diff --git a/src/asp.js b/src/asp.js
index 2c05289..655163e 100644
--- a/src/asp.js
+++ b/src/asp.js
@@ -13,8 +13,9 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
-import axios from 'axios'
+import axios, * as axiosMod from 'axios'
 import { decodeProtectedHeader, importJWK, compactVerify, calculateJwkThumbprint } from 'jose'
+import * as joseMod from 'jose'
 import { base32, base64url } from 'rfc4648'
 import { Claim } from './claim.js'
 import { Persona } from './persona.js'
@@ -57,12 +58,12 @@ export async function fetchASPE (uri) {
         responseType: 'text'
       }
     )
-      .then((/** @type {import('axios').AxiosResponse} */ response) => {
+      .then((/** @type {axiosMod.AxiosResponse} */ response) => {
         if (response.status === 200) {
           return response
         }
       })
-      .then((/** @type {import('axios').AxiosResponse} */ response) => response.data)
+      .then((/** @type {axiosMod.AxiosResponse} */ response) => response.data)
   } catch (e) {
     throw new Error(`Error fetching Keybase key: ${e.message}`)
   }
@@ -171,7 +172,7 @@ export async function parseProfileJws (profileJws, uri) {
 /**
  * Compute the fingerprint for JWK keys
  * @function
- * @param {import('jose').JWK} key
+ * @param {joseMod.JWK} key
  * @returns {Promise<string>}
  */
 export async function computeJwkFingerprint (key) {
diff --git a/src/claim.js b/src/claim.js
index b822c3d..fe3e0f2 100644
--- a/src/claim.js
+++ b/src/claim.js
@@ -18,6 +18,7 @@ import { isUri } from 'valid-url'
 import mergeOptions from 'merge-options'
 import { fetch } from './proofs.js'
 import { run } from './verifications.js'
+import * as verificationsMod from './verifications.js'
 import { list, data as _data } from './serviceProviders/index.js'
 import { opts as _opts } from './defaults.js'
 import { ClaimStatus } from './enums.js'
@@ -71,7 +72,7 @@ export class Claim {
      */
     this._status = ClaimStatus.INIT
     /**
-     * @type {import('./serviceProvider.js').ServiceProvider[]}
+     * @type {ServiceProvider[]}
      */
     this._matches = []
   }
@@ -245,6 +246,7 @@ export class Claim {
 
       let claimData = this._matches[index]
 
+      /** @type {verificationsMod.VerificationResult} */
       let verificationResult = null
       let proofData = null
       let proofFetchError
@@ -286,7 +288,7 @@ export class Claim {
         verificationResult = verificationResult || {
           result: false,
           completed: true,
-          proof: {},
+          proof: null,
           errors: [proofFetchError]
         }
       }
diff --git a/src/openpgp.js b/src/openpgp.js
index 40f7bdc..5ea0392 100644
--- a/src/openpgp.js
+++ b/src/openpgp.js
@@ -13,7 +13,7 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
-import axios from 'axios'
+import axios, * as axiosMod from 'axios'
 import { isUri } from 'valid-url'
 import { readKey, PublicKey } from 'openpgp'
 import HKP from '@openpgp/hkp-client'
@@ -129,12 +129,12 @@ export async function fetchKeybase (username, fingerprint) {
         responseType: 'text'
       }
     )
-      .then((/** @type {import('axios').AxiosResponse} */ response) => {
+      .then((/** @type {axiosMod.AxiosResponse} */ response) => {
         if (response.status === 200) {
           return response
         }
       })
-      .then((/** @type {import('axios').AxiosResponse} */ response) => response.data)
+      .then((/** @type {axiosMod.AxiosResponse} */ response) => response.data)
   } catch (e) {
     throw new Error(`Error fetching Keybase key: ${e.message}`)
   }
diff --git a/src/persona.js b/src/persona.js
index cff55de..5c14a95 100644
--- a/src/persona.js
+++ b/src/persona.js
@@ -27,7 +27,7 @@ import { Claim } from './claim.js'
 export class Persona {
   /**
    * @param {string} name
-   * @param {import('./claim.js').Claim[]} claims
+   * @param {Claim[]} claims
    */
   constructor (name, claims) {
     /**
@@ -68,7 +68,7 @@ export class Persona {
     this.themeColor = null
     /**
      * List of identity claims
-     * @type {import('./claim.js').Claim[]}
+     * @type {Claim[]}
      * @public
      */
     this.claims = claims
@@ -145,7 +145,7 @@ export class Persona {
 
   /**
    * @function
-   * @param {import('./claim.js').Claim} claim
+   * @param {Claim} claim
    */
   addClaim (claim) {
     this.claims.push(claim)
diff --git a/src/profile.js b/src/profile.js
index 698d09c..e4906a8 100644
--- a/src/profile.js
+++ b/src/profile.js
@@ -13,13 +13,22 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
-import { PublicKeyFetchMethod, PublicKeyEncoding, PublicKeyType } from './enums.js'
+import { PublicKey } from 'openpgp'
+import * as joseMod from 'jose'
+import { PublicKeyFetchMethod, PublicKeyEncoding, PublicKeyType, ProfileType } from './enums.js'
 import { Persona } from './persona.js'
 
+/**
+ * The online verifier instance of identity profiles like Keyoxide's web interface
+ * @typedef {Object} ProfileVerifier
+ * @property {string} name - Name of the profile verifier
+ * @property {string} url - URL to the profile verifier
+ */
+
 /**
  * A profile of personas with identity claims
  * @function
- * @param {Array<import('./persona.js').Persona>} personas
+ * @param {Array<Persona>} personas
  * @public
  * @example
  * const claim = Claim('https://alice.tld', '123');
@@ -30,9 +39,9 @@ export class Profile {
   /**
    * Create a new profile
    * @function
-   * @param {import('./enums.js').ProfileType} profileType
+   * @param {ProfileType} profileType
    * @param {string} identifier
-   * @param {Array<import('./persona.js').Persona>} personas
+   * @param {Array<Persona>} personas
    * @public
    */
   constructor (profileType, identifier, personas) {
@@ -44,7 +53,7 @@ export class Profile {
     this.profileVersion = 2
     /**
      * Profile version
-     * @type {import('./enums.js').ProfileType}
+     * @type {ProfileType}
      * @public
      */
     this.profileType = profileType
@@ -56,7 +65,7 @@ export class Profile {
     this.identifier = identifier
     /**
      * List of personas
-     * @type {Array<import('./persona.js').Persona>}
+     * @type {Array<Persona>}
      * @public
      */
     this.personas = personas || []
@@ -98,7 +107,7 @@ export class Profile {
       encodedKey: null,
       /**
        * The raw cryptographic key as object (to be removed during toJSON())
-       * @type {import('openpgp').PublicKey | import('jose').JWK | null}
+       * @type {PublicKey | joseMod.JWK | null}
        * @public
        */
       key: null,
@@ -130,7 +139,7 @@ export class Profile {
     }
     /**
      * List of verifier URLs
-     * @type {{name: string, url: string}[]}
+     * @type {ProfileVerifier[]}
      * @public
      */
     this.verifiers = []
diff --git a/src/proofs.js b/src/proofs.js
index b4aa450..b77bc49 100644
--- a/src/proofs.js
+++ b/src/proofs.js
@@ -17,6 +17,7 @@ import { isNode } from 'browser-or-node'
 import { fetcher } from './index.js'
 import { generateProxyURL } from './utils.js'
 import { ProxyPolicy, ProofAccessRestriction } from './enums.js'
+import { ServiceProvider } from './serviceProvider.js'
 
 /**
  * @module proofs
@@ -29,7 +30,7 @@ import { ProxyPolicy, ProofAccessRestriction } from './enums.js'
  * choose the right approach to fetch the proof. An error will be thrown if no
  * approach is possible.
  * @async
- * @param {import('./serviceProvider.js').ServiceProvider} data - Data from a claim definition
+ * @param {ServiceProvider} data - Data from a claim definition
  * @param {object} opts - Options to enable the request
  * @returns {Promise<object|string>}
  */
@@ -42,7 +43,7 @@ export async function fetch (data, opts) {
 }
 
 /**
- * @param {import('./serviceProvider.js').ServiceProvider} data - Data from a claim definition
+ * @param {ServiceProvider} data - Data from a claim definition
  * @param {object} opts - Options to enable the request
  * @returns {Promise<object|string>}
  */
@@ -85,7 +86,7 @@ const handleBrowserRequests = (data, opts) => {
 }
 
 /**
- * @param {import('./serviceProvider.js').ServiceProvider} data - Data from a claim definition
+ * @param {ServiceProvider} data - Data from a claim definition
  * @param {object} opts - Options to enable the request
  * @returns {Promise<object|string>}
  */
@@ -106,7 +107,7 @@ const handleNodeRequests = (data, opts) => {
 }
 
 /**
- * @param {import('./serviceProvider.js').ServiceProvider} data - Data from a claim definition
+ * @param {ServiceProvider} data - Data from a claim definition
  * @param {object} opts - Options to enable the request
  * @returns {Promise<object|string>}
  */
@@ -132,7 +133,7 @@ const createDefaultRequestPromise = (data, opts) => {
 }
 
 /**
- * @param {import('./serviceProvider.js').ServiceProvider} data - Data from a claim definition
+ * @param {ServiceProvider} data - Data from a claim definition
  * @param {object} opts - Options to enable the request
  * @returns {Promise<object|string>}
  */
@@ -171,7 +172,7 @@ const createProxyRequestPromise = (data, opts) => {
 }
 
 /**
- * @param {import('./serviceProvider.js').ServiceProvider} data - Data from a claim definition
+ * @param {ServiceProvider} data - Data from a claim definition
  * @param {object} opts - Options to enable the request
  * @returns {Promise<object|string>}
  */
diff --git a/src/serviceProvider.js b/src/serviceProvider.js
index 91e1835..aca19f1 100644
--- a/src/serviceProvider.js
+++ b/src/serviceProvider.js
@@ -13,6 +13,17 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
+import { ClaimFormat, ClaimRelation, EntityEncodingFormat, ProofAccessRestriction, ProofFormat } from "./enums"
+
+/**
+ * The method to find the proof inside the response data
+ * @typedef {Object} ProofTarget
+ * @property {ClaimFormat} format - How the response data is formatted
+ * @property {EntityEncodingFormat} encoding - How the response data is encoded
+ * @property {ClaimRelation} relation - How the proof is related to the response data
+ * @property {string[]} path - Path to the proof inside the response data object
+ */
+
 /**
  * A service provider matched to an identity claim
  * @class
@@ -104,7 +115,7 @@ export class ServiceProvider {
         fetcher: spObj.proof.request.fetcher,
         /**
          * Type of access restriction
-         * @type {import('./enums.js').ProofAccessRestriction}
+         * @type {ProofAccessRestriction}
          */
         accessRestriction: spObj.proof.request.accessRestriction,
         /**
@@ -120,13 +131,13 @@ export class ServiceProvider {
       response: {
         /**
          * Expected format of the proof
-         * @type {import('./enums.js').ProofFormat}
+         * @type {ProofFormat}
          */
         format: spObj.proof.response.format
       },
       /**
        * Details about the target located in the response
-       * @type {{format: import('./enums.js').ClaimFormat, encoding: import('./enums.js').EntityEncodingFormat, relation: import('./enums.js').ClaimRelation, path: string[]}[]}
+       * @type {ProofTarget[]}
        */
       target: spObj.proof.target
     }
diff --git a/src/signatures.js b/src/signatures.js
index 467494b..114dceb 100644
--- a/src/signatures.js
+++ b/src/signatures.js
@@ -13,7 +13,7 @@ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */
-import { readCleartextMessage, verify } from 'openpgp'
+import { CleartextMessage, PublicKey, readCleartextMessage, verify } from 'openpgp'
 import { Claim } from './claim.js'
 import { fetchURI } from './openpgp.js'
 import { Profile } from './profile.js'
@@ -28,10 +28,10 @@ import { Persona } from './persona.js'
  * Extract the profile from a signature and fetch the associated key
  * @async
  * @param {string} signature - The plaintext signature to parse
- * @returns {Promise<import('./profile.js').Profile>}
+ * @returns {Promise<Profile>}
  */
 export async function parse (signature) {
-  /** @type {import('openpgp').CleartextMessage} */
+  /** @type {CleartextMessage} */
   let sigData
 
   // Read the signature
@@ -84,7 +84,7 @@ export async function parse (signature) {
   if (sigKeys.length > 0) {
     try {
       obtainedKey.query = sigKeys[0]
-      /** @type {import('openpgp').PublicKey} */
+      /** @type {PublicKey} */
       obtainedKey.data = (await fetchURI(obtainedKey.query)).publicKey.key
       obtainedKey.method = obtainedKey.query.split(':')[0]
     } catch (e) {}
diff --git a/src/verifications.js b/src/verifications.js
index f54d04c..f7f329a 100644
--- a/src/verifications.js
+++ b/src/verifications.js
@@ -17,20 +17,42 @@ import { generateClaim, getUriFromString } from './utils.js'
 import { ClaimFormat, EntityEncodingFormat, ClaimRelation, ProofFormat } from './enums.js'
 import { bcryptVerify, argon2Verify } from 'hash-wasm'
 import { decodeHTML, decodeXML } from 'entities'
+import { ServiceProvider } from './serviceProvider.js'
 
 /**
  * @module verifications
  * @ignore
  */
 
+/**
+ * Parameters needed to perform the proof verification
+ * @typedef {object} VerificationParams
+ * @property {string} target
+ * @property {ClaimFormat} claimFormat
+ * @property {EntityEncodingFormat} proofEncodingFormat
+ * @property {ClaimRelation} [claimRelation]
+ */
+
+/**
+ * Result of the proof verification
+ * @typedef {Object} VerificationResult
+ * @property {boolean} result
+ * @property {boolean} completed
+ * @property {VerificationResultProof} [proof]
+ * @property {any[]} errors
+ */
+
+/**
+ * Information about the proof in the proof verification result
+ * @typedef {Object} VerificationResultProof
+ * @property {string} fetcher
+ * @property {boolean} viaProxy
+ */
+
 /**
  * @function
  * @param {string} data
- * @param {object} params
- * @param {string} params.target
- * @param {string} params.claimFormat
- * @param {string} params.proofEncodingFormat
- * @param {string} [params.claimRelation]
+ * @param {VerificationParams} params
  * @returns {Promise<boolean>}
  */
 const containsProof = async (data, params) => {
@@ -218,11 +240,7 @@ const containsProof = async (data, params) => {
  * @function
  * @param {any} proofData
  * @param {string[]} checkPath
- * @param {object} params
- * @param {string} params.target
- * @param {string} params.claimFormat
- * @param {string} params.proofEncodingFormat
- * @param {string} [params.claimRelation]
+ * @param {VerificationParams} params
  * @returns {Promise<boolean>}
  */
 const runJSON = async (proofData, checkPath, params) => {
@@ -272,12 +290,13 @@ const runJSON = async (proofData, checkPath, params) => {
 /**
  * Run the verification by finding the formatted fingerprint in the proof
  * @async
- * @param {object} proofData                                                - The proof data
- * @param {import('./serviceProvider.js').ServiceProvider} claimData   - The claim data
- * @param {string} fingerprint                                              - The fingerprint
- * @returns {Promise<object>}
+ * @param {object} proofData            - The proof data
+ * @param {ServiceProvider} claimData   - The claim data
+ * @param {string} fingerprint          - The fingerprint
+ * @returns {Promise<VerificationResult>}
  */
 export async function run (proofData, claimData, fingerprint) {
+  /** @type {VerificationResult} */
   const res = {
     result: false,
     completed: false,