Representations, generation and executable state

This reading path belongs to Phi9 / information and representation. It asks what an executable state preserves, what a generator supplies, and what a completed test can actually establish. The seed essay is an explanatory foundations piece, not a new empirical result.

Begin with the mechanism

What a seed can—and cannot—remember follows a declared seed through initialization, state updates, a latent code and readout. Five inline numbered references lead to the bibliography. Its three diagrams distinguish generation, lookup and learning. Foundations essay · working editorial edition · 3 October 2026.

Three different reading editions

What a rule actually says

Reader edition · 3 October 2026 · 10 pages. A short illustrated working companion (authorship unassigned in the retained edition): definitions before claims, a constructed projection, and a completed non-Gaussian target study. It is not the full technical archive or independent replication.

Read the illustrated HTML · Download the 10-page PDF

The world a model must keep

Learner edition 2 · 3 October 2026 · 67 pages · 14 chapters. Shubham Attri’s guided book includes traced examples, worked exercises and redrawn diagrams. All fourteen chapter titles were revised; the chapter order was reviewed and retained. Older technical passages and experiment results remain where needed. This assisted pedagogical rewrite is not fourteen new studies.

Download the 67-page learner edition. Earlier working and live editions remain separate; this file does not overwrite the earlier 54-page working book.

Composition is not reconstruction

Evidence-synthesis edition 3 · 3 October 2026 · 22 pages. A technical working manuscript, not a peer-reviewed or submitted paper. Its authorship remains unassigned. The separately labelled public working copy adapts only the pre-release status line and withholds private record identifiers; the scientific findings and earlier original remain unchanged. Website availability is not peer review or independent replication.

Download the 22-page public working copy.

This synthesis separates executable consistency, learning inside a supplied family, predictive sufficiency and reconstruction. Its tables retain strong comparators, information-access differences and negative results. The reader edition and full learner book are explanatory companions, not replacements for that technical record.

What the evidence supports—and where it stops

Constructed mathematics. Exact represented closure is a task-relative condition under specified actions, not a guarantee of reconstruction, learnability or an arbitrary new architecture. The supplied affine family and coordinates must remain visible.

Bounded checking. Sixteen exact Lean checks are bounded theorem checks. They are not validation of Bend floating-point behavior or an independent implementation; a recorded Bend verdict mismatch and arithmetic-order counterexample remain limitations.

Limited empirical findings. On NASA’s C-MAPSS FD001 simulator, one fixed 60/20/20 engine split gave compact four-channel engine-mean MSE 0.0131821, versus 0.0114382 for full ridge: 15.25% higher. The frozen narrow noninferiority test failed. Compact coefficients are not restricted sensor acquisition; all channels were loaded offline, and no physical sensing saving was measured. These are retained synthesis results, not tests rerun for this website release.

Failures stay visible. The earlier covariance gate failed: correlation −0.070475848, with fixed absolute bound 0.06. A 32-seed result about median paired contrasts does not establish population-mean benefit, rare-tail robustness or independent replication. A first-order information account is compatible with an endpoint advantage; it does not prove sole causation or complete mediation.

For a first accessible evidence trace, see the reader edition, pages 4–8. See the technical synthesis, page 3 for the covariance failure, pages 9–10 for FD001 methods/results, and pages 11–13 for cross-study limitations. No raw evidence ZIP, private record identifier or internal session log is released with this reading path.