Research-Stack/6-Documentation/docs/specs/UNIVERSE_MODEL_ORBIT_ZOOM_PROTOCOL.md

Universe Model Orbit-Zoom Protocol

Status: DRAFT_RECEIPT_PROTOCOL

Claim boundary: this is a navigation and receipt protocol for mapping a local problem into the nearest mathematical continent. It does not claim that the universe model uniquely proves the target math. It only defines how to zoom from coarse structure to checkable local laws without losing the distinction between assigned constants and derived consequences.

Orbit View

Use the unified equation as the orbital map:

Omega(n, theta, alpha) = Psi [ B(theta) tensor C(n, alpha) ] plus Delta(n, theta, alpha)

At orbit height, do not solve the problem. Classify it.

Signal seen from orbit	Likely continent	First local tool
Symmetric basis, no residual	fixed point / equilibrium	invariant check
Basis mismatch	torsional stress / gradient flow	beta-step correction
Context changes faster than basis	dynamical systems	velocity / damping law
Residual grows	instability / turbulence / FAMM	recovery gate
Residual shrinks	Lyapunov descent	energy monotonicity witness
Repeated structures preserve shape	algebra / topology	isomorphism witness
Many small states fold into receipts	Merkle/MMR/AMMR	replay proof

Zoom Ladder

Every descent layer must answer one question before the next zoom is trusted.

L0 Orbit:      What continent of math is this?
L1 Region:     Which local law family applies?
L2 State:      What variables are assigned?
L3 Derivation: What follows from the state?
L4 Receipt:    What can be replayed or refuted?
L5 Gate:       ADMIT, HOLD, or QUARANTINE

The most important distinction is:

assigned value != derived value

Assigned values are initial conditions, coefficients, capacities, or declared measurement scales. Derived values are consequences of the local law.

Torsional Fluid Baseline

Current repo anchors:

2-Search-Space/PIST/TorsionalPIST.lean
2-Search-Space/simulations/Newtonian-Superfluid-Simulation/custom_stack/superfluid_semantic_adapter.py

Assigned initial values:

q1 = 1
q2 = 1
q3 = 1
eta = 1.0 Q16.16 = 0x00010000
energy = 0
velocity = 0

Derived local values:

target = 0.5 * (q1 + q2) = 1
error = target - q3 = 0
attractForce = q2 - q1 = 0
correctionTorque = eta * error = 0
dimensionalTorque = eta * attractForce = 0
nextEnergy = norm(q1 - q2) + norm(error) = 0

So the correct baseline statement is:

E0 = 0        assigned
v0 = 0        assigned
eta0 = 1      assigned
tau0 = 0      derived from symmetry
DeltaE0 = 0   derived from the beta-step law

Continent Map For The Baseline

The torsional-fluid baseline lands in:

fixed point / equilibrium
+ zero-torque manifold
+ Lyapunov candidate surface
+ dynamical-systems stability check

It does not land in turbulence, shock, or FAMM recovery until symmetry breaks.

Pre-Fuzz Resolution

Before fuzz, the stack has two relevant resolution floors.

The arithmetic floor is the fixed-point lattice:

Q16.16 epsilon = 1 raw unit = 1 / 65536 ≈ 0.0000152587890625
Q16.16 one     = 0x00010000 = 65536 raw units

That is the smallest representable Q16.16 perturbation. Any claimed change smaller than one raw unit is below the deterministic lattice and must be treated as fuzz, interpolation, or an external measurement prior.

The torsional convergence floor currently used by TorsionalPIST_rgFlow is:

energy threshold = 0x00000100 = 256 raw units
                 = 256 / 65536
                 = 1 / 256
                 ≈ 0.00390625

So the pre-fuzz resolution is:

numeric resolution:       1 / 65536
torsional settle gate:    1 / 256

Interpretation:

0                         exact symmetric baseline
1 raw unit                smallest deterministic Q16.16 nudge
256 raw units             current torsional settle / no-more-zoom gate
anything below 1 raw unit fuzz-only
anything between 1 and 255 raw units deterministic but below current settle gate
anything at/above 256 raw units visible to the current torsional RG gate

This keeps fuzz honest. Fuzz is not allowed to invent a new baseline; it can only probe below, around, or above a declared resolution gate.

First Break Conditions

Use these as the first zoom-in tests:

Condition	Meaning	Next math continent
q1 != q2	basis split	torsional stress
q3 != 0.5 * (q1 + q2)	product/residual mismatch	beta-step correction
velocity != 0	state is moving	dynamics / damping
energy > 0	stored deformation exists	Lyapunov descent or instability
energy grows over steps	correction is not settling	FAMM / turbulence recovery
receipt missing	cannot replay claim	HOLD

Receipt Shape

Minimum orbit-zoom receipt:

{
  "protocol": "universe_model_orbit_zoom_v0",
  "orbit_class": "fixed_point_equilibrium",
  "local_law": "TorsionalPIST_torsionalBetaStep",
  "assigned": {
    "q1": "Quaternion.one",
    "q2": "Quaternion.one",
    "q3": "Quaternion.one",
    "eta_q16": "0x00010000",
    "energy_q16": "0",
    "velocity": "zero"
  },
  "derived": {
    "error": "0",
    "attractForce": "0",
    "correctionTorque": "0",
    "dimensionalTorque": "0",
    "nextEnergy": "0"
  },
  "decision": "ADMIT_BASELINE"
}

Working Rule

The universe model is successful at orbit height if it can say:

this belongs to this continent of math,
these are the assigned constants,
these values are derived,
these receipts are missing,
and this is the next local law to test.

It is not successful if it skips directly from metaphor to claimed theorem.