Capstone document connecting the session's conceptual framework to
all measured findings.
One-sentence statement: 'Computation in the space of invariants,
rather than in any specific representation.'
The matter→light move: nonlinear constraints (matter) → spectral
decomposition (light) → invariant extraction (truth).
The observerless observer = invariant geometry: computation defined
without privileging any representation. Results extracted by
choosing invariants that survive ALL representations. The Φ-metric
defines the geometry of observability.
Three 'endian' regimes = three projections of the same invariant
geometry:
- Big-endian: global invariants (QR/eigenvalues)
- Little-endian: local rules (KV cache/PPM)
- Water/block: continuous dynamics (golden spiral/SLOS)
Key limitation: symmetry group balance.
- Too much symmetry → no computation (cospectral graphs)
- Too little symmetry → no compression (text at 3.088 b/B)
Conservation law = invariant preservation:
total invariant information ≥ K(data)
Every session measurement maps to invariant language:
- Octagon (4/4) = Φ-metric converts nonlinear → spectral invariant
- Conservation (8 branches) = invariant preservation bound
- CRT (O(1)) = coprime invariant reconstruction
- p-adic = prime invariant decomposition
- Cospectral failure = same invariants, different objects
- Etesami-Haemers = invariant embedding at O(n²)
- GW SNR = signal invariant, noise representation-dependent
- Reaction primes = prime factorization = invariant decomposition
Pipeline = invariant extraction engine:
DNA (matter) → matrix (operator) → spectrum (light) → invariants (truth)
