# Own-trace fitting recovers inserted-state damage without a fitted latent advantage ## Scope The r/math_rlvr task asks whether a Qwen3-0.6B-Base model can obtain sustained mathematical reasoning gains from its own verifiable feedback. This paper studies a narrower prerequisite: when extra computation is inserted before the answer, can fitting verified own-model traces recover the resulting damage, and does that recovery exceed matched controls? The evidence supports a recovery interpretation but does not identify an exclusive mechanism. The paper makes no MATH-500 or general-capability claim. ## Design The frozen source contract uses 448 algebra questions from the supplied training pool, selected by ascending dataset index after a mechanical context and identity check. It collects four native categorical attempts per question at temperature 1 with a 1,024-token cap. The verifier retains every trace that is both boxed-correct and EOS-terminated; no answer selection or researcher-written supervision enters the targets. The source audit decodes, re-extracts and regrades every stored token path. It retains 940 traces from 349 covered questions out of 1,792 attempts. Later-RL and reserve identities are disjoint by the released index maps and contract hashes. The three arms share the same warm checkpoint, source traces, order and optimizer dose: 1. Text, with no inserted positions ($K=0$). 2. Latent, with $K=2$ deterministic continuous feedback positions. 3. Pause, with $K=2$ copies of existing token 151662 (`<|fim_pad|>`). There are no added trainable parameters. The supplied implementation is untied: token embedding and output head are separate tensors, totaling 751,632,384 parameters. In the latent arm, let $H(P)$ be the final normalized hidden state after prompt prefill with its KV cache. The first inserted state is $z_1=H(P)$, and the second is $z_2=H(P,z_1)$, where each $z_j$ is fed as the next input embedding through the same transformer block stack, RoPE positions and cache. Generation then begins from the final state. The pause arm instead appends two existing-token embeddings and runs the same transformer. The pause embedding row and all shared model parameters are updated during fitting. Each update minimizes the mean over questions, then retained traces within each question, then tokens within each trace: $$L=-\frac1{|B|}\sum_{q\in B}\frac1{|T_q|}\sum_{\tau\in T_q}\frac1{|\tau|}\sum_t\log p_\theta(\tau_t\mid P_q,\tau_{