16 KiB
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) and the implementation of the Deterministic Fibonacci search (ADR-0242), 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.
- 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: $$\psi_{ ext{context}}(X) = \sum_i c_i \psi_{ ext{token}_i}(X) - Holomorphic Dispersion: As
\\psi\_{ ext{context}}is injected, it propagates through theVocabManifold. Proximity and meaning are not calculated via nearest-neighbor vector scans. Instead, the wave disperses and performs parallel cross-correlation with the registered standing-wave modes{\\psi\_k}of the Hyperbolic Atlas, generating a spectrum of resonant coefficients: $$R_k = \int_M \langle \psi_{ ext{context}}(X) \widetilde{\psi}_k(X) angle_0 dX$$ This represents the instant, parallel projection of the input context onto the entire known semantic manifold.
2.2 Reasoning and Problem Solving: Hamiltonian Well Relaxation
Problem-solving is re-engineered as a Physical Wave-Field Relaxation Process, replacing probabilistic step-by-step tree search.
- The Problem Hamiltonian: The constraints and boundary conditions of a given problem (e.g. mathematical equalities, safety rules, or logical premises) are formulated as potential energy barriers or wells in a problem-specific Hamiltonian operator
\\mathcal{H}\_{ ext{problem}}. - Relaxation to Eigenstates: The ingress wave field
\\psi\_{ ext{context}}(X)is set as the initial state\\psi(X, 0). The system is allowed to evolve under the Algebraic Schrödinger Equation: $$\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.
- Thermodynamic Energy Classes: The Field Energy Operator (
H, defined in ADR-0006) 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.
- 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. - GoldTether Gate: Before any token or continuous action is permitted to exit the boundary, the GoldTether unit residual is evaluated: $$R_{ ext{GoldTether}} = \sup_{X \in M} \left| \psi_{ ext{steady}}(X) \widetilde{\psi}_{ ext{steady}}(X) - 1 ight|_F < 10^{-6}
If the generated state would introduce non-unitary drift (hallucination or ungrounded statements), the gate closes instantly, blocking the output and prompting a pre-ratified, safe fallback.
2.4 Speculative Contemplation and Non-Resonant Curiosity
Active thinking, self-reflection, and learning are modeled as Speculative Contemplation and Non-Resonant Curiosity, replacing classical gradient-descent backpropagation.
- Speculative Generation: During idle cycles, the contemplation loop (
core/contemplation/runner.py) speculatively generates wave-packets\\psi\_{ ext{speculative}}(X)representing potential hypotheses or analogical transfers. - Orthogonal Surprise Check: The non-resonant surprise residual of the speculative wave is evaluated: $$\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 aDiscoveryCandidateand 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), 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 theevals/andcalibration/quarantine zones until ratified by a signed human certificate.
5. References
docs/adr/ADR-0003-coordinate-system-dissolution.md— Relational fields replacing coordinate frames.docs/adr/ADR-0238-GoldTether-Modulated-Supervised-Autonomy.md— GoldTether residual monitoring.docs/adr/ADR-0239-Conformal-Procrustes-Surprise-Dual-Operator.md— Conformal Procrustes and surprise.docs/adr/ADR-0241-wave-field-driven-hyperbolic-atlas-and-resonant-cognition.md— Continuous wave-field framework.docs/adr/ADR-0242-deterministic-fibonacci-operators-and-evidence-gated-optimization.md— Fibonacci search contract.