WP37: the universal charge law - H_12.sin(phi) = q_anchor for every viable mixed sheet
WP36 derived the J-routing mechanism on the 303 u-class sheets. This
package extends the census and the law to all 955 viable block-diagonal
sheets (all anchors u/t/c, all orientations). Checker
checkers/wp37_universal_charge.py, results
results/wp37_universal_charge.json, 5/5 gates.
Universal structure (exact, machine floor)
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Phase-sector census (G1): EVERY viable block-diagonal sheet has its phase edge in the DOWN sector (955/955). Hu is real ensemble-wide; the loop phase lives only in Hd.
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Universal J-routing (G2): zeroing the Hu block off-diagonal c = H_12 kills J on every mixed sheet (848 sheets: u 232, t 192, c 424; residual J0/J < 2.5e-15) and leaves J exactly on every unmixed sheet (107: u 71, c 36; J0/J = 1 to machine precision). The up-sector 2x2 block mixing is the unique J valve.
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Exact commutator identity (G3, max err 2.1e-34) and first-harmonic Im(Hd) with magnitude-only factorization (G4) hold for all anchors.
The charge law (G5)
Per-sheet theorem of WP36: J.Du.Dd = c.sin(phi).M(mags). Ensemble readout shows the magnitude factor collapses to a class constant:
q_anchor = H_12 . sin(phi)
q_u = 3.621318e-02 within-class rel 2.9e-05 (EXACT, 232 sheets)
q_t = 1.125347e-06 within-class rel 1.7e-08 (EXACT, 192 sheets)
q_c = 3.245237e-03 within-class rel 1.0e-02 (APPROXIMATE, 424)
The c-class charge carries a genuine ~1% texture-level fluctuation, partially correlated with the block splitting Delta = H_22 - H_11 (corr 0.73); a linear Delta correction still leaves 0.87% residual. No exact refinement found - typed honestly as approximate.
What this explains about WP35
WP35's three-way theta typing is the q-law masked by Delta behavior:
- u: theta_u(phi) = q_u/(Delta.sin phi) with Delta class-constant at the fitted level -> the observed reciprocal law.
- t: q_t is exactly constant (1.7e-8) but Delta = H_22-H_11 is the tiny fitted yc^2-yu^2 difference and drifts 3-10% across phase groups -> the reciprocal law was real but hidden in WP35.
- c: q_c approximate at 1% -> per-class theta behavior.
Charge ratios: q_u/q_c = 11.15, q_c/q_t = 2885. Open: identify q_anchor as an explicit magnitude monomial and test the near-coincidence q_u/V_cb ~ q_c/V_ub ~ 0.87.
Typing
WP11 stands: phi remains chart data; nothing here claims descent to the physical quotient. The charge law is a chart-space statement about the scan ensemble's readout constraint, exact for u/t and approximate at ~1% for c.