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Stock-Based Compensation - Narrative (Details) - USD ($) $ / shares in Units, $ in Thousands |  | 3 Months Ended | 9 Months Ended | 12 Months Ended |  |  |  |
--- | --- | --- | --- | --- | --- | --- | --- | ---
Jun. 22, 2023 | Sep. 30, 2025 | Sep. 30, 2024 | Sep. 30, 2025 | Sep. 30, 2024 | Dec. 31, 2016 | Jun. 30, 2025 | Jan. 01, 2025 | Dec. 31, 2024 | Jan. 01, 2024
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Stock-based compensation expense |  |  | $ 13,100 | $ 27,803 | $ 35,617 |  |  |  |  |
2015 and 2016 and 2018 Equity Inducement Plan | Service Based Awards |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Share-based award, vesting period (in years) |  |  |  | 4 years |  |  |  |  |  |
Expiration term (in years) |  |  |  | 10 years |  |  |  |  |  |
2016 Equity Incentive Plan |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Annual percentage of additional shares |  |  |  |  |  | 5.00% |  |  |  |
Additional number of shares available for issuance (in shares) |  |  |  |  |  |  |  | 3,814,905 |  | 3,023,650
Common stock available for future issuance (in shares) |  | 10,880,124 |  | 10,880,124 |  |  |  |  |  |
Outstanding option awards (in shares) |  | 4,896,574 |  | 4,896,574 |  |  |  |  |  |
2018 Equity Inducement Plan |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Common stock available for future issuance (in shares) |  | 7,556,574 |  | 7,556,574 |  |  |  |  |  |
Outstanding option awards (in shares) |  | 6,637,231 |  | 6,637,231 |  |  |  |  |  |
2018 Equity Inducement Plan, Amended |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Common stock available for future issuance, additional amount authorized (in shares) |  |  |  |  |  |  | 750,000 |  |  |
Spyre 2023 Equity Incentive Plan |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Outstanding option awards (in shares) |  |  |  |  |  |  | 0 |  |  |
Spyre 2023 Equity Incentive Plan | Asset Acquisition |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Number of outstanding and unexercised stock options to purchase (in shares) | 2,734 |  |  |  |  |  |  |  |  |
Parapyre Option Obligation |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Stock-based compensation expense |  |  | $ 6,100 |  | $ 13,000 |  |  |  |  |
2024 Parapyre Option Obligation | Outstanding Parapyre warrants |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Warrants to purchase shares (in shares) |  | 1,532,591 |  | 1,532,591 |  |  |  |  | 848,184 |
Exercise price per warrant (in dollars per share) |  | $ 22.49 |  | $ 22.49 |  |  |  |  | $ 23.28 |
Number of warrants exercised (in shares) |  | 0 |  | 0 |  |  |  |  |  |
2016 Employee Stock Purchase Plan | 2016 ESPP | Employee Stock |  |  |  |  |  |  |  |  |  |
Share Based Compensation Arrangement By Share Based Payment Award [Line Items] |  |  |  |  |  |  |  |  |  |
Number of shares sold (in shares) |  | 17,298 | 14,053 | 34,175 | 16,383 |  |  |  |  |
Sale of stock, proceeds received |  | $ 200 | $ 0 | $ 600 | $ 300 |  |  |  |  |

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