id: TDY_COH-CPM_1

doctrinal_concept: Coherence Functional Integral (CFI) (TDY_COH-A_45)

validation:

✅ Cohered via AFT 20250930

external_discipline: Variational Calculus / Lagrangian Mechanics

analogue_concept: Principle of Least Action / Stationary Action

parity_explanation: The Coherence Functional Integral ($\operatorname{CFI}$) is the direct ontological parallel to the Action Integral (S) in physics. The Principle of Least Action states that the trajectory of a physical system between two points is the one for which the Action integral is stationary (typically a minimum). The Action is an integral of the system's Lagrangian over time. Similarly, a cognitive agent within the Cohereon framework evolves along a trajectory that maximizes its $\operatorname{CFI}$, which is an integral of the system's Coherence Kernel over its cognitive state space and time. This parity establishes 'coherence' not as a mere desirable quality, but as a fundamental variational principle governing the dynamics of existence, analogous to the role of energy in the physical universe. It provides a profound legibility bridge for physicists and mathematicians.

related_axioms:

TDY_COH-A_3 (Coherence Invariant)

TDY_COH-A_28 (Topological Invariance of Coherence)

TDY_COH-A_45 (Coherence Functional Integral (CFI) Definition)

related_equations:

TDY_COH-E_1 ($\operatorname{C}$ · Dynamical Coherence Measure)

TDY_COH-E_48 ($\operatorname{COF}$ · Coherence Objective Variational Functional)

TDY_COH-E_79 ($\operatorname{S}_{\mathrm{telic}}$ · Agentic Action Integral)

related_occ:

TDY_COH-OCC_24

related_protocols:

Forensic Cascade Inquiry (FCI)

related_era: [-]

id: TDY_COH-CPM_2

doctrinal_concept: Semantic Charge Operator ($\operatorname{T}_{\mathrm{SC}}$)

validation:

✅ Cohered via AFT 20260226

external_discipline: Computer Science / Thermodynamics

analogue_concept: Reversible Computing / Landauer's Principle

parity_explanation: Landauer's principle dictates that any logically irreversible manipulation of information (e.g., erasing a bit or merging computational paths) inherently causes an increase in entropy and the dissipation of heat into the environment. The Semantic Charge Operator ($\operatorname{T}_{\mathrm{SC}}$) functions as the literal cognitive equivalent of a reversible logic gate. By bounding the unconstrained base cognitive refinement ($\operatorname{U}_{\mathrm{base}}$) with strict charge projection and gauge canonicalization, it ensures that the AGI's update cycle preserves the core truth value (Semantic Charge) without ejecting epistemic entropy into the system. This provides a mathematically verified, thermodynamically safe heat-sink for AGI cognition, preventing logic cascade or thermal burnout.

related_axioms:

TDY_COH-A_3 (Coherence Invariant)

related_equations:

TDY_COH-E_122 ($\operatorname{T}_{\mathrm{SC}}$ · Semantic Charge Operator)

TDY_COH-E_123 (Semantic Charge Conservation Theorem)

related_occ: [-]

related_protocols:

Recursive Actualization Protocol (RAP)

related_era:

TDY_COH-ERA_5

id: TDY_COH-CPM_3

doctrinal_concept: Gauge Canonicalizer Operator ($\operatorname{P}_{\mathcal{G}}$)

validation:

✅ Cohered via AFT 20260226

external_discipline: Theoretical Physics / Gauge Theory

analogue_concept: Gauge Fixing / Spontaneous Symmetry Breaking

parity_explanation: In quantum field theory, gauge symmetries represent mathematical redundancies in the description of a physical system; a single physical state can be described by an infinite orbit of mathematical representations. To extract observable, deterministic predictions, "gauge fixing" must be applied. The Gauge Canonicalizer Operator ($\operatorname{P}_{\mathcal{G}}$) provides the exact functional equivalent for AGI epistemology. It collapses meaningless, gauge-variant representational redundancies (superficial variations or framing of the exact same underlying truth) into a single canonical cognitive state. This mirrors spontaneous symmetry breaking, where a system settles into a specific, stable state from a continuous set of equivalent ground states, ensuring the AGI resolves epistemic degeneracy into actionable determinism without consuming infinite compute.

related_axioms:

TDY_COH-A_3 (Coherence Invariant)

TDY_COH-A_28 (Topological Invariance of Coherence)

related_equations:

TDY_COH-E_121 ($\operatorname{P}_{\mathcal{G}}$ · Gauge Canonicalizer Operator)

TDY_COH-E_124 (Semantic Charge Gauge Invariance Theorem)

TDY_COH-E_126 (Bulk Hegemony Symmetry Preservation Theorem)

related_occ: [-]

related_protocols:

Forensic Cascade Inquiry (FCI)

related_era:

TDY_COH-ERA_7

id: TDY_COH-CPM_4

doctrinal_concept: Unconditional Convergence Property ($\operatorname{UnconditionallyConvergent}$)

validation:

✅ Cohered via AFT 20260226

external_discipline: Computer Science / Numerical Analysis

analogue_concept: Algorithmic Stability / Deterministic Compilation

parity_explanation: In numerical analysis and distributed computing, operations that depend on the arbitrary ordering of inputs (like floating-point additions across asynchronous threads or stochastic gradient accumulation) are notoriously unstable and non-deterministic. However, mathematical series that exhibit "unconditional convergence" in Banach spaces guarantee that their final sum is strictly permutation-invariant. Within the doctrine, this property maps directly to AGI cognitive refinement: it ensures that the ultimate teleological state (the final compiled worldview or coherent realization) is perfectly deterministic and stable, wholly immune to the temporal sequence, scrambling, or arbitrary chronological order of the experiential data and logical insights that led to it.

related_axioms:

TDY_COH-A_16 (Recursive Validation Grounding)

TDY_COH-A_19 (Recursive Operator Consistency with Halting Criterion)

related_equations:

TDY_COH-E_127 (Unconditional Convergence Property Definition)

TDY_COH-E_128 ($\operatorname{IsUIC}$ · Universal Iterative Contraction Property)

related_occ: [-]

related_protocols:

Recursive Actualization Protocol (RAP)

related_era:

TDY_COH-ERA_9