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Life sciences · Preprint
arXiv · September 8, 2026
Early or partial results. Treat as a signal, not a conclusion.
Deposon is a proposed scattering layer to create auditable records of LLM reasoning paths with formally guaranteed energy conservation (maximum deviation 2.2E-16). On synthetic trap benchmarks it achieves strong filtering gains (100% vs 7–10% baseline); on real benchmarks (GSM8K, StrategyQA) it performs identically to a simple six-keyword rule and offers value only in machine verifiability. Game-theoretic foundations—three formalized propositions—are falsified under pre-registered protocol; the potential-game claim survives only at approximate consistency level (median residual 0.669).
Methodological proposal with benchmarking validation (synthetic and real); no comparative controlled trial.. LLM reasoning paths on synthetic concept-decomposition traps and real-world reasoning benchmarks; no specification of LLM architecture, dataset sizes, or task domains beyond benchmark names.. Intervention: Deposon scattering layer with three-channel path filtering and auditable energy-conservation guarantee (max deviation 2.2E-16).. Compared with: Decoy-capture baseline (synthetic), six-keyword rule filter (GSM8K, StrategyQA), and fusion with semantic prior (physics benchmark)..
On synthetic trap benchmarks, Deposon achieves 100% path-filtering accuracy versus 7% and 10% for decoy-capture baseline. On real benchmarks (GSM8K and StrategyQA), Deposon performance is indistinguishable from a six-keyword rule (GSM8K 0.87 vs 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899). Maximum per-path energy-audit deviation is 2.2E-16 (machine epsilon) across all parameters.
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An unreviewed methodological proposal with mixed results: synthetic benchmarks show strong filtering gains, but real-world benchmarks find no advantage over a simple keyword filter, and game-theoretic claims are falsified or downgraded to approximate, limiting evidence of practical utility.
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Multi-step LLM reasoning lacks a machine-recheckable ledger: discarded reasoning paths leave no auditable record. We propose the Deposon scattering layer, which binds each node of an LLM-generated concept-decomposition graph to a two-parameter Deposon state; paths undergo three-channel scattering -- transmission, reflection, irreversible dissipation -- obeying T+R+A=1 for arbitrary parameters, with a maximum per-path energy-audit deviation of 2.2E-16 (machine epsilon). We report all three evidence tiers honestly. On synthetic trap benchmarks the path-filtering gain is closed (pre-registered): unified reaches 100% versus a decoy-capture baseline at 7%/10%. On real benchmarks the layer is indistinguishable from a trivial six-keyword rule filter (GSM8K 0.87 >= 0.85, McNemar p=0.5; StrategyQA 0.899 = 0.899); no difference is detected here, so we sharpen the claim to "the differential value lies solely in machine verifiability." Fusion yields a second negative result: convex combinations with a semantic prior never improve (physics 0.484 -> 0.452), and the apparent lambda=2 gain is an anti-field artifact; any fusion gain must be nonlinear. Modeling the reverse dynamics as a potential game on the graph, we evidence an auditable scalar's monotonicity and near-gradientness and quantify the empirical coordination ratio (ECR). The three formalized dynamical-equivalence propositions (P1a/P1b/T-P1c) are falsified under the pre-registered kill protocol, and the potential-game claim is downgraded to approximate (cyclic-graph median residual 0.669): only consistency-level evidence survives at the dynamical level. Code: github.com/zeroandcat/Deposon.
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