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Subsequent Events - Additional Information (Detail) - Subsequent Event - Sales Agreement With Jefferies LLC	Jul. 23, 2021 USD ($)
Subsequent Event [Line Items]
Common stock value subscriptions	$ 100,000,000
Percentage of agent compensation on gross proceeds from sale of common stock	3.00%

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- Definition

Percentage of agent compensation on gross proceeds from sale of common stock.

+ References

No definition available.

+ Details

Name:	tpst_PercentageOfAgentCompensationOnGrossProceedsFromSaleOfCommonStock
Namespace Prefix:	tpst_
Data Type:	num:percentItemType
Balance Type:	na
Period Type:	instant

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- Definition

Monetary value of common stock allocated to investors to buy shares of a new issue of common stock before they are offered to the public. When stock is sold on a subscription basis, the issuer does not initially receive the total proceeds. In general, the issuer does not issue the shares to the investor until it receives the entire proceeds.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 505
-SubTopic 10
-Section 45
-Paragraph 2
-URI http://asc.fasb.org/extlink&oid=65888546&loc=d3e21300-112643

Reference 2: 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(29))
-URI http://asc.fasb.org/extlink&oid=120391452&loc=d3e13212-122682

+ Details

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

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- Definition

Detail information of subsequent event by type. User is expected to use existing line items from elsewhere in the taxonomy as the primary line items for this disclosure, which is further associated with dimension and member elements pertaining to a subsequent event.

+ References

No definition available.

+ Details

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

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- Details

Name:	us-gaap_SubsequentEventTypeAxis=us-gaap_SubsequentEventMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

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- Details

Name:	us-gaap_TypeOfArrangementAxis=tpst_SalesAgreementWithJefferiesLlcMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: