v3.25.4

SCHEDULE OF RECONCILIATION OF ACTIVITY AND CHANGES IN FAIR VALUE (Details) - USD ($) | 3 Months Ended | 10 Months Ended | 12 Months Ended
--- | --- | --- | ---
Sep. 30, 2025 | Jun. 30, 2025 | Mar. 31, 2025 | Dec. 31, 2024 | Sep. 30, 2024 | Jun. 30, 2024 | Mar. 31, 2024 | Dec. 31, 2023 | Dec. 31, 2024
SAFE Note [Member] |  |  |  |  |  |  |  |  |
Fair Value, off-Balance-Sheet Risks, Disclosure Information [Line Items] |  |  |  |  |  |  |  |  |
Beginning balance |  |  |  |  | $ 6,367,200 | $ 5,520,100 | $ 5,212,200 |  | $ 5,212,200
Issuance of notes |  |  |  |  |  |  | 200,000 | 5,000,000 | 200,000
Change in fair value |  |  |  |  |  | 847,100 | 107,900 | 212,200 | 955,000
Sponsor earnout liability recognized on closing of Business Combination |  |  |  |  |  |  |  |  |
Issuance of common stock upon conversion |  |  |  |  | (6,367,200) |  |  |  | (6,367,200)
Ending balance |  |  |  |  |  | 6,367,200 | 5,520,100 | 5,212,200 |
Convertible Note [Member] |  |  |  |  |  |  |  |  |
Fair Value, off-Balance-Sheet Risks, Disclosure Information [Line Items] |  |  |  |  |  |  |  |  |
Beginning balance |  |  |  |  | 2,571,400 |  |  |  |
Issuance of notes |  |  |  |  |  | 2,100,000 |  |  | 2,100,000
Change in fair value |  |  |  |  |  | 471,400 |  |  | 471,400
Sponsor earnout liability recognized on closing of Business Combination |  |  |  |  |  |  |  |  |
Issuance of common stock upon conversion |  |  |  |  | (2,571,400) |  |  |  | (2,571,400)
Ending balance |  |  |  |  |  | 2,571,400 |  |  |
Sponsor Earnout Liability [Member] |  |  |  |  |  |  |  |  |
Fair Value, off-Balance-Sheet Risks, Disclosure Information [Line Items] |  |  |  |  |  |  |  |  |
Beginning balance | 4,700 | 4,700 | 532,700 | 2,972,800 |  |  |  |  |
Issuance of notes |  |  |  |  |  |  |  |  |
Change in fair value |  |  | (528,000) | (2,440,100) | (1,636,100) |  |  |  | (4,076,200)
Sponsor earnout liability recognized on closing of Business Combination |  |  |  |  | 4,608,900 |  |  |  | 4,608,900
Issuance of common stock upon conversion |  |  |  |  |  |  |  |  |
Ending balance | $ 4,700 | $ 4,700 | $ 4,700 | $ 532,700 | $ 2,972,800 |  |  |  | $ 532,700

X
- Definition Fair value measurement with unobservable inputs reconciliations recurring basis liability earn out liability value. + References No definition available. + Details
Name: | SDST_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityEarnOutLiabilityValue
Namespace Prefix: | SDST_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition Amount of issuances of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2G -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2G Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-3 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
Name: | us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityIssues
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition Amount of increase (decrease) of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-3 Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
Name: | us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPeriodIncreaseDecrease
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | na
Period Type: | duration

X
- Definition Amount of purchases of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2G -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2G Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-3 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c)(2) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
Name: | us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisLiabilityPurchases
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

X
- Definition Fair value of financial instrument classified as a liability measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 3 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-3 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (c) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
Name: | us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationsRecurringBasisLiabilityValue
Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

X
- 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/disclosureRef -Topic 825 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 11 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482907/825-10-50-11 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Topic 942 -SubTopic 825 -Name Accounting Standards Codification -Section 50 -Paragraph 1 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147478898/942-825-50-1 + Details
Name: | us-gaap_FairValueOffBalanceSheetRisksDisclosureInformationLineItems
Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

X
- Details
Name: | us-gaap_FinancialInstrumentAxis=SDST_SAFENoteMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FinancialInstrumentAxis=SDST_ConvertibleNoteMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_FinancialInstrumentAxis=SDST_SponsorEarnoutLiabilityMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |