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Note 15 - Related Party Transactions - Summary of Leasing Arrangements (Details) - Not-for-profit Corporation [Member] - Lease Term April 2022 Through December 2027 [Member] | 3 Months Ended
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Mar. 31, 2025 USD ($) ft²
Square Feet (Square Foot) | ft² | 6,006
Annual Rent | $ 51,051
Total commitment | $ 317,455

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- Definition The annual rent in a leasing arrangement. + References No definition available. + Details
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Namespace Prefix: | gyro_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- Definition Area of a real estate property. + References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | dtr-types:areaItemType
Balance Type: | na
Period Type: | instant

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- Definition Amount of lease payments to be received by lessor for operating lease. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Topic 842 -SubTopic 30 -Name Accounting Standards Codification -Section 50 -Paragraph 12 -Publisher FASB -URI https://asc.fasb.org/1943274/2147479773/842-30-50-12 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | debit
Period Type: | instant

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- Details
Name: | us-gaap_RelatedPartyTransactionsByRelatedPartyAxis=gyro_NotForProfitCorporationMember
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |

X
- Details
Name: | us-gaap_LeaseContractualTermAxis=gyro_LeaseTermApril2022ThroughDecember2027Member
Namespace Prefix: |
Data Type: | na
Balance Type: |
Period Type: |