Debt Conversion, Change In Control, Price Per Unit As A Percentage Of Lowest Price Offered

No definition available.

Name:	gemi_DebtConversionChangeInControlPricePerUnitAsAPercentageOfLowestPriceOffered
Namespace Prefix:	gemi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Conversion, Minimum Amount Of Proceeds Received For Issuance Of Convertible Preferred Securities That Triggers Automatic Conversion

+ References

No definition available.

+ Details

Name:	gemi_DebtConversionMinimumAmountOfProceedsReceivedForIssuanceOfConvertiblePreferredSecuritiesThatTriggersAutomaticConversion
Namespace Prefix:	gemi_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Debt Conversion, Non-Qualifying Financing Event, Option To Convert Notes, Percentage Of The Lowest Price Paid

+ References

No definition available.

+ Details

Name:	gemi_DebtConversionNonQualifyingFinancingEventMaximumAmountOfProceedsReceivedToTriggerOptionToConvertNotes
Namespace Prefix:	gemi_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Debt Conversion, Non-Qualifying Financing Event, Option To Convert Notes, Price Per Unit As A Percentage Of Lowest Price Per Unit Paid

+ References

No definition available.

+ Details

Name:	gemi_DebtConversionNonQualifyingFinancingEventOptionToConvertNotesPricePerUnitAsAPercentageOfLowestPricePerUnitPaid
Namespace Prefix:	gemi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Conversion, Note Holder Option, Conversion Price As A Percentage Of Lowest Price Paid

+ References

No definition available.

+ Details

Name:	gemi_DebtConversionNoteHolderOptionConversionPriceAsAPercentageOfLowestPricePaid
Namespace Prefix:	gemi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Conversion, Public Company Event, Price Per Unit As A Percentage Of Price Per Unit Implied In The Public Event

+ References

No definition available.

+ Details

Name:	gemi_DebtConversionPublicCompanyEventPricePerUnitAsAPercentageOfPricePerUnitImpliedInThePublicEvent
Namespace Prefix:	gemi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Conversion, Triggering Event, Percentage Of The Lowest Price Per Unit Paid

+ References

No definition available.

+ Details

Name:	gemi_DebtConversionTriggeringEventPercentageOfTheLowestPricePerUnitPaid
Namespace Prefix:	gemi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

Debt Instrument, Convertible, Conversion Price, Percentage Of Initial Public Offering Price

+ References

No definition available.

+ Details

Name:	gemi_DebtInstrumentConvertibleConversionPricePercentageOfInitialPublicOfferingPrice
Namespace Prefix:	gemi_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

The value of the financial instrument(s) that the original debt is being converted into in a noncash (or part noncash) transaction. "Part noncash" refers to that portion of the transaction not resulting in cash receipts or cash payments in the period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482913/230-10-50-3

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 50
-Paragraph 5
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482913/230-10-50-5

+ Details

Name:	us-gaap_DebtConversionConvertedInstrumentAmount1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The number of shares issued in exchange for the original debt being converted in a noncash (or part noncash) transaction. "Part noncash" refers to that portion of the transaction not resulting in cash receipts or payments in the period.

+ References

+ Details

Name:	us-gaap_DebtConversionConvertedInstrumentSharesIssued1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The price per share of the conversion feature embedded in the debt instrument.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 5
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-5

+ Details

Name:	us-gaap_DebtInstrumentConvertibleConversionPrice1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Face (par) amount of debt instrument at time of issuance.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 55
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482949/835-30-55-8

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 3: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69B

Reference 4: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69C
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69C

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482900/835-30-50-1

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482925/835-30-45-2

+ Details

Name:	us-gaap_DebtInstrumentFaceAmount
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Contractual interest rate for funds borrowed, under the debt agreement.

+ 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(22)(a)(1))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

+ Details

Name:	us-gaap_DebtInstrumentInterestRateStatedPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- 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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 815
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8A
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480434/815-10-50-8A

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 942
-SubTopic 235
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477314/942-235-S99-2

Reference 3: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-1

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S50
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480738/235-10-S50-4

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.12-04(a))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-3

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 235
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.4-08(f))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480678/235-10-S99-1

Reference 7: http://www.xbrl.org/2003/role/exampleRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 55
-Paragraph 8
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482949/835-30-55-8

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 9: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69B
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69B

Reference 10: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69C
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69C

Reference 11: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69E
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69E

Reference 12: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 55
-Paragraph 69F
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481568/470-20-55-69F

Reference 13: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 14: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 15: http://www.xbrl.org/2003/role/exampleRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 16: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (e)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 17: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (f)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 18: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1B
-Subparagraph (h)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1B

Reference 19: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

Reference 20: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

Reference 21: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1D
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1D

Reference 22: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 23: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 24: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1E
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1E

Reference 25: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 26: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 27: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 28: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1F
-Subparagraph (b)(2)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1F

Reference 29: http://www.xbrl.org/2003/role/disclosureRef
-Topic 470
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 1I
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481139/470-20-50-1I

Reference 30: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482925/835-30-45-2

Reference 31: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 835
-SubTopic 30
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482900/835-30-50-1

+ Details

Name:	us-gaap_DebtInstrumentLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The cash inflow from the issuance of a long-term debt instrument which can be exchanged for a specified amount of another security, typically the entity's common stock, at the option of the issuer or the holder.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-14

+ Details

Name:	us-gaap_ProceedsFromConvertibleDebt
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Per share amount received by subsidiary or equity investee for each share of common stock issued or sold in the stock transaction.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

Name:	us-gaap_LongtermDebtTypeAxis=us-gaap_ConvertibleDebtMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassBMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=gemi_SeptemberNoteUSDMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=gemi_NovemberNoteBTCMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=gemi_DecemberNoteUSDMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_DebtInstrumentAxis=gemi_MarchNoteBTCMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Related Party Loans and Convertible Notes - Convertible Notes (Details) - USD ($) $ / shares in Units, $ in Thousands, shares in Millions					1 Months Ended				2 Months Ended			9 Months Ended		12 Months Ended
	Sep. 11, 2025	May 15, 2025	Sep. 30, 2024	Nov. 30, 2023	Mar. 31, 2024	Dec. 31, 2023	Oct. 31, 2023	Sep. 30, 2023	Feb. 29, 2024	Feb. 29, 2024	Oct. 31, 2023	Sep. 30, 2025	Sep. 30, 2024	Dec. 31, 2024	Mar. 01, 2024	Dec. 27, 2023	Nov. 22, 2023	Sep. 15, 2023
Debt Instrument [Line Items]
Proceeds from related party convertible notes												$ 0	$ 24,568
Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering												804,297	$ 0
Class A common stock \| IPO
Debt Instrument [Line Items]
Share price per share (in dollars per share)	$ 28.00
Convertible Notes
Debt Instrument [Line Items]
Debt instrument, face amount	$ 228,000											200,000		$ 200,000
Proceeds from related party convertible notes												0		69,897
Stated interest rate		8.00%
Minimum amount of aggregate gross proceeds from issuance of convertible preferred units that trigger a qualified financing event		$ 50,000
Qualified financing event, conversion price as a percentage of the lowest price per unit paid by the other purchasers of the convertible preferred units		80.00%
Non-qualified financing event, maximum amount of proceeds received to trigger the option to convert the outstanding notes		$ 50,000
Non-qualified financing event, conversion price as a percentage of lowest price paid per unit by the purchasers of the convertible preferred units		80.00%
Note holder option, price of conversion as a percentage of the lowest original issue price		80.00%	80.00%
Change in control, conversion price as a percentage of the lowest price per unit offered in the change of control event		80.00%
Public company event, conversion price as a percentage of the price per common unit implied in the public company event		80.00%
Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering	$ 285,000											285,007
Convertible Notes \| Class B common stock
Debt Instrument [Line Items]
Number of shares resulting from conversion of debt (in shares)	10.2
Price per share resulting from converted debt (in dollars per share)	$ 22.40
Percentage of IPO price, resulting from converted debt	80.00%
September Note (USD) \| Convertible Notes
Debt Instrument [Line Items]
Debt instrument, face amount																		$ 50,000
Proceeds from related party convertible notes							$ 21,500	$ 28,500			$ 50,000	0		0
Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering												72,279
November Note (BTC) \| Convertible Notes
Debt Instrument [Line Items]
Debt instrument, face amount																	$ 54,671
Proceeds from related party convertible notes				$ 54,700								0		0
Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering												78,269
December Note (USD) \| Convertible Notes
Debt Instrument [Line Items]
Debt instrument, face amount																$ 50,000
Proceeds from related party convertible notes						$ 25,400			$ 24,600	$ 50,000		0		24,568
Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering												70,804
March Note (BTC) \| Convertible Notes
Debt Instrument [Line Items]
Debt instrument, face amount															$ 45,329
Proceeds from related party convertible notes					$ 45,300							0		$ 45,329
Conversion of related party loans and related party convertible notes to common stock in connection with initial public offering												$ 63,655