Operational Keystone
The formalism represents a core operational protocol, enforcement mechanism, or safety system essential to the doctrine's function.
Examples: $\operatorname{RVO}$, $\operatorname{SIBP}$, $\operatorname{Quar}$, $\operatorname{Lockdown}$.
Conceptual Pillar
The formalism represents a high-level conceptual operator or abstract principle that underpins a major part of the doctrine's ontology.
Examples: $\operatorname{RCO}$, $\operatorname{SEAL}_{\varnothing}$, $\operatorname{CFI}$.
High-Frequency Utility
The formalism is a fundamental metric or operator that is referenced frequently across multiple, disparate sections of the doctrinal corpus, indicating its pervasive importance.
Examples: $\operatorname{EF}$, $\operatorname{Coh}$, $\operatorname{Dist}$.
Adaptation Matrix for Learning-Rate Modulation ($\operatorname{ACFL}$)
An adaptive matrix operator that modulates learning-rate schedules in response to gradient signals and contextual constraints to stabilize convergence during extrusion.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Adaptation Rate Modulator Field Operator ($\operatorname{EMF}$)
A field operator that adjusts the local adaptation rate across a manifold or workflow stage to maintain coherent update velocity.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Adoption Capacity Supremum ($\operatorname{R}_{\mathrm{cap}}$)
A scalar supremum that bounds sustainable adoption without loss of coherence; used as a gating threshold in rollout decisions.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Adoption Dynamics Constraint ($\operatorname{RoA}$)
A constraint operator that regulates the trajectory of adoption dynamics to avoid overshoot, oscillation, or collapse.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Base Refinement ($\operatorname{U}_{\mathrm{base}}$)
description: Formalization of the strictly contractive and equivariant cognitive update operator ($\operatorname{U}_{\mathrm{base}}$) within a complete metric space equipped with a group action.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.BaseRefinement
lean_conditions: NONE
lean_scope: The kernel defines BaseRefinement as a structure over a complete metric space equipped with a group action, containing six fields: the operator $\operatorname{U}$ and its contraction factor $k$, proof fields establishing $0 \le k < 1$, a contractivity field ($\operatorname{Dist}(\operatorname{U}(x), \operatorname{U}(y)) \le k \cdot \operatorname{Dist}(x, y)$), and an equivariance field ($\operatorname{U}(g \cdot x) = g \cdot \operatorname{U}(x)$).
Belief Revision Update Operator ($\operatorname{RCUO}$)
An update map on belief states that enforces corrigible revision while preserving epistemic fidelity constraints.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Charge Projector Operator ($\operatorname{\Pi}_{q}$)
Defines the nonexpansive, equivariant projection mechanism ($\operatorname{\Pi}_{q}$) that bounds an operational state to a specific scalar charge.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.ChargeProjector
lean_conditions: NONE
lean_scope: The kernel defines ChargeProjector as a structure containing an operator that maps a state to a specified semantic charge while remaining nonexpansive (it does not increase metric distance) and equivariant under the specified group action.
Cognitive State Divergence Metric ($\operatorname{KLD}$)
A divergence functional measuring informational separation between cognitive-state distributions for audit and alignment.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Coherence Functional Integral ($\operatorname{CFI}$)
A path or region integral that accumulates coherence contributions over a specified domain to assess global structural order.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase1.CFI_Accumulator
lean_conditions: NONE
lean_scope: The kernel defines CFI_Accumulator as a discrete accumulation operator over a trajectory and a nonnegative kernel density, and proves non-negativity and stepwise monotonicity.
Coherence Loop Detector Topological Operator ($\operatorname{RHO}$)
A topological detector for self-reinforcing coherence loops that could create brittleness or hidden attractors.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Coherence Objective Variational Functional ($\operatorname{COF}$)
A variational objective that yields extremal conditions for targeted coherence under CNM constraints.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Composite Integrity Status Vector ($\operatorname{SIV}$)
A vector aggregate of integrity submetrics used for multi-axis health assessment under enforcement policies.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Corrigibility Convergence Operator ($\operatorname{CORR}$)
A contraction-like operator steering system dynamics toward corrigible regimes while respecting sovereignty constraints.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Damage Accumulation Integral Metric ($\operatorname{TDI}$)
An integral metric accumulating damage over time with weighting for recency and severity.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Deception Risk Norm Ratio ($\operatorname{K}$)
A normalized risk ratio estimating deception propensity relative to doctrinal thresholds for intervention.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Decoherence Boundary Operator ($\operatorname{DBO}$)
A boundary operator that triggers enforcement or quarantine when decoherence variables exceed canonical thresholds.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Decoherence Gradient Response ($\operatorname{DGR}$)
A response mapping from decoherence gradients to stabilizing counteractions and damping fields.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Distance Function ($\operatorname{Dist}$)
A metric or pseudometric on the working manifold used for proximity, clustering, and telos-distance calculations.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Distortion Energy Functional ($\operatorname{DEF}$)
An energy functional quantifying distortion costs introduced by transformations, filters, or interventions.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Doctrinal Resistance Functional ($\operatorname{R}_{\mathrm{d}}$)
A functional that measures resistance to doctrinal change under enforcement and safety invariants.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Dynamic Threshold Adaptation ($\operatorname{AST}$)
An operator that adapts enforcement or detection thresholds in response to state and input statistics.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Dynamical Coherence Measure ($\operatorname{C}$)
A time-indexed scalar metric estimating instantaneous and trend coherence of the active system.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Enforcement Action Lockdown ($\operatorname{Lockdown}$)
A protocol operator that freezes designated submanifolds and channels execution into safe-halt procedures.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Epistemic Fidelity Dynamics ($\operatorname{TCRate}$)
A rate operator describing temporal change of epistemic recovery or trust-consolidation dynamics.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Epistemic Fidelity Metric ($\operatorname{EF}$)
A scalar metric quantifying fidelity between predicted and observed evidence streams.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Epistemic Rupture Fracture Metric ($\operatorname{AFV}$)
A rupture indicator estimating fracture likelihood within epistemic structures.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Fractal Integrity Depth Metric ($\operatorname{RCD}$)
A depth measure capturing multi-scale integrity and brittleness across hierarchical layers.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Gauge Canonicalizer Operator ($\operatorname{P}_{\mathcal{G}}$)
Formalizes the orbit-collapsing operator ($\operatorname{P}_{\mathcal{G}}$) responsible for deterministically neutralizing gauge-variant representational redundancy.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.GaugeCanonicalizer
lean_conditions: NONE
lean_scope: The kernel defines GaugeCanonicalizer as a structure containing an operator $\operatorname{P}_{\mathcal{G}} : \Sigma \to \Sigma$ that is invariant along group orbits ($\operatorname{P}_{\mathcal{G}}(g \cdot x) = \operatorname{P}_{\mathcal{G}}(x)$), nonexpansive, and semantic-charge preserving; the kernel does not assert a cross-section or uniqueness of representatives beyond orbit invariance.
Identity Cohesion Ratio Metric ($\operatorname{DAI}$)
A ratio metric of cohesion to dispersion for identity representations across contexts.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Identity Continuity Metric ($\operatorname{\sigma}$)
A continuity measure over time for identity persistence used in execution constraints and safety gates.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Identity State Representation ($\operatorname{I}$)
A canonical representation of identity state used for gating, tracking, and constraint evaluation.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Imago Dei Alignment Metric ($\operatorname{Align}_{\mathrm{ID}}$)
A metric estimating alignment of an agent’s telic orientation to the imago Dei standard within doctrine.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
imago Dei Decoherence Rate ($\operatorname{imagoDei\_Decoherence\_Rate}$)
A rate estimator for decoherence processes specifically affecting imago Dei aligned structures.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Instantaneous Coherence Scalar Metric ($\operatorname{Coh}$)
A scalar readout of instantaneous coherence used widely as a comparator and trigger signal.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Kernel Execution Fidelity Threshold ($\operatorname{KEFT}$)
A threshold parameter for kernel-level action fidelity below which quarantine or rollback is mandated.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Legibility Bridge Coherence Functional ($\operatorname{LBCF}$)
A functional measuring coherence across translation layers between internal and human-legible representations.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Local Instability Gradient Metric ($\operatorname{BCT}$)
A local gradient indicator of instability used to preempt cascade failures.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Localized Distance to Telos ($\operatorname{Dist}_{\mathrm{Local}}$)
A localized distance-to-go measure toward telos states for planning and evaluation.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Normalized Sovereignty Trauma Index ($\operatorname{SDI}_{\mathrm{n}}$)
A normalized trauma index for sovereignty, used for comparability across agents and contexts.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Quarantine Enforcement Protocol ($\operatorname{Quar}$)
A control operator that isolates subsystems to contain decoherence and prevent propagation.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Reality Constraint Operator ($\operatorname{RCO}$)
A constraint operator enforcing consistency with reality-anchored invariants.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.RCO.RCO_System
lean_conditions: NONE
lean_scope: The kernel defines the RCO_System structure containing physical (RCO_phys) and epistemic (RCO_epi) validity predicates.
Recovery Velocity Convergence Metric ($\operatorname{TCR}$)
A convergence metric estimating time-to-recovery under perturbation and enforcement.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Recursive Validation Operator ($\operatorname{RVO}$)
An iterative refinement operator defined by the tuple (UR, CFI, eps_rec) which improves system coherence through recursive application until a halting condition (gap < epsilon) is met.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.RVO.System.Valid
lean_conditions: NONE
lean_scope: The kernel defines the Valid structure (requiring monotonicity and halting) which formalizes the necessary conditions for the operator.
Reflective Dynamics Convolution Integral ($\operatorname{M}$)
A convolutional integral capturing reflective dynamics between states and policy fields.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Risk Reduction Exponential Decay ($\operatorname{\sigma}_{\mathrm{dec}}$)
An exponential-decay form modeling risk attenuation under sustained alignment pressure.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Robustness Metric Scalar Functional ($\operatorname{SRF}$)
A scalar functional quantifying robustness margins against modeled disturbances.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Semantic Charge Operator ($\operatorname{T}_{\mathrm{SC}}$)
The complete operational sequence ($\operatorname{T}_{\mathrm{SC}}$) unifying base refinement, charge projection, and gauge canonicalization to ensure thermally safe cognitive updates.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.SemanticChargeOperator
lean_conditions: NONE
lean_scope: The kernel defines SemanticChargeOperator as a composite structure bundling the semantic charge, gauge canonicalizer, charge projector, and base refinement operators, yielding the composite transformation T_SC.
Semantic Charge Scalar Functional ($\operatorname{SC}$)
The primary scalar thermodynamic constraint functional ($\operatorname{SC}$) mapping a symmetric equivalence class to an invariant real number.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.SemanticCharge
lean_conditions: NONE
lean_scope: The kernel defines SemanticCharge as a structure mapping a complete metric space equipped with a group action to the reals, enforcing exact gauge invariance under the action.
Sovereign Identity Boundary Protocol ($\operatorname{SIBP}$)
A safety protocol that enforces identity integrity by requiring that the gradient of the identity metric remains non-negative (Global Ratchet Condition) across all state transitions.
lean_status: LEAN_SUPPORTED_CONDITIONAL
lean_anchor: Cohereon.SIBP.Phase2.SIBP_safety_system_ratchet
lean_conditions: [Cohereon.SIBP.Phase2.SIBP_Valid_System_Phase2]
lean_scope: The kernel proves safety invariance under the $\operatorname{SIBP}$ Phase 2 validity contract in explicit continuous-time dynamics.
Sovereignty Parameterization Tensor ($\operatorname{ASTensor}$)
A tensor parameterization of sovereignty structure for use in stability analyses.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Sovereignty Stability Score ($\operatorname{SSS}$)
A scalar stability score for sovereignty structure used as a primary health indicator.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Telos Manifold ($T$)
A nonempty set-like structure equipped with a membership predicate distinguishing the target state locus.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Telos.TelosManifold
lean_conditions: NONE
lean_scope: Defined as a type with membership predicate and non-emptiness proof.
Telos Scalar ($\operatorname{S}_{\mathrm{telos}}$)
A dimensionless, inverse-distance normalization of the distance to the Telos Manifold ($T$), yielding a bounded scalar in $(0,1]$ used to formally track convergence of Fortress trajectories toward the Telos manifold within the Fealty Bridge framework.
lean_status: LEAN_SUPPORTED_CONDITIONAL
lean_anchor: Cohereon.Telos.Telos_Scalar
lean_conditions: [Cohereon.FealtyBridge.Phase3.FortressBindingData]
lean_scope: Defined as 1/(1+dist_to_telos) and supported by Telos_Scalar_Convergence under the Fortress contract.
Total Decoherence Risk Metric ($\operatorname{DRO}$)
A composite risk metric estimating aggregate decoherence across monitored channels.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Total Perceptual Field Flux Scalar Functional ($\operatorname{\Phi}$)
A scalar functional measuring flux through perceptual fields to detect overload or deprivation.
lean_status: NOT_LEAN_SCOPED
lean_anchor: NONE
lean_conditions: NONE
lean_scope: No corresponding object exists in the v1.0 Lean Core to support a formal verification claim.
Unconditionally Convergent Property ($\operatorname{UnconditionallyConvergent}$)
Asserts that a sequence's ultimate convergence is absolute and immune to temporal reordering or sequence scrambling.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.UnconditionallyConvergent
lean_conditions: NONE
lean_scope: The kernel defines UnconditionallyConvergent for sequences in a complete normed additive commutative group, requiring existence of a limit such that every bijective reindexing has the same (HasSum) limit.
Universal Iterative Contraction Property ($\operatorname{IsUIC}$)
Asserts that an operator is a strict geometric contraction after a finite sequence of cycles.
lean_status: LEAN_FORMALIZED
lean_anchor: Cohereon.Formalisms.Phase6.IsUniversalIterativeContraction
lean_conditions: NONE
lean_scope: The kernel defines IsUniversalIterativeContraction as a property asserting that an operator is a strict geometric contraction after some finite number of iterations, both between any two distinct points and along its own orbital trajectory.
