Accrued and Other Current Liabilities (Details) - USD ($) $ in Thousands	Mar. 31, 2024	Dec. 31, 2023
Payables and Accruals [Abstract]
Accrued compensation	$ 2,506	$ 4,054
Accrued contracted research and development costs	18,149	7,092
Accrued professional and consulting fees	720	1,474
Accrued other	219	488
Total accrued and other current liabilities	$ 21,594	$ 13,108

Accrued contracted research and development costs.

No definition available.

Name:	syre_AccruedContractedResearchAndDevelopmentCosts
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- 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

- 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
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-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

- Definition

Carrying value as of the balance sheet date of the obligations incurred through that date and payable for employees' services provided. 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://www.xbrl.org/2003/role/exampleRef
-Topic 210
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 8
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483467/210-10-45-8

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-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_AccruedSalariesCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

Amount of expenses incurred but not yet paid classified as other, due within one year or the normal operating cycle, if longer.

+ References

+ Details

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

- References

No definition available.

+ Details

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