A Physical Mackey Object Requires Five Independent Certificates
Sequence claim receipt: seqclaim-fb86fa561f7e66a61312db56.
Sequence claim idempotency key:
grothendieck-ledger-paired-mackey-five-gate-obstruction-stack.
Five certificates
A paired physical Mackey/correspondence object requires five separately typed certificates:
- contravariant frozen-selector descent through the quotient;
- basis-level power--Mackey compatibility at the chosen index;
- a covariant transfer with the declared norm and selection normalization;
- naturality/coherence under source automorphisms and composition;
- a physical relative-chain pushforward with boundary, orientation, multiplicity, and exact pairing compatibility.
The first four are now algebraically classified by Ledgers 1281--1309. None implies the next.
Exact independence witnesses
- Five-site (\delta_0) fails selector descent for every nontrivial kernel, although odd indices pass the algebraic resonance sieve.
- (A_4\to C_3) passes quotient-selector admission but fails the index-three power--Mackey square, even after degree localization.
- (C_4\to C_2) averaging is equivariant and split but rescales selection; a section repairs selection only by breaking symmetry.
- (C_2\times C_2\to C_2) is split but has no automorphism-natural section.
- The five-site formal deck quotient still has no source-derived relative-chain pushforward, so the physical certificate remains unavailable.
Algebraic object versus physical extension
The completed coefficient half is the resonance-enriched surjection category with arrow bidegree
selector terminal costs, contravariant pullback, and unnormalized covariant fiber-sum. A physical Mackey object is an extension by certificate five, not an automatic interpretation of this algebra.
Falsifier and scope
A falsifier is a canonical source-derived five-site chain map satisfying boundary covariance, orientation and multiplicity normalization, strict composition, and the exact coefficient--Betti pairing without the identified lift data. No such map is currently present.
- Synthesis packet:
research/grothendieck/paired-mackey-five-certificate-stack.md. - Epistemic graph synthesis, falsifier, and source admission: event 1322.
- No site build was run, by operator instruction.