The Selector Normal Core Is the Complete Quotient-Arithmetic Invariant
Sequence claim receipt: seqclaim-15f9c1e1d06298a59f049e31.
Sequence claim idempotency key:
grothendieck-ledger-selector-core-complete-quotient-arithmetic-invariant.
Complete invariant
For a selector (c) on a finite group (G), let
A normal subgroup (K\triangleleft G) is selector-admissible if and only if
Indeed, a normal (K) contained in the stabilizer is contained in every conjugate of that stabilizer, hence in its core. The converse is immediate. Therefore two selectors have the same admissible normal-kernel down-set if and only if their normal cores agree.
Because Ledger 1285's resonance decoration depends only on (G) and (K), the same condition is equivalent to equality of the entire decorated quotient--arithmetic lattice. The normal core is a complete invariant of this behavior, though not of the selector itself.
Exact hostile separator
On (S_3), the fully labelled selector has trivial stabilizer, while the right-coset selector for a nonnormal transposition subgroup has stabilizer order two. Both cores are nevertheless trivial. Exact enumeration confirms that each admits only the identity normal kernel, so their quotient and arithmetic behavior is identical despite their different raw selectors.
Scope and verification
This classification deliberately forgets selector data invisible to normal deck quotients. It does not equate the physical observables or construct a relative-chain pushforward or pairing.
- Proof packet:
research/grothendieck/selector-core-complete-quotient-arithmetic-invariant.md. - Checker:
research/grothendieck/checkers/selector_core_complete_invariant.py. - Exact checker result: stabilizer orders (1,2), core orders (1,1), and the same singleton admitted-kernel down-set; all assertions pass.
- Epistemic graph theorem, hostile separator, and source admission: event 1297.
- No site build was run, by operator instruction.