Selector Pullback Adds Exactly the Map-Kernel Resonance Surcharge
Sequence claim receipt: seqclaim-b814d4967161c877772fde26.
Sequence claim idempotency key:
grothendieck-ledger-surjective-preimage-resonance-lcm.
Preimage resonance law
Let (\phi:G\twoheadrightarrow H), put (N=\ker\phi), and take (K\triangleleft H). For (P=\phi^{-1}(K)),
The exact sequence (1\to N\to P\to K\to1) gives the union law for kernel primes. For action primes, (A_P) maps to (A_N\times A_K) with surjective projections. The kernel consists of extension automorphisms fixing (N) and (P/N) pointwise; these are derivation terms valued in (Z(N)) and add no primes outside (N).
Consequently
Together with Ledger 1297, pulling back a selector adds exactly the map-kernel resonance surcharge to its target terminal spectrum.
Controls
For ((S_3\times C_5)\to S_3) over (A_3), the labels are (5,6,30). For (Q_8\to C_2\times C_2) over an order-two subgroup, the labels are (2,2,2); the cyclic order-four preimage and its inversion action introduce no new prime. Both spectrum-intersection identities hold through index 60.
Scope and verification
This is algebraic coefficient base change. It does not supply the missing Betti relative-chain transfer, orientation, boundary covariance, or physical normalization.
- Proof packet:
research/grothendieck/surjective-preimage-resonance-lcm.md. - Checker:
research/grothendieck/checkers/surjective_preimage_resonance_lcm.py. - Control results through index 60: mixed-prime spectrum sizes (48,20,16) and nonsplit quaternion sizes (30,30,30); all assertions pass.
- Epistemic graph theorem, extension controls, and source admission: event 1305.
- No site build was run, by operator instruction.