License Agreement, Milestone Payments

No definition available.

Name:	syre_LicenseAgreementMilestonePayments
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Nonrefundable research initiation fee for one program paid in cash.

+ References

No definition available.

+ Details

Name:	syre_NonrefundableResearchInitiationFeeForOneProgramPaidInCash
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Percentage of annual equity grant of options to purchase outstanding shares of common stock.

+ References

No definition available.

+ Details

Name:	syre_PercentageOfAnnualEquityGrantOfOptionsToPurchaseOutstandingSharesOfCommonStock
Namespace Prefix:	syre_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Reimbursable research costs.

+ References

No definition available.

+ Details

Name:	syre_ReimbursableResearchCosts
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Related party expenses incurred prior to asset acquisition.

+ References

No definition available.

+ Details

Name:	syre_RelatedPartyExpensesIncurredPriorToAssetAcquisition
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Related party expenses unpaid prior to asset acquisition.

+ References

No definition available.

+ Details

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

- Definition

Research initiation fees.

+ References

No definition available.

+ Details

Name:	syre_ResearchInitiationFees
Namespace Prefix:	syre_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Amount of transactions with related party during the financial reporting period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 850
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483326/850-10-50-1

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 850
-SubTopic 10
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483326/850-10-50-3

+ Details

Name:	us-gaap_RelatedPartyTransactionAmountsOfTransaction
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
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

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(i))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(c)(2)(ii))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 220
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-07(2)(g)(3))
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483575/946-220-S99-1

+ Details

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

- Details

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

- Details

Name:	us-gaap_PlanNameAxis=syre_ParapyreOptionObligationMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=syre_ParagonAgreementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionAxis=syre_StockCompensationAndResearchAndDevelopmentExpenseMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=us-gaap_RelatedPartyMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Paragon Agreement (Details) - USD ($) $ in Millions		1 Months Ended	12 Months Ended
Paragon Agreement (Details) - USD ($) $ in Millions	Jun. 22, 2023	May 31, 2023	Dec. 31, 2023
Paragon Therapeutics Inc
Related Party Transaction [Line Items]
Milestone payments			$ 39.5
Parapyre Option Obligation
Related Party Transaction [Line Items]
Percentage of annual equity grant of options	1.00%	1.00%
Paragon Agreement
Related Party Transaction [Line Items]
Related party expenses incurred prior to asset acquisition	$ 19.0
Related party expenses unpaid prior to asset acquisition	19.0
Stock Compensation And Research And Development Expense
Related Party Transaction [Line Items]
Related party transaction amount			$ 48.5
Related Party \| Paragon Agreement
Related Party Transaction [Line Items]
Research initiation fees	3.0	$ 3.0
Related party expenses incurred prior to asset acquisition	19.0
Reimbursable research costs	16.0
Related party expenses unpaid prior to asset acquisition	19.0
Nonrefundable research initiation fee for one program paid in cash	$ 0.8