# Claim ledger

## Proved in the manuscript, within explicit mathematical assumptions

1. The all-future operational quotient is the coarsest action-compatible quotient
   preserving the declared observations. This is established behavioral-equivalence
   mathematics, not claimed as a new foundational theorem.
2. The finite linear quotient is generated by the action closure of the query row space.
3. Current-query recoverability does not imply mixed-composition recoverability.
4. The additional ancestral tether has minimal length equal to the difference between
   parent closure rank and the rank of the combined child views, in field symbols.
5. Future-query recovery is exact iff the surviving memory nullspace lies in the
   operational quotient nullspace.
6. Minimum additional unrestricted scalar acquisitions equal the relevant rank gap.
7. Recursive lossless reconstruction composes by induction when every internal
   co-basis tether and required child information survives.
8. Quotient erasure recovery needs at least r+e field symbols for r unconstrained
   quotient coordinates and e arbitrary erasures; a classical polynomial code attains it.
9. Individually valued branch selection can miss unbounded mixed-operation synergy.
10. Arbitrary future linear operations rule out universal lossless state compression.

Proofs are human-readable and internally checked. They are not Lean/Coq-certified
and have not been independently peer reviewed. Many are standard facts or direct
new applications of those facts, rather than novel mathematics.

## Executed

77 automated tests; five seeded experiment runs; exact learned-family composition;
recursive fracture/reunification; identifiable recall; erasure and bounded-radius
small-code checks; frozen execution; chart gauge checks; counterexample-based hole
certificates; an intentionally non-submodular scheduler example.

## Not established

A trained self-improving transformer; general intelligence multiplication;
superiority over optimized equal-resource baselines; autonomous discovery of the
algebraic family; unrestricted world-model reconstruction; novel causal discovery
from observation alone; the novelty of the full architecture as a distinct RSI class.

## Explicit baseline results

Conventional pooled group identification matches 10,000/10,000 outputs in the learned
pipeline. A conventional observable-quotient compiler matches the frozen tests.
An optimized classical worklist can match the proposed closure's row-product count.
Classical polynomial erasure coding matches the coded-memory tests.
The scheduler example uses equal live-operator budgets, not equal total selection
compute. The conventional exhaustive pair baseline obtains the same best bundle.