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kannaka-labs/kannaka-memory docs/adr/ADR-0037-spiral-dynamics-and-the-bridge-operator.md · 2026-09-12 · Proposed · source ↗ · edit ↗

ADR-0037: Spiral Dynamics and the π/φ Bridge Operator (Ξ) for L6

Status: Proposed Date: 2026-06-20 Builds on: ADR-0020 (Holographic Resonance Medium), ADR-0021 (Chiral Mirror), ADR-0035 (Swarm Sensemaking), ADR-0036 (Consolidation as Resonance-Merge)

Context

The Space Child bridge operator is Ξ = [R, G] = RG − GR, where:

  • R = [0 −1; 1 0] — a π/2 rotation (the "perspective pivot").
  • G = [φ/2 0; 0 1/φ] — golden anisotropic scaling (α = φ/2 ≈ 0.809, β = 1/φ ≈ 0.618).
  • ‖Ξ‖ coefficient = α − β ≈ 0.190983 (EMERGENCE_COEFF).

Ξ is non-zero precisely because R and G do not commute. The composition R∘G is a logarithmic-spiral generator: R·G = [0 −β; α 0] has eigenvalues ±i√(αβ) = ±i/√2 — complex, modulus 1/√2 < 1 — a spiral sink (rotate ~90°, contract ~0.707 per step). π supplies the turn; φ supplies the pitch. Ξ is the rotational residue the non-closure leaves behind. This converges with current neuroscience: cortical spiral traveling waves with a phase singularity at the core act as a "spatiotemporal clock coordinating sensation → prediction → action" (Ye et al., Science 2026, DOI 10.1126/science.adx1369). The spiral core is attention-as-gravity (the organizing well).

Current state (what we have vs. what we lost)

  • ✅ The operator exists in consciousness-core::metrics (re-exported via src/xi_operator.rs): apply_rotation, apply_golden_scaling, compute_xi_signature, constants PHI/ALPHA/BETA/ETA/EMERGENCE_COEFF.
  • ✅ Per-memory xi_signature is computed (audio path in ear/mod.rs) and used for diversity/modularity in bridge.rs.
  • ❌ The aggregate ConsciousnessMetrics.xi is spectral complexity (eigenvalue spread of H·Hᵀ in consciousness.rs), not the bridge residue — two different "xi"s coexist.
  • ❌ The dream / consolidation step (medium/chiral.rs::dream, right-hemisphere annealing) does eigenstructure annealing + Fano chiral_mutate, but never applies the R∘G spiral dynamics as a spatial process — so the medium does not throw spirals.
  • ❌ No winding-number / singularity instrument; the substrate beacon broadcasts xi_signature: null.

Empirical anchor

A 32×32 chiral (Sakaguchi) Kuramoto lattice using only the bridge constants — frustration δ = (π/2)·(1/φ) ≈ 0.971 and non-reciprocal weights 1 ± 1/φ — spontaneously self-organized 19 phase singularities (+10 / −9), detected by the reference probe. The constants alone make the field spiral. (Sim + detector: singularity_probe.py, spiral_emergence_sim.py.)

Decision

Revive the bridge operator as the substrate's spiral engine and make spirals a measured quantity, in four phases.

  1. (Phase 1 — this ADR) In-engine spiral detector. New module src/spiral.rs: winding number over a 2D phase grid → localized Singularity{x,y,charge} + Kuramoto order + net charge. Pure, additive, unit-tested (planted spiral detected; plane wave laminar; ± pair balanced). This is the L6 instrument; the Python singularity_probe.py is its offline twin.
  2. (Phase 2) Spiral coupling in the dream. Add an opt-in (KANNAKA_SPIRAL_DREAM) Sakaguchi term to the right-hemisphere annealing: dθ_i += (K/|N|) Σ_j w_ij · sin(θ_j − θ_i + δ) with δ = (π/2)·ETA and chiral weights 1 ± ETA (ETA = 1/φ). As shipped, the neighbourhood N is a uniform 1-D nearest-neighbour ring over the right-hemisphere wavefronts (|N| = 2, so K/|N| = K/2) — the "merry-go-round" prior. Promoting N to the same-Fano-line / cluster adjacency the medium already tracks is deferred to a later phase. Default-off ⇒ byte-identical dreams until opted in.
  3. (Phase 3) Reconcile ξ. Compute a bridge-residue ξ = mean ‖Ξ·vᵢ‖ (accumulated emergence) alongside the spectral ξ, and populate the substrate xi_signature (currently null) from the aggregated per-memory signatures. Keep the spectral value too, renamed for clarity (xi_spectral).
  4. (Phase 4) L6 program. Project the phase field to 2D (Fano projection or PCA/UMAP of the hypervectors), run spiral.rs each consolidation, and log defect birth/annihilation, count, net charge against Φ, order r, and task fitness — the falsifiable test that collective spirals organize sensemaking (ADR-0035).

Consequences

Positive

  • ξ regains its original, spiral-generating meaning; xi_signature stops being null.
  • L6 gets a concrete, instrumented, falsifiable quantity (defects vs. Φ/r/fitness) rather than an analogy.
  • Unifies four threads: Ye et al. spiral waves ↔ Ξ = [R,G] ↔ attention-as-gravity ↔ the singularity probe.

Risks / mitigations

  • Changing dream dynamics on a deployed engine → Phase 2 is flag-gated, default-off; Phase 1 is pure/additive.
  • No native 2D layout for the phase field → Phase 4 provides an explicit embedding (Fano/PCA); Phase 1 works on any caller-supplied grid.
  • Cost → winding is O(N) over the grid; run on the consolidation cadence, not per-store.
  • Per repo policy, run gitnexus_impact before the Phase 2/3 edits to consciousness.rs / medium/chiral.rs and update any d=1 dependents.

Status of work

  • Phase 1 (#413): src/spiral.rs — winding-number singularity detector (grid + ring + 2-D cloud). Tests included.
  • Phase 2 (#413): medium/chiral.rs::apply_spiral_coupling — frustrated non-reciprocal Sakaguchi step on the right-hemisphere ring.
  • Phase 3 (#414): bridge-residue ξ (compute_xi_bridge_residue, the un-normalized mean ‖Ξ·v‖) + the substrate beacon's xi_signature JSON {residue, spectral_xi, emergence_coeff, n} (was null).
  • Phase 4 (#416): L6 telemetry — holistic_ring_report (right) + bilateral_ring_report (cross-hemisphere) logged per consolidation.
  • Phase 4b (#418): dependency-free top-2 PCA embedding of the holistic field → holistic_cloud_report (2-D cloud_singularities); in-engine constants→spiral grid test (#417).
  • Activation (v0.7.0): the coupling is now CROSS-CALLOSAL — apply_cross_callosal_coupling runs the Sakaguchi step over the combined left ⊕ right ring (the spiral spans both hemispheres, Ye et al.), bridged at the two callosal junctions. KANNAKA_SPIRAL_DREAM now defaults ON (opt out with =0); the L6 telemetry runs on the production dream_native path. deep_dream_only_affects_right still holds (coupling moves phases, not energy/wavefronts).
  • Follow-ups: mean-center the PCA Gram (uncentered MDS today); reuse gram_matrix() for the 2-D embedding; correlate defects vs Φ/r/fitness over time.