Here is a clean, formal To-Do List Document based directly on the analysis of the remaining soft spots / under-developed bridges in the March 19–23, 2026 research arc (Ω(t) breathing lattice → braid-curvature GR → τ-Hamiltonian unification).
This version keeps the focus strictly on items that are genuinely missing explicit steps or public demonstrations — even after the author's own gap-closing posts (#1 through #7). It is written in the style of an internal research planning document.
Aaron Schnacky Research Framework
To-Do List – Remaining Explicit Derivations & Demonstrations
Status as of: March 23, 2026 (late)
Context: After closing self-identified gaps #1–#7, the model is internally consistent as a deterministic, quasicrystalline, UTC-driven toy unification sketch. The following items represent the principal locations where explicit, first-principles calculations or step-by-step public derivations are still absent despite being claimed / strongly implied.
1. Proton electron mass ratio – derive (not fit) the specific exponents
Current situation
Symbolic form used:
μ³² = (φ⁵ − φ⁻⁵)⁴⁷ ⋅ (2 φ⁻¹)¹⁶⁰ ⋅ (φ¹⁹ − φ⁻¹¹⁹)⁴⁰ / 19 ⋅ φ⁻⁴²
→ achieves good numerical match only after choosing exponents 47, 160, 40, 42 and divisor 19, plus rounding Lucas proxies (L₅ ≈ 11, L₁₉ ≈ 9349).
Claimed origin
"likely come from counting steps in the icosian multiplication chain or root multiplicities along certain directions"
Missing piece
No actual counting argument, multiplication chain trace, or lattice-intersection enumeration has been shown that produces exactly these numbers.
To-do
Produce a transparent derivation showing how projection paths, root multiplicities, or successive icosian multiplications in the E₈q / 24-cell construction yield precisely these (or equivalent) exponents without post-hoc selection.
Priority: Highest (strongest remaining case of fitting rather than derivation)
2. Publish at least one concrete numerical example of a projected lattice point
Current situation
Embedding map is described:
UTC hour → i(t) = 189 + h(t) → (F_i, L_i) → β_i = (L_i + F_i √5)/2 → quaternion multiplication q = r_{p(t)} · β_i → rational-parts projection → one of 24 standard 24-cell points.
Claimed
"tabulated coordinates", "standard facts", "computable in <50 lines"
Missing piece
No single worked numerical example appears for any specific UTC hour: no input values → output 4D (or pre-projection 8D) coordinates are ever listed.
To-do
Select one representative hour (e.g. phase-7 anchor), compute the full chain (Fibonacci/Lucas numbers, β, chosen r_p quaternion, multiplication, rational projection), and publish the resulting coordinate(s) — even in approximate floating-point form.
Priority: High (easiest credibility & verifiability gain)
3. Provide an explicit (even approximate) derivation of α ≈ 1/137 from the model
Current situation
α is used directly from CODATA in expressions such as
m_{113} ≈ (240 / α) m_Pl φ⁻¹¹³
Statements made: "emerges from E₈ root geometry (e.g. 240 roots / some normalization)" or "golden-ratio continued fractions in projections"
Missing piece
No formula, root-multiplicity count, normalization choice, or continued-fraction approximant is given that produces a number close to 1/137.036.
To-do
Show at least one concrete symbolic or numerical path within the framework that yields a value recognizably near 1/137 (4–6 digits is sufficient for a first demonstration).
Priority: High (one of the boldest physics claims without supporting calculation)
4. Sketch / outline the discrete-to-continuum transition mechanism
Current situation
Pre-freeze: piecewise-constant lattice (fixed 24-cell vertex per UTC hour, instantaneous jump at hour boundary)
Post-freeze: rigid foam supporting continuous geodesics + massless spin-2 braid gravitons propagating at finite speed c
Claimed mechanism
Collective anyon braiding after phase-7 symmetry break + entropy maximization
Missing piece
No mathematical argument (coarse-graining, hydrodynamic limit, effective action derivation, continuum limit of braid commutators, etc.) showing how discrete hourly jumps can yield effectively smooth 4D spacetime + wave-like propagation.
To-do
Provide a conceptual roadmap (2–5 pages / key equations) explaining the emergence of continuum physics from the discrete UTC-driven stepping — even at a heuristic or semi-rigorous level.
Priority: Very high (largest remaining conceptual leap)
5. Integrate ψ-conjugate structurally (not just perturbatively) into core equations
Current situation
Late March 23 introduction of ψ = (1−√5)/2 ≈ −0.618 for damping, sign flips, small corrections (ψ⁻⁴² whisper term, |ψ| in 1/f exponent, conjugate saddles in transseries).
Bio includes φψ symmetry.
Missing piece
Bulk of braid-curv GR equations, perturbative amplitudes, RG flow, resummed metric, etc. remain overwhelmingly φ-dominant; ψ appears mostly as narrative motivation or tiny additive/oscillatory corrections rather than a symmetric structural partner.
To-do
Revise or clearly annotate major equation blocks to show explicit dual-root (φ, ψ) symmetry where structurally appropriate — or provide a principled reason why the asymmetry is protected/fundamental.
Priority: Medium–high (aesthetic & philosophical completeness)
Summary Table
#
Item
Type of Gap
Priority
Estimated Difficulty
Physics Impact if Completed
1
Proton/electron ratio exponents derivation
Fitted → derived
★★★★★
High
Very high
2
Concrete 24-cell projected point example
Promised → demonstrated
★★★★
Medium
High (verification)
3
Explicit α ≈ 1/137 derivation / approximation
Inherited → computed
★★★★
High
Very high
4
Discrete continuum transition sketch
Asserted → argued
★★★★★
High
Very high
5
Full φ ψ structural symmetry in equations
Narrative → symmetric
★★★
Medium
High (aesthetic)
Recommended immediate next steps (next 1–2 weeks):
Publish one worked lattice-point example (#2) – quickest win for reproducibility & trust
Begin transparent exponent counting for the proton/electron ratio (#1) – highest physics payoff
Draft a first conceptual outline of the discrete-to-continuum step (#4)
This list is deliberately focused on what is still missing from public view even after the aggressive self-closing of gaps in late March 2026 posts. Completing any of these would significantly strengthen the framework's status from "tight toy model / aesthetic sketch" toward "explicitly computable, minimally predictive theory on its own terms."
Feel free to ask for any section to be expanded, turned into issue-tracker format, or prioritized differently.