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Warrants outstanding, weighted average exercise price (in dollars per share Entity Address, State or Province Sublicense fees Sublicense Fees Sublicense fees Share-based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition (Year) Share-Based Payment Arrangement, Nonvested Award, Cost Not yet Recognized, Period for Recognition Unrecognized compensation cost weighted-average period of recognition Series A Preferred Stock [Member] Reverse Stock Split Reverse Stock Split, Policy [Policy Text Block] Reverse stock split, policy [Policy Text Block]. Notes to Financial Statements Disclosure Text Block [Abstract] Amendment Flag Equity Incentive Plans Share-Based Payment Arrangement [Text Block] Net Income (Loss) Available to Common Stockholders, Diluted [Abstract] Diluted net loss per common share Accrued director stipends Represents the amount of accrued director stipends as of the balance sheet date. Accrued director stipends Other income, net Other Nonoperating Income (Expense) Other Nonoperating Income (Expense), Total City Area Code Issuance of common stock in connection under Employee Stock Purchase Plan Maximum shares issued under ESPP Stock Issued During Period, Value, Employee Stock Purchase Plan Interest Expense, Nonoperating Interest Expense, Nonoperating, Total Interest expense pali_ClassOfWarrantOrRightForfeitedExpiredOrCancelledDuringPeriod The number of warrants or rights forfeited, expired or cancelled during period. Forfeited, expired or cancelled (in shares) Preferred Stock [Member] Preferred Stock [Member] Comprehensive Loss Comprehensive Income, Policy [Policy Text Block] Proceeds from Issuance of Common Stock Proceeds from issuance of common stock and warrants, net of underwriting discounts and commissions Proceeds from issuance of common stock Schedule of Stockholders' Equity warrant outstanding and exercisable. Schedule of Warrant Outstanding And Exercisable [Table Text Block] Tabular disclosure of warrants outstanding and exercisable. Prepaid subscriptions and fees. Prepaid Subscriptions and Fees Prepaid subscriptions and fees Operating Expenses [Abstract] Operating expenses: Common Stock, Par or Stated Value Per Share (in dollars per share) Common Stock, Par or Stated Value Per Share Common stock, par or stated value per share Deferred equity issuance costs included in accounts payable and accrued liabilities Deferred Equity Issuance Costs Included In Accounts Payable And Accrued Liabilities Deferred equity issuance costs included in accounts payable and accrued liabilities. RSUs and PSUs [Member] Restricted Stock Units and Performance Shares Units [Member] Restricted Stock Units and Performance Shares Units Member. Total current liabilities Liabilities, Current Noncash Investing and Financing Items [Abstract] Supplemental disclosures of non-cash investing and financing activities: Total cash, cash equivalents and restricted cash Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation Total cash, cash equivalents and restricted cash Cash, cash equivalents and restricted cash, end of period Cash, cash equivalents and restricted cash, beginning of year Segment Reporting [Text Block] Segment Information Reverse stock split fractional share settlement Stock Issued During Period, Shares, Reverse Stock Splits Reverse stock split fractional share settlement Collaborative Arrangement and Arrangement Other than Collaborative [Axis] Prepaid expenses and other current assets, other receivables. Prepaid Expenses and Other Current Assets Other Receivables Other current receivables Trading Symbol License Revenue Revenue from Contract with Customer, Including Assessed Tax Percentage cost in patent right Percentage Cost in Patent Right Percentage cost in patent right Entity Emerging Growth Company Additional Paid In Capital [Member] Additional Paid-in Capital [Member] Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block] Summary of Prepaid Expenses and Other Current Assets Cash consideration Cash Consideration Cash consideration. Plan Name [Domain] Milestone payment Milestone Payment Milestone payment. Prepaid Insurance Prepaid insurance Stock Issued During Period, Shares, Employee Stock Purchase Plans Shares issued under the ESPP. Issuance of common stock in connection under Employee Stock Purchase Plan (in Shares) Cover [Abstract] Service Based And Performance Based Restricted Stock Units [Member] Service-based and performance-based restricted stock units. Service Based And Performance Based Restricted Stock Units [Member] Stock Purchase Agreement [Member] Stock Purchase Agreement Member All Other Common Stock Warrants [Member] All other common stock warrants. All Other Common Stock Warrants [Member] Class of warrant or right exercised during period weighted average exercise price. Class of Warrant or Right Exercised During Period Weighted Average Exercise Price Exercised, weighted average exercise price Stock-based compensation and related charges Stock-based compensation Share-Based Payment Arrangement, Noncash Expense Share-based Payment Arrangement, Noncash Expense, Total Schedule of Fair Value of Options Granted Fair Value, Liabilities Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block] Additional Paid in Capital Additional Paid in Capital, Total Additional Paid in Capital, Beginning Balance Additional Paid in Capital, Ending Balance Additional paid-in capital Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract] Adjustments to reconcile net loss to net cash used in operating activities: Fair Value Disclosures [Abstract] Cash and cash equivalents Cash and Cash Equivalent Cash and Cash Equivalents, at Carrying Value, Total Cash and cash equivalents Registration Payment Arrangement by Arrangement [Axis] Cash Provided by (Used in) Financing Activity, Including Discontinued Operation Net cash provided by financing activities Net cash provided by (used in) financing activities Balance, Ending Balance, Beginning Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Liability Value Proceeds from Stock Plans Proceeds from issuance of common stock under Employee Stock Purchase Plan pali_ClassOfWarrantOrRightNumberOutstanding Represents the number of warrants or rights outstanding as of the specified date. Warrants outstanding Warrants outstanding, balance (in shares) Warrants outstanding, balance (in shares) Entity Filer Category December Two Thousand Twenty Four Offering [Member] December 2024 Offering. December 2024 Offering [Member] Segment Reporting, CODM, Profit (Loss) Measure, How Used, Description Lease Contractual Term [Axis] Increase (Decrease) in Accounts Receivable Accounts receivable Net Income (Loss) Available to Common Stockholders, Basic [Abstract] Basic and diluted net loss per common share: Revenue from Contract with Customer, Excluding Assessed Tax License revenue Percentage of Closing Price Percentage of closing price. Percentage of closing price Balance (in shares) Balance (in shares) Shares, Outstanding Issuance of stock during period Segment Reporting [Abstract] The number of warrants or rights issued during period. pali_ClassOfWarrantOrRightIssuedDuringPeriod Class of Warrant or Right, Issued During Period (in shares) Granted (in shares) Entity Address, Postal Zip Code Statement of Financial Position [Abstract] Local Phone Number