Discrete-Geometry Consistency Specialist
Budget: £750 – £1,500 GBP
TITLE: Request for Mathematical Consistency Evaluation of a Geometric Framework
I am seeking an applied mathematician to provide a mathematical integrity check on a constrained geometric framework I have developed.
The framework consists of:
• A 3-dimensional spherical octant domain.
• Six smooth surfaces, arranged as three fixed surfaces and three movable (“live”) surfaces.
• At every admissible state, the three live surfaces have a single unique intersection point, which must lie on a pre-defined radial axis within the octant.
• The displacements of the live surfaces are represented by three scalar parameters, which are always linked by one invariant constraint (formally: one equation in three variables).
• State evolution occurs in discrete steps, and the invariant must hold at each step.
Your task:
1. Determine whether such a system is mathematically self-consistent.
2. Determine whether a discrete update rule can exist that preserves the invariant and the radial constraint simultaneously.
3. Determine whether an extremal radial point (“saturation radius”) is mathematically admissible under these constraints.
This is not a physics problem.
It is a geometric consistency problem involving surfaces, invariants, constrained intersections, and discrete evolution.
No formulae or mechanisms are required from you — only an examination of:
• internal consistency,
• existence of valid configurations,
• and whether the stated constraints can coexist without contradiction.
The work is small, finite, and well-bounded.
If you are interested, I can supply the minimal formal definitions required (surfaces, domain, invariant structure) so you can proceed.
Skills required are 2D Discrete geometry: Invariants: Modelling: Algebra,
Calculus is not required.
Please outline your experience
Thank you,
James Hourihan
I am seeking an applied mathematician to provide a mathematical integrity check on a constrained geometric framework I have developed.
The framework consists of:
• A 3-dimensional spherical octant domain.
• Six smooth surfaces, arranged as three fixed surfaces and three movable (“live”) surfaces.
• At every admissible state, the three live surfaces have a single unique intersection point, which must lie on a pre-defined radial axis within the octant.
• The displacements of the live surfaces are represented by three scalar parameters, which are always linked by one invariant constraint (formally: one equation in three variables).
• State evolution occurs in discrete steps, and the invariant must hold at each step.
Your task:
1. Determine whether such a system is mathematically self-consistent.
2. Determine whether a discrete update rule can exist that preserves the invariant and the radial constraint simultaneously.
3. Determine whether an extremal radial point (“saturation radius”) is mathematically admissible under these constraints.
This is not a physics problem.
It is a geometric consistency problem involving surfaces, invariants, constrained intersections, and discrete evolution.
No formulae or mechanisms are required from you — only an examination of:
• internal consistency,
• existence of valid configurations,
• and whether the stated constraints can coexist without contradiction.
The work is small, finite, and well-bounded.
If you are interested, I can supply the minimal formal definitions required (surfaces, domain, invariant structure) so you can proceed.
Skills required are 2D Discrete geometry: Invariants: Modelling: Algebra,
Calculus is not required.
Please outline your experience
Thank you,
James Hourihan