genesis.py is an exploratory instrument for the Quantum Logical Framework: it starts from
the first distinction (one signed generator pair +g/−g), builds the exact closure census, treats
cycle-order as a frequency-octave hierarchy, and measures the fractal structure of closures at each
frequency. It computes real combinatorics and reports measured exponents — it does not prove
physics. Every printed result carries an epistemic tag ([EXACT], [MEASURED], [STRUCTURAL],
[LEAN] = machine-checked in the Lean layer, [OPEN]), and the sectors that show no signal say so.
Pure standard library, no network. Run: python3 genesis.py.
- The one genuine derivation — the spectral exponent (§2). The census fractal exponent is
−p/2, exactly, and this is not a fit:C(2m,m)·c_pair(p,m)is the closed-walk count onℤ^p, so the slope is thep-dimensional return-probability exponent. Three spatial pairs →−3/2; the 8-twist / 4-pair →−2. This is the strongest thing in the file and it is derived — and now Lean-anchored at the low orders (QLF_CensusWalk):p=1is the closure census, andp=2is the Vandermonde identityΣ_k C(m,k)² = C(2m,m)(sumChooseSq_eq_central), so the p=2 censusC(2m,m)²is the machine-checked π return density (census_p2_is_return_density, =QLF_PhysicalPi.returnDensity). The general-pclosed-walk identity and the−p/2asymptotic stay the Wallis residual. SeeAlpha.md. - census → π (§1, §5).
C(2n,n)/4ⁿ → 1/√(πn), soπ ≈ 1/(n·ratio²)with error falling as~1/n(7.85×10⁻⁶atn=10⁵). The census carries π. SeePhysical_Pi.md. - The swap-graph beyond 3-D — internal dimensions, not a negative (§4, §4b). The ball-growth
Ddoes not converge to 3; it climbs past 3 (D ~ k·log2/log k → ∞). This is not a failed 3-D probe: the external rendered dimension is the receipt quotient (→3-D,~2.94,Pointer_Swap_Fuzz.md); the excess beyond 3 is the internal gauge/color structure — dimensions not perceived as space, manifesting externally as stronger forces (the Kaluza-Klein reading). More internal DOF = stronger color binding = heavier. This feeds the particle map (below). (Genuine residuals that stay negative: no discrete-scale-invariance in the binary sector; the α0.036residual is not here,Alpha_Residual.md.) - Frequency = mass → the particle map (§3, §6).
m = 1/R = frequencyis a QLF identity, so the frequency-octave hierarchy is the mass spectrum; §6 maps internal structure → quantum numbers → zoo particle → mass relative tom_e(proton6π⁵, pion2/α, Koide τ — all with the measured value beside them). See below. §3's frequency-octave hierarchy is the closure spectrum of the harmonic-closure model — each octave a closure frequency, each closure a quantum-logical computation (Frequency_Synchronization.md§0,QLF_HarmonicClosure). - The
128 + d²census joint (§5).d=3 → 137, the only prime in the small family — the α cross-sector reading, tagged[STRUCTURAL]for the identification,[OPEN]for the residual.
genesis.py — ZFA landscape spectrum explorer
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1. THE FIRST DISTINCTION (binary closure census)
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n generated 4^n realized C(2n,n) ratio
1 4 2 0.500000
2 16 6 0.375000
3 64 20 0.312500
4 256 70 0.273438
6 4096 924 0.225586
8 65536 12870 0.196381
12 16777216 2704156 0.161180
16 4294967296 601080390 0.139950
[EXACT] ratio = C(2n,n)/4^n -> 1/sqrt(pi n). The first distinction's
closure fraction already carries pi; this is the alpha anchor.
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2. MULTI-PAIR CENSUS (spectral exponent counts conjugate pairs)
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p (pairs) fitted slope expected -p/2
1 -0.4919 -0.5000
2 -0.9839 -1.0000
3 -1.4762 -1.5000
4 -1.9694 -2.0000
[EXACT] slope -> -p/2: the census fractal exponent IS the pair count.
[STRUCTURAL] 3 spatial pairs -> slope -3/2 ; the 8-twist/4-pair -> -2.
[LEAN] anchored at low orders (QLF_CensusWalk): p=1 = the closure census;
p=2 = C(2m,m)^2 = the machine-checked pi return density (sumChooseSq_eq_central,
census_p2_is_return_density). General-p + the -p/2 asymptotic = Wallis residual.
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3. FREQUENCY-OCTAVE HIERARCHY (closure spectrum, p=1)
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octave j n=2^j closure-bits ratio
0 1 1.0000 5.000e-01
1 2 2.5850 3.750e-01
2 4 6.1293 2.734e-01
3 8 13.6517 1.964e-01
4 16 29.1630 1.399e-01
5 32 60.6686 9.935e-02
6 64 124.1714 7.039e-02
bits increment per octave : [1.585, 3.544, 7.522, 15.511, 31.506, 63.503]
successive increment ratio: [2.2362, 2.1224, 2.062, 2.0311, 2.0156]
[MEASURED] increment ratio -> 2 (each octave doubles n, ~doubles the
extensive 2n term): self-similar cascade across frequency.
[STRUCTURAL] m = 1/R = frequency (QLF_HiggsMechanism, mass_is_gauge_fold_delay):
this frequency hierarchy IS the mass spectrum -- frequency determines
mass. The particle assignments referenced to m_e are in sec 6.
log-periodic residual: peak power=6.712e-03, rms=1.683e-02
[MEASURED] no significant discrete-scale-invariance signal in the binary
sector. If DSI exists it lives in multi-pair / swap sectors.
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4. SWAP-GRAPH GROWTH (#62 dimension probe: measured, not assumed)
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multiset #nodes diam growth exponent D
(6, 6) 924 36 2.230
(8, 8) 12870 64 2.774
(10, 10) (too big)
(3, 3, 3) 1680 27 2.326
(4, 4, 4) 34650 48 2.930
(2, 2, 2, 2) 2520 24 2.386
(3, 3, 3, 3) (too big)
(6, 2) 28 12 1.248
(4, 2, 2) 420 20 1.926
[MEASURED] growth exponent D of the pointer-swap configuration space.
[STRUCTURAL] D>3 = INTERNAL (gauge/color) dimensions, not 3D space (Jim's reading):
the EXTERNAL 3D is the receipt quotient (#62, pointer_swap_fuzz.py ~2.94);
the excess beyond 3 is the internal color DOF = stronger forces (sec 6).
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4b. SWAP-GRAPH EXTRAPOLATION (does D converge? finite-size ladder)
======================================================================
k (=(k,k)) #nodes diam D(k)
4 70 16 1.6094
5 252 25 1.8808
6 924 36 2.2302
7 3432 49 2.5124
8 12870 64 2.7744
9 48620 81 3.0146 > 3
10 184756 100 3.2184 > 3
D increments D(k+1)-D(k): [0.271, 0.349, 0.282, 0.262, 0.24, 0.204]
linear slope of D vs k : 0.2728 (steady & positive)
[MEASURED] D does NOT converge -- it climbs past 3 and keeps rising
(~ k*log2/log k -> infinity). The '~3 at moderate size' is a CROSSING.
[STRUCTURAL] NOT a failed 3D probe (Jim's reading): the external 3D is the
receipt-quotient (~2.94, pointer_swap_fuzz.py); the growth beyond 3 is
the INTERNAL gauge/color structure -- more internal DOF = stronger
forces / more binding = heavier (frequency=mass, sec 6).
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5. CONSTANTS SECTOR (census meets physics; tagged)
======================================================================
census -> pi (pi ~ 1/(n*ratio^2)):
n= 10 pi ~ 3.221089 (err 7.95e-02)
n= 100 pi ~ 3.149456 (err 7.86e-03)
n= 1000 pi ~ 3.142378 (err 7.85e-04)
n= 10000 pi ~ 3.141671 (err 7.85e-05)
n= 100000 pi ~ 3.141601 (err 7.85e-06)
[EXACT] converges to pi in the limit (Wallis / Stirling).
alpha^-1 = 128 + d^2:
d=1 -> 129 composite
d=2 -> 132 composite
d=3 -> 137 prime <- 137, prime, elementary
d=4 -> 144 composite
d=5 -> 153 composite
[STRUCTURAL] d=3 substrate-derived (6+2 split); 128=2^7 selectivity.
[EXACT] the joint holds at exactly d=3 (cross-sector; see rigidity module).
[OPEN] the 0.036 residual (QED running) is NOT here; census-derivation open.
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6. PARTICLE MAP (frequency=mass; internal structure -> quantum #s -> m/m_e)
======================================================================
m = 1/R = frequency (QLF_HiggsMechanism): the sec-3 frequency hierarchy IS the
mass ladder. Internal dims (sec 4, D>3) = gauge/color, not 3D space. Every mass
is a ratio to the electron; proton & pion reuse THIS run's pi and 137 (sec 5).
particle internal quantum #s m/m_e QLF measured tag
electron min chiral loop L q=-1 gen1 1.00 1.00 [ref]
muon gen-2 lepton L q=-1 gen2 206.77 206.77 [depth]
tau 3-phase Koide L q=-1 gen3 3477.40 3477.23 [Derived]
proton 3 colors |S3|=6 B=+1 q=+1 1836.12 1836.15 [Derived]
pion+- 2 quarks |S2|=2 B=0 q=+-1 274.00 273.13 [Derived]
[Derived] proton 6*pi^5 = |S3|*pi^5 (3-colour permutation x internal angular,
QLF_LenzMassRatio, 0.002%); pion 2/alpha = |S2|/alpha (2 quarks x exposed
chirality, QLF_PionMassRatio); tau via Koide Q=2/3 given m_e,m_mu (QLF_Koide).
[STRUCTURAL] internal dimension = colour charge (Borromean 3, QLF_QuarkStructure);
charge in thirds from 3 colours; generations = 3 axis-pairs (= sec-2 p=3).
[Hypothesis] deeper internal (higher-D) structure = stronger colour binding = heavier;
swap-graph symbol-count <-> quark/colour content (falsifiable, untested).
[DEFEATER] every row shows the measured value; any mismatch falsifies that assignment.
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WHAT THIS COMPUTES vs CLAIMS (misses at full weight)
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COMPUTES [EXACT] : the closure census, the -p/2 spectral exponent,
census->pi convergence, the 128+d^2 joint at d=3.
READS : frequency=mass (m=1/R), so the octave hierarchy IS the
mass spectrum; D>3 = internal gauge/color (external 3D =
receipt quotient); particle map to m_e (sec 6).
DERIVED (reused) : proton 6*pi^5, pion 2/alpha, tau Koide -- ratios to m_e,
verified in QLF_LenzMassRatio/PionMassRatio/Koide.
HYPOTHESIS : swap-graph symbol-count <-> quark/color content; deeper
internal structure = stronger binding = heavier (untested).
STILL OPEN : DSI (none in binary sector); the alpha 0.036 residual; the
ABSOLUTE mass scale (needs closure depth + QCD, not census).
NOT A PROOF : an exploratory instrument. The Lean layer, not this,
is where the verified ratios live.
genesis.py's sectors are not separate from particle physics — each is the same combinatorial object a verified QLF module already rests on. Two identities carry the tie:
- Frequency = mass.
m = 1/R = frequency(QLF_HiggsMechanism,mass_is_gauge_fold_delay), so the §3 frequency-octave hierarchy is the mass spectrum — frequency determines mass (Per_Qubit_Mass_Quantum.md). - Internal dimensions = color/forces. The §4 swap-graph growth beyond the externally-rendered 3-D
(the receipt quotient) is the internal gauge/color structure — extra dimensions not perceived as
space, manifesting as the stronger (color) force (
QLF_StrongAlgebra; Borromean three-color necessitybaryon_needs_all_three_axes,QLF_QuarkStructure).
| genesis sector | the object | shared with (verified) | what it fixes |
|---|---|---|---|
§1 census C(2n,n) |
central-binomial closure count | string_mode_count (StringTheoryQLF) |
the string level-n mode degeneracy |
§2 −p/2 exponent |
conjugate-pair count | QLF_Generations, QLF_StrongAlgebra, QLF_SU5 |
the 6+2 split → colour SU(3), 3 generations, α's N=3² |
| §3 frequency hierarchy | m = 1/R ladder |
QLF_HiggsMechanism, QLF_PrimeResonance |
mass, and prime-frequency stability (proton n=3) |
§4 swap-graph D>3 |
internal config-space DOF | QLF_QuarkStructure, QLF_StrongAlgebra |
the internal color structure / strong force |
§5 128+d²=137 |
α from 6+2 |
QLF_FineStructureSubstrate |
EM coupling / fine structure |
- Color = the 3 internal axes (
QLF_StrongAlgebra); a baryon needs all three (baryon_needs_all_three_axes). - Electric charge = signed twist winding, quantized in thirds by the 3 colors (
down_quark_charge_third,QLF_QuarkStructure). - Baryon number = 3-axis winding (
QLF_BaryonWinding); proton+1. - Generation = the 3 spatial axis-pairs (= genesis §2's
p=3;num_generations_eq_three,QLF_Generations). - Spin = the half-spin closure (
QLF_Spin), 720° double cover.
Every mass is a ratio to the electron (the minimal chiral 4-twist loop, fold_electron). The proton and
pion ratios use genesis.py's own π (§5 census) and 137 (§5, 128+d²):
| particle | internal structure | quantum #s | m/m_e (QLF) |
measured | tag |
|---|---|---|---|---|---|
| electron | minimal chiral loop | L, q=−1, gen 1 |
1 (reference) |
1 | reference |
| muon | gen-2 lepton | L, q=−1, gen 2 |
206.77 |
206.77 | depth ratio |
| tau | 3-phase Koide | L, q=−1, gen 3 |
3477.4 |
3477.2 | [Derived] (Koide, given m_e,m_μ) |
| proton | 3 colors, |S₃|=6 |
B=+1, q=+1 |
6π⁵ = 1836.12 |
1836.15 | [Derived] (QLF_LenzMassRatio, 0.002%) |
| charged pion | 2 quarks, |S₂|=2 |
B=0, q=±1 |
2/α = 274 |
273.1 | [Derived] (QLF_PionMassRatio) |
[Hypothesis] (falsifiable, untested): deeper internal (higher-D) structure = stronger color
binding = heavier; the swap-graph symbol-type count maps to quark/color content. Defeater: every row
carries its measured value — any assignment that misses the PDG number falsifies that assignment.
Honest scope. The m_e-referenced ratios (6π⁵, 2/α, Koide) are machine-verified in the cited
Lean modules; genesis.py reuses and displays them (its own π and 137 feed the proton/pion rows). It
does not compute the absolute mass scale — that needs the closure depth + the QCD scale
(QLF_MassSpectrum, QLF_AlphaS), which is a
separate, in-progress input. So the answer to "can genesis.py's results be tied to the particle zoo?" is:
yes — the frequency ladder is the mass spectrum and the internal dimensions are the color/gauge
structure, with the specific mass ratios derived and referenced to the electron; the absolute scale
stays open. See Standard_Model.md, Quarks.md.
- The swap-graph cap is 60k nodes; raise it to resolve the finite-size drift further (the single most
informative extension).
swap_dimension_ladder(§4b) is the harness that fitsD(k)up the ladder — the extrapolation, not any single finiteD, is what bears on #62. - The multi-pair census memoizes
c_pair, so very largep×mgrows memory; everything else is O(seconds).
Pointer_Swap_Fuzz.md— the #62 swap-graph mechanism and the receipt-quotient (stabled).Alpha.md— the census sector: the−p/2spectral exponent and the128 + d²joint.Physical_Pi.md— census → π (Wallis / Stirling).Open_Problems.md— #62 status (the raw-graph divergence finding).