AAMT Working Paper Series

AsAManThinks Research · Mathematics of the MaiiaM Architecture

This repository is the canonical source for the AAMT Working Paper Series — 25 research working papers plus a 2-paper Experiments Series, establishing the mathematical foundations of the MaiiaM Alchemist architecture. Every paper is also permanently archived on Zenodo (DOI-linked below) and is clonable here as a single, version-controlled collection.

git clone https://github.com/wwhitehead/AAMT-Mathematics-Framework.git

---

What This Is

Modern AI treats optimization as brute-force statistics: trillions of parameters, datacenter-scale compute, and reward models that collapse under self-training feedback. The AAMT architecture replaces that with structural geometry.

The papers in this series define:

• TERA Algebra — a 4D symbolic coordinate system (Temporal, Emotional, Rational, Archetypal) that replaces learned softmax gates with closed-form geometric projections
• VortexGate MoE — zero-parameter routing via rank-1 product-Bernoulli measures on a 16-vertex Boolean hypercube
• HeartScale HCRS — per-token alignment filtering using hidden-state geometry, no reward model required
• Sign-Inversion Layer — the missing multiplicative operator M that transforms adversarial directions rather than deleting them; (−a)(−b) = ab
• Product-Bernoulli Hypercubes — a unified algebra showing 16-Meji / 64-State / Odu-256 are one parameterized family Hyp(d) at d = 4, 6, 8
• The .aamt Substrate (WP-23–25) — a memory-mapped hexadeca-tree binary format giving the TERA/Meji/Odu lattice a zero-copy, cross-platform artifact (native C++, Python, WebAssembly, and Unity all open the same bytes), with geometric mirror-pairing redundancy, GF(16) Reed–Solomon error correction, and CRDT-based multi-writer convergence
• A complete training and inference stack — phase scheduling, rank annealing, continual learning, model editing, semantic memory, federated dispatch, and consumer hardware inference — all grounded in the same number-theoretic and information-geometric foundations
• An Experiments Series (EXP-01–02) that tests specific operator claims directly, stating a falsifiable prediction before measuring it, and reporting corrections to its own earlier claims when the data disagrees

---

Core Mathematical Foundations

Zenodo anchor collection: 10.5281/zenodo.19600795

Five foundational papers establishing the dual-operator field equation ∂|ψ⟩/∂t = (M·F − R)|ψ⟩:

Paper	Title	File
I	Multiplicative Evaluation — The Zero-Veto Weighted Geometric Mean	Paper_I_Multiplicative_Evaluation.pdf
II	Toroidal Optimization — 4τ Permanence and the Breath Cycle	Paper_II_Toroidal_Optimization.pdf
III	Quadratic Scaling — The V(N) = αN − βN² Capacity Law	Paper_III_Quadratic_Scaling.pdf
IV	Generative Operator — Nonlinear Conservation in Dual-Operator Systems	Paper_IV_Generative_Operator.pdf
V	Unified Intelligence — Toward a Unified Field Theory	Paper_V_Unified_Intelligence.pdf

---

Working Paper Series (WP-01 – WP-25)

All papers are CC BY 4.0. Papers marked Rev 2 contain substantive corrections or extensions — those versions are in papers/ and on Zenodo as new versions under the same concept DOI.

WP	Title	Rev	Zenodo DOI	PDF
01	Vortex-Gated Mixture of Experts: Symbolic Zero-Parameter Routing via TERA Projection	Rev 2	10.5281/zenodo.20150167	↓
02	HeartScale Coherence Rejection Sampling: Inference-Time Alignment via Hidden-State Geometry	Rev 2	10.5281/zenodo.20150179	↓
03	Phase-Coherent Inference: Dynamic Compute Allocation via Phi-Twisted Toroidal Breath Scheduling	Rev 2	10.5281/zenodo.20150181	↓
04	Append-Only Lineage Graphs for Closed-Loop Model Improvement: Harvest, Gate, Retrain	Rev 2	10.5281/zenodo.20150193	↓
05	Odu-256 Archetypal Curriculum Mixing: Symbolic Taxonomic Weighting for Training Data Distribution	v1	10.5281/zenodo.20150195	↓
06	Provenance-Tracked Concept Directional Substitution: Lineage-Sourced Replacement Vectors for Auditable Model Editing	Rev 2	10.5281/zenodo.20484507	↓ · md
07	Merkle-Chained LoRA Genealogy and Hopfield Attractor Watermarking for Adapter Provenance Verification	v1	10.5281/zenodo.20484511	↓
08	Multiverse Superposition Inference: Chaos-Seeded Adapter Ensembles with HeartScale Affinity Blending	Rev 2	10.5281/zenodo.20484513	↓ · md
09	Compile-Gated DPO: Executable Verification as an Automated Preference Signal for Game-Engine Code Generation	v1	10.5281/zenodo.20484515	↓
10	Digital-Root Rotary Position Encoding: The 1→2→4→8→7→5 Cycle as a Basis for Sequence Position Representation	Rev 2	10.5281/zenodo.20484517	↓ · md
11	Shell-Coherent Expert Specialization: Alignment-Posture Assignment in Mixture-of-Experts Language Models	v1	10.5281/zenodo.20484519	↓
12	Filesystem-Mediated Multi-Agent Coordination: PID Registries, Cross-Repo Path Aliases, and Idempotent .env Injection	v1	10.5281/zenodo.20484527	↓
13	Inference on Consumer Silicon: Phase-Gated Compute, Shared-Base LoRA Sharding, and MPS Isolation for 2B-Parameter MoE Models	v1	10.5281/zenodo.20484529	↓
14	Federated Shell-Affinity Swarm Dispatch: Symbolic Alignment State as a Distributed Inference Routing Signal	v1	10.5281/zenodo.20484531	↓
15	Vortex-Addressed Semantic Memory: Retrieval by Archetypal Geometry Rather Than Embedding Similarity	Rev 2	10.5281/zenodo.20484533	↓ · md
16	Sign-Inversion as a Generative Safety Operator: The M-Operator and Reflect-Not-Mask Repair	v1	10.5281/zenodo.20710543	↓ · md
17	Product-Bernoulli Hypercubes: A Unified Algebra for Meji, 64-State, and Odu-256 Routing	v1	10.5281/zenodo.20710545	↓ · md
18	Number-Theoretic Scheduling for Diffusion Language Models: Void Descent, Digital-Root Cycles, and Commit Gating	v1	10.5281/zenodo.20710552	↓ · md
19	Channel Carving: Low-Resistance Attractor Formation Unifying Steering, Guidance, and Collapse	v1	10.5281/zenodo.20701845	↓ · md
20	Voxel-Addressable Memory: A Unified Spatial Index for Sovereign AI	v1	10.5281/zenodo.20887482	↓ · md
21	Voxel-Steered Autoregressive Generation: Overcoming the Quadratic Output Wall	v1	10.5281/zenodo.20945234	↓ · md
22	Odu Coverage Map: Session-Level Entropy Monitoring and Fisher–Rao Escape Steering for Semantic Loop Prevention	v1	10.5281/zenodo.20945238	↓ · md
23	The .aamt Substrate: Memory-Mapped Hexadeca-Tree Storage and Zero-Copy Geometric Routing (the Micro-VM Layer)	Rev 2	10.5281/zenodo.21316192	↓ · md
24	The AAMT Platform Architecture: Construction, Runtime, Ecosystem Integration, and Comparative Position	v1	10.5281/zenodo.21271708	↓ · md
25	Using the AAMT Substrate: Integration Points and Wiring Status	Rev 2	10.5281/zenodo.21316193	↓ · md

Zenodo concept DOIs (the WP-01–05 links above) always resolve to the latest version automatically. Papers marked Rev 2 link directly to the current version's DOI; the prior version stays permanently citable under the same concept DOI.

---

Experiments Series (EXP-01 – EXP-02)

A second series testing specific operator claims directly rather than assuming them — each paper states a falsifiable prediction before measuring it, and reports a correction to its own earlier claim when the data disagrees rather than leaving it standing.

#	Title	Rev	Zenodo DOI	PDF
01	Topological Trit Memory: Data Storage in a Chiral Field Lattice, and the √λ Depinning Law	v1	10.5281/zenodo.21185632	↓ · md
02	Echo Refocusing: When a Single Pulse Cancels TERA-Space Drift, and When It Provably Cannot	Rev 2	10.5281/zenodo.21316196	↓ · md

---

Architecture Map

Bottom-up dependency: each layer builds on the ones below. Gold = new unifier papers (WP-16–19). Six invariant spines (S1–S6) shown on the right connect papers across layers.

How the 22 papers form a unified stack:

FOUNDATIONS (Papers I–V)
  Dual-operator field: ∂|ψ⟩/∂t = (M·F − R)|ψ⟩
  TERA conservation law · 4τ permanence · quadratic scaling V(N)=αN−βN²
          │
          ▼
DISCRETE ALGEBRA (WP-17)
  Hyp(d) family: 16-Meji = Hyp(4) · 64-State = Hyp(6) · Odu-256 = Hyp(8)
  Unified Fisher–Rao metric · rank-1 losslessness · 64↔TERA Hopf bridge
          │
     ┌────┴──────────────────────────────┐
     ▼                                   ▼
ROUTING (WP-01, 11)             DATA & TRAINING SIGNAL (WP-05, 09)
VortexGate MoE                  Odu-256 curriculum mixing
Zero-param, rank-1 gate         Compile-gated DPO
     │                                   │
     ▼                                   ▼
ALIGNMENT OPERATORS (WP-02, 16)  POSITION & RANK (WP-10, 18)
  F  forward pass (WP-01)        DR-RoPE · φ-twist scheduling
  R  HCRS rejection (WP-02)      Golden-ratio macro clock
  M  Sign-Inversion Layer (WP-16) Digital-root micro basis
     │                                   │
     ▼                                   ▼
ENSEMBLING (WP-08)               TRAINING PIPELINE (WP-03, 04, 06, 07)
MSI = tensor rank-lift of WP-01  Phase scheduling · LACL lineage graphs
N product-Bernoulli ensemble     PT-CDS auditable model editing
                                 Merkle-LoRA provenance watermarking
          │
          └──────────────────────────────┐
                                         ▼
                               MEMORY & DISPATCH (WP-15, 14, 12, 13)
                               VASM archetypal-geometry retrieval
                               Shell-affinity swarm dispatch
                               Filesystem multi-agent coordination
                               Consumer silicon inference runtime
                                         │
                                         ▼
                                  UNIFIED DYNAMICS (WP-19)
                                  Channel Carving — steerability,
                                  mode collapse, and permanence
                                  as one τ-law: R(t) = R₀·e^{-t/τ}
                                          │
                                          ▼
                                GENERATIVE OUTPUT (WP-20, 21, 22)
                                Voxel-Addressable Memory (WP-20)
                                Rolling Output Eviction (WP-21)
                                Odu Coverage Map entropy monitor (WP-22)

---

Live Demos — HuggingFace Spaces

Space	What It Demonstrates	Link
AAMT Math Visualizer	Interactive simulations for WP-01 (VortexGate routing), WP-02 (HeartScale), WP-15 (VASM Fisher–Rao), WP-16 (Sign-Inversion), WP-17 (Hyp(d) geometry), WP-18 (scheduling curves), WP-20 (Voxel Memory octree), WP-21 (Voxel-Steer AR rolling output loop), WP-22 (Odu Coverage Map entropy monitor)	🤗 docwes1/aamt-math-viz-demo
HeartScale Gate	Live demo of the HCRS coherence filter (WP-02) — per-token alignment scoring, zero-veto multiplicative evaluator, no reward model	🤗 docwes1/heartscale-gate

---

Related Repositories

Repo	Purpose
wwhitehead/AAMT-Mathematics-Framework	This repo — full paper archive + markdown sources
wwhitehead/aamt-reproduce	Independent, runnable verification of WP-series claims — TERA/VortexGate, HeartScale, DR-RoPE
wwhitehead/aamt-space	Agent powering the AAMT HuggingFace Space visualizer
wwhitehead/maiiam-viewer	MaiiaM viewer application
wwhitehead/anything-llm-mwings	AnythingLLM fork with MaiiaM Wings integration

---

Repository Structure

AAMT-Mathematics-Framework/
├── README.md
├── LICENSE                                    (CC BY 4.0)
│
├── papers/                                    (WP-01 through WP-25 + EXP-01/02, latest versions)
│   ├── wp-01-vortex-gated-moe.pdf
│   ├── wp-02-heartscale-coherence-rejection-sampling.pdf
│   ├── ...
│   ├── wp-21-voxel-steered-autoregressive-generation.pdf
│   ├── wp-22-odu-coverage-map.pdf
│   ├── wp-23-aamt-substrate.pdf
│   ├── wp-24-aamt-platform-architecture.pdf
│   ├── wp-25-aamt-substrate-integration-guide.pdf
│   ├── exp-01-topological-trit-memory.pdf
│   ├── exp-02-echo-refocusing.pdf
│   └── sources/                               (Markdown source for revised + new papers)
│       ├── wp-01-vortex-gated-moe.md          (Rev 2)
│       ├── wp-06-concept-directional-substitution.md  (Rev 2)
│       ├── wp-16-sign-inversion-generative-operator.md
│       ├── wp-23-aamt-substrate.md            (Rev 2)
│       ├── wp-24-aamt-platform-architecture.md
│       ├── wp-25-aamt-substrate-integration-guide.md  (Rev 2)
│       ├── exp-01-topological-trit-memory.md
│       ├── exp-02-echo-refocusing.md          (Rev 2)
│       └── ...
│
├── foundations/                               (Mathematical Foundations Papers I–V)
│   ├── Paper_I_Multiplicative_Evaluation.pdf
│   ├── Paper_II_Toroidal_Optimization.pdf
│   ├── Paper_III_Quadratic_Scaling.pdf
│   ├── Paper_IV_Generative_Operator.pdf
│   └── Paper_V_Unified_Intelligence.pdf
│
└── provisional-patents/                       (USPTO provisional filings)
    ├── Provisional_1_Multiplicative_Evaluation.docx
    ├── Provisional_2_Breath_Cycle_Training.docx
    └── Provisional_3_Sign_Inversion_Layer.docx

---

Citation

For the full series (permanent Zenodo collection):

@misc{whitehead2026aamt,
  author    = {Whitehead, Weslyn Cory},
  title     = {{AAMT} Mathematical Foundations: A Unified Framework for
               Biological and Artificial Intelligence},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.19600795},
  url       = {https://doi.org/10.5281/zenodo.19600795}
}

For individual papers, use the per-paper DOI from the table above:

@techreport{whitehead2026vortex,
  author      = {Whitehead, Weslyn Cory},
  title       = {Vortex-Gated Mixture of Experts: Symbolic Zero-Parameter
                 Routing via {TERA} Projection},
  institution = {AsAManThinks Research},
  year        = {2026},
  type        = {Working Paper AAMT-WP-01, Revision 2},
  doi         = {10.5281/zenodo.20150167},
  url         = {https://doi.org/10.5281/zenodo.20150167}
}

---

Contact

Author: Weslyn Cory Whitehead Jr.
Research Hub: asamanthinks.com
ORCID: 0009-0005-7707-3210
Email: yarethewatchman@gmail.com

For licensing inquiries regarding TERA, VortexGate, HeartScale, or the Sign-Inversion Layer (patent pending), contact via email above.