XML 50 R43.htm IDEA: XBRL DOCUMENT
v3.25.2

Common Stock - Additional Information (Details) |  | 1 Months Ended | 3 Months Ended | 6 Months Ended | 12 Months Ended |  |
--- | --- | --- | --- | --- | --- | --- | ---
May 31, 2024 | Jun. 30, 2024 USD ($) $ / shares shares | Jun. 30, 2024 USD ($) $ / shares shares | Jun. 30, 2025 USD ($) shares | Dec. 31, 2024 USD ($) shares | May 30, 2024 shares | May 29, 2024 shares
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Common stock, shares authorized |  |  |  | 500,000,000 | 500,000,000 |  |
Reverse stock split conversion ratio | 0.11675 |  |  |  |  |  |
Common stock reserved for future issuance |  |  |  | one-for-8.5648 |  |  |
Net proceeds from public offering | $ |  | $ 157,600,000 |  |  |  |  |
2022 Stock Option and Grant Plan |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Number of common stock reserved |  |  |  | 2,663,841 | 2,713,368 |  |
2024 Stock Option and Grant Plan |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Number of common stock reserved |  |  |  | 5,742,280 | 3,814,618 |  |
2024 ESPP |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Number of common stock reserved |  |  |  | 690,045 | 324,243 |  |
IPO |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Underwriting discounts and commissions and offering costs | $ |  |  | $ 15,519,000 |  |  |  |
Private Placement |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Underwriting discounts and commissions and offering costs | $ |  |  | $ 1,297,000 |  |  |  |
Common Stock |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Voting right, description |  |  |  | Each share of common stock entitles the holder to one vote |  |  |
Dividends | $ |  |  |  | $ 0 | $ 0 |  |
Common stock, shares authorized |  |  |  |  |  | 500,000,000 | 250,000,000
Issuance of common stock from IPO |  |  | 9,200,000 |  |  |  |
Issuance of common stock from private placement |  |  | 1,058,824 |  |  |  |
Number of common stock reserved |  |  |  | 9,096,166 | 6,852,229 |  |
Common Stock | IPO |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Issuance of common stock from IPO |  | 9,200,000 |  |  |  |  |
Net proceeds from public offering | $ |  | $ 140,900,000 |  |  |  |  |
Shares issued, price per share | $ / shares |  | $ 17 | $ 17 |  |  |  |
Underwriting discounts and commissions and offering costs | $ |  | $ 15,500,000 |  |  |  |  |
Common Stock | Private Placement |  |  |  |  |  |  |
Subsidiary, Sale of Stock [Line Items] |  |  |  |  |  |  |
Issuance of common stock from private placement |  | 1,058,824 |  |  |  |  |
Net proceeds from private placement | $ |  | $ 16,700,000 |  |  |  |  |
Shares issued, price per share | $ / shares |  | $ 17 | $ 17 |  |  |  |
Underwriting discounts and commissions and offering costs | $ |  | $ 1,300,000 |  |  |  |  |

X
- Definition Stock issued during period, shares, private placement. + References No definition available. + Details
Name: | rapp_StockIssuedDuringPeriodSharesPrivatePlacement
Namespace Prefix: | rapp_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | duration

X
- Definition Aggregate number of common shares reserved for future issuance. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(29)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1 + Details
Name: | us-gaap_CommonStockCapitalSharesReservedForFutureIssuance
Namespace Prefix: | us-gaap_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition The maximum number of common shares permitted to be issued by an entity's charter and bylaws. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(29)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 946 -SubTopic 210 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.6-04(16)(a)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1 + Details
Name: | us-gaap_CommonStockSharesAuthorized
Namespace Prefix: | us-gaap_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | instant

X
- Definition Description of voting rights of common stock. Includes eligibility to vote and votes per share owned. Include also, if any, unusual voting rights. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 505 -SubTopic 10 -Section 50 -Paragraph 3 -Publisher FASB -URI https://asc.fasb.org/1943274/2147481112/505-10-50-3 + Details
Name: | us-gaap_CommonStockVotingRights
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Amount of paid and unpaid common stock dividends declared with the form of settlement in cash, stock and payment-in-kind (PIK). + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 505 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.3-04) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 2 -SubTopic 405 -Topic 942 -Publisher FASB -URI https://asc.fasb.org/1943274/2147477787/942-405-45-2 + Details
Name: | us-gaap_DividendsCommonStock
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition The cash outflow for cost incurred directly with the issuance of an equity security. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Topic 230 -SubTopic 10 -Section 45 -Paragraph 15 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482740/230-10-45-15 + Details
Name: | us-gaap_PaymentsOfStockIssuanceCosts
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition The cash inflow associated with the amount received from entity's first offering of stock to the public. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 14 -Subparagraph (a) -SubTopic 10 -Topic 230 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482740/230-10-45-14 + Details
Name: | us-gaap_ProceedsFromIssuanceInitialPublicOffering
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition The cash inflow associated with the amount received from entity's raising of capital via private rather than public placement. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 45 -Paragraph 14 -Subparagraph (a) -SubTopic 10 -Topic 230 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482740/230-10-45-14 + Details
Name: | us-gaap_ProceedsFromIssuanceOfPrivatePlacement
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | duration

X
- Definition Per share or per unit amount of equity securities issued. + References No definition available. + Details
Name: | us-gaap_SharesIssuedPricePerShare
Namespace Prefix: | us-gaap_
Data Type: | dtr-types:perShareItemType
Balance Type: | na
Period Type: | instant

X
- Definition Number of new stock issued during the period. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Name Accounting Standards Codification -Section 50 -Paragraph 2 -SubTopic 10 -Topic 505 -Publisher FASB -URI https://asc.fasb.org/1943274/2147481112/505-10-50-2 Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(28)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1 Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 210 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.5-02(29)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Topic 946 -SubTopic 505 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147478448/946-505-50-2 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Topic 946 -SubTopic 220 -Name Accounting Standards Codification -Section S99 -Paragraph 3 -Subparagraph (SX 210.6-09(4)(b)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3 Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Topic 946 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 3 -Subparagraph (SX 210.6-03(i)(1)) -Publisher FASB -URI https://asc.fasb.org/1943274/2147479886/946-10-S99-3 Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 505 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 1 -Subparagraph (SX 210.3-04) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480008/505-10-S99-1 + Details
Name: | us-gaap_StockIssuedDuringPeriodSharesNewIssues
Namespace Prefix: | us-gaap_
Data Type: | xbrli:sharesItemType
Balance Type: | na
Period Type: | duration

X
- Definition Ratio applied to the conversion of stock split, for example but not limited to, one share converted to two or two shares converted to one. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 505 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 4 -Subparagraph (SAB Topic 4.C) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480008/505-10-S99-4 + Details
Name: | us-gaap_StockholdersEquityNoteStockSplitConversionRatio1
Namespace Prefix: | us-gaap_
Data Type: | xbrli:pureItemType
Balance Type: | na
Period Type: | duration

X
- Definition Description of the reverse stock split arrangement. Also provide the retroactive effect given by the reverse split that occurs after the balance sheet date but before the release of financial statements. + References Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef -Topic 505 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 4 -Subparagraph (SAB Topic 4.C) -Publisher FASB -URI https://asc.fasb.org/1943274/2147480008/505-10-S99-4 + Details
Name: | us-gaap_StockholdersEquityReverseStockSplit
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Definition Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table. + References No definition available. + Details
Name: | us-gaap_SubsidiarySaleOfStockLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_PlanNameAxis=rapp_TwoThousandTwentyTwoStockOptionAndGrantPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_PlanNameAxis=rapp_TwoThousandTwentyFourStockOptionAndGrantPlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_PlanNameAxis=rapp_TwoThousandTwentyFourEmployeeStockPurchasePlanMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=us-gaap_IPOMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_SubsidiarySaleOfStockAxis=us-gaap_PrivatePlacementMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_StatementEquityComponentsAxis=us-gaap_CommonStockMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |