The amount of negotiating fee on costs incurred related to activities.

No definition available.

Name:	ppta_GovernmentAssistanceAmountOfNegotiatingFeeOnCostsIncurred
Namespace Prefix:	ppta_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

The amount of negotiating fee income earned on costs incurred.

+ References

No definition available.

+ Details

Name:	ppta_GovernmentAssistanceNegotiatingFeeIncomeEarnedOnCostsIncurred
Namespace Prefix:	ppta_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

The amount of cash inflow associated with reimbursement of certain costs incurred and fee income relating to grants.

+ References

No definition available.

+ Details

Name:	ppta_GovernmentAssistanceProceeds
Namespace Prefix:	ppta_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

- Definition

Percentage of reimbursement for negotiating fee.

+ References

No definition available.

+ Details

Name:	ppta_PercentageOfReimbursementForNegotiatingFee
Namespace Prefix:	ppta_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	instant

- Definition

Amount of asset from government assistance, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 832
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483507/832-10-50-3

+ Details

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

- Definition

Amount of increase in asset from government assistance.

+ References

+ Details

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

- Definition

Indicates line item in statement of financial position that includes increase in asset from government assistance.

+ References

+ Details

Name:	us-gaap_GovernmentAssistanceAssetIncreaseStatementOfFinancialPositionExtensibleEnumeration
Namespace Prefix:	us-gaap_
Data Type:	enum2:enumerationSetItemType
Balance Type:	na
Period Type:	duration

- Definition

Amount of government assistance awarded that comprises amount received, receivable, and to be received unless condition for government assistance is not met. Includes, but is not limited to, government grant, assistance, incentive, award, subsidy, and loan.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 832
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (c)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483507/832-10-50-3

+ Details

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

- Definition

Amount of decrease (increase) in expense from government assistance.

+ References

+ Details

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

- Definition

Indicates line item in statement of income or comprehensive income that includes decrease (increase) in expense from government assistance.

+ References

+ Details

Name:	us-gaap_GovernmentAssistanceExpenseStatementOfIncomeOrComprehensiveIncomeExtensibleEnumeration
Namespace Prefix:	us-gaap_
Data Type:	enum2:enumerationSetItemType
Balance Type:	na
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

+ Details

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

- Definition

Duration of government assistance transaction, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 832
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 4
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147483507/832-10-50-4

+ Details

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

- Details

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

- Details

Name:	us-gaap_GovernmentAssistanceTypeAxis=ppta_DefenseProductionActGrantUsDepartmentOfDefenseMember
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:	us-gaap_GovernmentAssistanceTypeAxis=ppta_DodOrdnanceTechnologyConsortiumGrantUsDepartmentOfDefenseMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_IncomeStatementLocationAxis=ppta_GovernmentGrantIncomeMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Government Grants (Details) - USD ($)			3 Months Ended		9 Months Ended
Government Grants (Details) - USD ($)	May 02, 2024	Aug. 18, 2023	Sep. 30, 2025	Sep. 30, 2024	Sep. 30, 2025	Sep. 30, 2024	May 28, 2025	Dec. 31, 2024	Jul. 25, 2023	Dec. 16, 2022
Government Grants
Government grants receivable			$ 1,915,015		$ 1,915,015			$ 2,489,421
TIA
Government Grants
Government grants receivable	$ 0
DPA
Government Grants
Amount of grants awarded	59,200,000
Estimated additional grant income	$ 34,400,000
Government Assistance, Asset, Increase, Statement of Financial Position [Extensible Enumeration]	Accounts Receivable, after Allowance for Credit Loss, Current
Government grant, reimbursement of certain costs incurred			$ 592,242	$ 11,667,011	$ 12,386,454	$ 16,417,506
Government Assistance, Expense, Decrease (Increase), Statement of Income or Comprehensive Income [Extensible Enumeration]			Government Assistance, Income, Increase (Decrease)	Government Assistance, Income, Increase (Decrease)	Government Assistance, Income, Increase (Decrease)	Government Assistance, Income, Increase (Decrease)
Government grants receivable								2,382,594
DPA \| Maximum
Government Grants
Amount of grants awarded									$ 24,800,000
DPA \| Maximum \| TIA
Government Grants
Amount of grants awarded										$ 24,800,000
DOTC
Government Grants
Amount of grants awarded		$ 22,400,000
Government assistance proceeds			$ 2,436,321	$ 39,329	$ 2,824,887	$ 4,505,821
Government grant, reimbursement of certain costs incurred			$ 2,175,287	$ 35,115	$ 2,522,221	$ 4,023,054
Government Assistance, Expense, Decrease (Increase), Statement of Income or Comprehensive Income [Extensible Enumeration]			Government Assistance, Income, Increase (Decrease)	Government Assistance, Income, Increase (Decrease)	Government Assistance, Income, Increase (Decrease)	Government Assistance, Income, Increase (Decrease)
Government grants receivable			$ 1,915,015		$ 1,915,015			$ 106,827
Period of performance		24 months
Reimbursement for negotiating fee (in percent)		12.00%	12.00%		12.00%
Reimbursement of fee income			$ 261,034	$ 4,214	$ 302,666	$ 482,767
DOTC \| Maximum
Government Grants
Amount of grants awarded		$ 15,500,000					$ 6,900,000
DOTC \| Government grant income
Government Grants
Reimbursement for negotiating fee (in percent)			12.00%		12.00%
Government assistance grant income			$ 357,039	$ 32,654	$ 496,401	$ 310,770