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Accrued Expenses and Other Current Liabilities (Details) - Schedule of Accrued Expenses and Other Current Liabilities - USD ($)	Mar. 31, 2024	Dec. 31, 2023
Schedule of Accrued Expenses and Other Current Liabilities [Abstract]
Accrued royalty (see Note 12)	$ 62,500	$ 150,000
Accrued payroll	36,056	22,481
Professional services	6,143,825	58,021
Engineering consulting		1,700
Business development	129,342	1,425
Accrued other	409,516	10,813
Total	$ 6,781,239	$ 244,440

X

- Definition

The amount of business development.

+ References

No definition available.

+ Details

Name:	airj_AccruedBusinessDevelopment
Namespace Prefix:	airj_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

The amount of engineering consulting.

+ References

No definition available.

+ Details

Name:	airj_AccruedEngineeringConsultingCurrent
Namespace Prefix:	airj_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- References

No definition available.

+ Details

Name:	airj_ScheduleOfAccruedExpensesAndOtherCurrentLiabilitiesAbstract
Namespace Prefix:	airj_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Amount of liabilities incurred to vendors for goods and services received, and accrued liabilities classified as other, payable within one year or the normal operating cycle, if longer.

+ References

No definition available.

+ Details

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

X

- Definition

Amount of expenses incurred but not yet paid nor invoiced, and liabilities classified as other.

+ References

No definition available.

+ Details

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

X

- Definition

Carrying value as of the balance sheet date of obligations incurred and payable for statutory payroll taxes incurred through that date and withheld from employees pertaining to services received from them, including entity's matching share of the employees FICA taxes and contributions to the state and federal unemployment insurance programs. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ 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(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

X

- Definition

Carrying value as of the balance sheet date of obligations incurred through that date and payable for professional fees, such as for legal and accounting services received. Used to reflect the current portion of the liabilities (due within one year or within the normal operating cycle if longer).

+ 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(20))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480566/210-10-S99-1

+ Details

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

X

- Definition

Carrying value as of the balance sheet date of obligations incurred through that date and payable for royalties.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Topic 942
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(15)(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478546/942-210-S99-1

+ Details

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