Common Stock, Shares, Outstanding, Percentage Available to Purchase on a Diluted Basis

No definition available.

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

- Definition

Development Cost Reduction, Percentage

+ References

No definition available.

+ Details

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

- Definition

Development Cost Reimbursement, Percentage

+ References

No definition available.

+ Details

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

- Definition

Minority interest ownership percentage by noncontrolling owners held in third party.

+ References

No definition available.

+ Details

Name:	syre_MinorityInterestOwnershipPercentageByNoncontrollingOwnersHeldInThirdParty
Namespace Prefix:	syre_
Data Type:	dtr-types1:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Related Party Transaction, Number Of Board Seats

+ References

No definition available.

+ Details

Name:	syre_RelatedPartyTransactionNumberOfBoardSeats
Namespace Prefix:	syre_
Data Type:	xbrli:integerItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount, after allowance for credit loss, of right to consideration from customer for product sold and service rendered in normal course of business.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 946
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (d)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147477802/946-310-45-1

Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(5))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 946
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.6-04(5)(b))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479170/946-210-S99-1

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 954
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479196/954-310-45-1

Reference 5: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 944
-SubTopic 210
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(3))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478777/944-210-S99-1

+ Details

Name:	us-gaap_AccountsReceivableNet
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Definition

Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479830/718-10-S99-1

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

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

- Definition

The equity interest of noncontrolling shareholders, partners or other equity holders in consolidated entity.

+ References

No definition available.

+ Details

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

- 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 310
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 13
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481990/310-10-45-13

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)(i))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-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)(c)(2)(ii))
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479134/946-220-S99-1

Reference 4: 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/1943274/2147479134/946-220-S99-1

+ Details

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

- Definition

Amount of noncash expense for share-based payment arrangement.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (a)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

+ Details

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

- Definition

Period over which grantee's right to exercise award under share-based payment arrangement is no longer contingent on satisfaction of service or performance condition, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days. Includes, but is not limited to, combination of market, performance or service condition.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardAwardVestingPeriod1
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Agreed-upon price for the exchange of the underlying asset relating to the share-based payment award.

+ References

No definition available.

+ Details

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

- Definition

Gross number of share options (or share units) granted during the period.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(01)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

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

- Definition

Percentage of vesting of award under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)(1)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

- Details

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

- Details

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

- Details

Name:	us-gaap_VestingAxis=us-gaap_ShareBasedCompensationAwardTrancheOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

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

- Details

Name:	srt_RangeAxis=srt_MaximumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_OwnershipAxis=syre_FairmountFundsManagementLlcMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Related Party Transactions - Narrative (Details)		3 Months Ended		9 Months Ended
Related Party Transactions - Narrative (Details)	Nov. 22, 2023 $ / shares shares	Sep. 30, 2024 USD ($) seat shares	Sep. 30, 2023 USD ($) shares	Sep. 30, 2024 USD ($) seat shares	Sep. 30, 2023 USD ($) shares	Apr. 01, 2024	Mar. 31, 2024
Related Party Transaction [Line Items]
Stock-based compensation		$ 13,100,000	$ 4,800,000	$ 35,617,000	$ 8,405,000
Options granted (in shares) \| shares		425,500	1,044,667	1,857,853	3,867,366
Stock-based compensation expense		$ 13,100,000	$ 4,785,000	$ 35,617,000	$ 8,405,000
Related Party
Related Party Transaction [Line Items]
Development cost reduction, percent						50.00%
Development cost reimbursement, percent							50.00%
Related Party \| Paragon Agreement
Related Party Transaction [Line Items]
Number of board seats held by related party \| seat		2		2
Amount of related party transaction		$ 1,200,000		$ 30,700,000
Stock-based compensation		6,100,000		13,000,000.0
Reduction in research and development expense		$ 5,900,000		$ 5,900,000
Common stock, shares outstanding, percentage available to purchase on a diluted basis		1.00%		1.00%
Related Party \| Subsequent to Asset Acquisition
Related Party Transaction [Line Items]
Amount of related party transaction		$ 7,400,000		$ 28,300,000
Related Party \| Consulting Agreement
Related Party Transaction [Line Items]
Options granted (in shares) \| shares	477,000
Exercise price (in dollars per share) \| $ / shares	$ 10.39
Vesting period	36 months
Stock-based compensation expense		$ 300,000	$ 0	$ 800,000	$ 0
Related Party \| Consulting Agreement \| Share-Based Payment Arrangement, Tranche One
Related Party Transaction [Line Items]
Vesting percentage	25.00%
Vesting period	1 year
Paragon Therapeutics Inc \| Maximum \| Related Party \| Paragon Agreement
Related Party Transaction [Line Items]
Percentage of ownership by noncontrolling owner		5.00%		5.00%
Fairmount Funds Management LLC \| Minimum \| Related Party \| Paragon Agreement
Related Party Transaction [Line Items]
Percentage of ownership by noncontrolling owner		5.00%		5.00%
Percentage of ownership held in third party		5.00%		5.00%