9 One continuous chain, with no hidden promotion
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The sensor story can now be followed without changing the meaning of a record midway through the argument.
Begin with eight candidate worlds \((b,s,n)\). The agent's initial display \(y\) determines its two-state predictive class under flips, but not the physical target bit. The first chapter proves both claims. The second gives the operator on the retained class and the coordinate map that becomes usable after calibration. Neither requires the nuisance bit.
When display and calibration observations arrive, candidate sets are filtered. The third chapter proves why the joint association must be retained, and why sixteen occupancy states suffice for the exact partition-evidence contract. Under a separately declared noisy calibration, four probability masses replace the occupancy bits. The same numerical posterior cannot be inferred from separate marginals. The enlarged chapter now requires a joint report/next-state law, not only correct separate marginals. Its finite refinement makes the required distinctions explicit, and its history bound states the separate price of conditioning on a rare report.
The fourth chapter places that posterior and any response approximation under one loss function. It also specifies what a recipient can decode from a message and its prior record. The fifth asks whether the sender can acquire the missing observation and transmit a successful artifact within a single online and stored-controller budget. The complete tree is counted even if an execution visits only one path. A separate noisy-calibration calculation then uses the exact same retained belief to select a finite expected-cost inquiry. Uniform whole-history error supports a quantitative policy comparison, but not an automatic hard-budget or zero-risk guarantee.
The sixth chapter then changes the discovery procedure rather than the hidden world. Checked equations can remove equivalent candidates while preserving every teacher proposal and counterexample. A separately justified capacity rule can stop reading an impossible diagnostic root. Neither step invents the primitive grammar, the teacher, or the theorem used to authorize pruning.
The seventh chapter binds those uses to their premises. Adding a universal repair changes the required diagnostic distinctions. The old lower bound becomes inapplicable; arithmetic identities need not. A fresh cost comparison may find a saving or a loss. The eighth chapter finally combines different participants' records and asks what actions they are entitled to perform under their declared institutional state. Safe indefinite operation and preservation of an authorized ending are checked separately.
9.1 A worked end-to-end record
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Take the actual illustrative world \((b,s,n)=(0,1,1)\). The complete protocol begins with all eight worlds possible:
| Event | Remaining worlds | What is justified |
|---|---|---|
| Before observation | All eight | No physical target identified. |
| Display \(y=1\) | Four worlds | Predict every later display flip. |
| Calibration \(s=1\) | Two worlds differing only in \(n\) | Physical target \(b=0\). |
| Send \(y\) to a recipient holding \(s\) | Same two worlds | Recipient computes \(b=0\) through its fixed XOR decoder. |
| Commit the authorized target action | As declared by its effect | One action justified across the current support. |
| Record the fulfilled obligation | Includes the action's receipt | Continuation or ending can refer to the actual completed act. |
The witness does not claim to have discovered its sensor semantics. Its exact checking confirms the stated scenario. Another physical process requires its own evidence. A failed receipt, an untrusted calibration, or an altered action effect changes the guarantee rather than being averaged away as a small numerical error.
9.2 Why the core is narrower than the archive
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This book does not append the old Neuralese experimental history, proposed PRISM architecture, full SRIC lineage, or every formal guide. Their presence would make the reader repeatedly switch between a proved conditional statement, a proposed mechanism, a historical execution, and an implementation plan. Those are useful source objects, but they are not one continuous proof.
Selected source results are restated and proved where they carry the argument. Selected stochastic-value arguments from AVOC enter through complete prose proofs and explicitly matched finite models. Their selected formal counterparts are identified in the companion; this does not import AVOC's complete formal development or the specialist Certified Bayesian Inference construction. Source pedigree alone supplies no blanket assurance for the wider source corpus.
Nor is a source excluded merely because it contains open questions. Its proved results can be considered individually. A claim enters when its exact form, dependencies, and evidence have been reviewed at the level promised for this edition. This is a stricter and more useful rule than treating every page of a final-named document as equally checked.
9.3 The result of the compilation
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The core establishes a connected conditional account of accessible state, meaningful operations, corrective memory, usable explanations, bounded investigations, justified search changes, and maintained obligations. The arguments share several elementary constructions, but each use preserves its distinct type and hypotheses.
No theorem here turns a semantic interface into a trained neural model, a finite investigation into general intelligence, a shared record into a collective subject, or an invariant into legitimate external authority. The mathematical contribution is the explicit chain and the failures that break it. Those failures can be investigated without changing the standard of proof or requiring a large implementation campaign.