Komorebi Methodology

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1 {
2   "scope": "Exposition-to-evidence map, not a Lean theorem ledger.",
3   "claims": [
4     {
5       "id": "KME01",
6       "location": "2: question sufficiency",
7       "claim": "Factorization through the image iff constancy on representation fibers.",
8       "evidence_kind": "written proof",
9       "current_support": "Finite set tests corroborate instances.",
10       "boundary": "Sets/functions on the declared domain, no computability claim."
11     },
12     {
13       "id": "KME02",
14       "location": "2: continuation",
15       "claim": "Represented dynamics factor iff represented successors are constant on fibers; iteration follows by induction.",
16       "evidence_kind": "written proof",
17       "current_support": "216 finite representation/transition scenarios.",
18       "boundary": "Unrestricted state claim distinguished from restricted initial states."
19     },
20     {
21       "id": "KME03",
22       "location": "2: coherent views",
23       "claim": "Every finite prefix of the inclusion tower has a section but no global compatible section exists.",
24       "evidence_kind": "written proof",
25       "current_support": "Finite prefixes illustrate but do not prove the infinite claim.",
26       "boundary": "Specified natural-number fibers and inclusion maps."
27     },
28     {
29       "id": "KME04",
30       "location": "3: returning coordinate",
31       "claim": "PT²P=(PTP)²+PTQTP for complementary projectors.",
32       "evidence_kind": "written proof",
33       "current_support": "Rational example and seeded finite matrix checks.",
34       "boundary": "Linear operators with P²=P and Q=I−P."
35     },
36     {
37       "id": "KME05",
38       "location": "3: memory formula, equation 2",
39       "claim": "Block elimination gives exact history terms and an initial-complement term.",
40       "evidence_kind": "written induction",
41       "current_support": "Direct block trajectories compared to memory trajectories, including perturbations and nonzero initial state.",
42       "boundary": "Finite sums at each time; no convergence or numerical-efficiency claim."
43     },
44     {
45       "id": "KME06",
46       "location": "3: defects, equation 3",
47       "claim": "Composite defect equals the two correctly transported defects.",
48       "evidence_kind": "written proof",
49       "current_support": "Typed finite matrix checks.",
50       "boundary": "Linear additive setting with matching maps."
51     },
52     {
53       "id": "KME07",
54       "location": "4: correction",
55       "claim": "Correction exists iff the defect class vanishes in the declared quotient image.",
56       "evidence_kind": "written proof",
57       "current_support": "Diagonal obstruction functional and enlarged-space solution.",
58       "boundary": "Protected correction uses D(ker p), not unrestricted image."
59     },
60     {
61       "id": "KME08",
62       "location": "4: stability",
63       "claim": "A vanishing residual need not imply distance to a true solution tends to zero.",
64       "evidence_kind": "written proof",
65       "current_support": "Unit-coordinate finite checks are illustrative.",
66       "boundary": "Bounded injective diagonal operator on ℓ²; no general stability theorem claimed."
67     },
68     {
69       "id": "KME09",
70       "location": "5: arithmetic",
71       "claim": "Euler parity transform and coefficientwise roots-of-unity selector.",
72       "evidence_kind": "written symbolic proof",
73       "current_support": "Exact integer/rational coefficient checks and an exact finite root specialization.",
74       "boundary": "No automatic integral or p-adic divisibility consequence."
75     },
76     {
77       "id": "KME10",
78       "location": "6: verification",
79       "claim": "Kernel acceptance, axiom policy, formal meaning, ordinary hypotheses, and reproduction are distinct.",
80       "evidence_kind": "official documentation and methodological explanation",
81       "current_support": "Current official-source consultation; historical project example attributed.",
82       "boundary": "No new Lean execution or independent kernel."
83     },
84     {
85       "id": "KME11",
86       "location": "7: proof fields",
87       "claim": "AND-premise dependencies, alternative justifications, and candidate edges have distinct roles.",
88       "evidence_kind": "defined finite illustration and cited project theory",
89       "current_support": "Finite certificate-closure checks and negative controls.",
90       "boundary": "Not a model of every human thought or recovered discovery history."
91     },
92     {
93       "id": "KME12",
94       "location": "8: collaboration",
95       "claim": "Inspectable records may improve handoff and reuse.",
96       "evidence_kind": "methodological proposal",
97       "current_support": "Operator case gives a concrete proposed handoff.",
98       "boundary": "No measured productivity advantage asserted."
99     },
100     {
101       "id": "KME13",
102       "location": "9: evaluation",
103       "claim": "Compare structured records with ordinary notes under declared tasks, budgets, and review.",
104       "evidence_kind": "proposed empirical protocol",
105       "current_support": "No comparative experiment conducted.",
106       "boundary": "Effectiveness remains open to testing and possible adverse results."
107     },
108     {
109       "id": "KME14",
110       "location": "source package",
111       "claim": "Complete-inventory verifier rejects targeted invalid archives.",
112       "evidence_kind": "executed implementation tests",
113       "current_support": "17 actual CLI fixtures with intended diagnostics.",
114       "boundary": "Integrity relative to manifest, not authentication or mathematical soundness."
115     }
116   ]
117 }

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