v3.25.1

Fair Value Measurements (Details) - USD ($)	12 Months Ended
Fair Value Measurements (Details) - USD ($)	Dec. 31, 2024	Dec. 31, 2023
Fair Value Measurements [Line Items]
Fair value of warrant liabilities (in Dollars)	$ 1,447,101	$ 241,183
Public Warrants [Member]
Fair Value Measurements [Line Items]
Warrants price increase	$ 0.18
Warrants price decrease		$ 0.06
Private Placement Warrants [Member]
Fair Value Measurements [Line Items]
Warrants price increase	$ 0.18
Warrants price decrease		$ 0.06

Amount of expense (income) related to adjustment to fair value of warrant liability.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 45
-Paragraph 28
-Subparagraph (b)
-SubTopic 10
-Topic 230
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482740/230-10-45-28

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 25
-Paragraph 13
-SubTopic 10
-Topic 480
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481766/480-10-25-13

+ Details

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

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 100
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482078/820-10-55-100

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-2

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147482106/820-10-50-3

+ Details

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

- Definition

Per share decrease in exercise price of warrant. Excludes change due to standard antidilution provision.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147481112/505-10-50-3

+ Details

Name:	us-gaap_WarrantExercisePriceDecrease
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Per share increase in exercise price of warrant. Excludes change due to standard antidilution provision.

+ References

+ Details

Name:	us-gaap_WarrantExercisePriceIncrease
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=aptm_PublicWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=aptm_PrivatePlacementWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Plum Acquisition Corp. III 10-K