Leases - Schedule of Maturity Analysis of Future Undiscounted Cash Flows (Details) - USD ($) $ in Thousands	Sep. 30, 2024	Dec. 31, 2023
Operating Leases
2024 (remaining)	$ 15,966
2025	53,485
2026	36,703
2027	23,116
2028	18,182
Thereafter	14,748
Total lease payments	162,200
Less: imputed interest	(12,391)
Total present value of lease liabilities	149,809	$ 176,061
Finance Leases
2024 (remaining)	1,006
2025	3,642
2026	2,985
2027	1,803
2028	718
Thereafter	38
Total lease payments	10,192
Less: imputed interest	(708)
Total present value of lease liabilities	$ 9,484

Finance lease liability payments due after year four.

No definition available.

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- Definition

Lessee operating lease liability payments due after year four.

+ References

No definition available.

+ Details

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Namespace Prefix:	psn_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- References

No definition available.

+ Details

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

- Definition

Present value of lessee's discounted obligation for lease payments from finance lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-6

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-1

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments for finance lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for finance lease to be paid in remainder of current fiscal year.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 50
-Paragraph 6
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478964/842-20-50-6

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for finance lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease to be paid in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payment for operating lease having initial or remaining lease term in excess of one year to be paid in remainder of current fiscal year.

+ References

+ Details

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

- Definition

Amount of lessee's undiscounted obligation for lease payments in excess of discounted obligation for lease payments for operating lease.

+ References

+ Details

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

- References

No definition available.

+ Details

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

- Definition

Present value of lessee's discounted obligation for lease payments from operating lease.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 842
-SubTopic 20
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479041/842-20-45-1

+ Details

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