Research-Stack/4-Infrastructure/NoDupeLabs/research-stack/gradient-models/doppler_gradient_integration_v0.md

Doppler Gradient Integration v0

Status

status: HOLD
source_type: visual_external_reference
source_uri: https://cf.v.redd.it/xv9gi3fv7rxg1/CMAF_1080.m3u8
authority_scope: visual_motif_to_model_requirement
proof_status: not_evidence
route_signature: gradient/doppler-shift/torsion/v0

Core observation

The linked reference should be treated as a geometry cue, not evidence. The usable requirement is:

Gradient models need explicit blue-shift / red-shift dynamics.

The visual-math translation is:

descending into a narrowing basin → local frequency increases → blue shift
escaping / relaxing outward → local frequency decreases → red shift
collision / phase boundary crossing → flash event
persistent angular path distortion → torsion accumulation

Why this belongs in the gradient models

Existing Research Stack material already has the right scaffold:

• SSMS_nD.lean defines variable-dimension manifolds and selects dimension by potential minimization, so the system already treats dimension choice as an energy descent process.
• SSMS.lean includes scalar nodes, Q16.16 hot-path arithmetic, recurrent state, ternary dot products, Betti Swoosh Hamiltonian, and ACI preservation.
• The Ricci-flow/turbulence notes define turbulence as unresolved metric/equivalence stress and identify Ricci flow as a metric-update engine.
• The HyperFabric route defines anisotropic torsional gradient flow, phase fields, locking, and stored torsional stress.
• The pulsar marble-jar route adds multiscale clocks, angular momentum conservation, glitch flashes, Doppler/beaming trace, and accessible phase-volume contraction.

This note connects those routes into one gradient requirement:

Every gradient step should track not only position and energy,
but also local frequency shift relative to the current basin metric.

Minimal equations

1. Loss-basin potential

E(x,t) = potential / free energy / routing cost

Descent still follows the existing rule:

x_{t+1} = x_t - η ∇E(x_t)

But the step is now instrumented by a shift factor.

2. Doppler-like shift proxy

For a gradient trajectory with velocity v_t along a local view direction n_t:

β_t = <v_t, n_t> / c_eff

shift_t = sqrt((1 + β_t) / (1 - β_t))

Interpretation:

shift_t > 1  → blue-shifted descent / compression / impact approach
shift_t < 1  → red-shifted retreat / relaxation / diffusion away
shift_t ≈ 1  → neutral drift

c_eff is not physical light speed unless the model is explicitly physical. In Research Stack it is an effective propagation limit or route-speed bound.

3. Gravitational-potential approximation

For basin-depth-only models:

Δf / f ≈ -ΔΦ / c_eff^2

Where:

Φ = basin potential
ΔΦ < 0 while falling inward → blue shift
ΔΦ > 0 while climbing outward → red shift

4. Torsion-coupled shift

shift*_t = shift_t · (1 + κ τ_t)

Where:

τ_t = torsion proxy / shell mismatch / angular route stress
κ   = torsion coupling weight

This keeps the old chandelier/pulsar insight:

narrowing basin raises torsion;
raised torsion sharpens the frequency shift;
frequency shift marks phase-boundary pressure.

5. Flash / phase boundary detector

A flash event occurs when the model crosses a combined shift/torsion threshold:

flash_t = (shift*_t > θ_blue and τ_t > θ_torsion)
       or (abs(Δphase_t) > θ_phase)
       or (route_changes_basin_t = true)

This should be logged as a phase event, not promoted to truth.

Required trace fields

Every gradient simulation that uses this route should emit:

time
state_id
basin_id
energy
energy_delta
gradient_norm
velocity_norm
torsion_proxy
accessible_phase_volume
beta_eff
doppler_shift
red_blue_label
flash_event
phase_boundary_id
route_weight_before
route_weight_after

Forest-map integration

visual cue
→ geometry requirement
→ Doppler gradient trace
→ torsion/phase flash detector
→ FAMM memory update
→ future routing bias

Authority boundary

TV / video imagery     → intuition only
Doppler equations      → borrowed mathematical structure
model trace            → engineering evidence
Lean theorem           → proof only if assumptions compile
real physical claim    → requires independent data

Outcome

Add Doppler-aware gradient instrumentation.
Do not treat the linked visual as proof.
Keep the route HOLD until code and validator exist.