V100 — A Structural Synthesis of the Arithmetic and Oscillatory Barriers in the Packet Shifted‑Family Endpoint Program

This paper consolidates the packet shifted‑family endpoint program into a single structural synthesis. The aim is not to claim a final unconditional endpoint theorem, but to organize the rigorous reductions already achieved into a clear hierarchy, separating proved components from conjectural or unresolved inputs.

The synthesis establishes the following:

1. The endpoint obstruction decomposes into an arithmetic component measured by the benchmark mass and an oscillatory reciprocal barrier.

2. The variation of strata amplitudes splits into four terms: support drift, weight drift, interval drift, and a genuinely oscillatory modulus‑shift term.

3. The oscillatory modulus‑shift contribution reduces to a weighted resonance‑counting problem.

4. The off‑core contribution factors through bounded‑variation estimates for strata amplitudes and square‑root partial‑sum bounds for completed rational sums.

The current state of the program is identified as follows: the completed rational‑sum side is largely reduced to square‑root cancellation and zero‑mode mass control, while the unresolved inputs are concentrated in (i) bounded variation of strata amplitudes and (ii) zero‑frequency weight mass bounds. These are formulated as explicit structural hypotheses. Once supplied, the off‑core contribution becomes power‑saving relative to the benchmark mass.

Conclusion: RH_V100 should be read as the stage where the arithmetic and oscillatory barriers are synthesized into a unified framework, clarifying what is rigorously proved and what remains as explicit unresolved inputs.