Edition README
KZFC and Residual Reflection
README.md
1 # Komorebi KZFC residual reflection v0.11.0 — multiverse residual layer
2
3 This checkpoint branches from the verified v0.10.0 depth-zero KZFC program and adds an
4 independent `Komorebi.Multiverse` layer. All 49 predecessor Foundation modules are preserved
5 byte-for-byte.
6
7 ## New formal content
8
9 The multiverse layer contains 11 Lean modules and 41 named theorem declarations covering:
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11 * reflexive/transitive world networks;
12 * upward amalgamation and dual/common-ground geometry;
13 * the finite amalgamation nerve;
14 * a concrete pairwise-but-not-joint triangle obstruction;
15 * transport systems and local/joint gluing;
16 * additive residuals and a triangle cocycle identity;
17 * logical disagreement residuals and invariant/common-core fragments;
18 * graded residual-descent theories and a proof that an unconstrained complete tower is vacuous;
19 * morphisms/pattern-embedding interfaces;
20 * externally indexed ZFC-world networks using the predecessor's explicit ZFC theory.
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22 The key example proves that three worlds can have all pairwise compatibility tests succeed while
23 no common upper world exists. With constant Unit coefficients all pairwise data residuals vanish,
24 yet the triple still fails to glue.
25
26 ## External set-theory alignment
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28 Mostowski's finite amalgamation-pattern theorem, as presented in *Set-Theoretic Blockchains*
29 (arXiv:1808.01509, Theorem 2.1), implies that the same triangle-boundary pattern is realizable by
30 Cohen extensions of a countable model of ZFC. That forcing construction is literature evidence,
31 not a theorem imported into the Lean kernel in this release.
32
33 Usuba's downward set-directedness theorem for grounds motivates keeping the upward and downward
34 world geometries distinct rather than imposing artificial symmetry.
35
36 ## Main correction discovered in this block
37
38 The bare statement "there exists a complete graded obstruction tower" is not a meaningful new
39 foundation. `packedFailureTheory_complete` proves that every gluing failure can be encoded at
40 degree zero. A nontrivial Komorebi axiom must therefore constrain the tower by an independently
41 specified construction such as locality, naturality, derived limits, or a sheaf/descent mechanism.
42
43 ## Next target
44
45 Build a finite oriented cochain complex over the amalgamation nerve, prove `d^2 = 0`, and separate
46 missing-simplex/world obstruction from coefficient cohomology. Only after that separation should
47 a new residual-descent axiom be proposed.
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49 See `MULTIVERSE_THEORY.md`, `MULTIVERSE_LITERATURE.md`, `BLOCK_11_REPORT.md`, and
50 `PROOF_BOUNDARY_v0.11.0.md`.