5.4 KiB
Non-Compressed Goxel Geometry Doctrine
Status: HOLD / conceptual geometry doctrine Authority: workbench definition; not formal proof Related:
docs/gcl/RunawayDigitalCellDivisionDoctrine.mddocs/gcl/HolyDiverGoxelMOIMBridge.mddocs/gcl/AVMFixedPointComplianceRemediation.mddocs/gcl/FederatedNanokernelSwarmDoctrine.md
Purpose
This document pins the corrected definition of a Goxel.
A Goxel is not a voxel with a different shape.
A Goxel is a non-compressed shape potential.
Core definition
Goxel = non-compressed geometry seed that can assume any admissible geometry before compression.
Equivalently:
A Goxel is a shape-agnostic pre-geometric unit.
It is not yet forced into voxel, hoxel, mesh, cube, shell, lattice, or fixed manifold form.
Negative definition
A Goxel is not:
a cube
a voxel
a hoxel
a mesh cell
a fixed 3D object
a preselected shape
a compressed lattice element
A Goxel becomes those things only after compression, locking, or projection.
Positive definition
A Goxel is:
non-compressed
shape-agnostic
pre-geometric
admissibility-seeking
compression-ready
boundary-undefined until constrained
Lifecycle
Goxel
-> assumes temporary admissible geometry
-> handles exchange / deformation / carrier flow
-> compresses into Voxel, Hoxel, lattice, shell, mesh, or manifold state
-> passes or fails ACI / Warden / Judge validation
Compression hierarchy
| Unit | Compression state | Geometric constraint | Role |
|---|---|---|---|
| Goxel | Non-compressed | Any admissible geometry | shape potential / buffer / seed |
| Voxel | Compressed | fixed 3D volume sample | local structural cell |
| Hoxel | Hyper-compressed | 4D or higher transition cell | temporal / manifold locking unit |
| Lattice | Regularized compression | repeated local rule | carrier / memory / routing medium |
| Manifold patch | validated compression | coordinate-compatible local geometry | admissible global surface |
Shock interpretation
Under shock, compression can reverse.
Voxel or Hoxel under shock
-> unlocks
-> decompresses into Goxel cloud
-> temporarily loses fixed boundary
-> maximizes exchange capacity
-> searches for admissible re-compression
This means the shock is not merely moving energy.
It is converting fixed geometry back into shape potential.
Immediate exchange interpretation
A non-compressed Goxel has high exchange capacity because it has not yet committed to one boundary.
uncompressed Goxel
-> high carrier flow
-> high geometry freedom
-> low rigidity
-> high risk of identity loss
Compressed state:
Voxel / Hoxel
-> lower geometry freedom
-> lower exchange capacity
-> higher rigidity
-> higher identity persistence
Partial compression
Partial compression is the transition state where a Goxel has started to become a constrained geometry but has not yet passed full validation.
Goxel cloud
-> partial compression
-> local boundary appears
-> carrier flow decreases
-> rigidity rises
-> ACI becomes passable
Partial compression must not be treated as full validation.
partial compression != ACI passed
partial compression = ACI becoming passable without losing bounded identity
Erdős / Ramsey reading
In an Erdős or Ramsey-style interpretation, a Goxel resembles a point in general position before a forced configuration appears.
Goxel cloud
-> unconstrained point-like seeds
-> density or shock pressure increases
-> admissible / unavoidable configurations emerge
-> compression selects one geometry
The compressed geometry is analogous to a forced pattern or convex configuration emerging from a sufficiently rich set.
Allowed claim:
Goxels can be modeled as pre-geometric shape potentials whose compression selects an admissible geometry from a larger possibility space.
Blocked claim:
Goxels literally have infinite physical degrees of freedom.
Implementation must use finite bounded representations.
Implementation rule
A practical Goxel implementation should not store arbitrary infinite shape.
It should store a bounded parameterization of shape potential:
energy
extent bound
admissible shape family
carrier flow capacity
compression state
boundary confidence
ACI residual
binding score
Candidate schema:
type GoxelState = {
id: string;
compression_state:
| "seed"
| "non_compressed"
| "partial_compression"
| "voxel_locked"
| "hoxel_validated"
| "collapsed"
| "repelled"
| "fused";
energy_q16: number;
uncompressed_extent_q16: number;
carrier_capacity_q16: number;
rigidity_q16: number;
binding_q16: number;
aci_residual_q16: number;
admissible_family: string[];
};
Collapse rule
A non-compressed Goxel is useful only while bounded.
if uncompressed extent grows without compression progress:
collapse
if ACI residual decreases and binding rises:
allow partial compression window
if ACI residual reaches zero or accepted tolerance:
allow lock / fuse / hoxel validation
Operating sentence
A Goxel is a non-compressed, shape-agnostic geometry seed: it can assume any bounded admissible geometry during exchange or shock response, then compress into voxel, hoxel, lattice, shell, or manifold form only after partial compression, binding recovery, and ACI-style validation.