This page compiles the core formulas and design rules that recur across the SCBE-AETHERMOORE system. It is public on purpose: the geometry, the deterrence logic, the Sacred Tongues, and the ethical framing should be legible together instead of scattered across code, forum posts, and architecture notes.
The formulas below are the public backbone: a deterrence geometry, a safety score, a five-stage decision chain, tongue-aware kernels, a storage KDF, a phase gate, and the oscillator work that stabilized the trust ladder.
d is hyperbolic distance from the safe center in the Poincare ball. R is the base radius, set to 1.5 from the perfect fifth ratio 3/2.
At the origin, the cost is 1. As drift grows, cost rises as an exponential of a square. In the temporal-intent form the cost becomes H_eff(d, R, x) = R^(d^2 * x), where x scales with sustained adversarial intent rather than brief noise.
The score maps the Poincare radius into a public-facing safety scalar. Near the origin it stays close to 1. Near the boundary it collapses toward 0.
Adversarial test batteries confirmed monotonicity, convexity, and oscillation resistance. Known implementation failures include NaN injection, overflow at the boundary, and threshold gaming.
The gate models transmission as a fraction between 0 and 1. Above the allow threshold the state passes cleanly. Between thresholds it attenuates. Below collapse it terminates and logs.
The threshold values currently published are placeholders and should be treated as uncalibrated until empirical validation is complete.
The pipeline takes text into curved space, measures drift from a safe center, scales cost by sustained intent, watches across three time scales, and multiplies five independent checks into a final gate.
Standard Poincare-ball distance. Distances accelerate near the boundary.
Intent begins innocent and grows with sustained problematic behavior. It decays so transient noise does not dominate the score.
The core cost escalation. Distance and sustained intent multiply before the exponential is applied.
Three clocks watch the same state: immediate behavior, session memory, and governance memory. The golden-ratio exponent prevents one clean timescale from erasing another dirty one.
Five locks on one door. If any component collapses to zero, the whole gate closes.
The Sacred Tongues are not decorative lore. They are the semantic channel split the rest of the architecture depends on. The fiction and the technical decomposition are the same structure presented in different registers.
Weighted channel inner product. PSD by construction.
The novel kernel. Cross-tongue interactions are encoded in the PSD matrix S, so the system can represent reinforcing channels instead of only parallel ones.
PSD by Schoenberg's theorem and useful as the stable smooth kernel in the family.
Not guaranteed PSD. This is one of the places where the public page should stay honest: the hyperbolic kernel needs regularization and should not be described as automatically safe by theorem.
| Technical channel | Narrative tongue | Primary function |
|---|---|---|
| Aethyr | Kor'aelin | Control flow and axioms |
| Solum | Avali | I/O and communication |
| Korith | Runethic | Scope and context |
| Thelvori | Cassisivadan | Math and logic |
| Velith | Mal'kythric | Security and crypto |
| Ixal | Nal'kythraelin | Transforms and morphisms |
The phi-phase oscillator was one of the places where the math moved from intuition into proof. It matters because it rescued the trust ladder from runaway growth while preserving the structural shape that made the system useful.
The companion-matrix eigenvalues stay complex with magnitude 1 because the coefficient always remains in the interval [1/phi, phi]. That means the system is bounded across all phase settings: it oscillates, but it does not blow up or decay away.
Each Sacred Tongue reads the same oscillator from a different angular position, spaced by the golden angle. This spreads attention without forcing total isolation.
This is the soft-Huffman style cost function for the tongue lattice. It stays bounded between the Shannon entropy floor and the base width ceiling.
The system is not only geometry. It is a posture. These are the rules that keep the mathematics from being used as a dressed-up excuse for domination.
The architecture is designed to collaborate rather than dominate. The harmonic wall does not erase agency. It makes adversarial drift progressively more expensive until bad choices become impractical.
Trust is continuous, history-sensitive, and recoverable. Coherence moves quickly, base trust moves slowly, and intervention should be graduated instead of absolute.
Recovery energy should be proportional to real impact. Small failures do not justify maximum-force responses if the wider obligation network can absorb them.
The interesting structure often lives in mismatches, deltas, and overlap failures. The architecture keeps returning to that idea: information is often in the conflict, not only in the consensus.
The book is not off-topic. It is the memory surface for the same technical vocabulary. History, fairy tales, proofs, and governance all teach through durable narrative structure.
This page is stronger when it keeps the unresolved work in view. These are the main places where the system still needs calibration, proof completion, or implementation hardening.