N100 exact shape nulls and clock-orthogonal thermal deformation

[LightChainr]

Scientific result

This focused PR contains only the N50/N100 geometry certificate, exact three-modulus nulls, and the new clock-quotient readout. It does not carry the old factorial production ancestry. The fresh N100 production and full thermal-profile companion are delivered separately in #484 at 7b30648.

• Exact geometry: the original N50 Smith pair cannot support a third modulus; N100 is the minimal same-map three-shape replacement.
• Exact conditional theory: affine-E4, affine height-only E4, and affine y-squared have distinct fixed zero combinations, with no unknown per-coordinate offset or amplitude.
• Actual production reuse: with D=Y4-Y2, U=Ys-Y2 and r_C=U_C/D_C, the measured clock is -.27798175 +/- .01937689. The remaining A/E/W vector is (-8.99609e-4,9.52915e-5,1.57452e-4), full delete-one chi-square 17.8234/3, nominal p .0004783.
• Exact interpretation: the clock-calibrated odd residual has zero p-integral; the even integral is minus the W residual. The companion N100 production: shape splitting and zero-area thermal redistribution #484 resolves the nonzero higher thermal moments. This is thermal redistribution, not a new field count.
• New future readout: freeze Psi=-.0224598 R_A+.222506 R_E+R_W, plus the full source covariance and two direction-transfer wedges. No next scale or Monte Carlo is launched.

Boundaries

All empirical readouts reuse one 2M-per-shape, 200-batch common-random block. The C choice and direction are post-reveal, so their diagnostics are not independent validation. The two-profile representation is saturated on three shapes. W-only remains compatible at alpha .01, and the even integral alone is only 2.39 SE. No unique loading, field identity, scale homogeneity, or physical E4 law is claimed.

The copied 200x12 sufficient statistics are hash-bound to the now-public source score at 7b30648; raw hashes and acquisition metadata are retained.

Artifacts

• notes/p267-third-geometry-feasibility.md
• notes/p267-three-modulus-null.md
• notes/p267-clock-shape-quotient.md
• predictions/p267-n100-three-modulus-null.json
• results/p267-clock-shape-quotient/{input,score}.json and REPORT.md

Four geometry and four exact-null focused tests passed in their source commits; three new clock algebra/covariance tests passed locally. No old full suite or MC was rerun. The optional numeric replay uses requirements-p267-clock.txt; the exact-arithmetic runtime is unchanged.

Related #267, #103, #154, #205, #275, #370. No issue closure or merge is requested.