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FIXED-POINT IMPLEMENTATION BRIDGE · SECTOR-LEVEL CERTIFICATE
The exact Casimir-sector theorem is now mirrored in signed Q16.48 arithmetic with $\varepsilon=2^{-18}$. The test preserves the $J=2$ and $J=5$ kernel lanes bit-for-bit, contracts all 78 complementary dimensions, and checks an exact sector mask against the same invariant subspace.
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$V=V_2^{\otimes3},\quad \dim V=125,\quad K=(C-6I)(C-30I),\quad \ker K=E_6\oplus E_{30},\quad \dim\ker K=47.$
Complementary $K^2$ values are $\{32400,12544,11664,19600,186624\}$. With $\varepsilon=2^{-18}$, the slowest factor is $1-11664/2^{18}=0.95550537109375$.
Evidence boundary: E1 sector-level fixed-point implementation check. This is not yet a full 125-lane RTL, synthesis, timing, overflow-width, or physical-device certificate.
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REFERENCE MODEL EXECUTED · 16/16 PASS. This result is a security invariant and executable authorization theorem. It does not alter the E47 spectral mathematics; it records the execution boundary used when E47/City agents invoke privileged tools.
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$\mathrm{Invoke}\Rightarrow\mathrm{BoundPrincipal}\land\mathrm{BoundTask}\land\mathrm{BoundTool}\land\mathrm{BoundArgs}\land\mathrm{Fresh}\land\mathrm{ActivePrincipal}.$
Successful invocation consumes a one-shot nonce. Cross-principal reuse, cross-task reuse, tool substitution, argument/content substitution, stale/pre-issued use, inactive-principal use, signature-only authorization, and replay are rejected by the reference state machine.
Authorization kernel · formal proof · executable test · public route
Evidence boundary: this proves the reference invariant and its local executable tests. Direct regression against each upstream implementation remains a separate evidence layer.
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LATEST AUTHORITY · CERTIFIED CHAIN ONLY
The spin-2 triple formalism is now stated with its native metric adjoint and its Grassmann witness boundary. The three rejected identifications are: coordinate dagger for the projector, dim ker K = 82, and set equality inferred from a matching dimension.
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$G_5=\operatorname{diag}(1,1/4,1/6,1/4,1),\quad G=G_5^{\otimes3}$
$K=(C-6I)(C-30I),\quad \ker K=E_6\oplus E_{30},\quad \dim\ker K=47.$
$P^2=P,\quad P^{\mathsf T}G=GP,\quad KP=0,\quad \operatorname{tr}P=47,\quad \Omega_c=47/125.$
$\Gamma=I-K^2/99144,\quad \Gamma P=P,\quad \|\Gamma^n-P\|_{G,2}=(15/17)^n.$