
+    ternary r136 1u32 r135 into r137;
+    div r0 r137 into r138;
+    add r135 r138 into r139;
+    div r139 2u32 into r140;
+    lt r140 r135 into r141;
+    ternary r141 r140 r135 into r142;
+    lte r142 65535u32 into r143;
+    assert.eq r143 true;
+    mul r142 r142 into r144;
+    is.eq r144 r0 into r145;
+    output r145 as boolean.private;
+
+function is_passing:
+    input r0 as u32.public;
+    input r1 as u32.public;
+    gt r0 r1 into r2;
+    output r2 as boolean.private;
+
+constructor:
+    assert.eq edition 0u16;
diff --git a/quadratic_vote/governance/build/program.json b/quadratic_vote/governance/build/program.json
new file mode 100644
index 0000000..a61840a
--- /dev/null
+++ b/quadratic_vote/governance/build/program.json
@@ -0,0 +1,9 @@
+{
+  "program": "governance.aleo",
+  "version": "0.1.0",
+  "description": "",
+  "license": "",
+  "leo": "4.0.1",
+  "dependencies": null,
+  "dev_dependencies": null
+}
diff --git a/quadratic_vote/governance/inputs/governance.in b/quadratic_vote/governance/inputs/governance.in
new file mode 100644
index 0000000..b3e895d
--- /dev/null
+++ b/quadratic_vote/governance/inputs/governance.in
@@ -0,0 +1,4 @@
+// cast_vote inputs: proposal_id (public field), token_balance (u32), approve (bool)
+1field
+1000u32
+true
diff --git a/quadratic_vote/governance/program.json b/quadratic_vote/governance/program.json
new file mode 100644
index 0000000..31e8fd0
--- /dev/null
+++ b/quadratic_vote/governance/program.json
@@ -0,0 +1,21 @@
+{
+    "program": "governance.aleo",
+    "version": "0.1.0",
+    "description": "Quadratic-voting governance program.",
+    "license": "MIT",
+    "leo": "4.0.1",
+    "dependencies": [
+        {
+            "name": "sqrt_math",
+            "location": "local",
+            "path": "../sqrt_math",
+            "edition": null
+        },
+        {
+            "name": "vote_math",
+            "location": "local",
+            "path": "../vote_math",
+            "edition": null
+        }
+    ]
+}
diff --git a/quadratic_vote/governance/src/main.leo b/quadratic_vote/governance/src/main.leo
new file mode 100644
index 0000000..c51b13b
--- /dev/null
+++ b/quadratic_vote/governance/src/main.leo
@@ -0,0 +1,40 @@
+program governance.aleo {
+    // Private on-chain receipt proving a participant voted on a proposal.
+    record Vote {
+        owner: address,
+        proposal_id: field,
+        weight: u32,
+        approve: bool,
+    }
+
+    // Cast a private vote on proposal `proposal_id`.
+    //
+    // `token_balance` is the caller's private holding; the quadratic voting
+    // weight is derived from it via vote_math::weight.  Returns a Vote receipt
+    // that proves participation without revealing the token balance on-chain.
+    fn cast_vote(public proposal_id: field, token_balance: u32, approve: bool) -> Vote {
+        assert(vote_math::weight::is_eligible(token_balance));
+        let profile: vote_math::cost::VoterProfile = vote_math::cost::build_profile(token_balance);
+        return Vote { owner: self.signer, proposal_id, weight: profile.weight, approve };
+    }
+
+    // Returns the credit cost of casting `votes` weighted votes under QV.
+    fn qv_cost(votes: u32) -> u32 {
+        return vote_math::cost::credits_for_votes(votes);
+    }
+
+    // Returns true when `token_balance` is a perfect square.
+    // Delegates directly to sqrt_math::checks, bypassing vote_math entirely,
+    // to illustrate that a program can reach into any library submodule.
+    fn has_perfect_sqrt(token_balance: u32) -> bool {
+        return sqrt_math::checks::is_perfect_square(token_balance);
+    }
+
+    // Returns true when weighted approvals exceed weighted rejections.
+    fn is_passing(public approvals: u32, public rejections: u32) -> bool {
+        return approvals > rejections;
+    }
+
+    @noupgrade
+    constructor() {}
+}
diff --git a/quadratic_vote/governance/tests/test_governance.leo b/quadratic_vote/governance/tests/test_governance.leo
new file mode 100644
index 0000000..0f6ee7d
--- /dev/null
+++ b/quadratic_vote/governance/tests/test_governance.leo
@@ -0,0 +1,121 @@
+import governance.aleo;
+
+program test_governance.aleo {
+    // A voter with 100 tokens gets weight floor(sqrt(100)) = 10.
+    @test
+    fn test_cast_vote_weight_10() {
+        let v: governance.aleo::Vote = governance.aleo::cast_vote(1field, 100u32, true);
+        assert_eq(v.weight, 10u32);
+        assert_eq(v.approve, true);
+    }
+
+    // A voter with 1 000 tokens gets weight floor(sqrt(1000)) = 31.
+    @test
+    fn test_cast_vote_weight_31() {
+        let v: governance.aleo::Vote = governance.aleo::cast_vote(1field, 1000u32, false);
+        assert_eq(v.weight, 31u32);
+        assert_eq(v.approve, false);
+    }
+
+    // Weight is capped at MAX_WEIGHT (100) for very large balances.
+    @test
+    fn test_cast_vote_cap() {
+        let v: governance.aleo::Vote = governance.aleo::cast_vote(1field, 10000u32, true);
+        assert_eq(v.weight, 100u32);
+    }
+
+    // A voter with 1 token (MIN_BALANCE) is eligible and gets weight 1.
+    @test
+    fn test_cast_vote_min_balance() {
+        let v: governance.aleo::Vote = governance.aleo::cast_vote(2field, 1u32, true);
+        assert_eq(v.weight, 1u32);
+    }
+
+    // A voter with 0 tokens must be rejected (MIN_BALANCE = 1).
+    @test
+    @should_fail
+    fn test_cast_vote_ineligible() {
+        let v: governance.aleo::Vote = governance.aleo::cast_vote(1field, 0u32, true);
+    }
+
+    // Casting 5 votes costs 5² = 25 credits.
+    @test
+    fn test_qv_cost_5() {
+        assert_eq(governance.aleo::qv_cost(5u32), 25u32);
+    }
+
+    // Casting 1 vote costs 1² = 1 credit.
+    @test
+    fn test_qv_cost_1() {
+        assert_eq(governance.aleo::qv_cost(1u32), 1u32);
+    }
+
+    // Casting 10 votes costs 10² = 100 credits.
+    @test
+    fn test_qv_cost_10() {
+        assert_eq(governance.aleo::qv_cost(10u32), 100u32);
+    }
+
+    // 1 024 = 32² is a perfect square.
+    @test
+    fn test_perfect_square_1024() {
+        assert(governance.aleo::has_perfect_sqrt(1024u32));
+    }
+
+    // 0 = 0² is a perfect square.
+    @test
+    fn test_perfect_square_0() {
+        assert(governance.aleo::has_perfect_sqrt(0u32));
+    }
+
+    // 1 000 is not a perfect square (31² = 961, 32² = 1 024).
+    @test
+    fn test_not_perfect_square_1000() {
+        assert(!governance.aleo::has_perfect_sqrt(1000u32));
+    }
+
+    // 2 is not a perfect square.
+    @test
+    fn test_not_perfect_square_2() {
+        assert(!governance.aleo::has_perfect_sqrt(2u32));
+    }
+
+    // 40 000 = 200² is a perfect square (covers convergence for larger inputs).
+    @test
+    fn test_perfect_square_40000() {
+        assert(governance.aleo::has_perfect_sqrt(40000u32));
+    }
+
+    // 65 536 = 256² is a perfect square (covers convergence near the u16 boundary).
+    @test
+    fn test_perfect_square_65536() {
+        assert(governance.aleo::has_perfect_sqrt(65536u32));
+    }
+
+    // 40 001 is not a perfect square (200² = 40 000, 201² = 40 401).
+    @test
+    fn test_not_perfect_square_40001() {
+        assert(!governance.aleo::has_perfect_sqrt(40001u32));
+    }
+
+    // A proposal with more approvals than rejections is passing.
+    @test
+    fn test_is_passing_true() {
+        assert(governance.aleo::is_passing(131u32, 15u32));
+    }
+
+    // A tied proposal is not passing (strict majority required).
+    @test
+    fn test_is_passing_tie() {
+        assert(!governance.aleo::is_passing(15u32, 15u32));
+    }
+
+    // A proposal with fewer approvals than rejections is not passing.
+    @test
+    fn test_is_passing_false() {
+        assert(!governance.aleo::is_passing(10u32, 20u32));
+    }
+
+    @noupgrade
+    constructor() {}
+}
diff --git a/quadratic_vote/run.sh b/quadratic_vote/run.sh
new file mode 100755
index 0000000..f680feb
--- /dev/null
+++ b/quadratic_vote/run.sh
@@ -0,0 +1,39 @@
+#!/bin/bash
+# Quadratic Vote — full walkthrough.
+# Run from the quadratic_vote/ directory.
+
+cd governance || exit 1
+
+echo ""
+echo "=== Step 1: Alice (1 000 tokens) approves proposal 1 ==="
+echo "    weight = floor(sqrt(1000)) = 31"
+leo run cast_vote 1field 1000u32 true
+
+echo ""
+echo "=== Step 2: Bob (225 tokens) rejects proposal 1 ==="
+echo "    weight = floor(sqrt(225)) = 15"
+leo run cast_vote 1field 225u32 false
+
+echo ""
+echo "=== Step 3: Carol (10 000 tokens) approves proposal 1 ==="
+echo "    weight = floor(sqrt(10000)) = 100  (hits MAX_WEIGHT cap)"
+leo run cast_vote 1field 10000u32 true
+
+echo ""
+echo "=== Step 4: Credit cost of casting 5 votes (= 5² = 25) ==="
+leo run qv_cost 5u32
+
+echo ""
+echo "=== Step 5: Does proposal 1 pass? (131 approvals vs 15 rejections) ==="
+leo run is_passing 131u32 15u32
+
+echo ""
+echo "=== Step 6: Perfect-square check via sqrt_math::checks ==="
+echo "    1024 = 32²  → true"
+leo run has_perfect_sqrt 1024u32
+echo "    1000 is not a perfect square  → false"
+leo run has_perfect_sqrt 1000u32
+
+echo ""
+echo "=== Step 7: Unit tests (leo test) ==="
+leo test
diff --git a/quadratic_vote/sqrt_math/program.json b/quadratic_vote/sqrt_math/program.json
new file mode 100644
index 0000000..0e786b7
--- /dev/null
+++ b/quadratic_vote/sqrt_math/program.json
@@ -0,0 +1,7 @@
+{
+    "program": "sqrt_math",
+    "version": "0.1.0",
+    "description": "Integer square root library.",
+    "license": "MIT",
+    "leo": "4.0.1"
+}
diff --git a/quadratic_vote/sqrt_math/src/checks.leo b/quadratic_vote/sqrt_math/src/checks.leo
new file mode 100644
index 0000000..2435163
--- /dev/null
+++ b/quadratic_vote/sqrt_math/src/checks.leo
@@ -0,0 +1,5 @@
+// Returns true when n is a perfect square (i.e., floor(sqrt(n))^2 == n).
+fn is_perfect_square(n: u32) -> bool {
+    let s: u32 = sqrt_math::newton::isqrt(n);
+    return s * s == n;
+}
diff --git a/quadratic_vote/sqrt_math/src/lib.leo b/quadratic_vote/sqrt_math/src/lib.leo
new file mode 100644
index 0000000..65e7a6d
--- /dev/null
+++ b/quadratic_vote/sqrt_math/src/lib.leo
@@ -0,0 +1,2 @@
+// Upper bound on floor(sqrt(n)) for any n: u32 (since sqrt(2^32 - 1) = 65535).
+const ISQRT_MAX: u32 = 65_535u32;
diff --git a/quadratic_vote/sqrt_math/src/newton.leo b/quadratic_vote/sqrt_math/src/newton.leo
new file mode 100644
index 0000000..4b93b4d
--- /dev/null
+++ b/quadratic_vote/sqrt_math/src/newton.leo
@@ -0,0 +1,19 @@
+// Returns floor(sqrt(n)) for any n: u32, including 0 and 1.
+// Result is always in [0, 65_535] since sqrt(2^32 − 1) = 65_535.
+//
+// Uses twenty iterations of Newton's method: x ← (x + n/x) / 2.
+// Starting from n/2 + 1 guarantees x ≥ 1 initially; twenty iterations
+// are sufficient to converge for all n: u32.
+// Because Aleo executes all loop iterations in circuit mode (no early exit),
+// the divisor must be guarded so that x = 0 (reachable only when n = 0)
+// never causes integer division by zero.
+fn isqrt(n: u32) -> u32 {
+    let x: u32 = n / 2u32 + 1u32;
+    for i: u8 in 0u8..20u8 {
+        let divisor: u32 = x == 0u32 ? 1u32 : x;
+        let next: u32 = (x + n / divisor) / 2u32;
+        x = next < x ? next : x;
+    }
+    assert(x <= sqrt_math::ISQRT_MAX);
+    return x;
+}
diff --git a/quadratic_vote/vote_math/program.json b/quadratic_vote/vote_math/program.json
new file mode 100644
index 0000000..1fdd1a2
--- /dev/null
+++ b/quadratic_vote/vote_math/program.json
@@ -0,0 +1,15 @@
+{
+    "program": "vote_math",
+    "version": "0.1.0",
+    "description": "Quadratic-voting weight and credit-cost library.",
+    "license": "MIT",
+    "leo": "4.0.1",
+    "dependencies": [
+        {
+            "name": "sqrt_math",
+            "location": "local",
+            "path": "../sqrt_math",
+            "edition": null
+        }
+    ]
+}
diff --git a/quadratic_vote/vote_math/src/cost.leo b/quadratic_vote/vote_math/src/cost.leo
new file mode 100644
index 0000000..6e13dab
--- /dev/null
+++ b/quadratic_vote/vote_math/src/cost.leo
@@ -0,0 +1,19 @@
+// Computed voting parameters for a participant.
+struct VoterProfile {
+    weight: u32,
+}
+
+// Returns the credit cost of casting `votes` weighted votes under QV.
+// Cost equals votes², so each additional vote is progressively more expensive.
+// votes must be ≤ 65_535 to avoid u32 overflow (65_535² = 4_294_836_225 < 2^32).
+fn credits_for_votes(votes: u32) -> u32 {
+    assert(votes <= 65535u32);
+    return votes * votes;
+}
+
+// Builds a VoterProfile for `token_balance`.
+// Uses vote_math::weight::compute for the capped QV weight.
+fn build_profile(token_balance: u32) -> VoterProfile {
+    let w: u32 = vote_math::weight::compute(token_balance);
+    return VoterProfile { weight: w };
+}
diff --git a/quadratic_vote/vote_math/src/lib.leo b/quadratic_vote/vote_math/src/lib.leo
new file mode 100644
index 0000000..0a7f9ef
--- /dev/null
+++ b/quadratic_vote/vote_math/src/lib.leo
@@ -0,0 +1,4 @@
+// Maximum vote weight any single participant may hold.
+const MAX_WEIGHT: u32 = 100u32;
+// Minimum token balance required to participate in a vote.
+const MIN_BALANCE: u32 = 1u32;
diff --git a/quadratic_vote/vote_math/src/weight.leo b/quadratic_vote/vote_math/src/weight.leo
new file mode 100644
index 0000000..dfb2d7d
--- /dev/null
+++ b/quadratic_vote/vote_math/src/weight.leo
@@ -0,0 +1,11 @@
+// Returns the quadratic-voting weight for `token_balance`.
+// Weight equals floor(sqrt(token_balance)), capped at vote_math::MAX_WEIGHT.
+fn compute(token_balance: u32) -> u32 {
+    let raw: u32 = sqrt_math::newton::isqrt(token_balance);
+    return raw < vote_math::MAX_WEIGHT ? raw : vote_math::MAX_WEIGHT;
+}
+
+// Returns true when `token_balance` meets the minimum participation threshold.
+fn is_eligible(token_balance: u32) -> bool {
+    return token_balance >= vote_math::MIN_BALANCE;
+}