QLF Flow Chart — a visual map of the framework

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 → eleven 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).

Master map — the substrate and its eleven domains ↑ top

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"]
  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 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

The five families: Foundations (1-2) · 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.

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 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).

1. Space, time, and the continuum ↑ top

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).

2. The fundamental constants ↑ top

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.

3. Forces ↑ top

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

4. Atoms and QED ↑ top

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

5. Gravity and GR ↑ top

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

6. Cosmology and the dark sector ↑ top

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 derived; SPARC.md). Dark energy is dynamicalρ_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).

7. Particles and the Standard Model ↑ top

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 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).

8. Quantum-gravity / TOE pillars ↑ top

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

9. The Millennium Prize program ↑ top

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.

10. Beyond the SM ↑ top

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

11. Chemistry, molecules and folding ↑ top

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).

See also ↑ top

- 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.