docs: add benchmarks page

apps/docs/package.json

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         "format:write": "remark ./**/*.mdx --output"
     },
     "dependencies": {
-        "@docusaurus/core": "3.1.1",
-        "@docusaurus/preset-classic": "3.1.1",
+        "@docusaurus/core": "3.5.2",
+        "@docusaurus/preset-classic": "3.5.2",
         "@mdx-js/react": "^3.0.0",
         "@semaphore-protocol/utils": "4.5.0",
         "@svgr/webpack": "^5.5.0",
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         "url-loader": "^4.1.1"
     },
     "devDependencies": {
-        "@docusaurus/module-type-aliases": "3.1.1",
-        "@docusaurus/tsconfig": "3.1.1",
+        "@docusaurus/module-type-aliases": "3.5.2",
+        "@docusaurus/tsconfig": "3.5.2",
         "@types/react": "^18.2.29",
         "remark-cli": "^12.0.0",
         "remark-frontmatter": "^5.0.0",

apps/docs/versioned_docs/version-V4/benchmarks.md

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+---
+sidebar_position: 8
+---
+
+# Benchmarks
+
+Semaphore v4 introduces new features and performance improvements. Detailed changes are available in the [release changelog](https://github.com/semaphore-protocol/semaphore/releases/tag/v4.0.0).
+
+The primary changes in benchmark values are driven by the two major protocol updates:
+
+-   New [Identity schema](https://github.com/semaphore-protocol/semaphore/tree/main/packages/identity).
+
+-   [LeanIMT](https://github.com/privacy-scaling-explorations/zk-kit/tree/main/packages/lean-imt): New optimized IMT.
+
+## New Identity schema
+
+Semaphore v4 includes a new schema for the identities allowing the creation and verification of signatures.
+
+Although the new Identity package is slightly slower than the one in Semaphore v3 (by just a few milliseconds), the trade-off is minimal considering the included functionality.
+
+The new identity schema adds additional constraints to the Semaphore v4 circuit; however, this does not negatively impact overall performance of the protocol.
+
+## LeanIMT
+
+Semaphore v4 uses the LeanIMT data structure for group operations, an improvement over the IMT used in v3.
+
+For further details, see the [LeanIMT paper](https://github.com/privacy-scaling-explorations/zk-kit/tree/main/papers/leanimt).
+
+The LeanIMT offers dynamic depth, resulting in faster and more cost-effective group operations, across Node.js, browser and smart contracts.
+
+Semaphore v4 support tree depths from 1 to 32, while v3 supports depths from 16 to 32, both for proof generation and verification.
+
+## System Specifications and Software environment
+
+All the benchmarks were run in an environment with these properties:
+
+**System Specifications**
+
+Computer: MacBook Pro
+
+Chip: Apple M2 Pro
+
+Memory (RAM): 16 GB
+
+Operating System: macOS Sequoia version 15.0.1
+
+**Software environment**
+
+Node.js version: 20.18.0
+
+Browser: Google Chrome Version 130.0.6723.92 (Official Build) (arm64)
+
+## Running the benchmarks
+
+### Javascript and Circom
+
+GitHub repository to the run Node.js, browser and Circom benchmarks: https://github.com/vplasencia/semaphore-benchmarks
+
+### Solidity
+
+GitHub repository to run the Solidity benchmarks: https://github.com/semaphore-protocol/semaphore
+
+## Node.js benchmarks
+
+### Identities
+
+![Identities](../../assets/img-benchmarks/node/identity-node-benchmarks.png)
+
+### Create Group
+
+Create group, either empty or with initial members.
+
+![Create Group](../../assets/img-benchmarks/node/create-group-node-benchmarks.png)
+
+### Add Member
+
+Add a member to groups with different sizes.
+
+![Add Member](../../assets/img-benchmarks/node/add-member-node-benchmarks.png)
+
+### Generate Proof
+
+Generate a proof using groups with different numbers of members.
+
+![Generate Proof](../../assets/img-benchmarks/node/generate-proof-node-benchmarks.png)
+
+### Verify Proof
+
+Verify a proof using groups with different numbers of members.
+
+![Verify Proof](../../assets/img-benchmarks/node/verify-proof-node-benchmarks.png)
+
+## Browser benchmarks
+
+Main functions used in the browser.
+
+![Browser benchmarks](../../assets/img-benchmarks/browser/browser-benchmarks.png)
+
+## Circuit benchmarks
+
+### Semaphore V3
+
+<img
+src={require('../../assets/img-benchmarks/circuits/semaphore-v3-circuits-benchmarks.png').default}
+alt="Circuit benchmarks Semaphore v3"
+style={{ width: '300px', height: 'auto' }}
+/>
+
+### Semaphore V4
+
+<img
+src={require('../../assets/img-benchmarks/circuits/semaphore-v4-circuits-benchmarks.png').default}
+alt="Circuit benchmarks Semaphore v4"
+style={{ width: '300px', height: 'auto' }}
+/>
+
+## Contracts
+
+<img
+src={require('../../assets/img-benchmarks/contracts/contract-benchmarks.png').default}
+alt="Contract Benchmarks"
+style={{ width: '590px', height: 'auto' }}
+/>
+
+### Semaphore V3 gas report
+
+![Contracts benchmarks Semaphore v3](../../assets/img-benchmarks/contracts/semaphore-v3-contracts-benchmarks.png)
+
+### Semaphore V4 gas report
+
+![Contracts benchmarks Semaphore v4](../../assets/img-benchmarks/contracts/semaphore-v4-contracts-benchmarks.png)

apps/docs/versioned_docs/version-V4/credits.md

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-sidebar_position: 12
+sidebar_position: 13
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 # Credits

apps/docs/versioned_docs/version-V4/faq.md

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-sidebar_position: 11
+sidebar_position: 12
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 # FAQ

apps/docs/versioned_docs/version-V4/glossary.md

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-sidebar_position: 8
+sidebar_position: 9
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 # Glossary

apps/docs/versioned_docs/version-V4/resources.mdx

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-sidebar_position: 9
+sidebar_position: 10
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 import Articles from '@site/src/components/Articles';

apps/docs/versioned_docs/version-V4/troubleshooting.md

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-sidebar_position: 10
+sidebar_position: 11
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 import Tabs from "@theme/Tabs"