Established in scope
Marking and necessary memory are connected within the given source
In the question: Historical: common source, state and event selection
Given source, grade and J>0; the two-time kernel is neither a physical measuring instrument nor a universal three-dimensional memory realization.
Read the exact result, assumptions and evidence
Result
Original grade and transport generate M4(C(S1)) with integer carry. Full H couples grade and carry. The GNS projection has K(t)=B*exp(itLQ)B with rank K(0)=3; its minimal temporal realization may be infinite-dimensional. No external memory is appended.
Required assumptions
- Declared native charge/scalar source
Fixed finite periodic spatial lattice source of rounds20–26 with original G, cocycle, neutral Z8 charges, scalar field and H=Hdiag+Hhop; a,m,beta>0 and original couplings are supplied. Nontrivial memory requires J>0. The original grade k is additionally retained, without presuming its selection from P1/P2.
Original evidence
- PROOF.md lines 31–151
Source checked at this snapshot
Original location and fingerprint
experiments/theory-contracts/native-mark-memory-20261014/PROOF.md
10492f2d34e93ffb8db2593b120ef120401e26bd5acc34db0cd9c7e8f15ec364
finding:native-grade-carry-and-memory