Number of shares issued by conversion of shares of acquiree entity during the period pursuant to merger process.

No definition available.

Name:	adgm_StockIssuedDuringPeriodConversionOfSharesOfAcquireeEntityInProcessOfMerger
Namespace Prefix:	adgm_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of additional shares issued and shares issued for reclassification of shares subject to non-redemption agreements and open market subscription agreements issued during the period pursuant to merger process.

+ References

No definition available.

+ Details

Name:	adgm_StockIssuedDuringPeriodSharesAdditionalSharesAndReclassificationOfShares
Namespace Prefix:	adgm_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of shares issued by conversion of temporary equity shares of acquiree entity during the period pursuant to merger process.

+ References

No definition available.

+ Details

Name:	adgm_StockIssuedDuringPeriodSharesConversionOfTemporaryEquityShares
Namespace Prefix:	adgm_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of shares of common stock outstanding. Common stock represent the ownership interest in a corporation.

+ 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(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 2
-Subparagraph (SX 210.6-05(4))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-2

Reference 4: http://www.xbrl.org/2009/role/commonPracticeRef
-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 5: 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

Reference 6: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 3
-Subparagraph (SX 210.6-09(7))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-3

+ Details

Name:	us-gaap_CommonStockSharesOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of shares of stock issued during the period pursuant to acquisitions.

+ 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(28))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

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(29))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 3: 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_StockIssuedDuringPeriodSharesAcquisitions
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of shares issued during the period as a result of the conversion of convertible securities.

+ 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(29))
-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(30))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

Reference 4: 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 5: 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 6: 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_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- 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

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

- Details

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

- Details

Name:	srt_CounterpartyNameAxis=adgm_PipeInvestorMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Mezzanine Equity and Stockholders' Equity (Deficit) - Number of shares outstanding (Details) - shares		12 Months Ended
	Jul. 31, 2024	Dec. 31, 2025	Dec. 31, 2024	Jul. 30, 2024
Mezzanine Equity and Stockholders' Equity (Deficit)
Total		22,210,459	15,198,232	779,908
Common Stock
Mezzanine Equity and Stockholders' Equity (Deficit)
Issuance of common shares, pre-funded warrants and warrants, net of issuance costs (in shares)	3,287,018	5,798,072
Conversion of ARYA convertible promissory Notes (in shares)	355,100
Conversion of ARYA Class A ordinary shares and Class B ordinary shares (in shares)	2,089,000
Conversion of Class A ordinary shares subject to redemption	123,520
Shares issued for acquisition of Legacy Adagio	6,771,769
Additional shares issued and reclassification of Class A ordinary shares subject to non-redemption agreements and open market subscription agreements	761,229
Total	13,387,636
Common Stock \| PIPE Investor
Mezzanine Equity and Stockholders' Equity (Deficit)
Issuance of common shares, pre-funded warrants and warrants, net of issuance costs (in shares)	3,287,018