Machine Native Reasoning: wider continuation

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1 
2 \chapter{Result and source map}\label{app:map}
3 The following map gives the role of each selected written result. Exact source anchors, excerpts, hashes, and detailed hypothesis review are in the accompanying machine-readable ledger and review files. Source relationships do not imply that every source page is admitted.
4 \small
5 \begin{longtable}{p{0.13\linewidth}p{0.39\linewidth}p{0.35\linewidth}}
6 \toprule Result & Preserved object & Source relationship\\\midrule\endhead
7 \ref{r:factor} & A target determined by an available record & GA, shared fibre criterion.\\
8 \ref{r:behavior} & Every declared finite continuation & GA and MU, consolidated.\\
9 \ref{r:packet} & Exact split encoding and named composition loss & SR, split and hidden-return identities.\\
10 \ref{r:transport} & Source operations and matched readouts & MU, with related uses in OSL and Neuralese use the same conditional principle.\\
11 \ref{r:common} & One output method across candidate dynamics & GA, common observable quotient.\\
12 \ref{r:positive-packets} & Probability interpretation of a complete packet family & LSM, positive packet criterion.\\
13 \ref{r:memory} & Every admitted future set correction & GA, correction-signature theorem.\\
14 \ref{r:occupancy} & Exact partition-evidence memory cardinality & GA, occupancy corollary.\\
15 \ref{r:bayes} & All posterior updates in the actual reporting chain & MU, finite channel factorization.\\
16 \ref{r:joint-refinement} & Coarsest partition closed for prediction and update & LSM and PRIQ, finite closure.\\
17 \ref{r:instrument} & Joint next-state/report law, posteriors and feedback & PRIQ and AVOC, selected composition.\\
18 \ref{r:history-bound} & Whole-history error and conditioning cost & LSM, law and normalization bounds.\\
19 \ref{r:risk} & One bounded-loss decision calculation & GA and MU, specialized common-risk bound.\\
20 \ref{r:recipient} & One artifact under fixed recipient procedures & MU, intersection and covering criterion.\\
21 \ref{r:inquiry} & One executable tree under all declared budgets & MU and SII, finite Pareto synthesis.\\
22 \ref{r:lowerbound} & A complete optimality claim for a checked tree & SII, binary singleton-repair scope.\\
23 \ref{r:belief-planning} & One optimal finite-horizon expected-cost inquiry & AVOC, projected values and finite plans.\\
24 \ref{r:policy-error} & Uniform policy evaluation before selection & LSM/AVOC, common-law specialization.\\
25 \ref{r:cegis} & Exact finite candidate rejection and acceptance & SII, finite counterexample refinement.\\
26 \ref{r:ordered} & The same proposed ASTs and teacher transcript & SII, sound equations and ordered quotient.\\
27 \ref{r:prefix} & The same completed ordered diagnostic search & SII, capacity and streaming arguments.\\
28 \ref{r:dependencies} & Applicability of dependency-bound witnesses & SII, complete declared dependency graph.\\
29 \ref{r:prices} & Gains under one complete additive ledger & SII, price-relative dominance.\\
30 \ref{r:lineage} & Conditional false-acceptance control & SII, adaptive lineage error budget.\\
31 \ref{r:reconstruction} & A target from jointly accessible linear records & SR and SRWT, target-relative specialization.\\
32 \ref{r:governance} & Legal action availability and label histories & MS, exact governance quotient.\\
33 \ref{r:ending} & Continued operation with an ending policy & MS, fully observed finite specialization.\\\bottomrule
34 \end{longtable}
35 \normalsize
36 
37 \clearpage
38 \section*{Selected core correspondence}\small
39 \begin{longtable}{@{}p{.11\linewidth}p{.55\linewidth}p{.25\linewidth}@{}}\toprule Result & Statement & Archived correspondence\\\midrule\endhead
40 \ref{r:factor} & A record determines a target exactly on its fibres & Accepted, scoped\\
41 \ref{r:behavior} & Evidence-initialized behavioral state & Accepted, scoped\\
42 \ref{r:packet} & Exact accounting of the discarded excursion & Accepted, scoped\\
43 \ref{r:transport} & Forward transport of a reusable method & Accepted, scoped\\
44 \ref{r:common} & A common observable quotient & Pending\\
45 \ref{r:positive-packets} & When complete packets are genuine probability components & Pending\\
46 \ref{r:memory} & Minimal exact memory for a correction contract & Accepted, scoped\\
47 \ref{r:occupancy} & The size of partition correction memory & Pending\\
48 \ref{r:bayes} & When a report preserves every Bayesian correction & Accepted, scoped\\
49 \ref{r:joint-refinement} & Least refinement closed under prediction and correction & Accepted, scoped\\
50 \ref{r:instrument} & One quotient for reports, posteriors, and feedback & Accepted, scoped\\
51 \ref{r:history-bound} & A whole-history bound with an explicit conditioning cost & Accepted, scoped\\
52 \ref{r:risk} & A decision bound for one actual approximation chain & Accepted, scoped\\
53 \ref{r:recipient} & A common artifact for fixed recipients & Accepted, scoped\\
54 \ref{r:inquiry} & Exact joint feasibility for explicit controllers & Accepted, scoped\\
55 \ref{r:lowerbound} & A candidate attaining both lower bounds is optimal & Accepted, scoped\\
56 \ref{r:belief-planning} & The same compressed belief supports the same inquiry & Accepted, scoped\\
57 \ref{r:policy-error} & Uniform model error controls a changed policy & Accepted, scoped\\
58 \ref{r:cegis} & What finite counterexamples establish & Accepted, scoped\\
59 \ref{r:ordered} & Ordered semantic compression preserves the teacher trace & Accepted, scoped\\
60 \ref{r:prefix} & A sound prefix exclusion & Accepted, scoped\\
61 \ref{r:dependencies} & Selective reuse with complete dependencies & Accepted, scoped\\
62 \ref{r:prices} & Which gains survive every admitted price? & Accepted, scoped\\
63 \ref{r:lineage} & A conditional error budget for a lineage & Accepted, scoped\\
64 \ref{r:reconstruction} & Target-relative joint reconstruction & Accepted, scoped\\
65 \ref{r:governance} & A quotient that preserves legal operations & Accepted, scoped\\
66 \ref{r:ending} & Safe continuation that retains an ending strategy & Pending\\
67 \bottomrule
68 \end{longtable}\normalsize
69 \chapter{Sources and references}
70 The named sources below identify the mathematical lineages used in this book. Exact editions, file hashes, source positions, and review records belong to the accompanying source register. A source citation does not import every result or every implementation in that source.
71 
72 \begin{description}[style=nextline]
73 \item[KS] Komorebi P. \emph{Komorebi Space: Coherent Realizations, Obstructions, and Descent}. The prologue uses strict coherent families, view evaluation, and attained-record factorization. The full analytic and descent theories are not assumed here.
74 \item[GA] Komorebi P. \emph{Grounded Abstraction: Identifiability, Representation Change, and the Limits of Learning}. Evidence access, predictive initialization, correction signatures, model uncertainty, and information required for migration.
75 \item[MU] Komorebi P. \emph{Machine Understanding: Representation, Explanation, and Transfer}. Reusable methods, recipient-relative artifacts, Bayesian reporting, and a common acquisition and resource contract.
76 \item[SII] Komorebi P. \emph{Self-Improving Intelligence: Representation, Discovery, and Recursive Revision}. Finite discovery, semantic compression, diagnostic pruning, dependency reuse, and resource and lineage bounds.
77 \item[MS] Komorebi P. \emph{Machine Societies: A Theory of Persistent Plural Computational Organization}. Selected joint-reconstruction, action-quotient, and continuation results. Institutional formation and external authority are not inferred from those finite results.
78 \item[SR] Komorebi P. \emph{Sufficient Resolution}. Split encodings, hidden-return identities, factorization, and target-relative reconstruction.
79 \item[SRWT] Komorebi P. \emph{Stratified Relational Workspace Theory}. The selected joint-reconstruction argument is used without importing the complete dynamics, emergence, persistence, or identity theory.
80 \item[LSM] Komorebi P. \emph{Large Signal Model Foundations}. The selected core's source anchors are the positive-packet criterion, joint prediction/correction closure, and whole-law and conditioning bounds. The source register retains the earlier edition actually used for those anchors, alongside the newer monograph. The larger observable-learning and domain-discovery program remains a separate source.
81 \item[PRIQ] Komorebi P. \emph{Hypergraph Lumpability and Bayesian Refinement for Dynamical Systems with Projector Resolutions}. Selected positive normalization and finite filtering arguments. The full nonlinear analytic and hyperedge theory is not imported.
82 \item[AVOC] Komorebi P. \emph{Artifact Value, Guarded Operations, and Calibrated Planning}. Selected conditioning, projected-value, and finite-planning mechanisms. The formal scope of the source implementation is distinct from the source-facing Machine Theory correspondence.
83 \item[PPT] Komorebi P. \emph{Proof Path Theory: Certificates, Compression, Discovery Fields, and Mathematical Memory}. Seeded closure, replay, obstruction witnesses, and typed certificate exchange. The selected trace-extension source and original formal concordance are retained in the companion.
84 \item[OSL] Komorebi P. \emph{Operator-Symbolic Language}. Used to identify the executable semantic interface and its remaining learned-translation boundary.
85 \item[NEU] Komorebi P. \emph{Neuralese: Recurrent Latent Operators, Causal Semantics, and Stability}. Used for its distinction between a specified semantic executor and a learned representation. Historical positive and failed scientific gates retain their original scope.
86 \item[SRIC] Komorebi P. \emph{Stratified Recursive Improvement Closure: Obstruction, Descent, Transport, and Evidence-Preserving Lineages}. A specialist source for recursive repair and evidence retention, not a blanket claim of unrestricted self-improvement.
87 \item[KLC] Leslie Pack Kaelbling, Michael L. Littman, and Anthony R. Cassandra. ``Planning and acting in partially observable stochastic domains.'' \emph{Artificial Intelligence} 101 (1998), 99--134. Classical context for belief-state planning and finite policies.
88 \end{description}
89 
90 These references are not an exhaustive literature or priority audit. Factorization, automata quotients, sufficient statistics, dynamic programming, program synthesis, closure systems, and controlled invariant sets have established mathematical foundations. The selected arguments are given with their hypotheses so that their use does not depend on an unstated attribution claim.
91 
92 \section*{Source treatment}
93 The original reviewed text and formal mappings are preserved separately. This monograph makes local type and domain assumptions explicit, repairs the path-level composition argument, and adds the subsequent integration chapters. The editorial record identifies those changes. Original source-suite runs remain historical evidence unless a new receipt records an actual rerun. The current finite regressions do not establish a fresh source-wide mathematical audit of every specialist manuscript.

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