Spectral Packets, State Sufficiency and Memory Leakage in a Two-Band Heat-Transport Model — BIT-FOURIER-NANO-IW-002 F0–F2 Closure

This report consolidates the closed F0–F2 stages of BIT-FOURIER-NANO-IW-002 and their terminal F5 handoff. The setting is a normalized, finite-volume heat-transport model with three spatial cells, two spectral bands and two directions, giving 12 nonnegative energy populations. Two distinct interfaces share the same calibration parameter. The prediction targets are the two interface currents at the normalized horizon h = 0.4. State–calibration dependence, hidden initial information and error budgets are retained.

Preserved results
F0 provides a counterexample: states with the same observation packet and both initial currents can produce different currents after propagation. F1 constructs a common, exact 12-to-8 linear reduction for both current trajectories over the declared nominal affine family A(theta). The original observation packet alone does not uniquely determine the reduced initial state.

F2 opens a narrower, structured family of time-independent local direction-flip rate errors within the declared generator-error budget. Exact block elimination separates the hidden-initial-state forcing, of order O(delta), from the feedback memory kernel, of order O(delta^2), using the verified nominal block decoupling. Keeping the initial forcing while omitting only the feedback kernel yields current-error bounds of 4.442661037762e-9 and 3.975012507471e-9 at h = 0.4. These are kernel-omission bounds, not total prediction errors. The kernel admits two decaying modes in this family; an exact realization uses eight retained variables, two dynamic memory variables and two static source parameters, not eight numbers in total.

Full uncertainty and negative results
Over the full declared rate-uncertainty box, FULL12, MEM8_SOURCE and DIRECT2 retain identical certified current enclosures after the stated source-error budgets: J1 in [0.354384706992, 0.477739754644] and J2 in [0.102447986263, 0.146838950960]. The eight-dimensional closed reduction does not extend to the entire enlarged directed-rate family. Initialization from the observation packet alone remains unresolved without a valid joint prior or additional measurements. No accuracy advantage over FULL12 or DIRECT2 is claimed.

All negative cost results are preserved. In the F1 reuse profile, QUOTIENT8 is slower than FULL12. In the F2 specified-rate scenario, MEM8_SOURCE is about 5.75% slower than DIRECT2; its approximately 2.32% faster result for the uncertain-rate box is a limited three-run observation, not an established total-cost advantage. Sensor, calibration, AI-resource, energy and peak-memory costs remain unmeasured.

Evidence and limits
The archive retains 36 historical wagers, 180 finite scientific-check records and the separate 119-item F5 artifact audit. These are not independent experiments or external peer review. Evidence remains DERIVED + SYNTHETIC and SELF_HARNESS; F3–F4 are NOT_OPENED. Preparation of this release introduces no new scientific derivation, simulation or benchmark. No general Hamiltonian derivation of Fourier’s law, continuous-PDE error certificate, material calibration, hardware authorization or scientific-priority claim is established. Source archives, initial-state terms, counterexamples and source-rights notices remain unchanged. Execution, compilation and editorial preparation were assisted by AI.