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Gyro Logic\n\n**A Stability-Based Framework for Representation Under Intrinsic Deviation**\n\n---\n\n## What is Gyro Logic?\n\nGyro Logic is a theoretical framework for modeling representation, meaning, and identity through the relation between **Structure**, **Slice**, and **Stability**.\n\nAt its core, Gyro Logic defines the following invariant structure:\n\n```text\nStructure → Slice → Stability\n```\n\nThis core principle is not replaced by later extensions.\nLoop, Operator, Orientation, Response, Deviation, Void, and Jump are defined as auxiliary concepts that extend or unfold this principle without changing it.\n\n---\n\n## Core Principle\n\n```text\nStructure → Slice → Stability\n```\n\n- **Structure** is an undifferentiated or multidimensional relational structure.\n- **Slice** is the act-concept by which Structure appears under a certain perspective, angle, granularity, or context.\n- **Stability** is the state quantity that appears in the result of Slice.\n\nStability is not an evaluator.\nIt is not the agent that decides, judges, or controls the next step.\n\n```text\nStability is evaluated.\nStability does not evaluate.\n```\n\n---\n\n## Gyro Unit\n\nA **Gyro Unit** is the minimal time-free theoretical unit of Gyro Logic.\n\n```text\nGyro Unit\n= Structure → Slice → Stability\n```\n\nIn Gyro Unit, the arrow does not primarily indicate physical time.\nIt indicates logical dependency or relational constitution.\n\nTemporal processes such as execution, computation, response, continuation, stopping, and jump do not belong to Gyro Unit itself.\nThey belong to Gyro Process or Gyro Loop.\n\n---\n\n## Gyro Process\n\nA **Gyro Process** is the time-including operational unfolding of Gyro Unit.\n\n```text\nStructure\n→ Operator Orientation\n→ slice-ing\n→ slice-done\n→ Stability\n→ Operator Response\n```\n\nGyro Process is a single operational cycle.\nIt is not yet a loop.\n\nTime appears mainly in:\n\n```text\nslice-ing\nOperator Response\n```\n\n---\n\n## Gyro Loop\n\nA **Gyro Loop** is the iterative structure formed when Gyro Processes are connected through Operator Response.\n\n```text\nGyro Process_n\n→ Operator Response_n\n→ Next Structure / Next Slice / Stop / Continue / Jump\n→ Gyro Process_n+1\n```\n\nGyro Loop does not replace the core principle:\n\n```text\nStructure → Slice → Stability\n```\n\nRather, Gyro Loop is the iterative extension of Gyro Process.\n\n---\n\n## Slice, slice-ing, and slice-done\n\nGyro Logic distinguishes between three layers of Slice.\n\n```text\nSlice\n= the general act-concept by which Structure appears\n```\n\n```text\nslice-ing\n= the time-including act-process in which Slice is being performed\n```\n\n```text\nslice-done\n= the completed result of Slice\n```\n\nStability appears in slice-done.\n\n```text\nslice-done = X + Δ\n```\n\nwhere:\n\n- **X** is the representation produced by Slice.\n- **Δ** is the deviation between Structure and Representation.\n\nThe time required for computation, observation, search, or transformation belongs to **slice-ing**, not to the logical result itself.\n\n---\n\n## Stability\n\nGyro Logic distinguishes between two layers of Stability.\n\n```text\nStability as property\n= the state quantity that appears in a single slice-done\n```\n\n```text\nStability over time\n= the persistence, variation, or trajectory of Stability across multiple Gyro Processes\n```\n\nIn a single Gyro Unit:\n\n```text\nσ = Stab(X, Δ)\n```\n\nIn a Gyro Loop:\n\n```text\n{σ_n}\n```\n\nStability remains a state quantity.\nIt does not decide the next Slice, Structure, continuation, stopping, or Jump.\nThe next action is determined by **Operator Response**.\n\nHigh Stability may indicate robustness, but excessive Stability may also indicate rigidity.\n\n---\n\n## Operator Orientation and Operator Response\n\nGyro Logic distinguishes between the pre-slice and post-stability roles of the Operator.\n\n```text\nOperator Orientation\n= the pre-slice directional condition by which an operator orients how Structure is sliced\n```\n\n```text\nOperator Response\n= the post-stability reaction by which an operator determines whether to continue, stop, adjust Slice, update Orientation, update Structure, or Jump\n```\n\nTheir temporal positions are:\n\n```text\nStructure\n→ Operator Orientation\n→ slice-ing\n→ slice-done\n→ Stability\n→ Operator Response\n→ Next\n```\n\nOperator Orientation is not Slice itself.\nOperator Response is not Stability itself.\n\n---\n\n## Time Structure\n\nGyro Logic separates time-free relational structure from time-including operational process.\n\n```text\nGyro Unit\n= time-free relational structure\n```\n\n```text\nGyro Process\n= time-including operational cycle\n```\n\n```text\nGyro Loop\n= time-including iterative structure\n```\n\nIn one sentence:\n\n```text\nGyro Logic defines its core structure as time-free, while time appears in Gyro Loop through slice-ing and Operator Response.\n```\n\n---\n\n## Deviation, Void, and Jump\n\n### Deviation\n\n```text\nΔ = deviation between Structure and Representation\n```\n\nA completed Slice may be represented as:\n\n```text\nslice-done = X + Δ\n```\n\n### Void\n\nVoid is the region where Stability is undefined, too low, or cannot be meaningfully evaluated.\n\n### Jump\n\nJump is a non-continuous reconstruction selected when existing Orientation, Slice, or Structure cannot resolve the current deviation or void.\n\n```text\nVoid / large Δ / unstable Stability\n→ Operator Response\n→ Jump\n```\n\nVoid does not jump by itself.\nJump is selected through Operator Response.\n\n---\n\n## Boundary Extension\n\nBoundary and Boundary State are auxiliary concepts for describing how distinctions become readable through Slice.\n\nThey do not replace the core principle:\n\n```text\nStructure → Slice → Stability\n```\n\n```text\nBoundary = Slice-relative readable distinction\nBoundary State = provisional relational state with respect to a Boundary\n```\n\nBoundary is not a fixed line inherent in Structure.  \nIt is generated, revealed, or stabilized by Slice, relative to Operator Orientation and Context.\n\nBoundary State describes how an object is provisionally positioned relative to that Boundary under the current Slice.\n\nDetailed notes:\n\n```text\ndocs/15_Boundary_20260610.md\ndocs/16_Boundary_State_20260610.md\n```\n\n---\n\n## Minimal Model\n\nTime-free Gyro Unit:\n\n```text\nX + Δ = O(S)\nσ = Stab(X, Δ)\n```\n\nTime-including Gyro Process:\n\n```text\nS(t0)\n→ B(t0)\n→ slice-ing(t0〜t1)\n→ X(t1) + Δ(t1)\n→ σ(t1)\n→ R(t1〜t2)\n```\n\nGyro Loop:\n\n```text\nP_n = (S_n, B_n, O_n, X_n, Δ_n, σ_n, R_n)\nP_{n+1} = L(P_n)\n```\n\nwhere the next state is selected through Operator Response, not by Stability itself.\n\n---\n\n## Layered Architecture\n\nGyro Logic is the theoretical layer.\n\n```text\nGyro Logic\n↓\nGyroOS\n↓\nGyroAuth\n```\n\n- **Gyro Logic**: theory layer\n- **GyroOS**: implementation layer\n- **GyroAuth**: application layer\n\nImplementation concerns from GyroOS must not redefine Gyro Logic.\nApplication concerns from GyroAuth must not be mixed into the theory layer.\n\n---\n\n## GyroAuth\n\nGyroAuth is an application layer built from Gyro Logic through GyroOS.\n\nIn GyroAuth:\n\n- Authentication = State Convergence\n- Identity = Stable Trajectory\n\nGyroAuth is not the definition of Gyro Logic.\nIt is one application of the theory.\n\n---\n\n## Current Focus\n\nThis release clarifies the theoretical distinction between:\n\n- Gyro Unit\n- Gyro Process\n- Gyro Loop\n- Slice / slice-ing / slice-done\n- Stability as property / Stability over time\n- Operator Orientation / Operator Response\n- Deviation / Void / Jump\n- Boundary / Boundary State\n\nThe purpose is to preserve the core principle:\n\n```text\nStructure → Slice → Stability\n```\n\nwhile making the temporal, iterative, and boundary-related extensions explicit.\n\n---\n\n## Figures\n\n![Gyro Logic Overview](./figures/v2.6/gyro_logic_overview.png)\n\n![GyroAuth Overview](./figures/v2.6/gyroauth_overview.png)\n\n---\n\n## Paper / Archive\n\nGyro Logic v2.6 introduced the Loop and dynamical-system direction.\nThis version clarifies the theoretical structure of Unit, Process, Loop, Slice, Stability, and Operator.\n\nReference archive:\nhttps://doi.org/10.5281/zenodo.19674468\n\n---\n\n## Repository Structure\n\n```text\n/docs\n/figures\n/paper\n```\n\n---\n\n## Minimal Summary\n\n```text\nGyro Logic begins with a time-free Gyro Unit:\nStructure → Slice → Stability\n\nIt unfolds into a time-including Gyro Process:\nStructure → Operator Orientation → slice-ing → slice-done → Stability → Operator Response\n\nIt becomes a Gyro Loop when Processes are iteratively connected through Operator Response.\n\nBoundary is a Slice-relative readable distinction.\nBoundary State is the provisional relational state of an object with respect to a Boundary.\n```\n\n---\n\n## License\n\nCC-BY-4.0","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fgitgyro-dev%2Fgyrologic","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fgitgyro-dev%2Fgyrologic","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fgitgyro-dev%2Fgyrologic/lists"}