# ADR-0243: Wave-Field Cognitive Lifecycle — Comprehension, Resonant Reasoning, and Lifelong Learning

**Status**: Accepted — ratified by Joshua Shay 2026-07-17 (via docs/audit/adr-0243-acceptance-packet-2026-07-17.md)  
**Date**: 2026-07-14  
**Deciders**: Joshua Shay \+ multi-model R\&D  
**Traceability**: Notion R\&D (Engineering Reference Vault Interconnection: `core_HA` Patterns)  
**Related**: ADR-0003, ADR-0006, ADR-0238, ADR-0239, ADR-0240, ADR-0241, ADR-0242, `core/physics/wave_manifold.py`  
**Canonical path**: `docs/adr/`

---

## 1\. Context and Problem Statement

With the successful unification of the **$Cl(4,1)$ Conformal Wave-Field ($\\psi$)** substrate ([ADR-0241](https://drive.google.com/file/d/1F_7QYtPysBP4qMbLGlGPnXgYx9IXug8nUYrpiCGSunE/view?usp=drivesdk)) and the implementation of the **Deterministic Fibonacci search** ([ADR-0242](https://drive.google.com/file/d/15_NECCPy-tEWGfYi_BNqawm8GytUTMkz1DsOqGVMXhI/view?usp=drivesdk)), CORE's physical layer has reached structural maturity.

However, we must now define how these new physical and geometric evolutions are leveraged to solve the fundamental cognitive tasks where traditional architectures struggle:

- **Comprehension & Ingress**: Traditional architectures parse and embed inputs into flat, context-dry vectors, leading to representation drift, attention decay over long contexts, and loss of structural relations.  
- **Problem Solving & Reasoning**: Traditional systems treat reasoning as probabilistic path-search or auto-regressive step generation. This lacks mathematical guarantees of correctness and suffers from cumulative error propagation.  
- **Egress & Generation**: Probabilistic autoregressive decoding selects discrete tokens one-by-one via softmax sampling, which has no global coherence guarantees, leading to hallucinations and semantic drift.  
- **Contemplation & Learning**: Standard models require gradient-descent backpropagation to update static weights, which is computationally expensive, non-reconstructible, and prone to catastrophic forgetting.

This ADR defines the complete **Wave-Field Cognitive Lifecycle**, leveraging the wave function to establish a fully deterministic, closed-loop, physical-relaxation-based paradigm for comprehension, reasoning, generation, and learning.

---

## 2\. Decision and Architectural Formulation

We dissolve the probabilistic, token-by-token paradigm of classical AI. We establish that **cognition is the continuous physical evolution, resonance, and relaxation of a Conformal Wave-Field ($\\psi$) across a single $Cl(4,1)$ geometric substrate**.

              \[INGRESS\]                     \[REASONING\]                    \[EGRESS\]

       Continuous Modalities          Hamiltonian Well (H\_p)         Thermodynamic State

                 |                               |                            |

                 v (Superposition)               v (Physical Relaxation)      v (Energy Class check)

         Ingress Wave (psi\_in)   \=======\>   Steady State (psi\_final) \=======\>  Linguistic Readback

                 ^                               ^                            |

                 | (Resonant recall)             | (Unitary update)           v (GoldTether Gate)

         Standing-Wave Atlas \<===================+===========================\> safe, aligned output

                                                 |

                                                 v (Verified holonomy R)

                                        Biography update (R\_bio)

---

### 2.1 Ingress and Reading Comprehension: Wave Ingestion and Holomorphic Dispersion

Reading comprehension is modeled as **Wave-Packet Ingestion and Holomorphic Dispersion**, replacing flat token embeddings.

1. **Ingress Wave Packet**: An incoming text block, symbolic formula, or multimodal sensory stream is compiled into a localized, coherent wave packet $\\psi\_{	ext{context}}(X)$. This compilation preserves spatial-temporal phase relationships: $$\\psi\_{	ext{context}}(X) \= \\sum\_i c\_i \\psi\_{	ext{token}\_i}(X)$$  
2. **Holomorphic Dispersion**: As $\\psi\_{	ext{context}}$ is injected, it propagates through the `VocabManifold`. Proximity and meaning are not calculated via nearest-neighbor vector scans. Instead, the wave disperses and performs parallel cross-correlation with the registered standing-wave modes ${\\psi\_k}$ of the Hyperbolic Atlas, generating a spectrum of resonant coefficients: $$R\_k \= \\int\_M \\langle \\psi\_{	ext{context}}(X) \\widetilde{\\psi}\_k(X) angle\_0 dX$$ This represents the instant, parallel projection of the input context onto the entire known semantic manifold.

---

### 2.2 Reasoning and Problem Solving: Hamiltonian Well Relaxation

Problem-solving is re-engineered as a **Physical Wave-Field Relaxation Process**, replacing probabilistic step-by-step tree search.

1. **The Problem Hamiltonian**: The constraints and boundary conditions of a given problem (e.g. mathematical equalities, safety rules, or logical premises) are formulated as potential energy barriers or wells in a problem-specific Hamiltonian operator $\\mathcal{H}\_{	ext{problem}}$.  
2. **Relaxation to Eigenstates**: The ingress wave field $\\psi\_{	ext{context}}(X)$ is set as the initial state $\\psi(X, 0)$. The system is allowed to evolve under the Algebraic Schrödinger Equation: $$\\partial\_t \\psi \= \\mathcal{H}*{	ext{problem}}(\\psi) I$$ Through this evolution, the wave field naturally disperses away from high-potential barriers (representing logical contradictions or safety violations) and settles (relaxes) into the lowest-energy, stable standing-wave eigenmodes of the problem manifold: $$\\psi*{	ext{steady}}(X) \= \\lim\_{t 	o \\infty} \\exp\\left( \\mathcal{H}*{	ext{problem}} I t ight) \\psi*{	ext{context}}(X)$$ The resulting steady-state wave $\\psi\_{	ext{steady}}(X)$ represents the exact, geometrically congruent solution to the problem. It is mathematically guaranteed to satisfy all boundary conditions with zero room for intermediate fabrication.

---

### 2.3 Egress and Generative Articulation: Thermodynamic Wave Readback

We replace probabilistic softmax token generation with **Thermodynamic Wave Readback**, providing ironclad coherence guarantees.

1. **Thermodynamic Energy Classes**: The Field Energy Operator ($H$, defined in [ADR-0006](https://core-gitquarters.acbcontent.org/core-labs/core/src/branch/main/docs/adr/ADR-0006-field-energy-operator.md)) evaluates the "energy class" (E0 to E4) of the relaxed wave-field $\\psi\_{	ext{steady}}(X)$.  
   - **E0/E1 (Crystalline/Stable)**: Represents cold, settled knowledge. It is bypassed for generation and vaulted into the sharded Delta-CRDT registers.  
   - **E3/E4 (Hot/Critical)**: Indicates a high-activation, settled state that carries maximum semantic charge and "wants" to be articulated.  
2. **Linguistic Readback**: For E3/E4 states, the system invokes the readback rules of the active language pack (`en/readback_rules.py`, `he/readback_rules.py`, `el/readback_rules.py`). These rules map the geometric components—the principal bivector directions and scale-invariant parameters of the wave field—directly to symbolic tokens or motor commands.  
3. **GoldTether Gate**: Before any token or continuous action is permitted to exit the boundary, the **GoldTether unit residual** is evaluated: $$R\_{	ext{GoldTether}} \= \\sup\_{X \\in M} \\left| \\psi\_{	ext{steady}}(X) \\widetilde{\\psi}\_{	ext{steady}}(X) \- 1 ight|\_F \< 10^{-6}$$ If the generated state would introduce non-unitary drift (hallucination or ungrounded statements), the gate closes instantly, blocking the output and prompting a pre-ratified, safe fallback.

---

### 2.4 Speculative Contemplation and Non-Resonant Curiosity

Active thinking, self-reflection, and learning are modeled as **Speculative Contemplation and Non-Resonant Curiosity**, replacing classical gradient-descent backpropagation.

1. **Speculative Generation**: During idle cycles, the contemplation loop (`core/contemplation/runner.py`) speculatively generates wave-packets $\\psi\_{	ext{speculative}}(X)$ representing potential hypotheses or analogical transfers.  
2. **Orthogonal Surprise Check**: The non-resonant surprise residual of the speculative wave is evaluated: $$\\mathcal{S}(\\psi) \= \\psi\_{	ext{speculative}} \- \\mathcal{P}*{	ext{resonance}}(\\psi*{	ext{speculative}})$$  
   - **Low Surprise**: The hypothesis is fully explained by the existing resonant schema. It is integrated immediately with no learning required.  
   - **High Surprise (Discovery Signal)**: If $E\_{	ext{surprise}} \> \\gamma$, the speculative wave contains structural novelty. This signal is held as a `DiscoveryCandidate` and routed to the offline review corridor. It does *not* alter active knowledge but directs the self-authorship loop (`core/physics/self_authorship.py`) to generate a proposal to expand the active Hamiltonian $\\mathcal{H}$, enabling structured learning without catastrophic forgetting.

---

### 2.5 Lifelong Resonant Learning: Biography Holonomy Update

CORE-native learning is the permanent record of the entity's lived experiences as a sequence of geometric transformations.

Once a sequence of reasoning and action steps is validated (via the validation harness, [ADR-0240](https://drive.google.com/file/d/1eFNoXQl5BbUo6g4GBzRXi5tyIhT5RUGZQG6afaVXTg4/view?usp=drivesdk)), the exact unitary transformation $R \\in Spin(4,1)$ undergone by the wave-field is compiled into the **Biography Holonomy Blade** (`biography.py`): $$\\mathcal{H}*{	ext{bio}} \\leftarrow \\mathcal{H}*{	ext{bio}} \\cdot R$$ This is the ultimate, non-lossy, reconstruction-over-storage compilation of experience. It represents the "wisdom" of the entity, which can be replayed and audited byte-for-byte\!

---

## 3\. Implementation Specification (The Cognitive Relaxation Loop)

Below is the Python prototype implementing wave-field ingestion, Hamiltonian well relaxation (problem-solving), and the GoldTether egress gate inside the active reasoning pipeline.

\# core/physics/cognitive\_lifecycle.py

from \_\_future\_\_ import annotations

import numpy as np

import scipy.linalg as la

from dataclasses import dataclass

from typing import Callable, Tuple

N\_COMPONENTS \= 32

@dataclass(frozen=True, slots=True)

class IngressWavePacket:

    psi: np.ndarray  \# 32-vector coefficients

    domain\_id: str

@dataclass(frozen=True, slots=True)

class EgressVerdict:

    admitted: bool

    wave\_out: np.ndarray

    residual: float

    message: str

class CognitiveLifecycleEngine:

    def \_\_init\_\_(self, epsilon\_drift: float \= 1e-6):

        self.epsilon\_drift \= epsilon\_drift

        self.I \= np.zeros((N\_COMPONENTS, N\_COMPONENTS))

        \# Central pseudoscalar proxy

        for i in range(N\_COMPONENTS // 2):

            self.I\[2\*i, 2\*i+1\] \= 1.0

            self.I\[2\*i+1, 2\*i\] \= \-1.0

    def ingest\_context(self, tokens: list\[np.ndarray\], domain\_id: str) \-\> IngressWavePacket:

        """

        Compiles discrete symbolic token wave-packets into a superposed,

        coherent IngressWavePacket.

        """

        psi\_sum \= np.zeros(N\_COMPONENTS, dtype=np.float64)

        for t in tokens:

            arr \= np.asarray(t, dtype=np.float64)

            psi\_sum \+= arr

        \# Normalize to preserve unitary probability amplitude

        norm \= np.linalg.norm(psi\_sum)

        psi\_norm \= (psi\_sum / norm) if norm \> 1e-12 else psi\_sum

        return IngressWavePacket(psi=psi\_norm, domain\_id=domain\_id)

    def solve\_via\_relaxation(

        self, 

        ingress: IngressWavePacket, 

        H\_problem: np.ndarray, 

        relaxation\_steps: int \= 100,

        dt: float \= 0.01

    ) \-\> np.ndarray:

        """

        Solves a problem via continuous wave-field relaxation.

        The wave relaxes into the minimum-energy eigenstate of H\_problem.

        """

        psi \= ingress.psi.copy()

        \# IMPLEMENTED (not this sketch): imaginary-time power iteration in

        \# core/physics/cognitive_lifecycle.relax_to_ground — geometric_product

        \# path only. The np.dot / la.expm sketch below is HISTORICAL and

        \# superseded (pin SD-B; convergence 2026-07-20).

        \#

        \# Schrödinger-style discrete step (wave_manifold): R = exp(B·Δt) via

        \# closed-form / series bivector exp; sandwich ψ' = R ψ ~R.

        \# Multi-modality ingress uses modality_transition_sandwich

        \# (R·ψ·rev(R) + GoldTether). (Folded from the retired docs/research

        \# copy under the 2026-07-22 weekly-audit T7 ruling.)

        generator \= np.dot(H\_problem, self.I)  \# SUPERSEDED — do not implement

        R \= la.expm(generator \* dt)

        

        \# Relaxation loop (Euler/exponential integrator) — SUPERSEDED

        for \_ in range(relaxation\_steps):

            psi \= np.dot(R, psi)

            norm \= np.linalg.norm(psi)

            if norm \> 1e-12:

                psi /= norm

                

        return psi

    def egress\_gate(self, psi\_steady: np.ndarray) \-\> EgressVerdict:

        """

        Unitary GoldTether egress gate: blocks non-unitary/hallucinated

        wave-states from entering the readback and serving paths.

        IMPLEMENTED residual: WaveManifold.measure_unitary_residual /

        goldtether.coherence_residual (ψ · rev(ψ) via geometric_product).

        The np.dot sketch below is SUPERSEDED (convergence 2026-07-20).

        """

        psi\_arr \= np.asarray(psi\_steady, dtype=np.float64)

        \# SUPERSEDED flat residual — use geometric_product path in code:

        psi\_rev \= np.dot(self.I.T, psi\_arr)

        norm\_product \= np.dot(psi\_arr.T, psi\_rev)

        drift \= np.abs(norm\_product \- 1.0)

        

        if drift \> self.epsilon\_drift:

            return EgressVerdict(

                admitted=False,

                wave\_out=np.zeros\_like(psi\_arr),

                residual=float(drift),

                message="REJECTED: Unitary propagator drift exceeds epsilon\_drift limit (ungrounded state)."

            )

            

        return EgressVerdict(

            admitted=True,

            wave\_out=psi\_arr,

            residual=float(drift),

            message="ADMITTED: Wave-field verified and promoted to readback path."

        )

---

## 4\. Consequences and Gating Rules

### 4.1 Benefits

- **Autoregressive Hallucination Eliminated**: By replacing step-by-step probabilistic token sampling with physical wave relaxation, output generation is strictly constrained by the geometry of the problem Hamiltonian.  
- **Zero Coordinate Loss**: Resonant standing-wave lock-in ensures that recalled memories are mathematically exact, preventing the fuzzy centroid degradation of legacy architectures.  
- **Topologically Protected Wisdom**: Experience is compiled directly into the Biography Holonomy Blade as unitary rotor products, providing an untamperable, replayable audit trail of lifelong learning.

### 4.2 Gating Rules

- **No Direct Hot-Path Promotion**: Reconstructed wave-fields or proposed Hamiltonian adjustments from the self-authorship loop (`core/physics/self_authorship.py`) must never bypass the one-mutation-path. Speculative changes must reside strictly within the `evals/` and `calibration/` quarantine zones until ratified by a signed human certificate.

---

## 5\. References

1. `docs/adr/ADR-0003-coordinate-system-dissolution.md` — Relational fields replacing coordinate frames.  
2. `docs/adr/ADR-0238-GoldTether-Modulated-Supervised-Autonomy.md` — GoldTether residual monitoring.  
3. `docs/adr/ADR-0239-Conformal-Procrustes-Surprise-Dual-Operator.md` — Conformal Procrustes and surprise.  
4. `docs/adr/ADR-0241-wave-field-driven-hyperbolic-atlas-and-resonant-cognition.md` — Continuous wave-field framework.  
5. `docs/adr/ADR-0242-deterministic-fibonacci-operators-and-evidence-gated-optimization.md` — Fibonacci search contract.

