A First-Principles Derivation of the Planck Constant from an Eleven-Dimensional Covariant Master Action

Planck's constant supplies one common normalization to quantum phase, canonical and graded algebras, and energy–angular-frequency conversion. We ask whether that common role can be selected from an eleven-dimensional covariant parent theory before a numerical unit of action is assigned. Information-projection dynamics first forms the active support, persistent finite objects, boundaries, temporal order, recovery, locking, and admissible readout that define the physical domain. On the selected finite, fixed-rank, fixed-capacity connected conservative component, these structures admit one seven-term covariant action. Varying the complete off-shell action before locking and constraint restriction gives the reduced action-dependent functional \[Q(a)=1/2[κ₊a+κinfoRinfoa⁻¹],info=ainfo⊗ 2.\] Its strict convexity selects the unique positive relative normalization \[a_{}=x_{}ainfo,_{}=0.061384295265890618… .\] The simultaneous active rescaling of the two action-line sections leaves the normalized parent record and \(x_{}\) unchanged. The physical result is therefore a positive action structure and its invariant relative selector; this active scale orbit is distinct from a passive change of basis on the one-dimensional action quantity line. On a faithful physical source quotient, the recurrent phase, same-solution Euclidean–Lorentzian transfer, occupied determinant line, conservative field–matter interactions, and flat normalization transport give \[σ={aq}{asrc}=1.\] The complete seven-term variation yields a closed mixed presymplectic form \[Ω₇ᵖʰʸˢ=Ωbg⁽⁷⁾+a_{}Fdet,δΩ₇ᵖʰʸˢ=0,\] whose normalized cohomology class is integral. The resulting prequantum line, determinant-line geometry, polarizations, boundary extension, Hamiltonian domain, and spectral calculus are transported consistently across the declared connected component. The same action element then appears in the phase law, bosonic and fermionic canonical structures, and the proper-time spectral relation: \[exp\!({iSphys}{a_{}}),[q,P]=ia_{},\{Ψ,Ψ^{}\}_{},Δ E=a_{}Ω.\] This simultaneous role identifies the reduced quantum of action and its full-cycle counterpart as \[UFT,sel=a_{},UFT,sel=2_{},σ=1.\] The energy–frequency result is a theorem for the same transported unitary family and is not counted as a second independent determination of the action scale. Cross-sector action weights are post-selection consequences and do not feed back into the primary derivation. The theorem applies to the selected finite connected component described above. The exact SI value of \(h\) is introduced only after the physical identification as a metrological coordinate. The present result does not assert an independent parameter-free prediction of the SI decimal, universality over disconnected roots, unrestricted continuum completion, or transport across rank-changing capacity transitions.