Original ledger status
QGEO.PERIODS.01
QGEO.PERIODS.01
The periods round -- the analytic layer of the cover is classical (one module, 6 checks, ~1 s; discovery probe periods_probe.py 6/6, verdict PERIODS-CLASSICAL). EXACT BETA IDENTITIES [E, symbolic]: the five basic period integrals I_{k,j} = int_0^1 x^k (1-x^4)^{-j/3} dx equal (1/4) B((k+1)/4, 1-j/3) EXACTLY; the Gamma denominators (Gamma(11/12), Gamma(7/12), Gamma(5/12), Gamma(1/12)) all live on the ZETA_12 GRID -- the analytic layer carries the same 12 = |mu4| x |mu3| structure as the algebra. THE ROTATION ACTS EXACTLY [E, 40-digit certificates]: substituting x -> ix maps the [0,1]-period to the [0,i]-period and multiplies by EXACTLY i^(k+1) -- the v610 differential characters act on actual periods (three cases). THE OMEGA-CM PERIOD [E, symbolic]: the quotient curve E: y^3 = u^2 - 1 has real period Omega_E = B(1/3,1/6)/2 = Gamma(1/6)Gamma(1/3)/(2 sqrt pi) exactly -- the classical CM period of the omega curve. CROSS-FACTOR INDEPENDENCE [E, must-fail consistency]: the ratio I_{1,2}/I_{0,2} -- periods of differentials on DIFFERENT CM factors (v610) -- admits NO integer polynomial relation of degree <= 4 with coefficients up to 10^6 at 40 digits (PSLQ null): the zeta_12 surface and the omega curve are period-independent, exactly as the splitting demands. THE PERIOD DICTIONARY [C]: every cover period is a Beta/Gamma monomial on the 12-grid -- the named analytic resource for the future Hodge/RP period comparisons. GATE.QGEO does not move; no marker changes. [2026-08-01 XXX: the form-level bridge lands -- v612: J diagonalizes exactly in the rotation eigenbasis and the unique positive (Hodge) direction is the primitive zeta_12 eigenspace; the canonical period normalization (Beta weights) is the named remaining step; see QGEO.POLFRAME.01.] [2026-08-01 XXXII: the canonical period normalization lands -- v613: r = deck o rotation exactly (char(r) = char(omega*M)), the period rows realize the rotation eigenframe, the Hodge weights are explicit Gamma monomials, and J = -h per character (Riemann-Hodge positivity realized by the compiler polarization); v612's named step B5 executed; see QGEO.PERNORM.01.]
Recorded status: Exact [E] symbolic Beta identities + 40-digit certificates + PSLQ-null consistency + [C] the period-dictionary reading
Dependencies, status detail and source
Canonical status: PERIODS-CLASSICAL: five Beta identities exact (zeta_12-grid Gamma denominators); rotation characters act on periods exactly; Omega_E = B(1/3,1/6)/2; cross-factor PSLQ null (splitting-consistent); period dictionary named; 6/6 checks
Dependencies: QGEO.LANDSCAPE.01; QGEO.COVER.01; v597; v610
Scripts: v611_periods.py
Location: tfpt_1;tfpt_2;tfpt_3
Original CSV, line 629