Co3
Re-discovering the method to the madness
Applications
◈
Hardware
λ
Software
Try Demo
RESEARCH STAGE · SPECCED NOT SHIPPED
◈

Terms of Access

Please review and accept the following terms to continue.

PROTOTYPE ACCESS AGREEMENT AND DISCLAIMER

Effective Date: January 2026

This Prototype Access Agreement and Disclaimer ("Agreement") is entered into by and between CO3 ONE LLC, an Arizona limited liability company ("Company," "we," "us," or "our"), and the individual accessing this prototype environment ("User," "you," or "your").

BY ACCESSING THIS PROTOTYPE, YOU ACKNOWLEDGE THAT YOU HAVE READ, UNDERSTOOD, AND AGREE TO BE BOUND BY THIS AGREEMENT. IF YOU DO NOT AGREE TO THESE TERMS, DO NOT ACCESS OR USE THIS PROTOTYPE.

1. EXPERIMENTAL NATURE OF PROTOTYPE

1.1. The software, tools, demonstrations, and materials accessible through this portal (collectively, the "Prototype") are experimental, developmental, and provided solely for testing, evaluation, and demonstration purposes.

1.2. The Prototype is provided "AS IS" and "AS AVAILABLE" without any warranties of any kind, whether express, implied, statutory, or otherwise, including but not limited to warranties of merchantability, fitness for a particular purpose, title, non-infringement, accuracy, reliability, or availability.

1.3. The Prototype may contain errors, bugs, defects, or inaccuracies. Outputs, calculations, analyses, recommendations, or other results generated by the Prototype should not be relied upon for any purpose and do not constitute professional, legal, financial, medical, or other advice.

2. NO CONFIDENTIALITY OF USER INPUTS

2.1. IMPORTANT NOTICE: ANY AND ALL INFORMATION, DATA, TEXT, OR OTHER CONTENT YOU ENTER INTO, SUBMIT TO, OR TRANSMIT THROUGH THIS PROTOTYPE ("USER INPUTS") IS NOT CONFIDENTIAL AND SHALL NOT BE TREATED AS CONFIDENTIAL BY THE COMPANY.

2.2. By submitting User Inputs, you acknowledge and agree that: (a) User Inputs may be stored, logged, analyzed, reviewed, or retained by the Company without limitation; (b) User Inputs may be used by the Company for any purpose, including but not limited to improving, developing, or training systems and models; (c) you have no expectation of privacy or confidentiality with respect to User Inputs; (d) you shall not submit any information that you consider confidential, proprietary, sensitive, or private.

2.3. You represent and warrant that you have all necessary rights to submit User Inputs and that such submission does not violate any third-party rights, confidentiality obligations, or applicable laws.

3. INTELLECTUAL PROPERTY

3.1. The Prototype, including but not limited to its underlying code, algorithms, methodologies, frameworks, theories, documentation, and user interface (collectively, "Company IP"), is the exclusive property of the Company and is protected by intellectual property laws, including patent-pending technologies.

3.2. This Agreement grants you a limited, non-exclusive, non-transferable, revocable license to access and use the Prototype solely for personal, non-commercial evaluation purposes during your authorized session.

3.3. You shall not: (a) copy, reproduce, modify, or create derivative works of the Prototype or Company IP; (b) reverse engineer, decompile, disassemble, or attempt to derive source code; (c) sublicense, sell, distribute, or transfer access to the Prototype; (d) use the Prototype for any commercial purpose; (e) remove or alter any proprietary notices or markings.

4. LIMITATION OF LIABILITY

4.1. TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, IN NO EVENT SHALL THE COMPANY, ITS MANAGERS, MEMBERS, EMPLOYEES, AGENTS, AFFILIATES, SUCCESSORS, OR ASSIGNS BE LIABLE FOR ANY INDIRECT, INCIDENTAL, SPECIAL, CONSEQUENTIAL, PUNITIVE, OR EXEMPLARY DAMAGES, INCLUDING BUT NOT LIMITED TO DAMAGES FOR LOSS OF PROFITS, GOODWILL, USE, DATA, OR OTHER INTANGIBLE LOSSES, ARISING OUT OF OR RELATING TO YOUR ACCESS TO OR USE OF (OR INABILITY TO ACCESS OR USE) THE PROTOTYPE.

4.2. TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, THE COMPANY'S TOTAL AGGREGATE LIABILITY ARISING OUT OF OR RELATING TO THIS AGREEMENT OR THE PROTOTYPE SHALL NOT EXCEED ONE HUNDRED UNITED STATES DOLLARS ($100.00).

4.3. THE LIMITATIONS IN THIS SECTION SHALL APPLY REGARDLESS OF THE THEORY OF LIABILITY, WHETHER BASED ON WARRANTY, CONTRACT, STATUTE, TORT (INCLUDING NEGLIGENCE), STRICT LIABILITY, OR ANY OTHER LEGAL OR EQUITABLE THEORY, AND WHETHER OR NOT THE COMPANY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

5. INDEMNIFICATION

5.1. You agree to indemnify, defend, and hold harmless the Company and its managers, members, employees, agents, and affiliates from and against any and all claims, damages, losses, liabilities, costs, and expenses (including reasonable attorneys' fees) arising out of or relating to: (a) your access to or use of the Prototype; (b) your User Inputs; (c) your violation of this Agreement; (d) your violation of any rights of any third party.

6. ACCESS REVOCATION

6.1. Your access to the Prototype is granted at the sole discretion of the Company and may be revoked, suspended, or terminated at any time, for any reason or no reason, without notice or liability.

7. GOVERNING LAW AND DISPUTE RESOLUTION

7.1. This Agreement shall be governed by and construed in accordance with the laws of the State of Arizona, without regard to its conflict of laws principles.

7.2. Any dispute arising out of or relating to this Agreement or the Prototype shall be resolved exclusively in the state or federal courts located in Maricopa County, Arizona, and you consent to the personal jurisdiction of such courts.

7.3. You waive any right to participate in a class action lawsuit or class-wide arbitration against the Company.

8. MISCELLANEOUS

8.1. This Agreement constitutes the entire agreement between you and the Company regarding the Prototype and supersedes all prior agreements and understandings.

8.2. If any provision of this Agreement is found to be unenforceable, the remaining provisions shall continue in full force and effect.

8.3. The Company's failure to enforce any right or provision of this Agreement shall not constitute a waiver of such right or provision.

8.4. This Agreement may be modified by the Company at any time. Continued access to the Prototype following any modification constitutes acceptance of the modified terms.

— End of Agreement —
✓

What if alignment drift were visible before evals caught it?

Co³ One develops formal methods for constraint-aware safety. We believe the difference between systems that stay aligned and systems that drift is geometric—and measurable—long before behavioral metrics register the change.

The Problem

Constitutional AI defines what a system should not do. But constraints alone don't tell you how close you are to violating them. Current evaluation methods capture snapshots. Drift is continuous. By the time a boundary is crossed, the trajectory that led there is already behind you.

The Method

Our research identified a structure that governs persistence under constraint: the relationship between a system's current state, its distance from failure boundaries, and the coherence of its trajectory over time. We formalized this as Restraint Continuity Observation Translation—a framework for seeing where a trajectory is headed, not just where it is. The math is simple. The applications are not.

The Evidence

We did not build this framework for AI. It emerged from work across physical systems, biological regulation, infrastructure resilience, and institutional dynamics. The same geometry held. That it applies to alignment is a consequence, not a premise.

The Artifact

Full documentation and licensing available for aligned research partners.

DISCOVER THE THEORY
CONTACT CO3 ONE

Constraint-based trajectory selection using TTBC — Patent Pending

Restraint Continuity Observation Translation

What happens next is whatever stays allowed, remains stable, and maintains distance from failure. Click any variable to see the same geometry across domains.

Interactive Constraint Geometry

Click a colored variable to explore
argmax d(y, ∂𝔽) + λ· CΔ + μ· ĊΔ
y ∈ 𝔽   subject to: Π (y) ≈ observed
where ∂𝔽 = failure boundary

Foundational Claim

Observed system behavior and its translations are governed by the persistence of admissible continuations under accumulating restraints. What remains continuous determines what can move and what can be consistently represented.

Mathematical Formulation

Symbolic Key

Xstate space
xcurrent state
𝔽(t,x)feasible continuation set
∂𝔽(t,x)feasibility boundary
d(y,∂𝔽)margin to violation
CΔ(t,y)coherence over window Δ
ĊΔ(t,y)coherence trend
Πprojection/translation map

Trajectory Rule

πt+Δt(x) = Π(
  argminy ∈ 𝔽(t,x) [
    d(y, ∂𝔽) − λ·CΔ(t,y) − μ·ĊΔ(t,y)
  ]
)

Binary Invariants

A 0–1 Pass / "Understood" Gating Framework

G := ∏m Im ∈ {0, 1}

Validity is structural rather than interpretive. Each invariant is encoded as a binary indicator Im ∈ {0,1}. Toggle to test the gate.

Sign coherence between prose and optimization direction
Nonempty-domain requirements for infimum or argmin
Explicit declaration and typing of the projection/translation map Π
Sufficient definition of coherence functional CΔ
Stated convention for boundary edge cases involving ∂𝔽
G = 1 × 1 × 1 × 1 × 1 = 1 (PASS)
United States Patent Application

System and Method for Constraint-Aware Trajectory Optimization

Application No.
19/448,772
Filing Date
January 14, 2026
Inventor
Ricardo Cruz Orozco
Status
Patent Pending
◈ This document is provided for reference only. Content is protected.

Abstract

A computer-implemented method for selecting trajectories within constrained systems is disclosed. The method generates a finite set of candidate trajectories, predicts time-to-boundary-crossing values for each candidate relative to a failure boundary, and selects a trajectory by comparative ordering that maximizes a minimum temporal margin over a future evaluation horizon. The approach preserves continued system operability and is applicable across physical, computational, and organizational domains.

Background of the Invention

Field of the Invention

[0003] The present invention relates to computational decision systems and, more particularly, to methods for selecting trajectories within constrained systems to preserve operability over time.

Description of Related Art

[0004] Existing trajectory planning and optimization techniques typically focus on minimizing cost or maximizing performance while satisfying constraints. Such methods may include model predictive control, safety filtering, and clearance-based planning. These approaches generally emphasize constraint satisfaction or spatial clearance and may not account for comparative temporal margins to system failure boundaries when selecting among multiple candidate trajectories. As a result, such systems may remain technically feasible while operating near failure boundaries with limited predictive robustness.

Summary of the Invention

[0005] The invention provides a computer-implemented method and system for selecting trajectories within constrained systems by generating a finite plurality of candidate trajectories, computing for each candidate a predicted time-to-boundary-crossing relative to a failure boundary, and selecting a trajectory by comparative ordering that maximizes a minimum predicted time-to-boundary-crossing over a future evaluation horizon to preserve operability.

[0006] The selected trajectory may be output in a form usable by an external control, scheduling, or decision process to reduce risk of boundary violation over time.

Detailed Description of the Invention

[0012] The invention operates by identifying constraints that define a feasible region of operation for a system. These constraints may be physical, computational, logical, policy-based, or organizational in nature, and collectively define conditions under which continued system operability is preserved.

[0013] Candidate trajectories are generated as discrete or continuous system evolutions computed from a current system state and constrained to remain initially within the feasible region. The set of candidate trajectories represents admissible future system behaviors for evaluation.

[0014] For each candidate trajectory, a predicted time-to-boundary-crossing (TTBC) value is computed. The TTBC represents an estimated future time at which the candidate trajectory would intersect a failure boundary associated with loss of operability if the trajectory were continued.

[0015] TTBC computation may be performed using forward simulation of system dynamics, interpolation between sampled trajectory states, or analytical evaluation of constraint functions over time. In discrete or stepwise systems, TTBC may be approximated by identifying the earliest timestep at which a constraint inequality defining the failure boundary is violated.

[0016] The TTBC metric differs from time-to-collision methods in that it evaluates temporal margin relative to abstract or system-defined boundaries rather than physical object collisions, and is applicable to non-physical domains including computational and organizational systems.

[0017] Candidate trajectories are comparatively ordered based on their TTBC values. In one embodiment, comparative ordering maximizes a minimum TTBC over a predefined evaluation horizon, thereby prioritizing trajectories that exhibit greater temporal robustness with respect to the failure boundary.

[0018] The selected trajectory is output in a form usable by an external system or decision process, including control execution, scheduling, or governance action, thereby enabling operational decisions that reduce the likelihood of boundary violation over time.

Figures

FIG. 1
System Architecture
Constraint Identification Trajectory Computation Boundary Evaluation Selection Module Output Translation

Trajectory selection architecture defining a feasible region and an associated failure boundary.

FIG. 2
Method Flow
Identify constraints defining a feasible region Compute candidate trajectories within the feasible region Evaluate proximity of candidate trajectories to failure boundary over prediction horizon Select trajectory based on preservation of distance from the failure boundary Generate an output representation corresponding to the selected trajectory

Trajectory generation module producing a finite plurality of candidate trajectories within the feasible region.

FIG. 3
Feasible Region and Trajectories
Failure Boundary FEASIBLE REGION CURRENT STATE CANDIDATE TRAJECTORY 1 CANDIDATE TRAJECTORY 2

Trajectory evaluation module computing predicted time-to-boundary-crossing values for candidate trajectories relative to the failure boundary.

FIG. 4
Selection Module
Candidate Traj. 1 Candidate Traj. 2 Candidate Traj. N Selection Module Output / Translation Module Output Repr.

Trajectory selection module comparatively ordering candidate trajectories based on predicted time-to-boundary-crossing values.

FIG. 5
Computing System
Computing System Processor Memory Constraint Identification Trajectory Computation Boundary Evaluation Selection Module Output / Translation

Output interface providing an output representation of the selected trajectory for use by an external system or decision process.

Claims

← Back to Theory
Constraint-Native Hardware
What if the physics did the math?
CLaSP
Constraint Lattice State Projection. Photonic mesh where settling is computation. Light finds feasible states because that's where it wants to be.
Spec: coupled SiN resonators · PCM barrier tiles · coherence-gated feedback
Current work: resonator coupling simulation, targeting MPW run.
apply
PrismForge
Hybrid optical compute. Not a GPU replacement—a successor for workloads that fit.
Spec: optical tensor cores · CLaSP coprocessor · electrical fallback · chiplet interconnect
apply
Fabrication Path
Real fabs. Real PDKs.
Targets: AIM Photonics (US) · imec iSiPP (EU) · LIGENTEC SiN (low-loss)
Built on RCOT

Restraint Continuity Observation Translation

Patent pending: US Application #19/448,772

Hardware provisionals pending

Explore RCOT Theory →

Toolkit
Proofs of concept. Domains where constraints define the problem.
Cognitive Prosthesis
The boundary between human and AI moves. When does assistance become override? Building the math for handoff.
Current work: fatigue-adaptive handoff in assisted movement.
apply
Autonomous Constraint Layers
Constraint layers for systems that act in the world. Reference architectures, not product.
Current work: drone no-fly enforcement that degrades safely, not abruptly.
apply
Spatial Training
Training that measures distance from failure, not just task completion.
Current work: crisis de-escalation with real-time margin feedback.
apply
Embodied Systems
Robots break things. Formalizing what not to do.
Current work: motion planning with dynamic collision boundaries.
apply
Built on RCOT

Restraint Continuity Observation Translation

Patent pending: US Application #19/448,772

OpenXR compatible · Unity integration path

CONTACT CO3 ONE

AI-MAPPED CROSS-DOMAIN CONSTRAINT GEOMETRY