Can Scalar-Field Memory Feed Back on Its Own Writing? An Order-of-Magnitude Feedback Estimate for the B3 Model

The main paper showed that a two-field scalar model (B3) can hold localized, history-dependent records in halos, and that halo formation may make those records observationally uninformative. Here we ask the next question: could a stored record modify its own local gravitational environment? Using the frozen B3 model and its held-out synthetic halo population, we estimate three feedback channels without new field evolution. Under a heuristic, approximately isothermal halo response, a record deepens its own fifth-force well, so the core becomes denser and the record moves away from its erase threshold. We compare this density response with each halo’s erase margin. The response is smaller than the typical erase margin unless the mediator’s fifth force inside halos is comparable to gravity. At a fifth force of 1% of gravity, it exceeds the erase margin for about 0.4% of written halos. The direct mediator interaction is short-ranged; consequences for infall and later writing elsewhere have not been calculated. The defensible conclusion is conditional: a history-dependent scalar-field record may modify its own local gravitational environment, potentially changing its resistance to erasure and producing a structural observable, depending on the mediator coupling and the halo response. This is an estimate, not a validated physical effect. Theoretical addendum to doi:10.5281/zenodo.23984771. Files: the note (PDF), the estimate script part3_B3_loopgain.py and its log. The script runs on the archived B3 tables and population code from the main record.