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

No definition available.

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

- Definition

Amount of estimated additional grant income.

+ References

No definition available.

+ Details

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

- Definition

The amount of negotiating fee income earned on costs incurred.

+ References

No definition available.

+ Details

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Namespace Prefix:	ppta_
Data Type:	xbrli:monetaryItemType
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- Definition

Number of grants awarded.

+ References

No definition available.

+ Details

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Namespace Prefix:	ppta_
Data Type:	xbrli:integerItemType
Balance Type:	na
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

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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

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Namespace Prefix:	ppta_
Data Type:	dtr-types:percentItemType
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Period Type:	instant

- Definition

Amount of increase in asset from government assistance.

+ 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

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

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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

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

- Details

Name:	us-gaap_GovernmentAssistanceTypeAxis=ppta_SmallBusinessInnovationResearchGrantUsDepartmentOfDefenseMember
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_TypeOfArrangementAxis=ppta_UndefinitizedTechnologyInvestmentAgreementMember
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
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Government Grants (Details)			1 Months Ended	3 Months Ended		9 Months Ended
Government Grants (Details)	May 02, 2024 USD ($)	Aug. 18, 2023 USD ($)	Sep. 30, 2022 USD ($) item	Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Sep. 30, 2024 USD ($)	Sep. 30, 2023 USD ($)	Jul. 25, 2023 USD ($)	Dec. 16, 2022 USD ($)
SBIR
Government Grants
Number of grants awarded \| item			2
Amount of grants awarded			$ 200,000
Estimated additional grant income over future periods						$ 0
DPA
Government Grants
Amount of grants awarded	$ 59,200,000			$ 20,000,000.0		20,000,000.0
Estimated additional grant income	$ 34,400,000
Government grant, reimbursed costs incurred				$ 11,667,011	$ 6,185,455	$ 16,417,506	$ 10,430,060
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)
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		$ 15,500,000
Government assistance proceeds				$ 39,329	$ 1,806,714	$ 4,505,821	$ 1,806,714
Government grant, reimbursed costs incurred				$ 35,115	$ 1,613,138	$ 4,023,054	$ 1,613,138
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)
Period of performance		24 months
Reimbursement for negotiating fee (in percent)		12.00%		12.00%		12.00%
Reimbursement of fee income				$ 4,214	$ 193,577	$ 482,767	$ 193,577
DOTC \| Maximum
Government Grants
Amount of grants awarded		$ 15,500,000
DOTC \| Government grant income
Government Grants
Reimbursement for negotiating fee (in percent)				12.00%		12.00%
Government assistance grant income				$ 32,654	$ 238,447	$ 310,770	$ 238,447