Exact Weil-Block Projective Capacity on Heisenberg Graphs: Resolving the Final Obstruction to δ Extraction

The O-series has progressively identified and resolved a sequence of obstructions preventing reliable extraction of the capacity exponent~ from discrete Heisenberg geometries: a geometric obstruction (O8--O9), an algorithmic obstruction (O10), and a residual representation-level ambiguity at the proxy stage (O11). O11 introduced a bidimensional Fourier-character proxy for the Weil-block decomposition, obtaining a stable estimate ₂₀₏ 3. 4 at q=307 while coarse-graining away the central coordinate~, thereby leaving open direction O11-O2. The present paper closes this observable gap by implementing the exact Weil projection. For each generic Weil block~Hc (c 0, i. e. \ non-trivial central character), we maintain a q q span tracker operating directly in the irreducible representation of Heis₃ (Z/qZ), at primes q\211, 307, 401\. We verify measurability conditions (E1) -- (E3), establish a stable pre-saturation decay window, and extract ₄ₗ₀₂ₓ via log-log regression. Robustness is assessed against fitting window, prime~q, block sampling density, and coarse-graining scheme. The converged exponent ₄ₗ₀₂ₓ 4. 4--4. 8 at q \29, 53, 61\ (with R² > 0. 98) exceeds the proxy value ₂₀₏ 3. 39 by approximately one unit, establishing Case~B: the exact Weil projection yields a larger exponent than the proxy, driven by the dynamically active central phase _ (n). Via the structural relation ^* = 1/ (+ 12) derived in O3--O7, this implies ^* 0. 19--0. 20, outside the phenomenological target ^* (0. 09, 0. 13). This incompatible outcome is most plausibly a finite-size artefact at q 61, motivating the extension to q 101 as the next step (O12-O1).