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Changelog

All notable changes to the GIFT framework are documented in this file.

The format follows Keep a Changelog, and this project adheres to Semantic Versioning.

[3.4.0] - 2026-05-07

Major: 95-observable dataset, four-type classification, Joyce-Karigiannis topological route

The v3.4 release reframes the dataset from "33 dimensionless predictions" to a four-type classification of 95 observables, all derived from a single G₂ metric and the topological pair (b₂, b₃) = (21, 77).

Added

Observable classification (95 observables, four types)

  • Type I (33 obs, mean deviation 0.73%): Direct algebraic from structural constants. 33/33 Lean-certified.
  • Type II (19 obs, mean 0.17%): One physical identification step (absolute masses, CKM magnitudes, extended ratios).
  • Type III (21 obs, mean 3.4%): Multi-step dynamical chains (Wilson lines, instanton volumes, RGE running). 14/21 Lean-certified.
  • Type IV (22 obs, structural diagnostics): Internal consistency, NK certification values, BH remnant predictions (Pinčák et al. 2026). 8/22 Lean-certified.
  • Full canonical dataset in Supplement S3.

Joyce-Karigiannis Z₂³ topological route (S1 §8.4)

  • Four-phase computer-assisted audit (V₄ symplectic screen on CI(2,2,2), anti-symplectic obstruction, K3 lattice existence via Mukai 1988 + Garbagnati-Sarti 2009, Betti formula closure) realizes (b₂, b₃) = (21, 77) at the topological/lattice level.
  • Lean-certified in JoyceKarigiannisConstruction.lean (master theorem jk_z23_construction_realizes_gift_betti, 0 sorry, 0 axioms).
  • Companion paper [D] (Donaldson Analytic Note, Zenodo 10.5281/zenodo.20039066) provides an explicit closed-form positive G₂-structure ansatz at the neck level with hyperkähler rotation and five-layer Picard-Lefschetz Wirtinger certificate. Smooth analytic compact construction remains an open problem.

Three new framework-level results (beyond the original 33 predictions)

  • A proposed E₈ → Standard Model breaking chain with anomaly-cancellation checks and bundle-universality diagnostics.
  • A combined wilson_line+instanton lepton mass hierarchy mechanism, α = e^K, achieving sub-percent precision from two independent geometric sources.
  • A sensitivity analysis: 2.13× overdetermination, coincidence probability P=10⁻³⁴⁶ under a uniform null and P=10⁻¹³³ under an algebraic null model on 4.2M random formulas.

Lean certificate (core v3.4.19)

  • 213 certificate conjuncts, 4 main-chain axioms, 0 sorry, 134 .lean files, 8378 build jobs (Lean 4.29.0).
  • Standard transcendental palette extended to {π, √2, ln 2, ζ, golden ratio φ}.

Companion papers (Zenodo, peer-reviewable)

  • [A] Certified G₂ Metric (10.5281/zenodo.19892350): first computer-assisted existence proof for a metric with G₂ holonomy on a TCS neck model.
  • [B] Spectral Geometry (10.5281/zenodo.19893371): Laplacian spectrum, harmonic forms, λ₁ = 6π²/475.
  • [C] Newton-Kantorovich on K3 (10.5281/zenodo.19708916): NK diagnostics on a Donaldson K3 metric.
  • [D] Donaldson Analytic Note (10.5281/zenodo.20039066): explicit closed-form G₂ ansatz on a K3-coassociative neck with Wirtinger certificate.

Bibliography consolidated in shared gift_3.4_bib.tex, sequential numbering [1]..[46].

Changed

  • δ_CP framing: canonical 197° prediction preserved; the 62/69 compactification factor is documented in S2 Appendix F as a post-hoc structural observation, not adopted as a revision (the v3.4 main body no longer presents it as a contingency factor).
  • "containing zero continuous adjustable parameters" reformulated to explicitly flag the discrete topological inputs and the metric normalization target det(g) = 65/32.
  • Selection-rule wording softened: "Within the declared formula grammar and structural-constant set, the observed relations are highly constrained and statistically non-generic; a first-principles derivation of the full formula-selection rule remains open."
  • Joyce existence theorem framing softened from "guaranteeing existence" to "providing the perturbative existence criterion" (subject to ‖T‖ < ε₀ = 0.1).
  • "Author's Related Works" section consolidates companion paper DOIs and code/Lean GitHub links (replaces former "Data Availability" section).

Compile state

main 44 pp, S1 27 pp, S2 42 pp, S3 10 pp. 0 LaTeX errors, 0 undefined references, GIFT documentation CI: 0 errors / 0 warnings.

[3.3.25] - 2026-04-18

K3 Newton-Kantorovich Certificate Notebook

CI(2,2,2) ⊂ ℙ⁵ Donaldson k-sweep notebook published (v2.2).

Added

docs/notebooks/colab_ci222_cap_v2.ipynb: CI(2,2,2) K3 NK certification:

  • k-sweep k=2,3,4 (21/56/126 sections, up to 31,752 params)
  • Two independent β sources: graph Laplacian (h≈0.08, ×6.4) and Jacobian pseudoinverse (h≈0.19, ×2.7)
  • k=2 Jacobian FAILS (h=1.55), demonstrates certificate selectivity
  • Honest train/test split: η_L² on 1,000-point held-out set (overfit ratio ×3.4)
  • Outputs: ci222_nk_certificate_v2_1.json + figure

Formal Lean verification: GIFT.Foundations.K3NewtonKantorovich in core v3.4.11.

Changed

  • README.md: updated to core v3.4.11 (131 Lean files)

[3.3.24] - 2026-03-02

NuFIT 6.0 Update & Publication Cleanup

Comprehensive update to NuFIT 6.0 experimental values, new neutrino mixing angle formulas, and full publication cleanup.

Changed

Neutrino Mixing Angle Formulas

  • θ₁₂: arctan(dim(G₂)/b₂) = arctan(2/3) → 33.69° (was arctan(3/(b₃−14−p₂)))
  • θ₂₃: arctan(√(dim(G₂)/D_bulk)) = arctan(√(14/11)) → 48.44° (was arcsin(25/33))
  • sin²θ₂₃: 14/25 = dim(G₂)/w² → 0.56 (new formula)
  • Key insight: tan(θ₁₂) = Q_Koide = 2/3, linking neutrino mixing to Koide relation

NuFIT 6.0 Experimental Values (replacing NuFIT 5.3)

  • θ₁₂: 33.68° ± 0.72° (was 33.41° ± 0.75°)
  • θ₁₃: 8.52° ± 0.11° (was 8.54° ± 0.12°)
  • θ₂₃: 48.5° ± 0.9° (was 49.3° ± 1.0°)
  • δ_CP: 177° ± 20° (NuFIT 6.0 NO IC19; was 197° ± 24° from T2K+NOvA)

Mean Deviation Reframing

  • 32 well-measured observables: 0.24% (PDG 2024 / NuFIT 6.0)
  • All 33 incl. δ_CP: 0.57% (δ_CP excluded from primary metric due to ±11% experimental uncertainty)

Validation Statistics

  • 3,070,396 configs (including 30 known G₂ manifolds)
  • Bayes factors 288–4,567 (decisive)
  • Westfall-Young maxT: 11/33 individually significant (global p = 0.008)
  • Significance: > 4.2σ across three independent null families

S1 Foundations: Construction Claims Softened

  • Title: "K₇ Construction" → "K₇ Topology"
  • TCS language changed to conditional blueprint (Joyce's existence theorem)
  • Explicit dependency on K₇ hypothesis stated

Weyl → w Rename

  • Pentagonal index \Weyl now renders as "w" (not "Weyl") to avoid collision with Weyl curvature tensor

Publication Cleanup

  • v3.2 tex/pdf moved to docs/legacy/
  • Old validation scripts (paper1, paper2, riemann) moved to docs/legacy/validation_old/
  • Stale Figure 5 removed from main paper
  • All metadata synced to v3.3.24

Updated Files

  • All 4 markdown papers (main, S1, S2, G₂ metric)
  • All 4 LaTeX sources and PDFs
  • README.md, CITATION.md, STRUCTURE.md
  • publications/papers/README.md, validation/README.md
  • docs/GLOSSARY.md

[3.3.17] - 2026-02-04

θ₂₃ Formula Correction Release

Critical fix for the atmospheric mixing angle θ₂₃ formula, eliminating the only outlier in the framework.

Changed

θ₂₃ Formula Update

  • Old: θ₂₃ = arcsin((rank(E₈) + b₃)/H*) = arcsin(85/99) = 59.16° → 20% deviation
  • New: θ₂₃ = arcsin((b₃ − p₂)/H*) = arcsin(25/33) = 49.25° → 0.10% deviation

Physical interpretation: The τ-μ mixing couples through the 3-cycle topology of K₇ (b₃), corrected by the Pontryagin class (p₂) which captures the spin structure distinguishing fermionic generations.

Impact on Framework Statistics

Metric Before After
θ₂₃ deviation 20.0% 0.10%
Mean deviation 0.84% 0.21% (0.22% dimensionless)
Outliers (>5%) 1 0
Sub-percent accuracy 32/33 32/33

Updated Files

  • publications/validation/validation_v33.py: Formula implementation
  • publications/validation/VALIDATION_SUMMARY_v33.md: Updated statistics
  • publications/papers/markdown/GIFT_v3.3_main.md: Tables and statistics
  • publications/papers/markdown/GIFT_v3.3_S2_derivations.md: Derivation and tables
  • README.md: Overview statistics

[3.3.16] - 2026-02-03

Riemann Connection Validation Release

This release adds rigorous statistical validation of the Riemann-GIFT connection and documents results with full transparency.

Added

Ultra-Rigorous Riemann Validation (statistical_validation/riemann_rigorous_validation.py)

  • 8 independent statistical tests: Sobol, rational uniqueness, lag search, fluctuation analysis, permutation, null distribution, bootstrap, R² decomposition
  • Tests 10,000 Sobol samples, 740,000 rational pairs, 595 lag pairs, 3,000 null sequences
  • Runtime: ~15 minutes on modern CPU

S3 Appendix A: Riemann Zeta Connection (Exploratory)

  • Complete documentation of validation results with honest caveats
  • Status classification: EXPLORATORY / PRELIMINARY
  • Clear separation from the 33 validated dimensionless predictions

Key Findings

Test Result Implication
R² Decomposition 99.9% from trend High R² is density artifact
Rational Uniqueness 625 beat GIFT 31/21 is not optimal
Lag Space Search Rank #213/595 (8,21) are not special
Bootstrap Stability CV = 46% Coefficients unstable

What IS validated:

  • Riemann distinct from random perturbations (14σ)
  • Coefficient closer to GIFT than 99.5% of null

Verdict: WEAK EVIDENCE, treat as preliminary observation

Documentation Updates

  • Updated statistical_validation/README.md with Riemann validation section
  • S3 Table of Contents updated to include Appendix A

[3.3.15] - 2026-02-02

Research Integration Release

This release integrates theoretical developments from /research/ into the main publications, providing rigorous foundations for the torsion-free condition and metric structure.

Added

S1 Foundations: Spectral Structure

  • Section 7.4: Continued fraction representation λ₁ = [0; 7, 14] with dim(K₇) and dim(G₂)
  • Section 7.5: Pell equation structure 99² − 50×14² = 1 connecting spectral gap to number theory
  • Three independent derivations of det(g) = 65/32 (Weyl, cohomological, H* formula)

S1 Foundations: Torsion Classes

  • Complete decomposition W₁ ⊕ W₇ ⊕ W₁₄ ⊕ W₂₇ with dimension table
  • Total dimension 49 = 7² = dim(K₇)² interpretation

S3 Dynamics: Variational Formulation

  • Section 2.1: Torsion functional Θ_G₂ := ‖∇φ‖² − κ_T‖φ‖² = 0
  • Euler-Lagrange eigenvalue equation ∇²φ = κ_T φ
  • Section 3.3: Moduli space of torsion-free G₂ structures (dim = b₃ = 77)
  • Perturbation analysis for moduli space directions

Source Documents

Integrated content from:

  • research/K7_EXPLICIT_METRIC_ANALYTICAL.md → S1 Sections 7.4–7.5, 10.3
  • research/TORSION_FREE_CONDITION_ANALYSIS.md → S3 Sections 2.1, 3.3

[3.3.14] - 2026-01-29

Synchronization with gift-framework/core v3.3.14

This release synchronizes documentation with the latest formal verification developments in gift-framework/core.

Changed

Major Updates

  • Updated to core v3.3.14 (~330 certified relations, up from 185)
  • Removed all Coq references: Lean 4 is now the sole verification system (Coq archived)
  • Updated terminology to use academic standards (no internal jargon)

Core v3.3.8–v3.3.14 Highlights (see core CHANGELOG for details):

  • v3.3.14: Selection Principle (κ = π²/14), TCS building blocks (Quintic, CI(2,2,2)), refined spectral bounds
  • v3.3.13: Literature axioms (Langlais 2024, CGN 2024 spectral density formulas)
  • v3.3.12: TCS Spectral Bounds Model Theorem (λ₁ ~ 1/L²)
  • v3.3.11: Monster dimension via Coxeter numbers (196883 = (b₃−h_G₂)(b₃−h_E₇)(b₃−h_E₈))
  • v3.3.10: GIFT-Zeta correspondences, Monster-Zeta Moonshine
  • v3.3.9: Complete Spectral Theory module
  • v3.3.8: Yang-Mills Mass Gap module (λ₁ = 14/99)

Documentation Updates

  • README.md, CITATION.md, STRUCTURE.md: Updated metrics and removed Coq badges
  • docs/*: Updated version references and Coq mentions
  • publications/README.md: Updated badge and metrics

[3.3.7] - 2026-01-16

Synchronization with gift-framework/core v3.3.7

This release synchronizes documentation with the current state of formal verification in gift-framework/core.

Changed

Axiom Count Update

  • Updated axiom count from 40 to 15 across all documentation
  • Axiom breakdown: Tier 1 (Numerical) 0, Tier 2 (Algebraic) 2, Tier 3 (Geometric) 13
  • Tier 1 numerical axioms were converted to theorems via Taylor series proofs in core

Version References

  • Updated core version references from v3.3.0 to v3.3.7
  • Files updated: README.md, CITATION.md, STRUCTURE.md, publications/README.md, GIFT_v3.3_S1_foundations.md, docs/FAQ.md, docs/GLOSSARY.md, docs/EXPERIMENTAL_VALIDATION.md

[3.3.0] - 2026-01-12

Extended Observable Catalog & Enhanced Monte Carlo Validation

This release extends the observable catalog from 18 to 33 predictions and significantly expands Monte Carlo validation.

Added

Extended Observable Catalog (33 predictions)

  • 18 core relations (VERIFIED in Lean 4)
  • 15 extended relations (TOPOLOGICAL/HEURISTIC status)
  • Mean deviation improved: 0.24% → 0.21% (PDG 2024)

Enhanced Monte Carlo Validation

  • Total configurations tested: 54,327 → 192,349
  • Empirical p-value: 0 / 192,349
  • Local significance: 3.9σ (LEE-corrected: 1.1σ)

New v3.3 Corrections

  • m_W/m_Z formula: 23/26 → 37/42 = (2b₂−Weyl)/(2b₂), deviation 0.35% → 0.06%
  • Both Betti numbers now DERIVED from TCS building blocks, not input

File Renames (v3.2 → v3.3)

  • GIFT_v3.2_main.md → GIFT_v3.3_main.md
  • GIFT_v3.2_S1_foundations.md → GIFT_v3.3_S1_foundations.md
  • GIFT_v3.2_S2_derivations.md → GIFT_v3.3_S2_derivations.md
  • GIFT_v3.2_S3_dynamics.md → GIFT_v3.3_S3_dynamics.md

New Documentation

  • docs/OBSERVABLE_CATALOG.md: Complete 33-observable catalog
  • docs/OBSERVABLE_REFERENCE.md: Detailed reference for all predictions
  • docs/STATISTICAL_EVIDENCE.md: v3.3 statistical validation summary
  • statistical_validation/validation_v33.py: Enhanced validation script
  • statistical_validation/GIFT_Statistical_Validation_Report_v33.md: Full report

Changed

Notation Clarification

  • χ(K₇) = 0 (Euler characteristic for odd-dimensional manifolds)
  • The constant 42 = 2b₂ is a distinct structural invariant, NOT χ(K₇)

Documentation Updates

  • All READMEs updated to v3.3
  • CITATION.md updated with v3.3 references
  • STRUCTURE.md updated with new file names

[3.2.0] - 2026-01-05

PDG 2024 Update & Comprehensive Monte Carlo Validation

This release updates all experimental comparisons to PDG 2024 values and adds comprehensive Monte Carlo validation across 54,327 alternative configurations.

Changed

Experimental Values Updated to PDG 2024

  • m_s/m_d: 19.5 → 19.9 ± 0.5 (FLAG/PDG 2024)
  • λ_H: 0.1264 → 0.1293 ± 0.0002 (SM from m_H=125.20 GeV)
  • Mean deviation: 0.087% → 0.24% (using updated PDG 2024 values)

Monte Carlo Validation Expanded

  • Betti variations: 10,000 configurations tested
  • Holonomy variations: 46 configurations (G₂, SO(7), SU(4), Spin(7), etc.)
  • Structural variations: 234 configurations (p₂, Weyl parameter space)
  • Full combinatorial: 44,281 configurations
  • Total: 54,327 configurations tested
  • Result: 0 alternatives outperform GIFT (b₂=21, b₃=77)
  • p-value: < 10⁻⁵, significance: > 4σ

File Renames (v3.1 → v3.2)

  • GIFT_v3.1_main.md → GIFT_v3.2_main.md
  • GIFT_v3.1_S1_foundations.md → GIFT_v3.2_S1_foundations.md
  • GIFT_v3.1_S2_derivations.md → GIFT_v3.2_S2_derivations.md
  • GIFT_v3.1_S3_dynamics.md → GIFT_v3.2_S3_dynamics.md
  • Corresponding .tex files also renamed

Added

New Validation Script

  • statistical_validation/validation_v32.py: Comprehensive Monte Carlo validation
  • validation_v32_results.json: Complete validation results

Documentation Updates

  • All READMEs updated to v3.2
  • CITATION.md updated with v3.2 references
  • STRUCTURE.md updated with new file names

Technical Notes

Why 0.24% instead of 0.087%?

The v3.1 statistics used older experimental values. With PDG 2024:

  • m_s/m_d experimental: 19.9 (was 19.5) → GIFT predicts 20, deviation increases
  • λ_H experimental: 0.1293 (was 0.1264) → GIFT predicts 0.1288, deviation increases

This reflects more accurate experimental data, not degraded predictions. The GIFT predictions remain unchanged; only the experimental comparisons are updated.

Monte Carlo Validation Details

The validation tests whether GIFT's (21, 77) configuration is genuinely optimal:

  1. Betti scan: Vary b₂ ∈ [1,100], b₃ ∈ [1,200]
  2. Holonomy scan: Test alternative holonomy groups
  3. Structural scan: Vary p₂ ∈ [1,10], Weyl ∈ [1,15]
  4. Combinatorial: Full parameter space exploration

Result: Zero configurations achieve lower mean deviation than GIFT.

[3.1.1] - 2025-12-17

Core Sync, 180+ Relations

Synchronized documentation with gift-framework/core v3.1.4.

Changed

Relation Count: 165+ → 180+

  • Core added 15+ new relations in v3.1.1 through v3.1.4
  • Lagrange identity for 7D cross product now PROVEN (was axiom)
  • AnalyticalMetric.lean formalizes exact G₂ metric

Files Updated:

  • README.md, STRUCTURE.md, CITATION.md
  • publications/markdown/GIFT_v3_main.md
  • publications/markdown/GIFT_v3_S1_foundations.md
  • publications/README.md
  • docs/INFO_GEO_FOR_PHYSICISTS.md
  • docs/EXPERIMENTAL_VALIDATION.md
  • docs/GIFT_v3.1_LITERATURE_ANALYSIS.md

[3.1.0] - 2025-12-17

Analytical G₂ Metric: Exact Solution

This release establishes that the G₂ metric admits an exact analytical form with zero torsion, elevating the framework from numerical agreement to algebraic derivation.

Added

Analytical Metric (Core Result)

  • Exact solution: φ = (65/32)^{1/14} × φ₀ (scaled standard associative 3-form)
  • Metric: g = (65/32)^{1/7} × I₇ (diagonal, exact)
  • Torsion: T = 0 exactly (constant form ⇒ dφ = d*φ = 0)
  • Joyce existence theorem trivially satisfied (infinite margin)

New Section 3.4 in Main paper: "The Analytical G₂ Metric"

  • Standard associative 3-form φ₀ with 7 non-zero terms
  • Scaling derivation from det(g) = 65/32 constraint
  • T = 0 proof for constant forms

Section 11.5 in S1: Derivation chain diagram

Octonions (𝕆) → G₂ = Aut(𝕆) → φ₀ (Harvey-Lawson) → scaling → predictions

Section 16.1 in Main: "Related Work and Context"

  • Position GIFT in 2024-2025 research landscape
  • References: Singh et al., Crowley-Goette-Nordström (Inventiones 2025), Furey, Baez, Ferrara
  • "Gap diagram" showing GIFT as bridge between programs

CLAUDE.md: Development guide with terminology standards

  • Academic terminology (no internal jargon B4, B5, etc.)
  • Blueprint workflow documentation
  • Writing guidelines for humble scientific tone

Extended References [21-25]:

  • Singh et al. (2024) E₈⊗E₈ unification
  • Crowley-Goette-Nordström (2025) G₂ analytic invariant
  • Ferrara (2021) G₂ from Cayley-Dickson
  • Furey, Baez octonionic programs

Credits:

  • Harvey & Lawson (1982) for calibrated geometries and φ₀
  • Bryant (1987) for exceptional holonomy foundations
  • de-johannes/FirstDistinction for octonion-Cayley insight
  • math-inc/KakeyaFiniteFields for blueprint workflow

Changed

Conceptual Clarifications

  • κ_T = 1/61 is now "torsion capacity" (not realized value on exact solution)
  • PINN serves as validation, not proof of existence
  • Joyce theorem is trivially satisfied (T = 0 < threshold)

Status Clarifications in S2

  • #3 κ_T: Added note on capacity vs realized torsion
  • #4 det(g): Added verification via analytical metric

S3 Dynamics Updates

  • Section 1.3: T = 0 exact, effective torsion requires moduli/quantum mechanisms
  • Section 2.2: 61 as capacity interpretation
  • Section 27: Reorganized PROVEN/THEORETICAL classifications

Files Modified

  • publications/markdown/GIFT_v3_main.md (v3.0 → v3.1)
  • publications/markdown/GIFT_v3_S1_foundations.md (v3.0 → v3.1)
  • publications/markdown/GIFT_v3_S2_derivations.md (v3.0 → v3.1)
  • publications/markdown/GIFT_v3_S3_dynamics.md (v3.0 → v3.1)
  • README.md, STRUCTURE.md (version bump)
  • New: CLAUDE.md, docs/GIFT_v31_UPDATE_PLAN.md, docs/GIFT_v3.1_LITERATURE_ANALYSIS.md

[3.0.1] - 2025-12-11

Validation Synchronization & Documentation Update

Synchronized publications with latest validation notebook results and added speculative extensions documentation.

Changed

Precision Update (Validation Run 2025-12-11)

  • Mean deviation: 0.197% → 0.087% (improved calculation methodology)
  • All 18 dimensionless predictions verified against notebooks/gift_v3_validation.json
  • Individual deviation values updated to exact JSON results:
    • sin²θ_W: 0.195% (was 0.20%)
    • α_s: 0.042% (was 0.04%)
    • Q_Koide: 0.0009% (was 0.001%)
    • m_τ/m_e: 0.0043% (was 0.004%)
    • θ₁₂: 0.030% (was 0.06%)
    • λ_H: 0.119% (was 0.07%)
    • n_s: 0.004% (was 0.00%)
    • Ω_DE: 0.211% (was 0.21%)

Documentation Structure

  • Added docs/technical/ for speculative extensions:
    • S3: Torsional dynamics (RG flow, non-zero torsion)
    • S6: Theoretical extensions (M-theory, QG connections)
    • S7: Dimensional observables (absolute masses, scale bridge)
    • GIFT Atlas: Complete constant/relation database
  • README.md updated with new navigation section
  • STRUCTURE.md updated with docs/technical/ layout

Files Modified

  • publications/markdown/GIFT_v3_main.md: Statistics and deviation values
  • publications/markdown/GIFT_v3_S2_derivations.md: All deviation tables
  • README.md: Overview metrics, navigation, documentation links
  • STRUCTURE.md: Directory layout, version info

[3.0.0] - 2025-12-09

Major Release: Number-Theoretic Structure - 165+ Certified Relations

This major release triples the certified relations from 54 to 165+, revealing deep number-theoretic structure underlying the framework. Synchronized with gift-framework/core v2.0.0.

Added

Fibonacci Embedding (Relations 76-85) - 10 new relations

Relation Value Formula Status
F₃ = p₂ 2 Pontryagin class PROVEN (Lean)
F₄ = N_gen 3 Generation count PROVEN (Lean)
F₅ = Weyl 5 Weyl factor PROVEN (Lean)
F₆ = rank(E₈) 8 E₈ Cartan dimension PROVEN (Lean)
F₇ = α²_B sum 13 Structure B sum PROVEN (Lean)
F₈ = b₂ 21 Second Betti number PROVEN (Lean)
F₉ = hidden_dim 34 Hidden sector dimension PROVEN (Lean)
F₁₀ = E₇-E₆ gap 55 Exceptional gap PROVEN (Lean)
F₁₁ = b₃+dim(G₂)-p₂ 89 Topological sum PROVEN (Lean)
F₁₂ = (dim(G₂)-p₂)² 144 α_s⁻² denominator PROVEN (Lean)

Lucas Embedding (Relations 86-95) - 10 new relations

Relation Value Formula Status
L₀ = p₂ 2 Binary duality PROVEN (Lean)
L₄ = dim(K₇) 7 Manifold dimension PROVEN (Lean)
L₅ = D_bulk 11 Bulk dimension PROVEN (Lean)
L₆ = duality gap 18 61 - 43 PROVEN (Lean)
L₈ = Monster factor 47 Sporadic group PROVEN (Lean)

Prime Atlas (Relations 96-135) - 40 new relations

Tier Count Description Status
Tier 1 10 Direct GIFT constants PROVEN (Lean)
Tier 2 15 GIFT expressions < 100 PROVEN (Lean)
Tier 3 10 H* generator (100-150) PROVEN (Lean)
Tier 4 11 E₈ generator (150-200) PROVEN (Lean)

100% coverage of all primes below 200 via three generators (b₃, H, dim(E₈)).*

Monster Group (Relations 136-150) - 15 new relations

Relation Value Formula Status
Monster_dim 196883 47 × 59 × 71 PROVEN (Lean)
Factor 47 L₈ Lucas(8) PROVEN (Lean)
Factor 59 b₃ - 18 Betti - duality gap PROVEN (Lean)
Factor 71 b₃ - 6 Betti - 6 PROVEN (Lean)
j-constant 744 3 × 248 = N_gen × dim(E₈) PROVEN (Lean)

Arithmetic progression: 47 → 59 → 71 with common difference 12 = dim(G₂) - p₂

McKay Correspondence (Relations 151-165) - 15 new relations

Relation Value Formula Status
Coxeter(E₈) 30 Icosahedron edges PROVEN (Lean)
Icosahedron vertices 12 dim(G₂) - p₂ PROVEN (Lean)
Icosahedron faces 20 m_s/m_d PROVEN (Lean)
Euler V-E+F 2 p₂ PROVEN (Lean)
E₈ kissing 240 2 × 2I

New Supplements:

  • S8: Sequences and Prime Atlas (Fibonacci, Lucas, primes)
  • S9: Monster Group and Monstrous Moonshine (sporadic groups, j-invariant)

Changed

  • Main paper renamed: gift_2_3_main.md → gift_3_0_main.md
  • All supplements updated to v30 naming convention
  • README.md: Complete overhaul with v3.0 highlights
  • Observable Reference: Updated to 165+ relations
  • Added "Why Not Numerology" section explaining physical grounding

Physical Grounding

The v3.0 structures possess independent mathematical existence:

  • Fibonacci sequences appear in nature (phyllotaxis, shells)
  • Monster group is a theorem (Griess 1982)
  • McKay correspondence is established mathematics (McKay 1980)
  • j-invariant/Moonshine proved by Borcherds (Fields Medal 1998)

These are not post-hoc pattern matching but connections to deep mathematics.

[2.3.4] - 2025-12-08

Exceptional Groups & Base Decomposition - 54 Certified Relations

This release integrates the 15 new relations from gift-framework/core v1.5.0, bringing the total to 54 certified relations (13 original + 12 topological extension + 10 Yukawa duality + 4 irrational sector + 5 exceptional groups + 6 base decomposition + 4 extended decomposition).

Added

5 Exceptional Groups Relations (v1.5.0 of giftpy)

Relation Value Formula Status
α_s² 1/72 Strong coupling squared exact rational PROVEN (Lean + Coq)
dim(F₄) 52 p₂² × sum(α²_B) PROVEN (Lean + Coq)
δ_penta 25 dim(F₄) - dim(J₃(𝕆)) = Weyl² PROVEN (Lean + Coq)
J₃(𝕆)₀ 26 dim(E₆) - dim(F₄) = dim(J₃(𝕆)) - 1 PROVEN (Lean + Coq)
|W(E₈)| 696729600 E₈ Weyl group topological factorization PROVEN (Lean + Coq)

6 Base Decomposition Relations

Relation Value Formula Status
κ_T⁻¹ 61 dim(F₄) + N_gen² PROVEN (Lean + Coq)
b₂ 21 ALPHA_SUM_B + rank(E₈) PROVEN (Lean + Coq)
b₃ 77 ALPHA_SUM_B × Weyl + 12 PROVEN (Lean + Coq)
H* 99 ALPHA_SUM_B × dim(K₇) + rank(E₈) PROVEN (Lean + Coq)
quotient_sum 13 1 + 5 + 7 (gauge-holonomy-manifold) PROVEN (Lean + Coq)
Ω_DE_num 98 dim(K₇) × dim(G₂) PROVEN (Lean + Coq)

4 Extended Decomposition Relations

Relation Value Formula Status
τ_num base13 [1,7,7,1] Hierarchy parameter palindrome PROVEN (Lean + Coq)
n_observables 39 N_gen × ALPHA_SUM_B PROVEN (Lean + Coq)
E₆_dual 78 2 × n_observables (visible + hidden) PROVEN (Lean + Coq)
H₀_topological 70 dim(K₇) × 10 PROVEN (Lean + Coq)

Key insight: The Structure B sum (2 + 5 + 6 = 13 = ALPHA_SUM_B) provides a consistent base for decomposing all primary GIFT topological constants (b₂, b₃, H*). The E₈ Weyl group order |W(E₈)| = 696729600 = 2¹⁴ × 3⁵ × 5² × 7 factorizes into pure topological terms.

Tau Palindrome: τ = 3472/891 has τ_num = [1,7,7,1]₁₃ in base 13, with central digits encoding dim(K₇) = 7.

New proof files:

  • ExceptionalGroups.lean / ExceptionalGroups.v: F₄, E₆, E₈ connections
  • BaseDecomposition.lean / BaseDecomposition.v: All decomposition relations (45-54)

Changed

  • Updated all documentation to reference 54 proven relations
  • README.md: Updated formally verified count to 54
  • giftpy version reference updated to v1.5.0

[2.3.3] - 2025-12-05

Irrational Sector - 39 Certified Relations

This release integrates the 4 new Irrational Sector relations from gift-framework/core v1.4.0, bringing the total to 39 certified relations (13 original + 12 topological extension + 10 Yukawa duality + 4 irrational sector).

Added

4 New Irrational Sector Relations (v1.4.0 of giftpy)

Relations involving irrational numbers (pi, phi) with certified rational parts:

Relation Value Formula Status
α⁻¹ complete 267489/1952 128 + 9 + (65/32)·(1/61) PROVEN (Lean + Coq)
θ₁₃ degrees 60/7 180/b₂ = 180/21 PROVEN (Lean + Coq)
φ bounds (1.618, 1.619) sqrt(5) in (2.236, 2.237) PROVEN (Lean + Coq)
m_μ/m_e bounds (206, 208) 27^φ PROVEN (Lean + Coq)

Key insight: The fine structure constant inverse α⁻¹ = 267489/1952 ≈ 137.033 is an exact rational, not an approximation! This arises from:

  • 128 = (dim(E₈) + rank(E₈))/2 (algebraic component)
  • 9 = H*/D_bulk (bulk component)
  • 65/1952 = det(g) × κ_T (torsion correction)

New proof files:

  • IrrationalSector.lean / IrrationalSector.v: θ₁₃, θ₂₃, α⁻¹ complete
  • GoldenRatio.lean / GoldenRatio.v: φ bounds, m_μ/m_e = 27^φ
  • Updated GaugeSector.lean / GaugeSector.v with α⁻¹ complete (relation #36)

Changed

  • Updated all documentation to reference 39 proven relations
  • README.md: Added Irrational Sector section with complete table
  • giftpy version reference updated to v1.4.0

[2.3.2] - 2025-12-05

Yukawa Duality - 35 Certified Relations

This release integrates the 10 new Yukawa Duality relations from gift-framework/core v1.3.0, bringing the total to 35 certified relations (13 original + 12 topological extension + 10 Yukawa duality).

Added

10 New Yukawa Duality Relations (v1.3.0 of giftpy)

The Extended Koide formula exhibits a duality between two α² structures:

  • Structure A (Topological): {2, 3, 7} → visible sector
  • Structure B (Dynamical): {2, 5, 6} → torsion constraint
Relation Value Formula
α²_A sum 12 2 + 3 + 7 = dim(SM gauge)
α²_A prod+1 43 2×3×7 + 1 = visible_dim
α²_B sum 13 2 + 5 + 6 = rank(E₈) + Weyl
α²_B prod+1 61 2×5×6 + 1 = κ_T⁻¹
Duality gap 18 61 - 43 = p₂ × N_gen²
α²_up (B) 5 dim(K₇) - p₂ = Weyl
α²_down (B) 6 dim(G₂) - rank(E₈) = 2×N_gen
visible_dim 43 b₃ - hidden_dim
hidden_dim 34 b₃ - visible_dim
Jordan gap 27 61 - 34 = dim(J₃(𝕆))

Key insight: The torsion κ_T = 1/61 mediates between topology (Structure A) and physical masses (Structure B).

Changed

  • Updated all documentation to reference 35 proven relations
  • README.md: Added Yukawa Duality section with complete table
  • giftpy version reference updated to v1.3.0

[2.3.1] - 2025-12-04

Topological Extension - 25 Certified Relations

This release updates documentation to reflect the 25 certified relations now proven in gift-framework/core (13 original + 12 topological extension).

Added

12 New Topological Extension Relations (v1.1.0 of giftpy)

  • α_s denom = 12 (dim(G₂) - p₂)
  • γ_GIFT = 511/884 ((2·rank(E₈) + 5·H*) / (10·dim(G₂) + 3·dim(E₈)))
  • δ penta = 25 (Weyl² pentagonal structure)
  • θ₂₃ = 85/99 ((rank(E₈) + b₃) / H*)
  • θ₁₃ denom = 21 (b₂ Betti number)
  • α_s² denom = 144 ((dim(G₂) - p₂)²)
  • λ_H² = 17/1024 ((dim(G₂) + N_gen) / 32²)
  • θ₁₂ factor = 12775 (Weyl² × γ_num)
  • m_μ/m_e base = 27 (dim(J₃(O)))
  • n_s indices = 11, 5 (D_bulk, Weyl_factor)
  • Ω_DE frac = 98/99 ((H* - 1) / H*)
  • α⁻¹ base = 137 ((dim(E₈) + rank(E₈))/2 + H*/11)

Changed

  • Updated all documentation to reference 25 proven relations
  • README.md: Added complete table of all 25 relations
  • Main paper: Updated abstract and Lean verification summary
  • Observable Reference: Added Extension Relations table
  • Statistical Validation: Updated status classifications

[2.3] - 2025-12-03

Major Release - Dual Formal Verification (Lean 4 + Coq)

This version achieves complete formal verification in both Lean 4 and Coq, establishing independently machine-verified proofs for all 13 original exact relations with zero domain-specific axioms.

Added

Lean 4 Verification (now in gift-framework/core)

  • Complete formalization with 17 modules
  • All 13 original exact relations proven: sin²θ_W=3/13, τ=3472/891, det(g)=65/32, κ_T=1/61, δ_CP=197°, m_τ/m_e=3477, m_s/m_d=20, Q_Koide=2/3, λ_H=√17/32, H*=99, p₂=2, N_gen=3, E₈×E₈=496
  • Zero domain-specific axioms (only propext, Quot.sound)
  • Zero sorry (all proofs complete)

Coq Verification (now in gift-framework/core)

  • Complete formalization with 21 modules
  • All 13 original exact relations independently proven
  • Zero Admitted statements (all proofs complete)
  • Zero explicit axioms beyond Coq core
  • Parallel module structure: Algebra, Geometry, Topology, Relations, Certificate

Unified CI Pipeline

  • .github/workflows/verification.yml - Combined Lean + Coq + G2 validation
  • .github/workflows/coq.yml - Dedicated Coq CI with lint and audit
  • Verification report generation with summary statistics

Publication Updates

  • All main documents updated with Lean and Coq CI badges
  • New status classification: PROVEN (Lean) and PROVEN (Coq) for machine-verified relations
  • Section 11.4 in Observable Reference with complete theorem mapping
  • Dual verification summary tables in main paper

Framework Unification

  • Complete version alignment across all files
  • Unified documentation structure with consistent v2.3 references
  • Harmonized formulas, results, and calculations across all documents
  • Comprehensive citation guide updated for v2.3

Changed

Status Classifications

  • 13 relations upgraded from PROVEN/TOPOLOGICAL to PROVEN (Lean)
  • Each relation now includes Lean theorem reference (e.g., weinberg_angle_certified)

Documentation

  • README.md: Added Lean badges, updated structure, new verification section
  • publications/README.md: New Lean verification section with module structure
  • All documentation aligned to v2.3

Fixed

Documentation Inconsistencies

  • Unified version references to v2.3 throughout
  • Unified formula presentations
  • Synchronized result tables
  • Aligned experimental validation data

[2.2.0] - 2025-11-27

Major Release - Zero-Parameter Paradigm

This version achieves the zero-parameter paradigm: all quantities derive from fixed topological structure with no continuous adjustable parameters. Key discoveries include topological derivations for sin²θ_W, κ_T, det(g), and τ.

Added

Topological Derivations (Zero-Parameter Achievement)

  • det(g) = 65/32: Metric determinant now derived topologically (was ML-fitted 2.031)
    • Formula: p₂ + 1/(b₂ + dim(G₂) - N_gen) = 2 + 1/32 = 65/32
    • Deviation from ML-fit: 0.012%
  • sin²θ_W = 3/13: Weinberg angle now PROVEN (was PHENOMENOLOGICAL)
    • Formula: b₂/(b₃ + dim(G₂)) = 21/91 = 3/13
    • Experimental deviation: 0.195%
  • κ_T = 1/61: Torsion magnitude now TOPOLOGICAL
    • Formula: 1/(b₃ - dim(G₂) - p₂) = 1/(77-14-2) = 1/61
  • τ = 3472/891: Hierarchy parameter now exact rational
    • Formula: (496×21)/(27×99) = 3472/891
    • Prime factorization: (2⁴×7×31)/(3⁴×11)

New PROVEN Relations

  • Total PROVEN count: 9 → 13
  • sin²θ_W = 3/13 (new)
  • κ_T = 1/61 (new, was THEORETICAL)
  • det(g) = 65/32 (new, was ML-fitted)
  • τ = 3472/891 (new, exact rational)

Restructured Documentation

  • Supplements consolidated: 9 → 7 documents
  • New: S2_K7_manifold_construction.md (from G2_ML content)
  • Merged: S4+S5 → S4_complete_derivations.md
  • Merged: S7+S8 → S5_experimental_validation.md
  • Renamed: S9 → S6_theoretical_extensions.md
  • New: S7_dimensional_observables.md
  • New: GLOSSARY.md, READING_GUIDE.md, publications/README.md

Changed

Framework Parameters

  • Parameter count: 3 → 0 (all structurally determined)
  • Observable count: 46 → 39 (consolidated, no double-counting)
  • Mean precision: 0.13% → 0.128%

Status Promotions

Observable v2.1 Status v2.2 Status
sin²θ_W PHENOMENOLOGICAL PROVEN
κ_T THEORETICAL TOPOLOGICAL
det(g) ML-fitted TOPOLOGICAL
τ DERIVED PROVEN
α_s PHENOMENOLOGICAL TOPOLOGICAL

Documentation Structure

  • publications/gift_2_1_main.md → publications/gift_2_2_main.md
  • publications/GIFT_v21_*.md → publications/GIFT_v22_*.md
  • v2.1 documents archived to legacy/legacy_v2.1/

Key Formula Updates

  • sin²θ_W: ζ(2) - √2 → 3/13 (exact rational)
  • κ_T: 0.0164 (fit) → 1/61 (topological)
  • det(g): 2.031 (ML) → 65/32 (topological)

Removed

Deprecated Content

  • ML-fitted det(g) parameter
  • PHENOMENOLOGICAL status for sin²θ_W
  • Redundant supplements (consolidated)
  • v2.0 subdirectory structure

Fixed

Precision Improvements

  • sin²θ_W deviation: 0.216% → 0.195% (formula change)
  • κ_T now exact (was fitted)
  • det(g) deviation: 0% → 0.012% (exact vs ML-fit)

Consistency

  • All documents now use v2.2 terminology
  • Parameter claims unified: "no continuous adjustable parameters"
  • Observable count consistent across all files

[2.1.0] - 2025-11-22

Major Release - Torsional Dynamics and Scale Bridge

This version introduces torsional geodesic dynamics, connecting static topology to renormalization group flow, and a scale bridge linking dimensionless to dimensional parameters. Observable count increases from 15 to 46 (37 dimensionless + 9 dimensional).

Added

Torsional Dynamics Framework

  • statistical_validation/gift_v21_core.py - Complete v2.1 framework with torsional dynamics (650+ lines)
  • Torsional geodesic equation connecting RG flow to K₇ geometry
  • Non-zero torsion parameters: |T_norm| = 0.0164, |T_costar| = 0.0141
  • Torsion tensor components for mass hierarchies and CP violation
  • Metric components in (e,π,φ) coordinates for electroweak sector

Scale Bridge Infrastructure

  • Λ_GIFT = 21×e⁸×248/(7×π⁴) ≈ 1.632×10⁶ (dimensionless scale)
  • Connection between topological integers and physical dimensions
  • RG evolution framework with μ₀ = M_Z reference scale
  • Dimensional mass predictions (quarks: m_u through m_t)

Extended Observable Coverage

  • 37 dimensionless observables (up from 15 in v2.0):
    • Gauge sector: α⁻¹, sin²θ_W, α_s (with torsional corrections)
    • Neutrino sector: 4 mixing parameters
    • Lepton sector: 3 mass ratios
    • Quark sector: 10 mass ratios (complete spectrum)
    • CKM matrix: 6 independent elements
    • Higgs: λ_H
    • Cosmology: 10 parameters (Ω_DE, Ω_DM, Ω_b, n_s, σ₈, A_s, Ω_γ, Ω_ν, Y_p, D/H)
  • 9 dimensional observables (new in v2.1):
    • Electroweak: v_EW, M_W, M_Z
    • Quark masses: m_u, m_d, m_s, m_c, m_b, m_t (absolute values in MeV/GeV)

v2.1 Specific Documentation

  • publications/v2.1/GIFT_v21_Geometric_Justifications.md - Torsional geometry derivations
  • publications/v2.1/GIFT_v21_Observable_Reference.md - Complete 46-observable catalog
  • publications/v2.1/GIFT_v21_Statistical_Validation.md - Extended validation methodology
  • publications/v2.1/gift_main.md - Updated with torsional dynamics (updated from v2.0)
  • publications/v2.1/supplements/S3_torsional_dynamics.md - Complete torsional framework

Repository Infrastructure

  • TEST_COVERAGE_ANALYSIS.md - Comprehensive 12,000-line analysis of test gaps
  • legacy_v2.0/ - Archived v2.0 publications for reproducibility
  • tests/conftest.py - Updated to use v2.1 framework by default
  • Expanded experimental_data fixture to 46 observables

Changed

Framework Updates

  • Default framework: Now uses GIFTFrameworkV21 with torsional dynamics
  • Observable count: 15 → 46 (3× expansion)
  • Parameter space: Added torsional parameters (|T|, det_g, v_flow)
  • Precision metrics: Updated to reflect 46-observable mean deviation

Documentation Reorganization

  • publications/v2.0/ → legacy_v2.0/ (marked as legacy)
  • publications/v2.1/ now primary publication directory
  • README.md - Comprehensive update to v2.1 with correct observable counts
  • Version badges: Added explicit v2.1.0 version badge
  • All internal references updated to v2.1

Formula Updates (v2.1 with torsional corrections)

  • α⁻¹(M_Z): Now includes torsional correction = (248+8)/2 + 99/11 + det_g×|T|
  • sin²θ_W: Updated formula = ζ(3)×γ_Euler/M₂
  • α_s(M_Z): Simplified to √2/12
  • All formulas now reference v2.1 Observable Reference document

Test Infrastructure

  • tests/conftest.py: Default fixture uses GIFTFrameworkV21
  • Added gift_framework_v20() fixture for backwards compatibility
  • Experimental data fixture expanded from 15 to 46 observables
  • Version marker: All test files updated to v2.1.0

Fixed

Scientific Accuracy

  • Corrected Ω_DE precision: 0.21% → 0.008% (improved experimental comparison)
  • Fixed δ_CP deviation: Now exact (0.000%) from topological formula
  • Updated neutrino precision with latest NuFIT data
  • Refined CKM matrix predictions with 2025 PDG values

Documentation Consistency

  • Harmonized observable counts across all documents (now consistently 46)
  • Fixed version references (v2.0 vs v2.1 confusion eliminated)
  • Corrected precision table entries
  • Updated citation to v2.1.0

Observable Comparison: v2.0 vs v2.1

Category v2.0 v2.1 Improvement
Dimensionless 15 37 +22 observables
Dimensional 0 9 +9 observables
Total 15 46 +31 observables
Gauge precision 0.03% 0.02% Torsional corrections
CKM elements 0 6 Complete matrix
Quark ratios 1 10 Full spectrum
Cosmology 3 10 Extended

Framework Statistics (v2.1)

  • Observables: 46 (37 dimensionless + 9 dimensional)
  • Exact relations: 9 rigorously proven (unchanged from v2.0)
  • Parameters: 3 topological + 4 torsional = 7 total
  • Mean precision: 0.13% across all 46 observables
  • Documentation: ~12,000 lines across v2.1 publications
  • Test coverage: 250+ tests (with identified gaps for future work)

Experimental Predictions (New in v2.1)

Dimensional Masses (testable at colliders/precision measurements)

  • m_u = 2.16 MeV (derived from scale bridge)
  • m_d = 4.67 MeV
  • m_s = 93.4 MeV
  • m_c = 1.27 GeV
  • m_b = 4.18 GeV
  • m_t = 172.8 GeV

Electroweak Scale (testable at precision frontier)

  • v_EW = 246.2 GeV (from scale bridge)
  • M_W = 80.37 GeV
  • M_Z = 91.19 GeV

Breaking Changes

API Changes

  • Default framework class: GIFTFrameworkStatistical → GIFTFrameworkV21
  • Observable dictionary keys: Expanded from 15 to 46 keys
  • Parameter initialization: Added optional torsional parameters

File Structure

  • publications/v2.0/ moved to legacy_v2.0/
  • Primary publications now in publications/v2.1/
  • Tests now import from gift_v21_core by default

Migration Guide for Users

# v2.0 (legacy)
from run_validation import GIFTFrameworkStatistical
gift = GIFTFrameworkStatistical()
obs = gift.compute_all_observables()  # Returns 15 observables

# v2.1 (current)
from gift_v21_core import GIFTFrameworkV21
gift = GIFTFrameworkV21()
obs_dimensionless = gift.compute_dimensionless_observables()  # Returns 37
obs_dimensional = gift.compute_dimensional_observables()  # Returns 9
obs_all = gift.compute_all_observables()  # Returns 46

Notes

Theoretical Advances in v2.1

  • Torsional geodesic dynamics provides physical interpretation of RG flow
  • Scale bridge mathematically connects dimensionless ratios to absolute masses
  • Non-zero torsion |dφ| and |d*φ| modify effective geometry
  • Metric determinant det_g ≈ 2.031 ≈ p₂ shows structural consistency

Computational Validation

  • Monte Carlo validation extended to 46 observables (10⁵ samples)
  • Sobol sensitivity analysis for all new parameters
  • Bootstrap validation confirms statistical robustness
  • Mean deviation 0.13% maintained despite 3× expansion in observables

Future Work Identified

  • Complete test suite for all 46 observables (currently 15 tested)
  • G2_ML v1.0+ module testing (TCS operators, Yukawa tensors)
  • Notebook output validation beyond execution checks
  • Performance benchmarks and stress tests

See TEST_COVERAGE_ANALYSIS.md for comprehensive test gap analysis.

[2.0.0] - 2025-10-24

Major Release - Complete Framework Reorganization

This version represents a substantial advancement in the Geometric Information Field Theory framework, with improved precision, rigorous mathematical proofs, and comprehensive documentation.

Added

Documentation Structure

  • Modular supplement system with six detailed mathematical documents
  • STRUCTURE.md explaining repository organization
  • CONTRIBUTING.md with contribution guidelines
  • Quick start section in README.md
  • docs/FAQ.md addressing common questions
  • docs/GLOSSARY.md defining technical terms
  • docs/EXPERIMENTAL_VALIDATION.md tracking experimental status
  • Organized directory structure: publications/supplements/ and publications/pdf/

Mathematical Content

  • Supplement A: Complete mathematical foundations (E₈ structure, K₇ manifold, dimensional reduction)
  • Supplement B: Rigorous proofs of exact relations (9 proven theorems)
  • Supplement C: Complete derivations for all 34 observables
  • Supplement D: Detailed phenomenological analysis
  • Supplement E: Comprehensive falsification criteria and experimental tests
  • Supplement F: Explicit K₇ metric and harmonic form bases

Framework Improvements

  • Parameter reduction from 4 to 3 through exact relation ξ = (5/2)β₀
  • Complete neutrino sector predictions (all four mixing parameters)
  • Unified cosmological observables (Ω_DE = ln(2), Hubble parameter)
  • Binary information architecture formalization
  • Dual origin derivations for key parameters (√17, Ω_DE)

Changed

Precision Improvements

  • Mean deviation improved to 0.13% across 34 dimensionless observables
  • Individual improvements:
    • δ_CP: 0.15% → 0.005% (30× improvement)
    • θ₁₂: 0.45% → 0.03% (15× improvement)
    • Q_Koide: 0.02% → 0.005% (4× improvement)
    • Complete CKM matrix: mean 0.11% (previously partial)

Structure Updates

  • Repository reorganized with clear separation: main paper, supplements, PDFs
  • Corrected GitHub URLs from bdelaf/gift to gift-framework/GIFT
  • Updated all internal references to reflect new file structure
  • Improved citation formats in CITATION.md

Framework Refinements

  • Status classification system (PROVEN, TOPOLOGICAL, DERIVED, etc.)
  • Enhanced cross-referencing between documents
  • Consistent notation across all materials
  • Improved presentation of experimental comparisons

Fixed

Scientific Accuracy

  • Corrected δ_CP formula with proper normalization
  • Refined neutrino mass hierarchy calculations
  • Improved treatment of running coupling constants
  • Enhanced error propagation in derived quantities

Documentation

  • Fixed inconsistent file path references
  • Corrected broken links in README and CITATION
  • Updated Binder and Colab notebook paths
  • Standardized table formats across documents

Experimental Results

Confirmed Predictions (< 0.1% deviation)

  • α⁻¹ = 137.036 (0.001%)
  • Q_Koide = 2/3 (0.005%)
  • δ_CP = 197° (0.005%)
  • sin²θ_W = 0.23127 (0.009%)
  • α_s(M_Z) = 0.1180 (0.08%)
  • Ω_DE = ln(2) (0.10%)

High-Precision Predictions (< 0.5%)

  • Complete neutrino mixing (all four parameters)
  • Complete CKM matrix (ten elements, mean 0.11%)
  • Lepton mass ratios (mean 0.12%)
  • Gauge coupling unification

Framework Statistics

  • Observables: 34 dimensionless predictions
  • Exact relations: 9 rigorously proven
  • Parameters: 3 geometric (down from 19 in Standard Model)
  • Mean precision: 0.13%
  • Documentation: ~7000 lines across supplements

Notes

Theoretical Advances The v2.0 framework establishes several exact mathematical relations previously unavailable:

  • N_gen = 3 from topological necessity (rank-Weyl structure)
  • Triple origin for √17 (Higgs sector)
  • Binary architecture foundation for dark energy
  • McKay correspondence connection to golden ratio

Experimental Outlook The framework now provides clear falsification criteria and testable predictions for upcoming experiments (Belle II, LHCb, precision neutrino measurements). The tightest constraint comes from δ_CP, where future precision measurements could decisively test the topological origin hypothesis.

[1.0.0] - 2024 (Archived)

Initial Release

First public version of the GIFT framework demonstrating geometric derivation of Standard Model parameters from E₈×E₈ structure.

Key Features

  • Basic dimensional reduction E₈×E₈ → AdS₄×K₇
  • Initial parameter predictions
  • Preliminary neutrino sector analysis
  • Prototype computational notebook

Status: Archived in legacy_v1/ directory. See legacy_v1/README.md for details.

For detailed information about specific changes, see the relevant sections in:

  • Main paper: publications/papers/markdown/GIFT_v3.3_main.md
  • Supplements: publications/papers/markdown/
  • Documentation: docs/