READING_NOTES.md
Self-Improving Intelligence: visual guide
READING_NOTES.md
1 # Reading notes and page index
2
3 Self-Improving Intelligence — Visual Guide v1.0.0
4
5 These notes accompany the diagrams. Full hypotheses and proofs remain in the source manuscript.
6
7 ## 01. Self-Improving Intelligence: A Visual Guide
8
9 A standalone visual companion.
10
11 **Interpretation.** Four different objects improve across the finite chain.
12
13 **Boundary.** No claim of general intelligence or indefinite recursive acceleration.
14
15 Source: [S] First-edition scope, pp. ii-iii
16
17 ## 02. The route through this guide
18
19 Read the worked world first. Then follow the discovery procedure outward, keeping the supplied machinery in view.
20
21 **Interpretation.** Every plate identifies its source section. Manuscript page numbers are the printed numbers, not the PDF viewer index.
22
23 **Boundary.** A solid arrow is a specified transition or dependency. Dashed paths are explicitly labeled as recurrence or a qualified extension. Counts retain their original units.
24
25 Source: [S] Scope guide; §§1-3 | manuscript pp. iii, 1-4
26
27 ## 03. A better system is not always a better improver
28
29 Changing a library and changing the procedure that uses it answer different questions. A crossed comparison keeps them separate.
30
31 **Interpretation.** Holding the library fixed isolates a change in the improvement procedure. The combined descendant may improve for a different reason.
32
33 **Boundary.** Use comparable starting solvers, task laws, installed information, and budgets. A stronger base model or an extra library is another changed component.
34
35 Source: [S] §3; Counterexample 3.2 | manuscript pp. 3-4
36
37 ## 04. One defect. Eight possible cells.
38
39 The procedure cannot see the defect index. It receives only the reports of the questions it is allowed to ask.
40
41 **Interpretation.** Retain an executable way to find a justified repair in a later episode. Do not install the next episode’s hidden answer.
42
43 **Boundary.** The binary sensors and repair meanings come from a declared finite model. The 88 query-table entries are supplied, not learned through executed calibration.
44
45 Source: [S] §4; §32 | manuscript pp. 4, 49-51
46
47 ## 05. Two investigations, the same installed sensors
48
49 Equality-first testing and coordinate queries use the same declared language. Their paths have different depths, but their complete trees have the same size.
50
51 **Interpretation.** Equality-first: seven questions, then repair. Coordinate queries: three questions, then repair. Total costs are eight and four calls.
52
53 **Boundary.** Both full binary trees have eight repair leaves and seven query nodes: fifteen records. These are literal tree records, not bytes or minimal program sizes.
54
55 Source: [S] §4; Theorem 32.1 | manuscript pp. 4, 49-50
56
57 ## 06. Follow one episode: the defect is at cell 5
58
59 This page follows the canonical coordinate policy. The procedure knows the reports, not the hidden index shown to the reader.
60
61 **Interpretation.** The three reports select a repair for this episode. The reusable artifact is the branching procedure that works for every allowed starting cell.
62
63 **Boundary.** The shipped compiler can use an equality query at the last two-case branch. It has the same cost. This plate deliberately shows the canonical all-coordinate tree.
64
65 Source: [S] §4; §32; Appendix A | manuscript pp. 4, 49-54
66
67 ## 07. The path is not the stored program
68
69 A single successful run touches four records. Its complete reusable controller still contains all fifteen.
70
71 **Interpretation.** Execution follows one branch. Literal storage sums every branch. The highlighted path for reports 1, 0, 1 reaches repair 5.
72
73 **Boundary.** Immutable cases, binary observations, a different successful repair for each case, and one record per node. Shared code or state-reset operations change the model.
74
75 Source: [S] §6; Theorem 11.1; §28 | manuscript pp. 6-7, 14-15, 44
76
77 ## 08. A residual is a question, not a diagnosis
78
79 The same mismatch can be consistent with several causes. A useful next experiment separates repair-relevant explanations.
80
81 **Interpretation.** Retain competing explanations. Seek an admitted observation whose possible outcomes change which correction is justified.
82
83 **Boundary.** A representation cannot recover a distinction unavailable in its complete transcript. With disjoint repairs and identical transcript laws, equal-prior success is at most one half.
84
85 Source: [S] §5; Proposition 5.1 | manuscript pp. 5-6
86
87 ## 09. The best question need not identify the most
88
89 A repair may work for several hidden cases. The right stopping condition is a common successful action, not complete knowledge of the state.
90
91 **Interpretation.** The 2/2 question has more information about four equally likely cases, but one branch still mixes incompatible repairs.
92
93 **Boundary.** Both questions cost one unit and preserve the state. The 3/1 question supports a correct repair after one observation in every case.
94
95 Source: [S] Counterexample 6.3; §5.1 | manuscript pp. 6-8
96
97 ## 10. One tree must satisfy both resource limits
98
99 The synthesis combines complete child policies. Worst-case execution takes a maximum. Stored controller size takes a sum.
100
101 **Interpretation.** This illustrative root has cost 1. Its children cost (2 calls, 3 records) and (4 calls, 7 records). The combined tree costs (5 calls, 11 records).
102
103 **Boundary.** This is an illustration of the recurrence, not a new optimality result. A real child must be valid on the actual post-experiment support, and every possible branch needs a witness.
104
105 Source: [S] Theorem 6.2 | manuscript pp. 6-7
106
107 ## 11. An unknown sensor needs a reference
108
109 A correct procedure for each known model need not give a common procedure when the model itself is unknown.
110
111 **Interpretation.** The report o = x ⊕ θ cannot distinguish (x,θ) = (0,0) from (1,1). They require different repairs. Repeating that same reading adds no information.
112
113 **Boundary.** A reference reports θ at cost 2. An ordinary query costs 1, then repair costs 1. Total work is 4, and the complete binary controller stores 7 records.
114
115 Source: [S] Theorem 7.1; Counterexample 7.2 | manuscript pp. 8-10
116
117 ## 12. Transport the investigation, not only the repair
118
119 A translated answer can be correct while the observation needed to obtain it is unavailable in the target system.
120
121 **Interpretation.** Experiment permissions, report labels, state effects, successful-repair meanings, and costs. Correspondences are supplied in this finite theorem.
122
123 **Boundary.** Copying the two possible repairs into a world with no bit-revealing observation does not transport the policy that chooses between them.
124
125 Source: [S] Theorem 9.1; Counterexample 9.2 | manuscript pp. 12-13
126
127 ## 13. Now improve the procedure that builds the tree
128
129 A checked candidate can end an exhaustive search only when it is valid and attains the relevant global lower bounds.
130
131 **Interpretation.** For n immutable cases with binary unit-cost queries and singleton repairs, a valid tree attaining both 1 + ceil(log₂ n) calls and 2n − 1 records closes the frontier.
132
133 **Boundary.** An invalid scope, missing candidate, or unattained bound sends control to the exact parent. That preliminary work still counts.
134
135 Source: [S] Theorem 11.1; §11.2 | manuscript pp. 14-15
136
137 ## 14. What the shortcut actually reads
138
139 On the sixteen-case model, both compilers return an optimal controller with 5 execution calls and 31 stored records.
140
141 **Interpretation.** The recorded compilation count is 576,128 reads for the parent and 1,728 for the shortcut. Both include completed witness checking.
142
143 **Boundary.** Each also pays 320 common input-validation reads. Selection among all candidates costs 21,124 development reads. Table accesses are not total CPU instructions.
144
145 Source: [S] Proposition 12.1; §13.3 | manuscript pp. 16, 19
146
147 ## 15. A fallback preserves meaning, not free speed
148
149 A preliminary shortcut can fail to prove an optimum and then spend extra work before invoking the same exact parent.
150
151 **Interpretation.** With four cells and only singleton queries, the shortcut falls back. Both return the same optimum. The wrapper uses 472 reads instead of 402.
152
153 **Boundary.** A successful witness, a proved finite-horizon impossibility, and an interrupted search are different results. A timeout cannot certify infeasibility.
154
155 Source: [S] Counterexample 13.1; §16.2 | manuscript pp. 18, 24-25
156
157 ## 16. Sometimes the search state is too coarse
158
159 No longer formula can recover a feature the learner was never given. Here, the missing distinction is remaining branch capacity.
160
161 **Interpretation.** Both contexts have (a,b,m) = (0,3,4). With capacity 2 the root must fail. With capacity 4, a completion with branch sizes (1,3) is possible.
162
163 **Boundary.** Capacity is exposed from a supplied feature registry. This repairs an internal search representation, not a physical sensor model or the definition of depth.
164
165 Source: [S] Proposition 14.1; Counterexample 14.2 | manuscript pp. 20-21
166
167 ## 17. Four proposals, three counterexamples
168
169 The learner composes an arithmetic predicate. Retained counterexamples prevent it from proposing the same rejected behavior again.
170
171 **Interpretation.** The final five-node expression is max(a,b) > C. The reference learner visits 190 of 3,960 candidates and makes four teacher calls.
172
173 **Boundary.** The teacher checks 198 developmental contexts. That certifies this finite agreement, not validity at every larger capacity. Installation needs a separate scope argument.
174
175 Source: [S] Theorem 15.1; §15.2; rule trace | manuscript pp. 21-23
176
177 ## 18. Stop reading when no suffix can rescue the root
178
179 Eight cases must fit into two branches of capacity four. After five equal reports, the outcome is already decided.
180
181 **Interpretation.** Counts cannot decrease. Once one count exceeds C, no unread report can bring that branch back within capacity. The suffix cannot change rejection.
182
183 **Boundary.** Passing the capacity test does not prove that the remaining query library can separate either child. The compiler must still search and verify complete subtrees.
184
185 Source: [S] Proposition 16.1; Theorem 16.3 | manuscript pp. 23-25
186
187 ## 19. A training-perfect rule can prune the answer
188
189 A dangerous shortcut is not made safe by a final answer checker: it may delete the only successful candidate before that checker sees it.
190
191 **Interpretation.** At (a,b,m,C) = (0,5,16,8), the bounded-cap formula rejects. But the unread cases can complete both branches to eight, so capacity remains feasible.
192
193 **Boundary.** Examples help select a formula. A proof with applicable premises authorizes deleting possibilities. The supplied structural gate accepts only the supported rule form.
194
195 Source: [S] Counterexample 16.2 | manuscript pp. 23-24
196
197 ## 20. Fewer model reads can still mean more work
198
199 The same ordered compiler returns the same literal controller. Streaming changes when impossible roots are abandoned.
200
201 **Interpretation.** At 64 cases, streaming avoids 8,287 model rows. The returned controller still costs 7 online calls and 127 stored records.
202
203 **Boundary.** Streaming also adds 14,209 comparisons in the conservative account. At equal prices for reads and comparisons, that isolated modification costs more.
204
205 Source: [S] §18; Theorem 16.3 | manuscript pp. 24-28
206
207 ## 21. Count repair distinctions, not hidden states
208
209 If one repair fixes a pair of cases, a diagnostic policy need not identify which member of the pair occurred.
210
211 **Interpretation.** Put nonnegative weights on cases so every repair-success set has total at most 1. A successful leaf then carries at most 1 unit. Binary depth h supports at most 2ʰ leaves.
212
213 **Boundary.** Adding a universal repair makes the old total weight of 4 violate its success-set constraint. Recheck the weights before using the old pruning rule.
214
215 Source: [S] Propositions 17.1, 22.1; Theorem 22.2 | manuscript pp. 25, 33-35
216
217 ## 22. A useful equation begins as a proposal
218
219 The next acquired object is a task-independent library of equations. Evaluations suggest candidates; derivations decide which can be used.
220
221 **Interpretation.** The finite proposer constructs 1,068 equations from equal probe vectors. The limited proof procedure admits 336 with replayable arithmetic derivations.
222
223 **Boundary.** The remaining 732 may be false, valid only on a narrower scope, or simply beyond this proof search. The primitive arithmetic axioms and checking machinery are supplied.
224
225 Source: [S] §§19-20 | manuscript pp. 29-30
226
227 ## 23. Keep the earliest checked representative
228
229 Equivalent expressions can share a search representative without changing the original program submitted to the teacher.
230
231 **Interpretation.** The exact proposed program trees, retained counterexamples, final result, and exhaustion outcome. Removed later equivalents would already fail a retained counterexample.
232
233 **Boundary.** Pure total arithmetic, sound equations, fixed order, an extensional deterministic teacher, and no forgotten counterexamples. It does not preserve every possible cost-sensitive objective.
234
235 Source: [S] Theorems 21.1-21.2 | manuscript pp. 30-32
236
237 ## 24. Less repetition. The same corrective evidence.
238
239 The quotient changes which redundant candidates are evaluated. It does not change the task teacher or smuggle in the target rule.
240
241 **Interpretation.** Both learners begin the new task with no task-specific counterexamples. They submit the same four programs and receive the same three counterexamples.
242
243 **Boundary.** Equation discovery, proof admission, quotient preparation, dispatch, and storage must be charged separately. The ten targets are finite tasks in one arithmetic language.
244
245 Source: [S] §21.1; Theorem 21.2 | manuscript pp. 30-32
246
247 ## 25. One chain, not multiplied headline gains
248
249 The representation that speeds up rule acquisition feeds a separately certified compiler change. Each link keeps its own comparison.
250
251 **Interpretation.** If the quotient preserves rule acquisition and the acquired rule passes the unchanged compiler gate, the complete chain returns the same rule and controller.
252
253 **Boundary.** Let K be extra preparation. The composite saves work in a common additive unit only if (A − A′) + (D − D′) > K. Do not multiply ratios from different baselines or units.
254
255 Source: [S] Proposition 23.1; §25 | manuscript pp. 35-40
256
257 ## 26. A certificate has a dependency address
258
259 When a premise changes, mark the affected claims and their descendants. Reuse unaffected witnesses only under a complete dependency declaration.
260
261 **Interpretation.** Arithmetic equations and a repair-weight witness belong to different branches. A change in one branch need not invalidate everything.
262
263 **Boundary.** This is not automatic discovery of every dependency in arbitrary code. An omitted premise can leave a registry green while its claim becomes false. Hashes do not repair missing semantics.
264
265 Source: [S] Theorem 24.1; §24.2 | manuscript pp. 37-38
266
267 ## 27. A stronger repair can invalidate an old proof
268
269 The conclusion “this controller is valid” and the conclusion “this change saves work” do not automatically survive together.
270
271 **Interpretation.** For the 32-case paired model, adding a universal repair invalidates the old weight constraints. Rebuilt weights permit a one-step, one-record controller.
272
273 **Boundary.** The earlier assessment referred to another controller and compilation. The replacement needs a new comparison. The unaffected arithmetic equation library remains applicable.
274
275 Source: [S] Counterexample 22.3; §24.3 | manuscript pp. 35, 38-39
276
277 ## 28. The same controller, opposite cost conclusions
278
279 Before claiming improvement, choose a common ledger and state the prices used to combine its event counts.
280
281 **Interpretation.** These are old-minus-new search events on the same 32-case weighted problem. Scope and witness checks are equal and cancel only in this isolated difference.
282
283 **Boundary.** Weight preparation, equation acquisition, installed programs, storage, and revision management do not become free. Event counts alone do not determine processor time or energy.
284
285 Source: [S] Proposition 25.1; Counterexample 25.2 | manuscript pp. 39-40
286
287 ## 29. Do not turn selection evidence into a fresh audit
288
289 What the improver has already inspected belongs to its developmental history, even when the inner solver never saw it.
290
291 **Interpretation.** A proof supports a conditional statement. A checker validates a finite witness. A fresh performance audit supports a comparison on a declared task law.
292
293 **Boundary.** Repeatedly reading a “holdout” exposes it to the outer loop. A correct proof does not establish its physical premises. Finite algorithm counters are not independent neural trials.
294
295 Source: [S] §26; Proposition 26.1 | manuscript pp. 41-42
296
297 ## 30. An audit can stop early without betting in hindsight
298
299 Choose the evidence update before seeing its paired score. Stopping after observing evidence is a different operation.
300
301 **Interpretation.** Freeze the comparison, choose the next bet from past information, observe the next paired score, then update the evidence process.
302
303 **Boundary.** With four fair ± scores, betting only after seeing a positive doubles the evidence on positives. The nominal threshold 4 is crossed on 11 of 16 paths, not at most 1/4.
304
305 Source: [S] Theorem 27.1; Counterexample 27.2 | manuscript pp. 42-43
306
307 ## 31. Safe repetition is not guaranteed progress
308
309 An authorized attempt must be selected before its outcome is known. One policy must meet the continuation requirement on every allowed branch.
310
311 **Interpretation.** Given fully observed lineage states, a finite attempt catalogue, and separately justified progress marks, the recurrence decides whether one policy guarantees k gains within h attempts.
312
313 **Boundary.** If every attempt can reject and return to the same safe state, any finite horizon admits an all-rejection path. Safety can hold without a bounded sure gain.
314
315 Source: [S] Theorem 29.1; Counterexample 29.2 | manuscript pp. 45-46
316
317 ## 32. Positive gains need not accelerate
318
319 Recursion, continued improvement, and increasing productivity per unit resource are separate claims.
320
321 **Interpretation.** The gains 1/2, 1/4, 1/8, … are all positive. Their accumulated total remains below 1 after every finite number of steps.
322
323 **Boundary.** Faster improvement requires a claim about gain divided by complete discovery-and-acceptance cost. More headroom or a successful feedback loop does not establish it.
324
325 Source: [S] Proposition 30.1; §30 | manuscript pp. 46-47
326
327 ## 33. The learned semantic bridge is still a research target
328
329 A commuting square specifies meaningful reuse. It does not discover the representation, learn the operations, or demonstrate their use by a neural system.
330
331 **Interpretation.** If the domain is invariant, every admitted operation commutes with q, and q preserves the required output, the relation extends to every finite operation sequence.
332
333 **Boundary.** Learning encoders, operations, experiment selectors, and proposers is a separate problem. The complete learned Neuralese–OSL bridge is not implemented in this edition.
334
335 Source: [S] §31; Proposition 31.1; §34 | manuscript pp. 48-49, 52-53
336
337 ## 34. Locate the recursive achievement exactly
338
339 The finite chain acquires objects at several levels. It does not erase the supplied foundations of the next outer level.
340
341 **Interpretation.** A generated equation library changes the search representation used to acquire later discovery rules, while preserving the specified evidence and final programs.
342
343 **Boundary.** General intelligence, learned physical semantics, autonomous invention of the primitive proof system, and indefinite improvement of the equation learner remain open.
344
345 Source: [S] First-edition scope; §§23, 34 | manuscript pp. iii, 35-36, 52-53
346
347 ## 35. A small vocabulary for reading the proofs
348
349 Use these distinctions to avoid turning several different achievements into one word such as “intelligence” or “success.”
350
351 **Interpretation.** The repair changes a target. The compiler discovers a policy. The learner can change a compiler rule. The equation library can change the learner’s candidate representation.
352
353 **Boundary.** A witness is checked under a model. A proof has hypotheses. A resource claim has a ledger. A generalization claim needs evidence beyond semantic relabeling.
354
355 Source: [S] Definitions 3.1, 6.1; §§5, 24-25 | manuscript pp. 3, 5-7, 37-40
356
357 ## 36. Return to the source at the right level
358
359 This companion prioritizes mechanisms and counterexamples. The first-edition manuscript is the authority for complete hypotheses and proofs.
360
361 **Interpretation.** All substantive claims are restatements or worked illustrations of [S]. Source statistics are attributed to the supplied first-edition records, not presented as new learning runs.
362
363 **Boundary.** The guide’s examples and numerical transcriptions were checked separately. The full original 336,867-assertion suite was not rerun to make this visual companion.
364
365 Source: [S] Komorebi P., Self-Improving Intelligence, v1.0.0, 8 October 2026.