Entity date of incorporation.

No definition available.

Name:	crtx_EntityDateOfIncorporation
Namespace Prefix:	crtx_
Data Type:	xbrli:gYearMonthItemType
Balance Type:	na
Period Type:	duration

- Definition

Organization consolidation and presentation of financial statements disclosure line items.

+ References

No definition available.

+ Details

Name:	crtx_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureLineItems
Namespace Prefix:	crtx_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of investment in debt security measured at fair value with change in fair value recognized in other comprehensive income (available-for-sale), classified as noncurrent.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 326
-SubTopic 30
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=121558606&loc=SL82898722-210454

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 320
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=121553693&loc=d3e26626-111562

+ Details

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

- Definition

Cash includes currency on hand as well as demand deposits with banks or financial institutions. It also includes other kinds of accounts that have the general characteristics of demand deposits in that the customer may deposit additional funds at any time and effectively may withdraw funds at any time without prior notice or penalty. Cash equivalents, excluding items classified as marketable securities, include short-term, highly liquid Investments that are both readily convertible to known amounts of cash, and so near their maturity that they present minimal risk of changes in value because of changes in interest rates. Generally, only investments with original maturities of three months or less qualify under that definition. Original maturity means original maturity to the entity holding the investment. For example, both a three-month US Treasury bill and a three-year Treasury note purchased three months from maturity qualify as cash equivalents. However, a Treasury note purchased three years ago does not become a cash equivalent when its remaining maturity is three months. Short-term investments, exclusive of cash equivalents, generally consist of marketable securities intended to be sold within one year (or the normal operating cycle if longer) and may include trading securities, available-for-sale securities, or held-to-maturity securities (if maturing within one year), as applicable.

+ References

+ Details

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

- Definition

Number of shares issued for each share of convertible preferred stock that is converted.

+ References

+ Details

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

- Definition

The cash outflow for cost incurred directly with the issuance of an equity security.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 15
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3291-108585

+ Details

Name:	us-gaap_PaymentsOfStockIssuanceCosts
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The cash inflow associated with the amount received from entity's first offering of stock to the public.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 14
-Subparagraph (a)
-URI http://asc.fasb.org/extlink&oid=121586364&loc=d3e3255-108585

+ Details

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

- Definition

The cash inflow from the additional capital contribution to the entity.

+ References

+ Details

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

- Definition

The cumulative amount of the reporting entity's undistributed earnings or deficit.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 210
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.5-02(30)(a)(3))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 65
-Paragraph 15
-Subparagraph (g)(2)
-URI http://asc.fasb.org/extlink&oid=121322162&loc=SL121327923-165333

Reference 3: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-03(a)(23)(a)(4))
-URI http://asc.fasb.org/extlink&oid=120400017&loc=d3e572229-122910

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 40
-Section 65
-Paragraph 2
-Subparagraph (h)(2)
-URI http://asc.fasb.org/extlink&oid=121370832&loc=SL117420844-207641

Reference 5: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section S99
-Paragraph 1
-Subparagraph (SX 210.3-04)
-URI http://asc.fasb.org/extlink&oid=120397183&loc=d3e187085-122770

Reference 6: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 40
-Section 65
-Paragraph 2
-Subparagraph (g)(2)(i)
-URI http://asc.fasb.org/extlink&oid=121370832&loc=SL117420844-207641

+ Details

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

- Definition

Date the subsidiary or equity investee issued or sold stock, in CCYY-MM-DD format.

+ References

No definition available.

+ Details

Name:	us-gaap_SaleOfStockTransactionDate
Namespace Prefix:	us-gaap_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share or per unit amount of equity securities issued.

+ References

No definition available.

+ Details

Name:	us-gaap_SharesIssuedPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	num:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of new stock issued during the period.

+ References

+ Details

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

- Definition

The number of securities classified as temporary equity that have been issued and are held by the entity's shareholders. Securities outstanding equals securities issued minus securities held in treasury. Temporary equity is a security with redemption features that are outside the control of the issuer, is not classified as an asset or liability in conformity with GAAP, and is not mandatorily redeemable. Includes any type of security that is redeemable at a fixed or determinable price or on a fixed or determinable date or dates, is redeemable at the option of the holder, or has conditions for redemption which are not solely within the control of the issuer. If convertible, the issuer does not control the actions or events necessary to issue the maximum number of shares that could be required to be delivered under the conversion option if the holder exercises the option to convert the stock to another class of equity. If the security is a warrant or a rights issue, the warrant or rights issue is considered to be temporary equity if the issuer cannot demonstrate that it would be able to deliver upon the exercise of the option by the holder in all cases. Includes stock with put option held by ESOP and stock redeemable by holder only in the event of a change in control of the issuer.

+ References

+ Details

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

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_IPOMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_OverAllotmentOptionMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_SubsidiarySaleOfStockAxis=us-gaap_PrivatePlacementMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Organization - Additional Information (Details) - USD ($) $ / shares in Units, $ in Thousands		1 Months Ended	9 Months Ended
	May 13, 2019	Feb. 29, 2020	Sep. 30, 2020	Sep. 30, 2019	Dec. 31, 2019
Organization Consolidation And Presentation Of Financial Statements Disclosure [Line Items]
Entity incorporation date			2012-06
Proceeds from issuance of common stock, net of underwriting discounts and commissions and offering expenses				$ 77,827
Accumulated deficit			$ (126,099)		$ (69,805)
Cash, cash equivalents, and short-term investments			137,800
Long term investments			$ 60,133		$ 16,763
IPO
Organization Consolidation And Presentation Of Financial Statements Disclosure [Line Items]
Issuance of stock (in shares)	5,073,800
Offering price per share	$ 17
Proceeds from issuance of common stock, net of underwriting discounts and commissions and offering expenses	$ 77,800
Conversion of redeemable convertible preferred stock to common stock	18,161,027
Convertible redeemable preferred stock, shares outstanding	0
Underwriters
Organization Consolidation And Presentation Of Financial Statements Disclosure [Line Items]
Issuance of stock (in shares)	661,800
Private Placement
Organization Consolidation And Presentation Of Financial Statements Disclosure [Line Items]
Issuance of stock (in shares)		2,500,000
Offering price per share		$ 50.00
Agreement date		Feb. 10, 2020
Proceeds from issuance of common stock		$ 125,000
Costs related to offering		$ 7,400