Open Problems, Scope, and Closing
This page gathers the volume's open problems in one place: the dynamics of the quasi-longitudinal gamma branch, the absolute-scale calibrations marked open, the spacing choice, and the unclaimed origin questions. Scope is restated plainly — the volume describes present physics and does not claim cosmic origins. Each open item is a gap or conditional, not a hidden contradiction.
Gathered here are the volume's open problems — the quasi-longitudinal branch's dispersion, the absolute-scale items graded open, and the choice between candidate spacings — alongside a restated scope: present physics, origins unclaimed. The closing position is that every open item is a stated gap or conditional, audited in the irreproducibility ledger, not a softened contradiction. Open items span the dispersion dynamics, absolute scale, and the 1/r² gravity normalization.
Open problems (gathered)
- The quasi-longitudinal gamma dispersion (Ch 2): the angle account (physics volume
§10.9.1) classifies gamma as a quasi-longitudinal mode, which reframes the Fermi tension—but the
dispersion relation ω(k) of that branch is not derived, so whether it is effectively
dispersionless (reconciling the Fermi bound) or again strongly dispersive is undetermined.
Its observational side is to be registered against the physics volume's open observation gate
G-ISO(§10.9.2), item (iv) (consistency with precision propagation data). The most important open problem. Advanced (v2):ch2_gamma_collective.pyshows the collective (soliton) mode is dispersionless by the leading-front diagnostic (peak ×2.84, width ×0.50, versus a linear packet's ×0.45/×1.25), and that independent modes would smear 10MeV vs 10keV by 3×10¹⁹s over 130Mly (the Fermi tension) whereas the collective mode keeps the broadband packet within the GW170817 window (<1.7s). The microscopic ω(k) is still not derived; the residual is observational (whether real GRB gamma is always collective). - The cosmological cavity length L≈150Mpc (Ch 14, 15): the single quantitative
gap behind both the CMB acoustic peaks and the BAO ruler. Sharpened (this version):
derive_acoustic_length.pyattacks the program's three criteria head-on. It closes two of them—a genuine resonant-cavity standing wave (eigenmodes kₙ=nπ/L, baryon-loaded Θ=(1+R)cos kL-R) reproduces the 1:2:3 peak-height alternation that isolated shells cannot (heights 1.00,0.20,0.91,0.17 with odd>even, versus a monotonic |sin/|² shell), and the 150Mpc background sits 41 orders of magnitude below the γ-ray scale so it cannot worsen the Chapter 2 dispersion limit. The third criterion does not close: a scale audit of every framework length finds only the microscopic inflow clock (c/νₚ≈10³km) and the Hubble length (≈4300Mpc), with 150Mpc requiring the latter divided by ≈28.6 —an order-ten factor with no forced origin in the π-chain. No constant was moved to manufacture it; the missing object is named precisely as a cosmological boundary/cavity length, not a vague conflict. Further (this version): a Big-Bang-free interpretation is now on record at hypothesis level (acoustic_length_hypothesis_interpretation.py): the companion fluid volume's selected-length mechanism (L_(*)=2π√2√(σ/ε), attractor x_(*)=2/π, slope -(π/2)⁵, same 81+1 lattice) reads the scale as a 2D-rotational→3D-isotropic crossover—the anisotropic-web-to-homogeneity transition—so the mechanism (and the forced prefactor 2π√2) close, while five independent routes agree the absolute 150Mpc keeps requiring the matter distribution's amplitude. Several forced-constant forms fit the needed factor 28.6 to under 1%, so none is claimed. The standing of the chapters is therefore upgraded: mechanism closed (\textsf{HYP}), with the absolute value reclassified as an empirical normalisation—the same out-of-scope category as BBN, the absolute g, and the absolute 2.725K. Mechanism resolved; absolute value an honest out-of-scope normalisation. - The lattice scale for light (Ch 2): whether D=4.8526 pm or a=6.33×10⁻¹⁹m governs light propagation is unresolved (it sets the dispersion scale). One datum is now on record (v2): at optical wavelengths the mass-free closure of the reality-mapping note (§(realmap)) uses D alone — the 632.99/532 pair closes on λ/D with zero fit freedom — so D is the mapping scale for the visible band; the gamma branch remains the open half.
- The a₀ wavelength identification (Ch 6): the factor 2π in a₀=cH₀/2π is derived—the framework's full-cycle constant 2π=α/δ=(2/π)/(1/π²) (the cosine-integral rectification ratio, physics vol.\ §13.5.5), the same 2π as in mₚ/mₑ=2π·3π⁴, arising in the wave picture as the wavenumber→full-wavelength factor. The residual is a modelling choice: that the relevant length is the full background wavelength λ_(bg)=2π/κₒₚₜ rather than the reduced R_H=1/κₒₚₜ (which would give the bare cH₀); the wave picture and the 90% match support it, and the empirical scale sits in the consistent band k≈5–7.
- The absolute value of G (Ch 3): the mechanism of the saturating restoring channel and of a critical radius is now shown by simulation (gate physics, §(gate)); the absolute value of G/g_(*) (the “four-wall” question) is still not derived from first principles and is fixed empirically through κ. The physics volume (v0.6.0) quantifies the computational wall behind this (event spacing 10¹¹–10¹³, quantum resolution 10¹², signal size 10²⁵, throughput 10¹⁷ short; <10² recoverable from C rewrites) and opens a recovery program R1–R4 for the historical full-physics claim — its §17.4.4, where the absorption-momentum rule now also carries a decision table (candidate on record: conserving transfer).
- Mercury's 3:2 capture probability (Ch 5): the 1:1 lock and the 3:2 resonance are
both reproduced—at e=0.206 the 3:2 is the dominant non-synchronous resonance, a stable lock,
and the captured state, versus 1:1 for a circular orbit (
ch5_spin_tidal.py, part D). What remains open is the probability of capture into the 3:2, which depends on the initial phase and on the tidal-response model (constant-Q vs. constant-lag) and triaxiality; the framework favours but does not force the observed 3:2. Computed (v2):ch5_mercury_capture.pygives the standard, model-dependent probability—≈7% (constant-Q, Goldreich–Peale) to ≈55–73% (core friction, Correia–Laskar)—quantifying “favours but does not force.” - The Bullet Cluster (Ch 8): a deficit transport model (§(colliding)) now
demonstrates the lensing/gas offset in a toy simulation under stated separation
conditions, but the quantitative cluster gate (χ² against real lensing+X-ray) is not
run; the offset is degenerate with collisionless dark matter, with post-merger reattachment a
proposed discriminator. Mechanism shown, not claimed as a quantitative success.
Magnitude computed (v2):
ch8_bullet_offset.pygives a lensing–gas offset of ≈0.2–0.6Mpc from ram-pressure stripping for physical cool-core parameters—the observed Bullet range, with no particle dark matter. The full χ² against real maps is still not run. - Lensing sign and the no-slip matching (Ch 8): the sign is now fixed by the
GR-matched index n≃1-4Φ_(eff)/c²>1 (post-Newtonian γ=1); the open
item is whether this no-slip matching survives a joint rotation-curve+lensing fit, an
equation-of-state question for the physics volume. Consistency shown (v2):
ch8_lensing_consistency.pyon NGC 2403 finds the rotation-fitting deficit is a positive, well-behaved mass that lenses with γ=1 (vs γ→0.2 for baryons-only); the joint fit against measured lensing for the same systems is the data-limited residual. - Reciprocity in an absorbing medium (Ch 7): the d_A=d_L/(1+z)² relation behind the angular-size minimum needs justification when photons are absorbed.
- The Hubble-tension parameters (Ch 7): the line-of-sight-averaging mechanism reaches
the observed 73/67 order but does not fix the sensitivity η or the local contrast
δ_(loc) independently; the predicted correlation of H₀ with local density and
with direction is the test. Demonstrated (v2):
ch_hubble_tension.pyreproduces the 73/67 magnitude (ηδ_(loc)≈0.08) and exhibits the predicted H₀–density correlation; the η–δ_(loc) degeneracy and the sign of η are broken only by measuring it. - The absolute CMB temperature 2.725K (Ch 9): the mechanism is now shown by
simulation—a light-bathed lattice holds a nonzero floor while the deficit cores reach absolute
zero (
ch9_cmb_floor.py), unifying the microwave floor with the cold darkness of Chapter 8—and the Stefan–Boltzmann energy balance is self-consistent (u_(CMB)≈80u_(*)⇒2.725K). What remains open is the absolute value: the floor is anchored to the observed radiation density, and that density (the factor 80) is not derived from the lattice's absolute emission rate. Mechanism shown and balance consistent; absolute value still anchored. - Jet launching (Ch 9): the collimation geometry is shown; the acceleration mechanism
is qualitative. Feasibility shown (v2):
ch_jet_acceleration.pytreats the rotating-inflow funnel as a relativistic de Laval nozzle and integrates the Bernoulli invariant Γw=w₀; the flow accelerates to Γ_(∞)=w₀, recovering AGN (Γ 10) and GRB (Γ 10²–10³) jets with opening angle 1/Γ. The acceleration and collimation are thus feasible; the energy loading of the base enthalpy w₀ (the launching step) remains speculative. - Spin-rate history (Ch 5): present spin rates depend on formation history and tidal
evolution, which are not derived. The galactic one-sided inflow—a tunable parameter, disclosed
openly in
ch_galactic_spin.py—is negligible for planetary spin (its tidal gradient is 10⁻¹³–10⁻¹⁸ of the Sun's), so it is not invoked to fit spins. Pattern derived (v2):ch_spin_locking.pyshows the locked-vs-free dichotomy is not contingent—comparing τ_(lock)∝ a⁶/Mₚ² (Eq. (taulock)) to the 4.5Gyr age with a single fiducial parameter set sorts all twelve test bodies correctly (the Moon, Galilean moons, Titan, Charon, Phobos, Mercury locked; Earth, Mars, giants free), no per-body tuning. Only the intrinsic spin (initial rate, and the sign in anomalies like Venus) stays formation-contingent. - Solar activity (App E, \textsf{HYP}/\textsf{SPEC}): an inflow-sink reproduces the
sunspot phenomenology (converging inflow/downdraft, field concentration, cooling, Wilson
depression) and a flare picture at order of magnitude, but is degenerate with standard
magnetoconvection on every observable; the one distinguishing claim (the inflow organises the
field) faces the observed flux-emergence-first sequence. A conjecture, not a result.
Checked (v2):
ch_solar_activity.pymakes the negative explicit. The cycle is an 11/22-yr oscillation, which requires a clock—an intrinsic frequency. Reduced to its lowest mode the αΩ dynamo has eigenvalues -1± i√(|D|), an intrinsic oscillation of period 2π/√(|D|), with no inflow term; a steady inflow (the source of unchanging gravity) has no imaginary eigenvalue and cannot supply such a clock. With flux-emergence-first this favours the dynamo. Honest verdict: this item does not close—the inflow conjecture is degenerate-at-best for steady features and cannot account for the cycle's periodicity.
Scope, restated
This volume explains present, observable facts by present physics, to a precision it holds
below the ten-percent level. It does not reconstruct cosmic origins: the deep past cannot
be verified to that standard, and the volume does not pretend otherwise. It asserts no cosmic
history—no “steady state,” no alternative beginning. It does raise one objection,
grounded entirely in present black-hole physics: if even a black hole cannot confine energy to a
point (finite jammed density; energy returned as jets), it is a legitimate physical question how
the Big Bang's initial singularity could have existed (Ch 9). That objection stands on present
facts; the answer about the past does not, and is left to evidence that can settle it. All
microscopic foundations are imported, by single-sentence citation rather than re-derivation, from
the physics volume, DOI \href{https://doi.org/10.5281/zenodo.17932566}{10.5281/zenodo.17932566}.
Closing
The honest standing of the volume is this. It takes a single input—a per-nucleon vacuum inflow rate (Ch 1)—and from it recovers gravity and the orbits (Ch 3, Ch 4), treats spin as a first-class phenomenon (Ch 5), derives the galactic acceleration scale and the radial acceleration relation (Ch 6), fits the supernova distances without dark energy (Ch 7), reinterprets dark matter as a vacuum deficit whose darkness is absolute zero (Ch 8), and accounts for the microwave background and black holes as present phenomena (Ch 9). Much of this is degenerate with the standard accounts and is offered as consistency, not proof. A few results are genuinely distinguishing and testable. One—vacuum dispersion—is the sharpest tension: read as a transverse mode it conflicts with the Fermi bound, but the framework's own angle account places gamma in a quasi-longitudinal branch, downgrading the conflict to an open dynamical item; that two-layered status is stated as plainly as the successes. The volume is therefore not a finished theory but a coherent, falsifiable, present-facts framework with explicit predictions and an explicit list of what would break it.
Reproducibility
\begin{sloppypar}
Every quantitative claim in this volume is reproduced by the accompanying package
(VP_reproducibility): thirty-four standalone scripts—the per-chapter scripts ch1–ch9,
the chapter-2 light-and-burst dynamics suite (light emergence and angle, the collective disturbance, the
Goldstone/Maxwell account, the stiffness ceiling, the relativistic law, and the burst energetics, spectrum,
propagation, jamming, and up-conversion tests), the post-Newtonian and gravitational-wave checks
(ch10_post_newtonian, ch11_grav_waves) and the puzzle, light-element,
CMB-anisotropy, and large-scale-structure checks of Ch 12–15 (ch12_puzzles,
ch13_bbn, ch14_cmb_aniso, ch15_lss_bao), the Ch 5 transparency test ch_galactic_spin, the
Appendix E conjecture ch12_sunspot, and the cross-scale ch_accuracy_dashboard, and the ledger renderer ch10_ledger—two real
datasets (SPARC NGC2403_rotmod.dat; Pantheon+ Pantheon+_extract.tsv), and a
reproducibility map listing each claim, its script, and its exact expected output—including the
vacuum-dispersion tension, the §10.9.1 angle table, the collective-disturbance mechanism, the
burst energetics and gravitational-wave link (§(burststiff)), the
Goldstone/Maxwell account, the collective-stiffness ceiling, the relativistic energy–velocity law, and the accuracy dashboard of §(dashboard), which the package makes reproducible rather than hides. The scripts use
symplectic integrators, fixed (un-tuned) constants except where a single fit is explicitly noted,
and no random seeds for the deterministic results. This closing chapter adds no new simulation; its
figure is rendered by ch10_ledger.py and summarises the ledger above.
\end{sloppypar}
10.5281/zenodo.17932566}.
\appendix