Passive fault tolerance at 4K. Glass-box AI. One mathematical correction -- replacing continuous geometry with ultrametric tree geometry -- addresses two multi-billion-dollar problems. All evidence is open-access. All demos are interactive. All code is MIT-licensed.
All 19 resources healthy -- 9 demos live · 10 publications verified · 19/19 online · See demos
Ternary Bruhat-Tits tree encoding produces zero logical errors at depth 7 (2,187 leaves), validated at physical error rates up to 40%. The strong triangle inequality geometrically prevents error accumulation.
DOI: Symmetric Extension →Encoding one logical bit across q=128 leaves reduces logical error rate by 48× -- achieved by exploiting existing hyperfine levels. Zero additional physical qubits required.
DOI: Symmetric Extension →Complete neutral atom hardware specification: ternary tree depth 3, Rydberg blockade gates, 4K operation. Within demonstrated experimental capabilities at Harvard, Caltech, PASQAL.
Try: Hardware Visualizer →Q-PNA linear mapping with cophenetic loss beats transformer 6.6× on hierarchical classification. STC verification: 100% detection rate, 0 false positives.
DOI: Q-PNA v2.0 →Scrollable charts from computational validation runs. All data from published results with registered DOIs.
Ternary Bruhat-Tits tree, p_err=0.2. LER drops to zero at depth 7 (2,187 leaves). DOI
Single logical bit, varying encoding leaves q. 48x reduction at q=128 -- zero additional qubits. DOI
Glass-box Q-PNA beats black-box transformer 6.6x on hierarchical classification. DOI
| Test | Metric | Result | Pass |
|---|---|---|---|
| Ultrametric containment | Triadic inequality | 649/649 triples pass | YES |
| Error detection | STC detection rate | 100% | YES |
| False positive rate | STC false alarms | 0 | YES |
| Hierarchical classification | Accuracy vs baseline | 6.6x | YES |
| Scatter reduction | Encoding gain q=128 | 48x | YES |
| Tree depth scaling | LER at d=7 | 0 (zero) | YES |
STC = Syntactic Token Calculus. Cross-referenced: The Tree Is Real, Q-PNA v2.0
Don't read about it. Watch it happen. Each demo demonstrates a key QWAV result in 30 seconds.
Watch ultrametric geometry suppress errors in real time. Adjust error rates and tree depth with sliders.
Explore glass-box AI decision trees. Train on sample data. See WHY each classification was made.
Watch particles cluster inevitably in ultrametric space -- and random-walk forever in Euclidean.
Compare cophenetic, ultrametric, and Euclidean distances. Discover triadic rigidity by clicking leaves.
Rotate and zoom a 40-atom neutral atom tree. See how Rydberg gates map to tree vertices.
One geometry, six domains. Explore how the same tree structure emerges independently in QEC, spin glasses, proteins, cosmology, cognition, and language.
One-command DOI registration. Publish papers to Zenodo without leaving the terminal.
All artifacts cross-linked: Error Confinement · Q-PNA · Convergence · Tree Distance · Hardware · Tree Universality · Virtual Qubit Showdown
All papers open-access on Zenodo with registered DOIs. Full archive at zenodo.org/communities/qwav/ (145+ records). Searchable catalog: Publication Hub → (35 publications, filter by domain, level, DOI)
| Title | Date | DOI | Code |
|---|---|---|---|
| Computational Validation of Ultrametric Error Confinement | 2026-05-12 | 10.5281/zenodo.20134944 | GitHub |
| Symmetric Extension -- Ternary Tree Architecture | 2026-05-16 | 10.5281/zenodo.20208437 | -- |
| Ultrametric Quantum Computing Foundations | 2026-05-15 | 10.5281/zenodo.20154557 | -- |
| Cross-Domain Synthesis: Ultrametric Geometry as Common Structure | 2026-05-17 | 10.5281/zenodo.20265907 | -- |
| Tree Distance Cophenetic | 2026-05-18 | 10.5281/zenodo.20213043 | -- |
| When Proofs Deceive -- A Taxonomy of Mathematical Certainty | 2026-05-18 | 10.5281/zenodo.20266032 | -- |
| Q-PNA Research Specification v2.0 | 2026-05-19 | 10.5281/zenodo.20287742 | GitHub |
| Convergence, Consilience, and the Hierarchical Architecture of Reality | 2026-05-20 | 10.5281/zenodo.20302276 | -- |
Each phase links to published work. Items marked [SPECULATIVE] are forward projections -- honest about what's verified vs planned.
Delivered: Zero logical errors at depth 7 (2,187 leaves). 48× error reduction at q=128. 40-atom hardware specification for neutral atom platforms. 6 interactive demos deployed (including Tree Universality Explorer). 30-publication prior work catalog curated. 8+ publications with registered DOIs on Zenodo. Symmetric Extension | Error Confinement Validation | The Tree Is Real | Tree Universality Explorer
Larger trees (d=8-10, multi-million leaf). Multi-prime validation (p=2,3,5,7). New error models: depolarizing, amplitude damping, correlated. Q-PNA v2.1 with new hierarchical classification datasets. First inbound contact milestone for hardware collaboration. [SPECULATIVE: Timeline depends on external validation velocity]
Expanded domain coverage: biology (protein folding hierarchies), linguistics (Nested Semantic Trees, Few Become One), cosmology (hierarchical structure formation). New spinoffs from Issues.md. Strategy refresh at 6-month mark. Evidence deck with scrollable charts [DELIVERED: this site]. [SPECULATIVE: Domain expansion depends on collaborator availability]
If inbound contact converts: hardware validation on actual neutral atom or trapped ion platforms. Entity formation if funding triggers (grant, fellowship, institutional affiliation). Publication archive reaches 700+ (current trajectory). Convergence Consilience framework extended. [SPECULATIVE: All 2027 items are contingent on external factors]
30 key publications forming the QWAV research foundation. Full archive at zenodo.org/communities/qwav/ (145+ records). Organized by discovery thread.
| # | Publication | Date | Relevance to QWAV |
|---|---|---|---|
| 1 | Validation of Ultrametric Error Confinement | 2026-05-12 | First computational validation: zero logical errors at depth 7. p_ad=0.05-0.40 range. |
| 2 | Symmetric Extension of Ultrametric Error Confinement | 2026-05-16 | Formal proof of strong triangle inequality error suppression. 48x reduction at q=128. |
| 3 | Ultrametric Quantum Computing Foundations | 2026-05-15 | Complete formalism: Bruhat-Tits encoding, p-adic valuation, logical qubit mapping. |
| 4 | The Tree Is Real | 2026-05-21 | 649 triples computational validation -- all triples satisfy ultrametric inequality. |
| 5 | TREE OF FREQUENCIES | 2026-05-06 | Physical tree concept: microwave/RF spectral encoding in ultrametric trees. |
| 6 | How Geometry Creates Memory | 2026-05-06 | Threshold Principle: ultrametric geometry prevents information leakage by design. |
| 7 | Ultrametric Quantum Computation (April) | 2026-04 | Early formalism: p-adic quantum mechanics and Bruhat-Tits tree encoding. |
| 8 | Bruhat-Tits Quantum Processor | 2026-05 | Hardware architecture: Rydberg atoms on Bruhat-Tits tree vertices. |
| # | Publication | Date | Relevance to QWAV |
|---|---|---|---|
| 9 | Q-PNA Research Specification v2.0 | 2026-05-19 | Neural architecture: p-adic valuation encoding, ultrametric attention, cophenetic loss. |
| 10 | Symmetry as a Grammatical Function | 2026-05-08 | Symmetry emerges from grammatical constraints -- formal basis for STC detection. |
| 11 | Few Become One | 2026-05-22 | Polysynthetic communication and ultrametric language architecture. Nested Semantic Trees. |
| 12 | Language as Information Architecture | 2026-05-12 | Entropy gradient, mutual exclusion principle -- quantitative language foundation. |
| 13 | The Tree at the Bottom of Thought | 2026-05-21 | Synthesis: ultrametric branching across all cognitive domains. |
| # | Publication | Date | Relevance to QWAV |
|---|---|---|---|
| 14 | Tree Distance Cophenetic | 2026-05-18 | Mathematical formalization of cophenetic distance on rooted trees. |
| 15 | Ultrametric Geometry as Common Structure | 2026-05-17 | Cross-domain synthesis: ultrametric trees in 5 disparate domains. |
| 16 | Convergence, Consilience, and Hierarchical Architecture | 2026-05-20 | Meta-analysis of convergence/consilience as signatures of hierarchical reality. |
| 17 | When Proofs Deceive | 2026-05-18 | Taxonomy of mathematical certainty -- epistemic foundation for ultrametric claims. |
| 18 | Hierarchical Universe | 2026-05 | Cosmological ultrametric structure: galaxy clusters, dark matter halos as tree nodes. |
| 19 | Hierarchical Geometry of Numbers | 2026-05 | p-adic valuation as natural hierarchical measure on integers. |
| 20 | Bruhat-Tits Tree as Unifying Geometric Object | 2026-05 | Mathematical synthesis: the B-T tree as bridge between p-adic analysis and physics. |
| 21 | Fine-Structure Constant as a Cross-Ratio | 2026-05 | Cross-ratio invariant on p-adic trees -- physical constants from geometry. |
| 22 | Adelic Constraints on QFT (Phases 1-3) | 2026-05 | Three-phase program: adelic constraints on quantum field theory. |
| # | Publication | Date | Relevance to QWAV |
|---|---|---|---|
| 23 | Force-Multiplier Playbook | 2026-05 | Solo deep-tech strategy: how one person competes with institutional labs. |
| 24 | An Introvert's Deep-Tech Startup Path | 2026-05 | Non-traditional research career path -- QWAV's operational model. |
| 25 | A Different Geometry for Computing | 2026-05 | Accessible introduction: why changing geometry changes everything. |
| 26 | Two Ways of Measuring | 2026-05 | Ultrametric vs Euclidean distance -- philosophical and mathematical contrast. |
| 27 | Every Point is the Center of its Own Universe | 2026-05 | Ultrametric topology: every ball is a center -- philosophical implications. |
| 28 | Road Not Taken | 2026-05 | Historical: why ultrametric geometry was overlooked in 20th-century physics. |
| 29 | Statistical Genesis of Appearance | 2026-05 | How continuous appearance emerges from discrete hierarchical structure. |
| 30 | Ultrametric Paradigm | 2026-05 | Programmatic overview of ultrametric geometry as paradigm shift. |
30 key publications curated from the QWAV corpus. Each maps to the ultrametric tree framework. Full catalog with DOIs and relevance statements: 0.3.md
| # | Publication | Domain | Key Finding |
|---|---|---|---|
| 1 | Computational Validation of Ultrametric Error Confinement | QEC L2 | Zero errors at depth 7 via Bruhat-Tits tree encoding |
| 2 | Symmetric Extension of Ultrametric Error Confinement | QEC L2 | Ternary architecture, 48x scatter reduction, 40-atom pathway |
| 3 | Parisi -- Infinite Number of Order Parameters (1979) | Spin Glass L3 | Nobel 2021: independently discovered ultrametric tree of pure states |
| 4 | Frauenfelder/Wolynes -- Energy Landscapes (1991) | Protein L4 | Protein folding as diffusion on hierarchical energy tree |
| 5 | Springel et al. -- Millennium Simulation (2005) | Cosmology L5 | Cosmic merger trees: cophenetic correlation > 0.85 |
| 6 | Cross-Domain Synthesis: Ultrametric Geometry as Common Structure | Synthesis L5 | 5 integration points mapping tree geometry across 5 domains |
| 7 | The Tree Is Real -- Computational Validation of Ultrametric Convergence | Meta L2 | Computational meta-analysis: hierarchy produces ultrametric signatures |
| 8 | The Tree at the Bottom of Thought | Cognition L5 | Semantic memory as cophenetic tree with triadic rigidity |
| 9 | Few Become One -- Polysynthetic Communication | Language L5 | Morpheme scope relations form ultrametric branching architecture |
| 10 | The Tree and Its Shadow -- Unified Phase Diagram | Synthesis L1 | Phase diagram of ultrametric organization vs. noise |
Full 30-publication catalog with DOIs at ultrametric-tree-universality/0.3.md