CLAIMS.md
ABC: global RR8 branch
CLAIMS.md
1 # Local arithmetic claims and their boundaries
2
3 This route starts from the current Komorebi Space definitions of a view
4 functor, protected partial section and compatibility differential, together
5 with Block03's local Teichmuller carry formulas. PROOF_NOTE.md constructs the
6 new incidence diagrams and proves the following statements.
7
8 | ID | Exact result | Scope |
9 | --- | --- | --- |
10 | W1 | t_N:k->R_N is the unique normalized multiplicative residue section, and its reductions commute | Every prime p and N>=1; t_0 is only the zero-tail notation |
11 | W2 | C_N takes values in R_(N-1), is a normalized symmetric cocycle, and reduces naturally | All primes and precisions; C_1 is zero |
12 | W3 | The protected carry quotient injects into the actual Komorebi protected-obstruction quotient for the declared finite additive diagram | The raw graph, fibers, restrictions and protected seed are fixed explicitly |
13 | W4 | That additive extension problem is empty at N>=2, while the carry-and-multiplication Set-valued diagram has one exact normalized realization | The nonzero carry is retained; multiplication corrections are not treated as an additive subgroup |
14 | W5 | Both operation tables and obstruction classes form coherent precision towers | Naturality is proved for the actual finite diagrams and quotient maps |
15 | W6 | Teichmuller digit coordinates k^N reconstruct every element of R_N, and their inverse-limit ring is Z_p | Local p-adic arithmetic, with explicit addition and multiplication recursions |
16 | W7 | Uniform radical-controlled archimedean height cost | Open; neither local existence nor an inverse limit proves it |
17
18 W1 and the carry formulas have classical arithmetic content already present
19 in the predecessor. This checkpoint supplies the actual finite view-system
20 construction, its protected obstruction injection and the precision-natural
21 realization theorem. No priority claim over classical Teichmuller or Witt
22 arithmetic is made.
23
24 No new Lean execution or finite mathematical experiment is asserted. Earlier
25 Block03 receipts have a different scope and do not verify these new diagrams.
26 The focused independent review records the exact raw proof revision it checks.