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Note 13 - Equity (Details Textual) - USD ($) |  |  |  |  |  |  | 3 Months Ended | 6 Months Ended |  |
--- | --- | --- | --- | --- | --- | --- | --- | --- | --- | ---
Jun. 16, 2025 | Apr. 30, 2025 | Apr. 28, 2025 | Mar. 28, 2025 | Feb. 13, 2025 | Feb. 12, 2025 | Jun. 30, 2025 | Jun. 30, 2024 | Jun. 30, 2025 | Jun. 30, 2024 | Dec. 31, 2024 | Dec. 20, 2024
Class of Warrant or Right, Exercise Price of Warrants or Rights (in dollars per share) |  |  |  |  |  |  | $ 11.16 |  | $ 11.16 |  | $ 11.54 |
Proceeds from Warrant Exercises |  |  |  |  |  |  |  |  | $ 8,828,000 | $ 0 |  |
Deemed Dividend Liability, Current |  |  |  |  |  | $ 4,410,000 | $ 0 |  | 0 |  | $ 0 |
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Grant Date Fair Value |  |  |  |  |  |  |  |  |  | 0 |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value |  |  |  |  |  |  | 0 |  | 0 |  |  |
Share-Based Payment Arrangement, Option [Member] |  |  |  |  |  |  |  |  |  |  |  |
Share-Based Payment Arrangement, Expense |  |  |  |  |  |  | (43,000) | $ 58,000 | 43,000 | 148,000 |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Grant Date Fair Value |  |  |  |  |  |  |  |  | 34,000 |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Intrinsic Value |  |  |  |  |  |  |  |  |  |  | $ 0 |
Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount |  |  |  |  |  |  | 119,000 |  | $ 119,000 |  |  |
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition (Year) |  |  |  |  |  |  |  |  | 1 year 9 months |  |  |
Restricted Stock Units (RSUs) [Member] |  |  |  |  |  |  |  |  |  |  |  |
Share-Based Payment Arrangement, Expense |  |  |  |  |  |  | 70,000 | 0 | $ 71,000 | 0 |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Grant Date Fair Value |  |  |  |  |  |  |  |  | 1,051,000 | 0 |  |
Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount |  |  |  |  |  |  | 980,000 |  | $ 980,000 |  |  |
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition (Year) |  |  |  |  |  |  |  |  | 2 years 10 months 13 days |  |  |
Deferred Stock Units (DSUS) [Member] |  |  |  |  |  |  |  |  |  |  |  |
Share-Based Payment Arrangement, Expense |  |  |  |  |  |  | 50,000 | $ 0 | $ 167,000 | 0 |  |
Share-Based Payment Arrangement, Nonvested Award, Option, Cost Not yet Recognized, Amount |  |  |  |  |  |  | $ 41,000 |  | $ 41,000 |  |  |
Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition (Year) |  |  |  |  |  |  |  |  | 3 months |  |  |
Share-Based Compensation Arrangement by Share-Based Payment Award, Equity Instruments Other than Options, Grant Date Fair Value |  |  |  |  |  |  |  |  | $ 209,000 | $ 0 |  |
Evoke Neuroscience, Inc. [Member] |  |  |  |  |  |  |  |  |  |  |  |
Stock Issued During Period, Shares, Acquisitions (in shares) |  | 857,142 |  |  |  |  |  |  |  |  |  |
Shares Issued, Price Per Share (in dollars per share) |  | $ 3.2 |  |  |  |  |  |  |  |  |  |
The 2025 PIPE Warrants [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Warrants or Rights (in shares) |  |  |  | 547,737 |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) |  |  |  |  |  |  |  |  | $ 4 |  |  |
Class of Warrant or Right, Issued During Period (in shares) |  |  |  |  |  |  |  |  | 547,737 |  |  |
March 2025 Warrants [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Each Warrant or Right (in shares) |  |  |  | 1 |  |  |  |  |  |  |  |
Class of Warrant or Right, Exercise Price of Warrants or Rights (in dollars per share) |  |  |  | $ 4 |  |  |  |  |  |  |  |
Warrants and Rights Outstanding, Term (Year) |  |  |  | 3 years |  |  |  |  |  |  |  |
March 2025 Broker Warrants [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Warrants or Rights (in shares) |  |  |  | 25,958 |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) |  |  |  |  |  |  |  |  | $ 3.8 |  |  |
Class of Warrant or Right, Issued During Period (in shares) |  |  |  |  |  |  |  |  | 25,958 |  |  |
Three Fifty Warrant [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) |  |  |  |  |  |  |  |  | $ 3.5 |  |  |
Class of Warrant or Right, Issued During Period (in shares) |  |  |  |  |  |  |  |  | 400,000 |  |  |
Four Warrant [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) |  |  |  |  |  |  |  |  | $ 4 |  |  |
Class of Warrant or Right, Issued During Period (in shares) |  |  |  |  |  |  |  |  | 400,000 |  |  |
PIPE Warrants [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Warrants or Rights (in shares) |  |  |  |  |  |  | 823,529 |  | 823,529 |  |  |
Class of Warrant or Right, Exercise Price of Warrants or Rights (in dollars per share) |  |  |  |  |  |  | $ 6.83 |  | $ 6.83 |  |  |
Proceeds from Warrant Exercises |  |  |  |  |  | $ 5,625,000 |  |  |  |  |  |
Convertible Promissory Note Warrants [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Warrants or Rights (in shares) |  |  |  |  |  |  |  |  |  |  |  | 800,000
Class of Warrant or Right, Exercise Price of Warrants or Rights (in dollars per share) |  |  |  |  |  |  |  |  |  |  |  | $ 4
Proceeds from Warrant Exercises |  |  |  |  | $ 3,200,000 |  |  |  |  |  |  |
Private Placement [Member] |  |  |  |  |  |  |  |  |  |  |  |
Stock Issued During Period, Shares, New Issues (in shares) |  |  |  | 547,737 |  |  |  |  |  |  |  |
Equity Offering, Unit Price (in dollars per share) |  |  |  | $ 3 |  |  |  |  |  |  |  |
Proceeds from Issuance or Sale of Equity |  |  |  | $ 1,643,000 |  |  |  |  |  |  |  |
Equity Offering, Issuance Costs |  |  |  | $ 179,000 |  |  |  |  |  |  |  |
Inducement Agreement [Member] |  |  |  |  |  |  |  |  |  |  |  |
Stock Issued During Period, Shares, New Issues (in shares) |  |  | 340,000 |  |  |  |  |  |  |  |  |
Securities Purchase Agreement [Member] |  |  |  |  |  |  |  |  |  |  |  |
Stock Issued During Period, Shares, New Issues (in shares) | 340,000 |  |  |  |  |  |  |  |  |  |  |
Equity Offering, Unit Price (in dollars per share) | $ 3 |  |  |  |  |  |  |  |  |  |  |
Proceeds from Issuance or Sale of Equity | $ 1,200 |  |  |  |  |  |  |  |  |  |  |
Equity Issuance, Units, Number of Units (in shares) | 400,000 |  |  |  |  |  |  |  |  |  |  |
Units Issued, Common Stock Per Unit (in dollars per share) | $ 1 |  |  |  |  |  |  |  |  |  |  |
Units Issued During Period, New Issues (in shares) | 400,000 |  |  |  |  |  |  |  |  |  |  |
Securities Purchase Agreement [Member] | Pre-funded Warrants [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Each Warrant or Right (in shares) | 1 |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) | $ 0.0001 |  |  |  |  |  |  |  |  |  |  |
Units Issued, Warrants Per Unit (in dollars per share) | $ 1 |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued During Period (in shares) | 60,000 |  |  |  |  |  |  |  |  |  |  |
Securities Purchase Agreement [Member] | Three Fifty Warrant [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Each Warrant or Right (in shares) | 1 |  |  |  |  |  |  |  |  |  |  |
Warrants and Rights Outstanding, Term (Year) | 5 years |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) | $ 3.5 |  |  |  |  |  |  |  |  |  |  |
Units Issued, Warrants Per Unit (in dollars per share) | $ 1 |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued During Period (in shares) | 400,000 |  |  |  |  |  |  |  |  |  |  |
Securities Purchase Agreement [Member] | Four Warrant [Member] |  |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Number of Securities Called by Each Warrant or Right (in shares) | 1 |  |  |  |  |  |  |  |  |  |  |
Warrants and Rights Outstanding, Term (Year) | 5 years |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued, Exercise Price (in dollars per share) | $ 4 |  |  |  |  |  |  |  |  |  |  |
Units Issued, Warrants Per Unit (in dollars per share) | $ 1 |  |  |  |  |  |  |  |  |  |  |
Class of Warrant or Right, Issued During Period (in shares) | 400,000 |  |  |  |  |  |  |  |  |  |  |
Conversion of Promissory Note to Common Stock [Member] |  |  |  |  |  |  |  |  |  |  |  |
Debt Conversion, Converted Instrument, Shares Issued (in shares) |  |  |  |  | 800,000 |  |  |  |  |  |  |
Debt Instrument, Convertible, Conversion Price (in dollars per share) |  |  |  |  | $ 3 |  |  |  |  |  |  |
Exercise of Conversion Options, Transaction Costs, Additional Paid-in-capital |  |  |  |  | $ 39,000 |  |  |  |  |  |  |

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