This is a one-page visual map of the Quantum Logical Framework (QLF) — a
formal proof system, machine-verified in Lean 4 across more than a hundred modules with zero sorry,
that derives quantum mechanics and spacetime from a single selection principle: Zero Free Action
(ZFA) balance. Every chart below shows one domain; the boxes are clickable
(this is a PDF/HTML perk — GitHub disables Mermaid node links), and each Open
line lists the documents that derive that domain.
How to read it: one substrate → five families → twelve domains → the individual results. Click a box to jump to its section or open its source document; use the table of contents to navigate. To save as PDF: open this file in a browser, then File → Print → Save as PDF (keep “Background graphics” on).
flowchart LR S["The QLF Substrate 8-twist alphabet - ZFA closure - synthesized spacetime"] S --> FND["Foundations"] S --> MAT["Matter and forces"] S --> EMR["Emergent matter"] S --> GRV["Gravity and the cosmos"] S --> FRN["Frontiers"] FND -->|"renders"| D1["1 Space, time and the continuum"] FND -->|"fixes"| D2["2 The fundamental constants"] FND -->|"sums"| D12["12 Quantum field theory and renormalization"] MAT -->|"projects"| D3["3 Forces"] MAT -->|"binds"| D4["4 Atoms and QED"] MAT -->|"structures"| D7["7 Particles and the Standard Model"] EMR -->|"assembles"| D11["11 Chemistry, molecules and folding"] GRV -->|"weighs"| D5["5 Gravity and GR"] GRV -->|"expands"| D6["6 Cosmology and the dark sector"] FRN -->|"meets"| D8["8 Quantum-gravity / TOE pillars"] FRN -->|"resolves"| D9["9 The Millennium Prize program"] FRN -->|"predicts"| D10["10 Beyond the SM"] click D1 "#1-space-time-and-the-continuum" click D2 "#2-the-fundamental-constants" click D12 "#12-quantum-field-theory-and-renormalization" click D3 "#3-forces" click D4 "#4-atoms-and-qed" click D7 "#7-particles-and-the-standard-model" click D11 "#11-chemistry-molecules-and-folding" click D5 "#5-gravity-and-gr" click D6 "#6-cosmology-and-the-dark-sector" click D8 "#8-quantum-gravity--toe-pillars" click D9 "#9-the-millennium-prize-program" click D10 "#10-beyond-the-sm" click S "https://github.com/rchain-community/quantum-logical-framework/blob/main/README.md" _blank
Jump to: 1 Space, time and the continuum · 2 The fundamental constants · 3 Forces · 4 Atoms and QED · 5 Gravity and GR · 6 Cosmology and the dark sector · 7 Particles and the Standard Model · 8 Quantum-gravity / TOE pillars · 9 The Millennium Prize program · 10 Beyond the SM · 11 Chemistry, molecules and folding · 12 Quantum field theory and renormalization
The five families: Foundations (1-2, 12) · Matter and forces (3, 4, 7) · Emergent matter (11) · Gravity and the cosmos (5-6) · Frontiers (8-10).
Emergent matter is the one family that is not fundamental physics. The other four ask what the
substrate is; this one asks what it assembles once atoms exist — and it earns a family of its own
precisely because nothing in it is a new law. Chemistry, polymers and folding all run on the rule domains
3–4 already established, which is the claim being made by putting them on the map at all.
Open: README.md
Root reading: everything derives from the 8-twist substrate under Zero Free Action —
Philosophy.md (possibilist ontology, and §3a the working method: things happen every
way that closes, and what happens in the most ways happens first), WHITE_PAPER.md.
The method's limit, proven: Law_Of_Exceptions.md — *a system with more
states can always break a finite closure*, so every restrictive law has a real, constructed exception and
no finite closure is final (QLF_LawOfExceptions). Capacity turns out to
be an excursion budget (QLF_ClosureDepthLaw), which is why the
proton dissolves at T_c and baryon number at T_EW while electric charge — whose proof carries no
capacity — has no exception at any scale. Corollary for everything below: **construction proves
possibility, not uniqueness.**
An application of that same capacity machinery: Mpemba.md — anomalous relaxation, where
relaxation time is the maximum excursion, giving a proven no-go (none for the imbalance measure), a
proven enabler (no scalar determines relaxation), and proven instances (more energy closing strictly
faster) — while the ensemble effect and the water phenomenon stay open
(QLF_Mpemba).
Foundational logic & mathematics: the substrate's logic is quantum logic — argued as the correct
foundation of mathematics (bottom-up, sound vs. exploding) in Quantum_Logic_Foundations.md,
with the minimal quantum logic MO2 machine-verified on the substrate (orthomodular + non-distributive,
lean/QLF_QuantumLogic.lean); and ordinary mathematics emerging from it (ℕ,
the ring, μ₄, su(2)/su(3), the continuum as completion) in the companion Mathematics_From_QLF.md.
The category-theoretic shape — the causal-set base category, ZFA as an equalizer, the capacity-horizon
bifibration whose free prime-factorisation forces self-similarity (and closes the log-periodic channel,
so the α-residual weight w = 1/2 is structural), the Tannakian/anabelian layer, RhoQuCalc as a dagger SMC —
is collected in Category_Theory_QLF.md (a description, not an axiom).
Truth is objective across observers, and in two ways (lean/QLF_MultiObserver.lean,
no axioms): whether a history closes, and the phase it carries, are the same in every observer's frame
(the discrete axis-permutation × gauge-swap group) — so two or more perspectives agree on the truth
(observers_agree), witnessed by two independent invariants, the count verdict and the Pauli scalar
(truth_from_two_perspectives_in_two_ways). The /solve "meeting of minds" consensus is a theorem.
It from bit: the unit of information is the two-valued ½-spin closure — one bit (log 2 for the spinor
alphabet {+I,−I}) vs zero for a single-valued vector {+I} — the 2π double-valuedness reproven from the
explicit rotation matrices and grounding the spinor Cartan discovered in 1913 as the carrier of information
(lean/QLF_SpinorInformation.lean, Mathematics_From_QLF.md §Rung 5a).
Harmonic-closure model: reality and constructable truth are the closing spectrum of frequency-component closures — each frequency f = 1/R is one ZFA closure, i.e. a quantum-logical computation (a set of Feynman diagrams: path integral = generate, ZFA closure = the firebreak selecting the physical ones) (Frequency_Synchronization.md §0).
flowchart TD S["8-twist substrate - ZFA"] S -->|"causal order"| R["Closure-reachability pre-geometric causal set"] R -->|"faithful 3-D render"| D["3 spatial dimensions"] S -->|"logical latency"| T["Time = per-event Planck tick"] D -->|"synthesize"| SP["Synthesized spacetime"] T -->|"synthesize"| SP S -->|"RCA_0 floor"| CN["No continuum / no Choice"] click S "https://github.com/rchain-community/quantum-logical-framework/blob/main/README.md" _blank click R "https://github.com/rchain-community/quantum-logical-framework/blob/main/SpaceTime.md" _blank click D "https://github.com/rchain-community/quantum-logical-framework/blob/main/SpaceTime.md" _blank click T "https://github.com/rchain-community/quantum-logical-framework/blob/main/SpaceTime.md" _blank click SP "https://github.com/rchain-community/quantum-logical-framework/blob/main/SpaceTime.md" _blank click CN "https://github.com/rchain-community/quantum-logical-framework/blob/main/TheContinuum.md" _blank
Open: README.md · SpaceTime.md · TheContinuum.md
3 is the minimal dimension that renders any relational structure faithfully — and it reappears
everywhere below (SpaceTime.md §3a).
flowchart TD SP["6+2 split -> 3 spatial axes"] SP -->|"N = 3^2"| AL["alpha = 1/137"] SP -->|"spatial 3/8"| WK["sin^2theta_W = 3/8"] SP -->|"gauge 2/8"| OL["Omega_Lambda = log 2"] SP -->|"surface ~ r^2"| NW["Newton 1/r^2"] SP -->|"l = 3"| MG["nuclear magic numbers"] S2["3-quark Borromean closure"] --> MP["m_p/m_e = 6pi^5"] AL -->|"2/alpha"| MPI["m_pi/m_e = 274"] click SP "https://github.com/rchain-community/quantum-logical-framework/blob/main/SpaceTime.md" _blank click AL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Alpha.md" _blank click WK "https://github.com/rchain-community/quantum-logical-framework/blob/main/Weak_Force.md" _blank click OL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Cosmological_Constant.md" _blank click NW "https://github.com/rchain-community/quantum-logical-framework/blob/main/Gravity_From_Delay.md" _blank click MG "https://github.com/rchain-community/quantum-logical-framework/blob/main/Magic_numbers.md" _blank click MP "https://github.com/rchain-community/quantum-logical-framework/blob/main/Proton_Resonance_R_e.md" _blank click MPI "https://github.com/rchain-community/quantum-logical-framework/blob/main/Pion_QLF.md" _blank click S2 "https://github.com/rchain-community/quantum-logical-framework/blob/main/Proton_Resonance_R_e.md" _blank
Open: SpaceTime.md · Alpha.md · Weak_Force.md · Cosmological_Constant.md · Gravity_From_Delay.md · Magic_numbers.md · Proton_Resonance_R_e.md · Pion_QLF.md · Genesis.md
The census spectrum explorer Genesis.md exercises the constants sector end-to-end: the exact −p/2 census spectral exponent (Lean-anchored, QLF_CensusWalk), census → π, and α⁻¹ = 128 + d² (d = 3 → 137).
α's full story (derivation, IR/3-D scale, the running, the no-drift theorem, 4D/5D
over-determination): Alpha.md. The +0.036 residual is now healed to its honest shape
(Alpha_Residual.md §9c): the bracket is two-sided and machine-checked both ends
(137.01587 < α⁻¹ < 137.04813), the equal-weight prediction 137.032 is structural (w = ½ forced
by the free-monoid bifibration, not fitted), and 0.036 is existence-proven (reachable by a prime
resummation) with its multiplicity open — which resummation = the continuum vacuum-polarisation
running, the Standard Model's own frontier. Every substrate mechanism swing is closed; CODATA is an
estimate of the missing count, not a target.
flowchart TD AX["3 spatial axes + 2 gauge"] AX -->|"abelian"| EM["U1 - electromagnetism"] AX -->|"non-abelian, chiral"| WK["SU2 - weak"] AX -->|"colour, confined"| ST["SU3 - strong"] AL["alpha derived"] --> CPL["dimensionless couplings"] EM -->|"projection"| UNI["one force, three projections"] WK -->|"projection"| UNI ST -->|"projection"| UNI click AX "https://github.com/rchain-community/quantum-logical-framework/blob/main/Forces_From_Three_Axes.md" _blank click EM "https://github.com/rchain-community/quantum-logical-framework/blob/main/Electricity.md" _blank click WK "https://github.com/rchain-community/quantum-logical-framework/blob/main/Weak_Force.md" _blank click ST "https://github.com/rchain-community/quantum-logical-framework/blob/main/Forces_From_Three_Axes.md" _blank click AL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Alpha.md" _blank click CPL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Forces_From_Alpha.md" _blank click UNI "https://github.com/rchain-community/quantum-logical-framework/blob/main/Forces_From_Three_Axes.md" _blank
Open: Forces_From_Three_Axes.md · Electricity.md · Weak_Force.md · Alpha.md · Forces_From_Alpha.md
flowchart TD AL["alpha = 1/137"] AL -->|"1/2alpha^2m_e c^2"| RY["Rydberg / Bohr"] AL -->|"~ alpha^2"| DI["Dirac fine structure"] AL -->|"loop alpha"| LA["Lamb shift"] AL -->|"alpha/2pi"| GM["g-2"] AL -->|"Z_0/2alpha"| VK["von Klitzing R_K"] AL -->|"~ alpha^4"| HF["hyperfine / 21 cm"] click AL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Alpha.md" _blank click RY "https://github.com/rchain-community/quantum-logical-framework/blob/main/Hydrogen.md" _blank click DI "https://github.com/rchain-community/quantum-logical-framework/blob/main/Dirac_Correction.md" _blank click LA "https://github.com/rchain-community/quantum-logical-framework/blob/main/Lamb_Shift.md" _blank click GM "https://github.com/rchain-community/quantum-logical-framework/blob/main/g_minus_2.md" _blank click VK "https://github.com/rchain-community/quantum-logical-framework/blob/main/Electricity.md" _blank click HF "https://github.com/rchain-community/quantum-logical-framework/blob/main/Magnetism_Spatial_Dynamics.md" _blank
Open: Alpha.md · Hydrogen.md · Dirac_Correction.md · Lamb_Shift.md · g_minus_2.md · Electricity.md · Magnetism_Spatial_Dynamics.md
flowchart TD HO["Holographic event-counting + log 2"] HO -->|"G = L_P^2c^3/hbar"| NG["Newton's law + G"] NG -->|"43''/century"| ME["Mercury perihelion"] HO -->|"deltaQ = T deltaS"| EE["Einstein equations equation of state"] EE -->|"causal order -> metric"| CV["Curvature"] EE -->|"spin-2, v = c"| GW["Gravitational waves"] click HO "https://github.com/rchain-community/quantum-logical-framework/blob/main/Gravity_From_Delay.md" _blank click NG "https://github.com/rchain-community/quantum-logical-framework/blob/main/Gravity_From_Delay.md" _blank click ME "https://github.com/rchain-community/quantum-logical-framework/blob/main/Mercury_Perihelion.md" _blank click EE "https://github.com/rchain-community/quantum-logical-framework/blob/main/Einstein_Equations.md" _blank click CV "https://github.com/rchain-community/quantum-logical-framework/blob/main/Curvature.md" _blank click GW "https://github.com/rchain-community/quantum-logical-framework/blob/main/Einstein_Equations.md" _blank
Open: Gravity_From_Delay.md · Mercury_Perihelion.md · Einstein_Equations.md · Curvature.md
flowchart TD EV["ZFA event synthesis w = -1"] EV -->|"gauge 2/8"| OL["Omega_Lambda = log 2 closes the 10^122 catastrophe"] EV -->|"high-V epoch"| IN["Inflation same field"] EV -->|"denser logic"| DM["Dark matter no particle"] OL -->|"residual w = -1"| DE["Dark energy"] EV -->|"event rate"| AGE["Age ~ 13.8 Gyr"] EV -->|"freeze-out n/p"| NS["^4He fraction Y_p ~ 1/4"] OL --> CORE["Concordant with LCDM data CMB BBN age Omega_Lambda w = -1"] AGE --> CORE NS --> CORE DM --> DIV["Divergent on LCDM interpretation particle CDM and static Lambda"] DE --> DIV EV --> TG["Thermodynamic gravity Jacobson Bekenstein derives 8piG and Lambda = log 2"] click EV "https://github.com/rchain-community/quantum-logical-framework/blob/main/Cosmological_Constant.md" _blank click OL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Cosmological_Constant.md" _blank click IN "https://github.com/rchain-community/quantum-logical-framework/blob/main/Curvature.md" _blank click DM "https://github.com/rchain-community/quantum-logical-framework/blob/main/DarkMatter.md" _blank click DE "https://github.com/rchain-community/quantum-logical-framework/blob/main/DarkMatter.md" _blank click AGE "https://github.com/rchain-community/quantum-logical-framework/blob/main/AgeOfUniverse.md" _blank click NS "https://github.com/rchain-community/quantum-logical-framework/blob/main/Fusion.md" _blank
Open: Cosmological_Constant.md · Curvature.md · DarkMatter.md · SPARC.md · AgeOfUniverse.md · Fusion.md · Mysteries_Of_Physics.md §3a
Dark matter is the closure-balance RAR, blind-tested parameter-free on 147 SPARC galaxies (a₀ = cH₀/2π, the 2π derived; SPARC.md). Dark energy is dynamical — ρ_Λ ∝ H² (Lean-anchored, QLF_DynamicalDarkEnergy) — so QLF sits in the resolution-favorable class of the Hubble tension, and its dark-matter fit votes local (H₀ ≈ 72.9); a reframe + vote, not a numeric resolution (DarkMatter.md §5a).
Convergence with accepted cosmology (the ledger, Mysteries_Of_Physics.md §3a). QLF is concordant with ΛCDM's observational core — the hot Big Bang, CMB, BBN (Y_p = 1/4), the ≈13.8 Gyr age, Ω_Λ = log 2 ≈ 0.69, and the w≈−1 accelerating expansion are all reproduced or left intact (a Big-Bang-singularity alternative, not a hot-Big-Bang-observation alternative). It diverges only on ΛCDM's two interpretive pillars — particle cold dark matter (→ the RAR/MOND reading above) and a static Λ (→ dynamical ρ_Λ ∝ H²), i.e. the open, contested questions. Its deeper convergence is with accepted thermodynamic/emergent gravity (Jacobson 1995, Bekenstein–Hawking, holography), from which it derives the Einstein 8πG coefficient and Λ = log 2 (QLF_EinsteinEquations).
flowchart TD TH["3 spatial axes the same 3"] TH -->|"axis count"| GEN["3 fermion generations"] GEN -->|"Q = 2/3"| KO["Koide -> m_tau"] GEN -->|"3 angles + CP"| MX["CKM / PMNS mixing"] TH -->|"self-conjugate"| NU["neutrino is Majorana"] NU -->|"DeltaL = 2"| BD["beta-decay / 0nubetabeta"] TH -->|"one scale x ratios"| MS["mass spectrum"] SP["spin = the twists"] --> HG["mass Higgs mechanism"] SP -->|"log 2 = one bit"| BIT["spin-1/2 = one bit - it from bit"] click TH "https://github.com/rchain-community/quantum-logical-framework/blob/main/Standard_Model.md" _blank click GEN "https://github.com/rchain-community/quantum-logical-framework/blob/main/Standard_Model.md" _blank click KO "https://github.com/rchain-community/quantum-logical-framework/blob/main/Standard_Model.md" _blank click MX "https://github.com/rchain-community/quantum-logical-framework/blob/main/Standard_Model.md" _blank click NU "https://github.com/rchain-community/quantum-logical-framework/blob/main/Beta_Decay_Neutrino_Nature.md" _blank click BD "https://github.com/rchain-community/quantum-logical-framework/blob/main/Beta_Decay_Neutrino_Nature.md" _blank click MS "https://github.com/rchain-community/quantum-logical-framework/blob/main/Per_Qubit_Mass_Quantum.md" _blank click SP "https://github.com/rchain-community/quantum-logical-framework/blob/main/Spin_QLF.md" _blank click HG "https://github.com/rchain-community/quantum-logical-framework/blob/main/Higgs.md" _blank click BIT "https://github.com/rchain-community/quantum-logical-framework/blob/main/Mathematics_From_QLF.md" _blank
Open: Standard_Model.md · Beta_Decay_Neutrino_Nature.md · Per_Qubit_Mass_Quantum.md · Spin_QLF.md · Higgs.md · Mathematics_From_QLF.md
It from bit — information is the ½-spin closure. The unit of information is the two-valued spinor closure: one bit (log 2) for {+I,−I} vs zero for a single-valued vector {+I} (a single-valued object cannot express a distinction). The 2π double-valuedness is reproven from the explicit rotation matrices (spinor_double_valued_vector_blind: +I on the vector SO(3) rep, −I on the spin-½ SU(2) rep), grounding Cartan's 1913 spinor as its carrier. Priority runs abstraction → physical: information is the distinction, the ½-spin closure its minimal realization (lean/QLF_SpinorInformation.lean, Mathematics_From_QLF.md §Rung 5a).
flowchart TD S["substrate"] S -->|"j = 1/2 spin network"| LQ["Loop Quantum Gravity"] S -->|"C(2n,n) modes"| ST["String theory"] S -->|"Q = half-spin shift"| SU["Supersymmetry"] S -->|"closure floor mu^2=1/2"| PL["Planck scale"] click S "https://github.com/rchain-community/quantum-logical-framework/blob/main/README.md" _blank click LQ "https://github.com/rchain-community/quantum-logical-framework/blob/main/LQG_QLF.md" _blank click ST "https://github.com/rchain-community/quantum-logical-framework/blob/main/StringTheory.md" _blank click SU "https://github.com/rchain-community/quantum-logical-framework/blob/main/SUSY_QLF.md" _blank click PL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Planck_Scale.md" _blank
Open: README.md · LQG_QLF.md · StringTheory.md · SUSY_QLF.md · Planck_Scale.md
flowchart TD CC["Continuum = UV catastrophe RCA_0 core + boundary axiom"] CC -->|"critical line"| RH["Riemann hypothesis"] CC -->|"log 2 gap quantum"| YM["Yang-Mills mass gap"] CC -->|"rank = ord"| BS["Birch-Swinnerton-Dyer"] CC -->|"balanced => algebraic"| HOD["Hodge conjecture"] CC -->|"generate != verify"| PN["P vs NP"] CC -->|"no blow-up"| NV["Navier-Stokes"] click CC "https://github.com/rchain-community/quantum-logical-framework/blob/main/Continuum_Choice_Fallacy.md" _blank click RH "https://github.com/rchain-community/quantum-logical-framework/blob/main/Riemann-Conjecture-Proof.md" _blank click YM "https://github.com/rchain-community/quantum-logical-framework/blob/main/YangMills_MassGap_QLF.md" _blank click BS "https://github.com/rchain-community/quantum-logical-framework/blob/main/BSD_QLF.md" _blank click HOD "https://github.com/rchain-community/quantum-logical-framework/blob/main/Hodge_QLF.md" _blank click PN "https://github.com/rchain-community/quantum-logical-framework/blob/main/P_vs_NP_QLF.md" _blank click NV "https://github.com/rchain-community/quantum-logical-framework/blob/main/NavierStokes_QLF.md" _blank
Open: Continuum_Choice_Fallacy.md · Riemann-Conjecture-Proof.md · YangMills_MassGap_QLF.md · BSD_QLF.md · Hodge_QLF.md · P_vs_NP_QLF.md · NavierStokes_QLF.md
Overview: Millennium.md.
flowchart TD B["Beyond the Standard Model"] B -->|"not free"| D1["derived: alpha, Koide, theta-bar=0, Omega_Lambda"] B -->|"test now"| P1["Majorana neutrino -> 0nubetabeta"] B -->|"scale-free by construction"| P2["no cosmological drift of alpha0"] B -->|"soft"| P3["dark matter is not a particle"] click B "https://github.com/rchain-community/quantum-logical-framework/blob/main/Beyond_Standard_Model.md" _blank click D1 "https://github.com/rchain-community/quantum-logical-framework/blob/main/Beyond_Standard_Model.md" _blank click P1 "https://github.com/rchain-community/quantum-logical-framework/blob/main/Beta_Decay_Neutrino_Nature.md" _blank click P2 "https://github.com/rchain-community/quantum-logical-framework/blob/main/Alpha.md" _blank click P3 "https://github.com/rchain-community/quantum-logical-framework/blob/main/DarkMatter.md" _blank
Open: Beyond_Standard_Model.md · Beta_Decay_Neutrino_Nature.md · Alpha.md · DarkMatter.md
flowchart TD V["valence = closures an atom can share"] V -->|"saturate"| BD["shared closure = bond"] BD -->|"H2O, CO2, graphite, rust"| MOL["molecules and carbon allotropes"] BD -->|"Pauli holds them apart"| XL["crystals and condensates"] V -->|"(v-2)/2 each"| CC["closure count b1 = E - V + 1"] CC -->|"b1 counts them"| DOU["double bond = ring = one closure"] CC -->|"only k is free"| RX["reaction class = change in molecule count"] V -->|"free valence for water?"| HP["hydrophobic / polar"] V -->|"valence 2 is neutral"| CH["divalent -> chains"] CH -->|"backbone carries none"| FOLD["folding: a contact is a ZFA closure"] HP -->|"only H-H pays"| FOLD click V "https://github.com/rchain-community/quantum-logical-framework/blob/main/Chemistry.md" _blank click BD "https://github.com/rchain-community/quantum-logical-framework/blob/main/Chemistry.md" _blank click MOL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Chemistry.md" _blank click XL "https://github.com/rchain-community/quantum-logical-framework/blob/main/Geometry_Of_Space.md" _blank click CC "https://github.com/rchain-community/quantum-logical-framework/blob/main/Chemistry.md" _blank click DOU "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_Unsaturation.lean" _blank click RX "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_Unsaturation.lean" _blank click HP "https://github.com/rchain-community/quantum-logical-framework/blob/main/Chemistry.md" _blank click CH "https://github.com/rchain-community/quantum-logical-framework/blob/main/Chemistry.md" _blank click FOLD "https://github.com/rchain-community/quantum-logical-framework/blob/main/Protein_Folding.md" _blank
Open: Chemistry.md · Protein_Folding.md · lean/QLF_Unsaturation.lean · lean/QLF_Folding.lean · hydrocarbon_census.py · protein_census.py
The counting layer. An atom's valence is what it contributes to a molecule's closure count,
(valence − 2)/2, and the cycle rank b₁ = E − V + 1 counts the closures the molecule carries. That
identification does three things at once: the textbook degree of unsaturation is that count (with
oxygen absent from the formula because its contribution is zero); a **ring and a double bond are one
phenomenon**, so C₆H₁₂ is a single census class; and since a balanced reaction pins V and E, a
reaction's change in closure count is its change in molecule count — addition, elimination and
substitution are that one number (QLF_Unsaturation, no axioms).
Up to folding. Valence 2 is the neutral element of the count, which is why a divalent monomer makes a
chain and why the peptide bond — closure-neutral, 2 molecules in and 2 out — leaves a polypeptide
backbone carrying no closure of its own. So every closure a folded chain has is a contact, and a
contact is a ZFA closure in the literal sense: zero net displacement, count-balanced, Pauli-closed by the
keystone (QLF_Folding). The lattice-protein parity rule and the log 2 contact
quantum follow; the mirror no-go — counting cannot select a handedness — bounds what the census can
ever answer (Protein_Folding.md).
flowchart TD PT["path integral = the possibility tree - phase-weighted ZFA closures"] PT -->|"grade by closure"| ORD["expansion order = closure structure - length, vertices, depth"] ORD -->|"IsDiagram order 0"| C1["tree level = the closure census"] ORD -->|"single binding"| C2["one loop = the 2/3pi coefficient"] PT -->|"listen at capacity R"| RG["renormalization = the capacity horizon"] RG -->|"A_R+1 minus A_R"| CT["counterterm = one finite term, never a divergence"] RG -->|"Q(R) = Q0 2^R"| RUN["running: QED log = census octave count"] PT -->|"prefix-free code"| KR["Kraft bound: the series converges"] KR -->|"no mode continuum"| DYS["Dyson divergence = continuum artefact"] click PT "https://github.com/rchain-community/quantum-logical-framework/blob/main/QFT_QLF.md" _blank click ORD "https://github.com/rchain-community/quantum-logical-framework/blob/main/Perturbation_Theory_QLF.md" _blank click C1 "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_FractalDiagram.lean" _blank click C2 "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_VacuumPolarization.lean" _blank click RG "https://github.com/rchain-community/quantum-logical-framework/blob/main/Perturbation_Theory_QLF.md" _blank click CT "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_ExactRG.lean" _blank click RUN "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_VacuumPolarizationTower.lean" _blank click KR "https://github.com/rchain-community/quantum-logical-framework/blob/main/lean/QLF_KraftMeasure.lean" _blank click DYS "https://github.com/rchain-community/quantum-logical-framework/blob/main/TheContinuum.md" _blank
Open: QFT_QLF.md · Perturbation_Theory_QLF.md · lean/QLF_ExactRG.lean · lean/QLF_FractalDiagram.lean · lean/QLF_VacuumPolarization.lean · lean/QLF_RunningCouplings.lean · TheContinuum.md
The perturbation series is the possibility tree, graded not by an external coupling but by **closure
structure** — continuation length, diagram order (IsDiagram, the closure↔Feynman-diagram map), or
closure depth (Perturbation_Theory_QLF.md). Two orders are proven against
QED: the tree level is exactly the closure census (order_zero_iff_closure), and the **one loop is the
2/(3π) vacuum-polarization coefficient** (orderOneWeight_eq), census-sourced and committed before
comparison (QLF_FractalDiagram, QLF_VacuumPolarization).
Renormalization is Wilsonian and finite. The regulator is the capacity horizon R — a listener of
capacity R hears the closures of depth ≤ R; the counterterm for the step R → R+1 is a single finite
term A_{R+1} − A_R, never a subtracted infinity; the running is Q(R) = Q₀·2^R, so the QED logarithm
is the census octave count (QLF_VacuumPolarizationTower).
And the substrate's series converges absolutely in its cylinder measure — twist_kraft plus
|A| ≤ W — so no Borel resummation, and the Dyson divergence is exposed as an artefact of the mode
continuum the substrate does not have (QLF_ExactRG, the exact-RG recursion +
finiteness + convergence, no axioms). The α residual is the worked calibration of the bridge line
(Alpha_Residual.md §9c): QLF proves the census space (two-sided bracket) and proves
w = ½ → 137.032 structural; the open piece is the multiplicity — which continuum resummation — not a
census-truncation rule. Existence proven, multiplicity open — the exact shape of every Millennium bridge,
run to convergence in a case with a measured answer. Every substrate mechanism swing is closed; the
turbulence swing produced a side-derivation (She–Léveque C₀ = 2 from /solve axis-minimality).
Contrast, once: the rigorous continuum QFT (a Wightman /
Osterwalder–Schrader theory on ℝ⁴) is not constructed here — that step is the Yang–Mills boundary axiom of
domain 9. What the reformulation proves is that the discrete substrate the continuum is the limit of, plus
the one explicit crossing, carries QFT's empirical content.
- README.md · lean/README.md — project overview + the full Lean module
table.
- Open_Problems.md — the honest gap registry (closed / principled-boundary / open).
- Beyond_Standard_Model.md — the derived / predicted / open scorecard.
- Alpha.md — one result mapped end to end, as a worked example.
- Chemistry.md · Protein_Folding.md — domain 11 end to end: one
rule (a bond is a shared closure) up through the closure count to a fold as a closure census.
- Fredkin_QLF.md — conservative logic on the substrate: Fredkin's conservation law
is ZFA count balance (QLF_Fredkin, no axioms), so a reversible computer
runs free and only erasure is charged. Run it: fredkin_machine.html.