A Beacon Without a Shared Language: Bootstrapping the Interpretation of Planetary-Scale Optical Signals

Planetary-scale optical modulation could carry persistent, low-rate interstellar signals, but recognizing a repeated pattern does not establish its organization or meaning. This paper specifies a candidate primer linking timing and framing cues to counts, numerals, and arithmetic demonstrations. Six computational studies separate sequence recovery, known-waveform detection, and exact-token numerical transfer under disclosed receiver assumptions. Initial pilots identify sensitivity to observing gaps, null-model calibration, and the permitted rule family. Prospectively frozen refinements address those weaknesses without changing the earlier results. Across eight fixed observing-window periods, one balanced schedule recovered all payloads in 865 of 1600 paired trials, versus 482 for repeated ordering and 667 for shifted ordering, without dominating every regime. Freshly calibrated original and first-difference detectors satisfied a simultaneous 1% false-alarm confidence-bound criterion across nine specified synthetic mixtures. Differencing increased power against the tested nonwhite backgrounds at moderate amplitude but reduced white-noise power; the weakest injections supplied no additional flags beyond paired nulls. With three added teaching lessons, four targeted finite rule families each correctly predicted all 42 fresh expressions, including thirty untaught output numerals. Cubic and lookup alternatives remained, and quadratic uniqueness depended on coefficient bounds. A standard finite-example argument explains the unrestricted ambiguity. The longer learning waveforms were not jointly evaluated with channel or detection studies. These results support conditional reconstruction and finite-family transfer, while leaving codebook-free acquisition, physical detectability, and unrestricted interpretation unresolved. License scope: The paper, original data and figures are licensed under CC BY 4.0. Original simulation source code is licensed under MIT. Third-party components retain their own licenses, as detailed in the accompanying package.