C-0029 Under review MODERATE certainty
A jump-navigation loop for alpha Centauri A converges in three jumps to the quality of the orbit solution, and no further: with the catalogue as the only input, jump 1 misses by 486 au RMS — priced almost entirely by the adopted parallax, along the line of sight. One onboard astrometric re-fix later (1 mas assumed, parameterised), the AB pair itself acts as a known-baseline rangefinder — the pair's angular separation grows as 1/d, so range error falls as sigma_fix * d^2/separation — bringing jump 2 to 1.15 au. Jump 3 lands on the 0.300 au floor set by the quality of the Pourbaix-Boffin orbital elements, and jumps 4-5 buy nothing: past that point the limit is the ephemeris, not the instrument. A 100-fold better sensor changes nothing at jump >= 3; only a better AB orbit solution does. Monte Carlo (4000 samples, persistent catalogue errors, exact 1/parallax nonlinearity) agrees with the closed-form covariance budget to 0.982-0.996 across all legs; with a perfect sensor the loop converges to 0.3001 au = the ephemeris floor, not to zero. The instant-jump image-aiming offset of 33.54 au reproduces targeting_sim exactly. Legs shorter than ~10x the pair separation are flagged out-of-regime for the small-angle model rather than reported.
Standing our derivation · numerical result · TRL 2 Assumes orbital elements from Pourbaix & Boffin 2016 (S-0012) with the 0.300 au element-quality floor measured in navigation_requirements_alpha_cen.py; onboard re-fix accuracy 1 mas as a PARAMETER (sensitivity: results scale with it only down to the ephemeris floor); departure epoch 2026.6, dwell 1 yr between jumps; geometric jump sequence dividing the remaining distance; jump arrival epoch = departure epoch (a convention a jump theory would have to fix; flagged, not derived); small-angle rangefinder model, honest only for leg distance >~ 10x the AB separation Stops applying any epoch where the Pourbaix-Boffin solution is superseded (the floor moves with it); legs shorter than ~10x the pair separation; and any statement about jump PHYSICS — this is geometry and astrometry conditional on a jump mechanism existing Computed in compute/jump_targeting.py, tests/test_jump_targeting.py, report/jump_targeting.json Note Front 1 deliverable (CEO directive 2026-08-10: fully described navigation system with jump-position algorithms). Computed by a delegated agent, then re-run and re-verified by the asserter from a clean shell (10/10 tests, table reproduced digit-for-digit). The 0.300 au floor comes from navigation_requirements_alpha_cen.py section 2 (element quality), SIMBAD parallax cache sha a187495ca935 embedded for offline reproducibility. Jump-theory-dependent conventions (arrival-epoch simultaneity, exact execution, proper-time behaviour across a jump) are parameterised hooks flagged as open problems in the JSON, not assumptions smuggled in. Full architecture draft with [SOURCE-PENDING] queue (SEXTANT X-ray pulsar navigation results, Gaia DR4 bright-star performance) awaits source ingestion before the system document enters report/.
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