[amaybaum]

This PR narrows book/ch18-beyond.md:114 (§18.4) and its FULL mirror, as the owner decided on 2026-10-26. It branches from main at 52e2db40; the head is e871c5d0.

Merge is not authorized. It needs green CI and the owner's approval at an exact SHA. The independent review passed (see below).

Why

ch18-beyond.md:114 said that the randomness "is unpredictable by any embedded observer regardless of its origin".

OI-PE-1 / PE-01 (#923) refutes that universal form with a finite witness:

• Generator: a self-clocked shift-register generator, G_clk, n = 5.
• Observer: an embedded active observer with two bits of memory.
• Result: advantages 1/8, 5/32, 5/32 and 1/8 over the window K′ ∈ [4, 7], at a footprint of 6 = n+1.

Both the governing verdict and the signed sensitivity verdict are COUNTEREXAMPLE.

The change

Old

New

"The randomness is unpredictable by any embedded observer regardless of its origin, so the cryptographic properties depend on unpredictability rather than on ontic vs epistemic status."

"What these applications rely on is unpredictability to the parties who can observe or act on the source, not the ontic or epistemic status of its randomness. Determinism does not by itself guarantee that unpredictability: an embedded observer whose actions reach the hidden state driving a deterministic source can, for some sources, predict its output better than chance. Whether a source stays unpredictable to observers of bounded memory, whether they act on it or only read it, depends on the source, and the framework does not establish it for the hidden sector of the physical realization."

What each sentence does:

• The paragraph's point is kept: the applications depend on unpredictability, not on the ontic or epistemic status of the randomness.
• The broad claim is removed and PE-01's counterexample is stated as an existence claim.
  • It carries no resource bound, no family-wide property and no claim about C2–C4, so it does not contradict PE-01's scope limits: K1 only, 31 table bits uncharged, C2–C4 unchecked, one cell.
  • "Whose actions reach the hidden state" matches PE-01's observer, which reaches the hidden sector only through the dynamics.
• The open question is marked, not asserted.
  • It is open for observers of bounded memory, whether they act on the source or only read it, for the physical realization's hidden sector.
  • Within its own bounded scope, PE-01 also found read-only predictors that fail only the footprint condition. So it does not separate acting from reading in general.

Kept as written:

• the paragraph's heading and conclusion;
• :108, "The randomness is unavoidable for any embedded observer". A better-than-chance advantage is not full prediction, so PE-01 does not bear on it.

Corpus sweep: no paraphrase of the old universal claim remains. appendix-c-objections.md:150 is consistent with the new text.

Files

• book/ch18-beyond.md:114 and its mirror book/The-Incompleteness-of-Observation-FULL.md:4934.
• FULL .tex/.pdf, regenerated with build.sh:
  • the word diff holds only this paragraph and the hash stamp;
  • the page count is unchanged at 553;
  • pdftotext finds the new text and none of the old.

Independent review

The review of 4d8ff648 returned ACCEPT WITH NITS, with no required changes.

Nit	Disposition
N1, recommended	Applied at e871c5d0. The third sentence no longer contrasts acting with reading.
N2, optional: "parties who can observe or act on the source" read literally includes full control	Kept. The second sentence already limits the claim to "for some sources".
N3, optional: "no practical consequences" rests on the proposal-level 10⁻³² estimate of §18.2	Not in this PR's scope. Noted for a later pass.
N4: "physical realization" is also used at :112	Kept. Both uses refer to the framework's physical realization of the substratum.
N5: commit messages	Commit 4d8ff648 says "§18.x"; it should be §18.4. It also calls the read-only bounded-memory question "untested", which holds only for the physical realization. Pushed commits are not rewritten; this note records the correction.

Checks

These ran locally on e871c5d0: architecture_check (259 invariants, 0 violations), mirror_check, claims_check, voice_check and duplicate_check.

Interaction with #932

#932 (F29) also regenerates FULL .tex/.pdf. Whichever PR lands second merges main and rebuilds FULL with build.sh; generated files are never merged by hand.

🤖 Generated with Claude Code

https://claude.ai/code/session_013T6pfKuv5mi3MXtKjH2tZb