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Note 8 - Derivative Liabilities - Fair Value of Derivative Liability (Details)

v3.23.1

Note 8 - Derivative Liabilities - Fair Value of Derivative Liability (Details) - Derivative Financial Instruments, Liabilities [Member] - USD ($)	3 Months Ended	6 Months Ended
	Mar. 31, 2023	Mar. 31, 2022
Series G Warrant [Member]
Beginning balance at September 30, 2022	$ 748,275
Exchange of warrants into common stock	(13,948)
Adjustments to estimated fair value	(734,327)
Ending balance at March 31, 2023	0
Series G Warrant [Member] \| Fair Value, Inputs, Level 3 [Member]
Beginning balance at September 30, 2022		$ 748,275
Issuances		0
Adjustments to estimated fair value		0
Ending balance at March 31, 2023		748,275
Expiration of derivative liability		0
Series F Warrant [Member] \| Fair Value, Inputs, Level 3 [Member]
Beginning balance at September 30, 2022		1,000,000
Issuances		0
Adjustments to estimated fair value		0
Ending balance at March 31, 2023		0
Expiration of derivative liability		(1,000,000)
Series H Warrant [Member]
Beginning balance at September 30, 2022	459,200
Exchange of warrants into common stock	(35,330)
Adjustments to estimated fair value	(423,870)
Ending balance at March 31, 2023	$ 0
Series H Warrant [Member] \| Fair Value, Inputs, Level 3 [Member]
Beginning balance at September 30, 2022		459,200
Issuances		0
Adjustments to estimated fair value		0
Ending balance at March 31, 2023		459,200
Expiration of derivative liability		$ 0

- Definition

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

+ References

No definition available.

+ Details

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

- Definition

Amount of gain (loss) recognized in income from derivative asset (liability) after deduction of derivative liability (asset), measured at fair value on recurring basis using unobservable input (level 3).

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (c)(1)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

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

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- Definition

Amount of issuances of financial instrument classified as a derivative asset (liability) after deduction of derivative liability (asset), measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-SubTopic 10
-Topic 820
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-3

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- Definition

Amount of settlements of financial instrument classified as a derivative asset (liability) after deduction of derivative liability, measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

+ Details

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- Definition

Fair value of financial instrument classified as derivative asset (liability) after deduction of derivative liability (asset), measured using unobservable inputs that reflect the entity's own assumption about the assumptions market participants would use in pricing.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Topic 820
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (b)
-SubTopic 10
-Topic 820
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-3

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