Exact positions at epoch 2026.0 retain at most 10.1% of 365.25-day signal information in seven NANOGrav models with fixed noise and free proper motion

Can one independent position at a late epoch restore annual planet-signal information in old pulsar records? We use 82,598 times of arrival from seven isolated pulsars in NANOGrav release 2.1.0. We hold noise values fixed and use a linear angular-motion model without acceleration. An exact position at Julian TDB epoch 2026.0 retains 0.94% to 10.08% of the reference information across targets and phases. Both proper-motion components remain free. The reference fixes position and motion, but fits all other delivered free timing terms, including parallax. The signal period is 365.25 TDB days. The exact-position result bounds every finite single-position error covariance at that epoch if no extra motion information is supplied. At epoch 2030.0, the retained range is 0.38% to 5.97%. With an exact 2026.0 position, independent motion errors of 0.86 to 12.74 microarcseconds per year recover half the reference information. These are target-specific standard errors per coordinate, with recovery required at every phase. Two independent positions at 2026.0 and 2030.0 require errors of 2.04 to 27.48 microarcseconds per coordinate and epoch. We provide epoch curves, precision thresholds, and small kernels for other independent constraints. Direct timing fits and an offline rerun check the calculation. Annual signal loss and the need for motion information are known from earlier work. This study adds bounds and tools for seven selected public models. It does not search residuals, detect a planet, or set mass limits. The package preserves code, input data, source notices, figures, provenance, and reproduction instructions.

pulsar timing · annual planet signals · astrometry epoch · proper motion · NANOGrav · Fisher information · independent astrometry · reproducible sensitivity calculation