References

WHAT THIS PAGE IS

This is the single consolidated bibliography for TSO v11.1. It gathers every external reference cited across the foundation, math, house, and roof pages, and adds several recent papers whose findings are independently consistent with TSO themes without being designed to test the framework. It also indexes the public Colab notebooks that implement TSO's calculations, so any reader can reproduce or challenge the numerical results.

Honest literature context. None of the external papers cited here directly tests or falsifies TSO. The framework is too new to have been engaged by published work. Recent literature searches (April 2026) found no paper that contradicts a specific TSO axiom, prediction, or mathematical claim, and no paper that validates one in a way that was not retrofitted. The alignments noted below are indirect resonances — independent results that echo TSO themes such as percolation transitions in quantum systems, vacuum coupling effects, coherence at criticality, and conditional topological stability. They are not proof of anything. They are the backdrop against which TSO's claims will eventually be tested.

TSO primary documents
Percolation theory and lattice mathematics
Quantum foundations, measurement, and decoherence
Quantum percolation and criticality (experimental)
Gravity, quantum gravity, and collapse
Particle physics and the Standard Model
Biology at criticality
Crystallization kinetics and cosmology
CMB birefringence and cosmological observables
TSO public Colab notebooks

1. TSO PRIMARY DOCUMENTS

Pepin, J. (original paper). Two State Ontology. Self-published. incapp.org/twostatetheory.pdf The foundational paper. Introduces S + W = 1, the continuum between quantum and classical states, and the original phenomenological parameter λ ≈ 10⁻¹¹ m²/s. Predates the Z = 7 lattice formulation and the tension asymmetry. Required reading for anyone evaluating how the framework has evolved.
Pepin, J. (Fire Model). TSO Fire Model Framework. Self-published. incapp.org/TSO_Fire_Model_Framework.pdf The intermediate framework with γ₀ as the base decoherence rate and α = 2d as the geometric constant. Most of its specific numerical values have been superseded by the dimensionless Pip formulation in v11.1, but the conceptual structure remains the bridge between the original paper and the current version.

2. PERCOLATION THEORY AND LATTICE MATHEMATICS

Stauffer, D. & Aharony, A. (1994). Introduction to Percolation Theory. Taylor & Francis, 2nd revised ed. DOI:10.1201/9781315274386 The standard reference for percolation thresholds and critical exponents. The value p_c ≈ 0.3116 used throughout TSO is the 3D site percolation threshold from this textbook. Not cited as evidence for TSO — cited because it is the source of the dimensionless constant the framework is built on.
Grimmett, G. (1999). Percolation. Springer, 2nd ed. DOI:10.1007/978-3-662-03981-6 Rigorous mathematical treatment of percolation theory. Relevant for the correlation-length critical exponent ν ≈ 0.88 used in TSO's sigmoid prediction (3D site percolation universality, corrected from the previously-asserted κ = 4/3 in v11.8 — see Prediction 40) and for understanding why spanning clusters fail cooperatively at threshold rather than gradually.
Fayfar, S. P., Bretaña, A., & Montfrooij, W. (2022). Protected percolation: a new universality class pertaining to heavily-doped quantum critical systems. J. Phys. Commun. 6, 075009. arXiv:2008.08258 Closest published prior art to TSO's wave-to-solid percolation mechanism — and as of v11.9, the structural basis for the epi-matter identification (Prediction 42). Defines a new percolation universality class where once a cluster breaks off the spanning cluster, its sites become "protected" and cannot be removed — the same physical structure as TSO's irreversible crystallization (wave→solid). For 3D simple cubic protected percolation, the measured exponents (β', γ', ν', τ') differ from standard 3D percolation; the susceptibility exponent γ' = 1.3066(19) is suggestively close to 4/3 but distinguishably different at high precision. Physical motivation comes from heavy-fermion quantum-critical systems (Ce(Fe,Ru)₂Ge₂, UCu₄Pd) where isolated magnetic clusters are protected from Kondo screening. TSO v11.9 proposes that the same protected percolation regime they characterized in condensed matter has a cosmological analog: what cosmology calls dark matter is epi-matter, substrate sitting in this protected regime at cosmological scales. The framework's MC tests (Notebook 3) explicitly compare against this baseline. Contacting Montfrooij's group (Missouri) is a natural outreach step; the v11.9 Euclid prediction notebook is written with this audience in mind.
Bianconi, G. & Dorogovtsev, S. N. (2024). Theory of percolation on hypergraphs. Phys. Rev. E 109, 014306. DOI:10.1103/PhysRevE.109.014306 General theory of percolation on hypergraphs (3-uniform and higher). Relevant to TSO because the Fano plane is a 3-uniform hypergraph — each of the seven Fano lines is a 3-element hyperedge. The paper shows that on hypergraphs the node-percolation threshold differs from the hyperedge-percolation threshold, which is the right machinery for analyzing percolation on the Z = 7 Fano lattice rigorously. Not yet applied to TSO; flagged as the standard reference for the next theoretical pass on the Fano-bond model.

3. QUANTUM FOUNDATIONS, MEASUREMENT, AND DECOHERENCE

Gleason, A. M. (1957). Measures on the closed subspaces of a Hilbert space. Indiana University Mathematics Journal, 6(4), 885–893. JSTOR link Gleason's theorem. TSO inherits the Born rule from this result and from CPⁿ geometry rather than deriving it independently. Cited to make the inheritance explicit — TSO does not claim to derive Born probabilities from scratch.
Zurek, W. H. (2003). Decoherence, einselection, and the quantum origins of the classical. Reviews of Modern Physics, 75, 715. arXiv:quant-ph/0105127 The environment-as-witness framing of decoherence. TSO's description of the observer as one γ_c,i contribution among many is consistent with Zurek's picture, with one addition: the framework makes the closing irreversible at the microscopic level, which gives the arrow of time without an extra postulate.
Gundhi, A., Navas-Garcia, J. L. G., & Smirne, A. (2024). Decoherence due to the Casimir effect? Physical Review D, 110, 116001. arXiv:2409.03866 Argues that previously-claimed Casimir-induced decoherence arises from sudden boundary switching rather than from continuous vacuum fluctuations in static geometries. Compatible with TSO's view that Casimir is one γ_c channel among many, insufficient in isolation to drive a typical system past p_c — additional γ_c contributions from thermal, photonic, or contact coupling are generally required. Found via independent literature search (Grok, April 2026) as the strongest potentially-adverse paper; on inspection it is not actually adverse.
Kincaid, J. M., McKenzie, R. H., & White, G. (2016). Measurement-induced decoherence and information in double-slit interference. American Journal of Physics, 84, 522. DOI:10.1119/1.4947254 Reference for the path-rotation reanalysis on the roof. TSO's P = cos²(θ) formula is exact to machine precision on this dataset, though mathematically equivalent to the standard Fubini-Study projection.

4. QUANTUM PERCOLATION AND CRITICALITY (EXPERIMENTAL)

The following papers show experimental results in quantum systems that exhibit percolation-like transitions, criticality-enhanced coherence, or unexpected phases at critical coupling. None was designed as a TSO test. Their relevance is indirect — they demonstrate that the physics TSO proposes is not, in principle, at odds with what is actually measured in the lab.

Feng, Z., et al. (2023). Direct observation of quantum percolation dynamics. Nanophotonics, 12(16), 3343–3353. De Gruyter — Nanophotonics Femtosecond-laser-written photonic lattices with up to 1,600 waveguides. The quantum percolation threshold is measured at ~80%, significantly higher than the classical threshold of ~63%. Resonates with TSO's claim that quantum spanning clusters require denser connectivity than classical ones to remain stable. Not a test of p_c = 0.3116 — the thresholds here are in a different observable — but an experimental confirmation that quantum and classical percolation thresholds can differ and that quantum systems have well-defined percolation transitions.
O'Rourke, M. J., & Chan, G. K.-L. (2023). Entanglement in the quantum phases of an unfrustrated Rydberg atom array. Nature Communications, 14, 5397. DOI:10.1038/s41467-023-41166-0 Square lattice of Rydberg atoms exhibits an unanticipated nematic phase stabilized by short-range entanglement and an "order-from-disorder" mechanism. Some predicted phases are destabilized while new ones appear. Echoes TSO's picture of unexpected phase richness near p_c — the spanning cluster topology can stabilize orders that mean-field analysis misses.
Liang, R., et al. (2026). Frustrated Rydberg Atom Arrays Meet Cavity-QED: Emergence of the Superradiant Clock Phase. Physical Review Letters (2026); preprint at arXiv (2025). PRL homepage Rydberg array coupled to an optical cavity produces a novel "superradiant clock" phase through cavity-mediated long-range interactions. Resonates with TSO's Γ_C accumulation picture: adding a γ channel (the cavity) shifts the system past a critical threshold and produces a new phase that did not exist without the extra coupling. Relevant because it shows phase transitions driven by adding coupling channels, which is exactly how TSO describes crystallization.
Vattay, G., Kauffman, S., & Niiranen, S. (2014). Quantum Biology on the Edge of Quantum Chaos. PLOS ONE, 9(3), e89017. DOI:10.1371/journal.pone.0089017 Systems near a critical quantum chaos transition (between integrable and chaotic regimes) can maintain quantum coherence orders of magnitude longer than expected at room temperature. Tested on the FMO light-harvesting complex. This is the strongest independent resonance for TSO's "life at p_c" claim — it provides an experimentally-tested mechanism by which coherence is enhanced precisely at criticality, which is what TSO requires biology to exploit.
Kim, K., Kim, M., Park, J., Byun, A., & Ahn, J. (2024). Quantum computing dataset of maximum independent set problem on king lattice of over hundred Rydberg atoms. Scientific Data, 11, 111. DOI:10.1038/s41597-024-02926-9 | Open access. Data: figshare CORRECTION (May 20, 2026): A previous version of this page cited this reference as "Kim et al. 2024, Nature 631, 536–541, DOI:10.1038/s41586-024-07700-w" — an antiferromagnetic Ising Rydberg simulator paper that could not be verified. That DOI points to an unrelated biology paper. The correct citation is the open-access Scientific Data MIS dataset paper above (same KAIST group, Jaewook Ahn corresponding author). The dataset contains 582,916 Rydberg-atom measurements with adiabatic sweeps across the transverse antiferromagnetic Ising Hamiltonian. A prior TSO session claimed a reanalysis of this dataset showed tanh beating exponential by 2.75× (ΔAIC > 30) — that claim has been withdrawn from predictions.html pending independent audit of the fitting procedure on the correct dataset. The public figshare data is available for independent verification.

4. QUANTUM PERCOLATION AND CRITICALITY (EXPERIMENTAL)

Feng, Z., et al. (2020). Experimental realization of quantum percolation transitions using photonic lattices. arXiv:2001.00268. Link → Direct measurement of quantum vs classical percolation thresholds on a photonic chip (up to 1,600 waveguides, hexagonal lattice). Quantum threshold = 80%, classical = 63%, gap = 0.104. Benchmark for TSO quantum percolation predictions. The IBM ibm_marrakesh run (May 2026) reproduced the same gap structure on a different platform and topology (heavy-hex, gap = 0.161).
Xia, Z., et al. (2025). Krylov complexity phase transition in quantum circuits near the percolation threshold. Recent preprint. Link → In interacting fermionic quantum circuits, the Krylov complexity phase transition is separated from the classical percolation threshold and governed by different scaling exponents. Directly consistent with TSO's p_q > p_c gap — quantum information requires more connectivity than classical spanning to transmit.
Travěnec, I. (2003). Quantum percolation in two dimensions. Physical Review B. DOI → Confirms all 2D quantum percolation states become localized for any positive disorder in large enough samples (no metal-insulator transition in 2D). Honest caveat for TSO: the IBM 2D Anderson gap is a finite-size effect in 2D, not a thermodynamic transition. In 3D it becomes a true threshold — where TSO's p_q should be measured.

5. GRAVITY, QUANTUM GRAVITY, AND COLLAPSE

Aziz, A., & Howl, R. (2025). Classical gravity can transmit quantum information. Nature Communications, 16. DOI:10.1038/s41467-025-58503-0 Shows that when matter is treated with full quantum field theory, classical gravity can generate entanglement between masses. This directly defuses the Feynman argument ("if gravity entangles, gravity must be quantum"). TSO predicts exactly this result because gravity couples to the T and ∅ paths — which are always open by construction — so gravitational "entanglement" is shared open paths, not quantized gravitons.
Donadi, S., Piscicchia, K., Curceanu, C., Diósi, L., Laubenstein, M., & Bassi, A. (2021). Underground test of gravity-related wave function collapse. Nature Physics, 17, 74–78. DOI:10.1038/s41567-020-1008-4 Gran Sasso X-ray measurements rule out the parameter-free Diósi-Penrose gravitational collapse model. TSO predicts this result because gravity alone is never enough to drive collapse in the framework — the transition condition is Γ_net < −p_c, a sum over all coupling channels, not γ_gravity specifically. The Penrose framing makes gravity privileged; TSO demotes it to one channel among many.
Petruzziello, L., & Illuminati, F. (2021). Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale. Nature Communications, 12, 4449. DOI:10.1038/s41467-021-24711-7 Derives a universal decoherence mechanism from a fluctuating minimal length at the Planck scale. Maps onto TSO's effective dimensionality d_eff = 7W approaching 2 at the holographic floor — the fluctuations in this picture are the percolation dynamics near the ice/water boundary in TSO's picture. Not a validation, but a structurally similar argument from an independent starting point.
't Hooft, G. (1993). Dimensional reduction in quantum gravity. Salam Festschrift; preprint at arXiv:gr-qc/9310026 Original statement of the holographic principle. TSO's prediction that d_eff = 7W → 2 at the ice floor (W → 2/7) is a lattice-level statement consistent with 't Hooft's dimensional-reduction argument, approached from an entirely different direction.
Susskind, L. (1995). The World as a Hologram. Journal of Mathematical Physics, 36, 6377. arXiv:hep-th/9409089 The canonical formulation of holography in string theory. See note on 't Hooft 1993 above.

6. PARTICLE PHYSICS AND THE STANDARD MODEL

Particle Data Group. (2024). Review of Particle Physics. Progress of Theoretical and Experimental Physics, 2024(8), 083C01. pdg.lbl.gov The canonical reference for Standard Model particle content, charges, masses, and mixing. All TSO comparisons to "the SM" use PDG values. The topology enumeration matches the PDG charge spectrum {0, ±1/3, ±2/3, ±1} but should be understood in light of the null hypothesis test — the match is largely a consequence of n_spatial = 3 in the charge formula Q = χ_spatial/3, not uniquely a property of the Z = 7 lattice.
Sakharov, A. D. (1967). Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe. JETP Letters, 5, 24. Sakharov conditions (summary) The three conditions necessary for baryogenesis. TSO's baryon asymmetry calculation via Walton-Chalmers / Avrami crystallization mathematics is an alternative mechanism that does not depend on CP violation in the particle sector — it depends on competitive crystal growth in the cosmic solidification process. Whether this is physically correct remains open.
Macedonia, C. (2025). A Geometric Derivation of the Weinberg Angle from Discrete Octonionic Operators. Preprints.org, November 2025. Link → Independent derivation of sin²θ_W from Fano/octonionic geometry (Kosmoplex Theory). Obtains sin²(1)/√(3π) ≈ 0.23064 with zero free parameters. TSO independently obtains 3/13 = 0.23077 by a structurally different route (integer degree counting vs transcendental functions). TSO is closer to the measured value (0.23100). Convergence of two independent groups on the same geometric substrate is either evidence the substrate is real, or evidence the number space near 0.231 has a higher-than-expected density of natural-looking geometric expressions. The 19.2σ Z-pole discrepancy acknowledged in the paper itself (0.25% off at tree level). Both results are proposed; neither has a formal proof.
Burgdörfer, J., Březinová, I., et al. (TU Wien) (2024). Attosecond entanglement dynamics in helium photoionization. Physical Review Letters, October 2024. Coverage → First measurement of quantum entanglement formation time: 232 attoseconds. "The electron doesn't just jump out of the atom — it is a wave that spills out, and that takes a certain amount of time. It is during this phase that entanglement occurs." Directly consistent with TSO: entanglement formation is the physical process of γ_o,stored latching — the formation cost of a correlated state. The 232 as timescale is the time for dp/dt to go from positive (wave expanding) to zero (spanning cluster locked). TSO's claim that entanglement is a physical process with finite formation time, not an instantaneous mathematical correlation, receives its first direct experimental support.

7. BIOLOGY AT CRITICALITY

Hutchison, C. A., Chuang, R.-Y., Noskov, V. N., et al. (2016). Design and synthesis of a minimal bacterial genome. Science, 351(6280), aad6253. DOI:10.1126/science.aad6253 The JCVI-syn3.0 minimal bacterial genome with 473 genes, of which 149 had unknown function at publication. TSO's Monte Carlo of a minimal spanning cluster on Z = 7 gives 475 ± 36 nodes, and the unknown fraction 149/473 = 0.315 matches p_c to 1.1%. The match was noticed after the Monte Carlo result was computed, not fitted. The follow-up annotation audit of the 149 unknowns found 73% connectivity/maintenance proteins — consistent with a scale-free spanning cluster near criticality.
Zhang, Z., et al. (2021). Protein-protein interaction networks of minimal cells are scale-free. PLOS Computational Biology. PLOS Comp Bio Minimal and synthetic cell interaction networks consistently show scale-free topology — a signature of networks at or near percolation criticality. Supports the life-at-p_c claim independently of syn3.0 gene count.
Vattay, G., Kauffman, S., & Niiranen, S. (2014). Quantum Biology on the Edge of Quantum Chaos. PLOS ONE, 9(3), e89017. DOI:10.1371/journal.pone.0089017 Already cited under quantum percolation above; also the cleanest independent support for the life-at-p_c claim.
Levin, M. (ongoing). Bioelectric networks in morphogenesis and regeneration. Tufts University. drmichaellevin.org The most grounded of the speculative biology connections on the roof. Levin's work on bioelectric signalling provides a concrete example of biological systems using spanning-cluster-like topological patterns to encode morphological information. Not a test of TSO, but a useful source of experimental patterns to compare against.

10. TSO PUBLIC COLAB NOTEBOOKS

Every numerical result in TSO is implemented in a public Colab notebook. Any reader can reproduce, challenge, or modify the calculations. If any notebook produces a different result than claimed on the website, please report it — several previous retirements (including the Γ_c retirement on April 4, 2026) came from exactly this kind of independent verification.

Topology Enumeration (Sector A/B/C). Colab notebook Enumerates all equivalence classes of closed-path configurations on Z = 7, reduces by SO(3) × Z₂ × C symmetry, and produces the TSO particle spectrum. Cited on house and roof-particles.
Null Hypothesis Test — Topology Enumeration. Colab notebook Tests whether the SM charge spectrum match is specific to Z = 7 or generic across reasonable lattice choices. Result (April 5, 2026): 22.7% of parameter combinations produce exact matches to the SM charge set, and all matches have n_spatial = 3. The charge match is a consequence of the /3 in the charge formula, not a specific feature of Z = 7. The talking point "SM charge spectrum from pure combinatorics on Z = 7" needs to be downgraded. Detailed class structure (three generations, color multiplicity) has not yet been subjected to a similar test.
Baryon Asymmetry via Walton-Chalmers / Avrami. Colab notebook Computes η = 7.26 × 10⁻¹⁰ from lattice constants and cosmic parameters. Zero fitting. Result within 19% of observed.
Antimatter / Annihilation Mathematics. Colab notebook Mirror-topology enumeration and annihilation consistency checks. 5/6 passed as of v11.0.
syn3.0 Annotation Audit. Colab notebook Audit of the 149 unknown genes in JCVI-syn3.0. Finds 73% connectivity/maintenance enrichment (7.6× baseline, p < 0.0001). Depends on current gene function annotations, which are continuously updated.
Life at p_c Calculations. Colab notebook Monte Carlo of the minimal spanning cluster (475 ± 36 nodes), the kBT ≈ δW temperature calculation, and the Goldilocks-zone analysis.
Internal Consistency Check. Colab notebook 54/55 internal consistency tests across all major TSO results. The one failure was a code bug in a charge-spectrum comparison, not a physics inconsistency.
Pip Catalog and Γ_c Retirement. Colab notebook Introduces the dimensionless Pip unit (1 Pip = p_c/1000) and contains the verification computation showing that the claimed α³ m_ec²/(2ℏ) formula for the retired Γ_c = 1.5 × 10¹⁵ Hz is off by a factor of 10.
Thermodynamic Dynamics — V(p), equation of motion, cosmological trajectory. Colab notebook (May 2026) Establishes γ_o and γ_c as forces on a potential energy landscape. V(p) with minimum at W_dm=2/7 and saddle at p_c. Equation of motion dp/dt = γ_o - γ_c. Cosmological trajectory from Big Bang (maximum stored γ_o) to heat death. Pip scale for tension measurements.
Weinberg Angle sin²θ_W = 3/13 from Fano Degree Counting. Colab notebook (May 2026) Pure Fano degree counting. d_U(1)=3, total gauge degrees=13. sin²θ_W = 3/13 = 0.23077. Measured 0.23100. Δ = 0.09%. Zero free parameters. Status: proposed.
TSO State of the Framework v11.4 (STARRED — complete summary). Colab notebook Complete derivation chain, exact results, proposed results, open problems, falsification conditions, and confidence assessment as of v11.4. Starting point for understanding the full framework.
∅ Path as "HERE" — measurement, photon propagation, decoherence. Colab notebook (May 2026) Establishes ∅ as the null coordinate required to specify quantum position. Photon propagation as open ∅. Decoherence as Γ_close > Γ_open. Lindblad anticommutator = ∅ contribution to zero-point floor. Gogberashvili (2022) validation.
TSO as Intermediate Theory — M-theory, G2, σ = 6/√1104. Colab notebook (May 2026) Establishes TSO as intermediate theory between M-theory and QM/CM. σ = 6/√1104, proposed by Joshua Osborne as the bulk friction ratio (interpretation, not confirmation; formula provenance unverified). 6 = non-null paths, 1104 = Anderson gap in Pips. CY fourfold trail: Sethi-Vafa-Witten, Freudenthal Det, Kreuzer-Skarke. Fano = [7,4,3] Hamming code.
Sethi, S., Vafa, C., Witten, E. (1996). Constraints on Low-Dimensional String Compactifications. Nuclear Physics B, 480(1–2), 213–224. arXiv:hep-th/9606122. Link → For M-theory compactified on a Calabi-Yau fourfold X, the tadpole condition N = χ(X)/24 must be a non-negative integer. Integrality requires χ divisible by 6 (at minimum). TSO tadpole N = 15 (from total Fano degrees = 15 = p₁/2) implies χ(CY4) = 360 for the specific CY fourfold whose G2 boundary is the TSO 7-path space. This paper is the entry point into the Calabi-Yau fourfold trail identified by Joshua Osborne.

Colab notebook

Nine numerical tests of the γ_o/γ_c tension asymmetry. As of v11.1, all nine pass — but three of the nine are primarily self-consistency checks rather than contact with external reality. Honest caveat: generating synthetic TSO data and then recovering it with a TSO fit is circular and confirms only that curve fitting works.

WHAT THIS PAGE IS

Contents

1. TSO PRIMARY DOCUMENTS

2. PERCOLATION THEORY AND LATTICE MATHEMATICS

3. QUANTUM FOUNDATIONS, MEASUREMENT, AND DECOHERENCE

4. QUANTUM PERCOLATION AND CRITICALITY (EXPERIMENTAL)

4. QUANTUM PERCOLATION AND CRITICALITY (EXPERIMENTAL)

5. GRAVITY, QUANTUM GRAVITY, AND COLLAPSE

6. PARTICLE PHYSICS AND THE STANDARD MODEL

7. BIOLOGY AT CRITICALITY

8. CRYSTALLIZATION KINETICS AND COSMOLOGY

9. CMB BIREFRINGENCE AND COSMOLOGICAL OBSERVABLES

10. TSO PUBLIC COLAB NOTEBOOKS

HONEST LITERATURE ASSESSMENT