Outstanding problems
Outstanding problems of fundamental physics, and the DCT position on each
A matrix of 22 long-standing open problems, the mainstream-physics status, the DCT mechanism, the predicted observable, the current empirical status, and the per-observable sub-page and cluster paper that carry the derivation.
This page is the “what does DCT actually solve” index. Every row links into a per-observable sub-page (with measurement, residual, methodology, and a runnable Python script) and into the cluster paper that owns the derivation. Empirical-status verdicts use the four-bin scorecard from /scorecard/ —
PASS (HIT or SOFT), FAIL (MISS), OPEN (untested or unresolved), FORWARD (a discriminating prediction not yet adjudicated by data). Status verdicts are post-amendment (see Updates for the temporal Avrami \(P(z)\) reversion and its consequences).
Cosmology
| Outstanding problem | Mainstream status | DCT mechanism | Predicted observable | Empirical status | Sub-page | Cluster paper |
|---|---|---|---|---|---|---|
| Hubble tension — SH0ES vs Planck 5\(\sigma\) gap on \(H_0\) | Open since \(\sim\!2018\); no consensus mechanism in \(\Lambda\)CDM | Conformal-frame mapping in scalar–tensor gravity. The condensate fraction \(P_0 = \cos(36^\circ)/\cos(18^\circ) = 0.850651\) sets \(H_{\rm phys} = H_E/\sqrt{P_0}\), with zero free parameters. | \(H_{\rm phys} = 73.019\) km/s/Mpc; SH0ES Cepheid measures \(73.04 \pm 1.04\) | PASS — 0.02\(\sigma\) | /observables/h-phys/ | DCT-COS-01 |
| 17-method H0 spread — multi-method H0 values do not lie on a single \(\Lambda\)CDM line | Generally treated as systematics; no first-principles model | Each method probes a different effective condensate density along its line of sight; DCT predicts a tight slope of \(H_0\) vs the inferred condensate-density marker. | 17-method \(H_0\)-vs-density correlation slope | PASS — 7.34\(\sigma\); \(\Lambda\)CDM null \(p = 3 \times 10^{-8}\) | /observables/h-phys/ | DCT-COS-01 |
| \(S_8\) structure-growth tension — weak-lensing low compared to Planck-extrapolated \(\Lambda\)CDM | Open; multiple proposed extensions (e.g. interacting DE) | Linearised perturbation kernel on a \(\Lambda\)CDM background: \(\mu_b(a) = 1/P\), \(\mu_{\rm DM}(a) = 1/[P(1+\beta)]\), \(\Sigma(a) = 1/\bar P\). Constant-\(P_0\) suppresses late-time growth by \(\sim\!1{-}P_0\). | \(S_8 \approx 0.776\) (canonical); KiDS-Legacy 2025 measures \(0.815 \pm 0.018\) | FAIL — \(\sim\!2\sigma\) tension under canonical constant-\(P_0\) | /observables/s-8/ | DCT-COS-01 |
| Background BAO under DCT | BAO is an external check on any non-\(\Lambda\)CDM cosmology | For homogeneous \(P(t)\) in \(\tilde g = P g\), photon comoving \(\chi(z)\) is unchanged (null cancellation). Operational \(H_{\rm phys}\) targets must not be reverse-engineered into the BAO \(\chi\) integral. Perturbation-level kernels remain the live scored framework. | 12-bin DESI Y1 \(D_M(z)/r_d\) | PASS / neutral — homogeneous background; legacy \(\Delta\chi^2\) branch retracted | /observables/bao/ | DCT-BAO-01 |
| Dark-energy / cosmological-constant problem — \(\rho_\Lambda\) observed is \(\sim\!10^{120}\) below QFT estimate | Long-standing “vacuum-catastrophe”; no accepted resolution | Polytope-derived holographic prefactor: \(\Lambda_P = 2\pi^2 \cdot \rho_{\rm QFT} \cdot (\ell_P/L)^2\). The \(2\pi^2\) coefficient is the only ingredient beyond known scales; closes the gap to within \(\sim\!14\%\). | \(\Lambda_P/\rho_{\rm crit}\) within order-unity of unity | PASS (SOFT) — \(\sim\!14\%\) closure; geometric prefactor still on the OPEN derivation list | /observables/lambda-vacuum/ | DCT-COS-01 |
| Equation of state \(w(z)\) — deviation from \(w = -1\) under DESI | DESI 2024 hints at \(w_0\) \(\ne\) \(-1\), \(w_a \ne 0\) | DCT predicts an exact \(w_0 = -1\), \(|w_a| < 10^{-4}\) at the background level; any nonzero \(w_a\) detection beyond \(\sim\!10^{-4}\) falsifies the theory's late-time vacuum. | DESI Y1 \(w_0\), \(w_a\) joint posterior | OPEN / FORWARD — awaiting DESI Y3 | /observables/w-0/ · /observables/w-a/ | DCT-COS-01 |
| CMB low-quadrupole anomaly — \(C_2\) observed is below \(\Lambda\)CDM expectation | Open; usually attributed to cosmic variance | Conformal-wall theorem: SM-sector observables that cross the \(P\)-conformal boundary are protected; large-angular-scale modes inherit a small suppression from the topological boundary condition. | \(C_2\) suppression \(\sim\!15\%\) below \(\Lambda\)CDM | PASS (SOFT) — directional agreement with Planck 2018 | /observables/cmb-low-quadrupole/ | DCT-CMB-01 |
| CMB lensing amplitude \(A_L\) — Planck finds \(A_L \approx 1.18\) vs unity | Open; persistent ~\(\sigma\)-level excess | The lensing kernel in the perturbation-level programme picks up a small \(\Sigma(a) = 1/\bar P\) enhancement; predicts the right sign. | \(A_L\) excess \(\sim\!10{-}15\%\) over unity | PASS (SOFT) — directional agreement with Planck 2018 | /observables/a-l-cmb/ | DCT-CMB-01 |
| Globular-cluster ages — HD140283 sits near or above the \(\Lambda\)CDM age of the universe | Tension at \(\sim\!2{-}3\sigma\) when systematics are folded | Constant-\(P_0\) integration of \(H(z)\) gives \(t_{\rm univ} = 12.69\) Gyr. An interim Avrami \(P(z)\) extension that closed the tension at 13.7 Gyr was reverted on as non-canonical. | \(t_{\rm univ}\) vs HD140283 13.5 \(\pm\) 0.2 Gyr | FAIL — \(\sim\!2.9{-}4.0\sigma\) tension under canonical constant-\(P_0\) | /observables/t-univ-avrami/ | DCT-COS-01 |
Dark sector and galactic dynamics
| Outstanding problem | Mainstream status | DCT mechanism | Predicted observable | Empirical status | Sub-page | Cluster paper |
|---|---|---|---|---|---|---|
| Dark-matter direct-detection null — XENONnT, LZ, PandaX find nothing | Open; the WIMP miracle window is closed | The corpus contains no particle DM. Galactic dynamics arise from the spatial Avrami profile of the tie field, \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\); the disformal matter-tie coupling carries no fermion-number current and has no nuclear recoil signal. | \(\sigma_{\rm SI}^{\chi N} = 0\) structurally | PASS — consistent with all current direct-detection nulls | /observables/lz-dm-null/ · /pandax-dm/ · /xenon1t/ | DCT-DM-01 |
| Radial Acceleration Relation (RAR) — tight \(g_{\rm obs}\) vs \(g_{\rm bar}\) curve across SPARC | Empirical; explained phenomenologically by MOND | Single Avrami profile \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) with \(g_\dagger\) set by canonical constants; no per-galaxy free parameter. | RAR \(g_{\rm obs}\) vs \(g_{\rm bar}\) on SPARC | PASS — mean \(\chi^2/N = 0.97\) over 175 galaxies | /observables/g-dagger/ | DCT-DM-01 |
| MOND scale \(a_\dagger \approx 1.2 \times 10^{-10}\) m/s\(^2\) | Empirical; no first-principles derivation in mainstream physics | \(g_\dagger = c \, H_{\rm phys}/(2\pi\sqrt{P_0})\) from canonical constants only | \(g_\dagger = 1.224 \times 10^{-10}\) m/s\(^2\); Milgrom \(1.20 \times 10^{-10}\) | PASS — 2.0\(\%\) (0.81\(\sigma\)) match | /observables/g-dagger/ | DCT-DM-01 |
| Galaxy scaling relations — baryonic Tully–Fisher, Faber–Jackson, Fundamental Plane | Empirical; usually fitted per-relation | Same single Avrami \(P(g)\) that fits the RAR derives all three slopes with no per-relation parameter. | BTFR slope, FJ exponent, FP orientation | PASS on all three | /baryonic-tully-fisher/ · /faber-jackson/ · /fundamental-plane/ | DCT-DM-01 |
| Bullet Cluster lensing offset | Empirical; conventionally cited as evidence for collisionless DM | Spatial \(P(g)\) profile is sourced by the baryon distribution but propagates through the conformal weight; the lensing-vs-X-ray offset is reproduced without a particle DM halo. | Lensing-baryon offset profile | PASS (SOFT) — reproduces the offset within the publicly-released maps | /observables/bullet-cluster/ | DCT-DM-01 |
| Lens-to-dynamical mass turnover \(M_{\rm lens}/M_{\rm dyn}(z\!\sim\!1.5) = 1.30\) | Not predicted by \(\Lambda\)CDM; would be a discriminating signature | The perturbation-level kernel \(\Sigma(a) = 1/\bar P\) and \(\mu_{\rm DM}(a) = 1/[P(1+\beta)]\) generate a redshift-dependent split between strong-lensing mass and stellar/galaxy-dynamics mass that turns over near \(z \sim 1.5\). | Euclid 2027–2029 \(M_{\rm lens}/M_{\rm dyn}(z)\) | FORWARD — discriminating prediction; awaiting Euclid | /observables/m-lens-m-dyn/ | DCT-BAO-01 |
Standard Model and particle physics
| Outstanding problem | Mainstream status | DCT mechanism | Predicted observable | Empirical status | Sub-page | Cluster paper |
|---|---|---|---|---|---|---|
| Three-generation count and gauge structure | Open; no SM-internal explanation for exactly three generations or for \(SU(3)\!\times\!SU(2)\!\times\!U(1)\) | McKay correspondence on the binary icosahedral group \(2I\) \(\to\) \(E_8\) \(\to\) SM. The 600-cell vertex partition fixes both the generation count and the gauge labels. | Three-generation structure plus SM gauge group | PASS — structural identity | /observables/mckay-2i-e8/ | DCT-SM-01 |
| CKM mixing structure — Wolfenstein parameters and Jarlskog \(J\) | Empirical; no SM-internal derivation | \(\mathbb{Z}_3\) symmetry of the 600-cell vertex partition fixes the CKM hierarchy; the Jarlskog invariant is the structural \(\mathbb{Z}_3\) invariant of that partition. | \(J = 3.27 \times 10^{-5}\); PDG \(3.18 \times 10^{-5}\) | PASS — 3\(\%\) (0.6\(\sigma\)) | /observables/jarlskog/ | DCT-SM-01 |
| Proton-to-electron mass ratio \(m_p/m_e\) | Empirical 1836.15267343; no SM-internal derivation | Three-term polytope identity \(z\!\cdot\!153 + 1/\varphi^4 + 1/z^2\) where \(z = 12\) is the 600-cell vertex valence and \(\varphi\) is the golden ratio. | \(m_p/m_e = 1836.152501\); CODATA \(1836.15267343 \pm 0.00000011\) | PASS — 92 ppb match | /observables/m-p-m-e/ | DCT-SM-01 |
| Matter–antimatter asymmetry \(\eta_B\) | Open; no SM mechanism for the observed \(\eta_B \approx 6.1 \times 10^{-10}\) | Polytope-derived combination with a \(1/\varphi^4\) post-hoc correction (currently a partial derivation; full first-principles route is OPEN, see E3 family). | \(\eta_B \approx 6 \times 10^{-10}\) | PASS (SOFT, post-hoc) — flagged as OPEN derivation question | /observables/eta-baryon/ | DCT-SM-01 |
| Strong-CP problem — why is \(|\bar\theta_{\rm QCD}| \lesssim 10^{-10}\)? | Open; conventional resolution invokes a Peccei–Quinn axion not yet detected | Conformal-wall theorem protects \(\theta_{\rm QCD}\) at the boundary; the axial \(U(1)\) current acquires a topological boundary condition that drives \(\bar\theta\) to zero without an axion. | \(\bar\theta_{\rm QCD} \to 0\) structurally | OPEN — mechanism stated; numerical bound below current EDM limit not yet computed | /observables/strong-cp/ | DCT-SM-01 |
| Hierarchy problem — why \(M_{\rm EW} \ll M_{\rm Pl}\)? | Open; SUSY and extra-dimension routes have not closed | Brans–Dicke stiffness theorem (DCT-SBD) protects the EW scale across cosmological evolution: \(\Delta M_{\rm EW}/M_{\rm EW}\) integrated over the age of the universe is bounded below the observational reach. | \(d \ln M_{\rm EW}/d \ln a\) bound | PASS (SOFT) — theorem proved; observational bound consistent | /observables/sbd-stiffness/ | DCT-SBD-01 |
| Neutrino mass ordering / CP phase \(\delta_{CP}\) | Open; \(\delta_{CP}\) hint of \(-\pi/2\) from T2K, NOvA | SM leading-log running window 7\(^\circ\)–12\(^\circ\) brackets the residual on \(\delta_{CP} = \pi/3\); structural identity from the 600-cell complex-conjugation pair. | \(\delta_{CP}\) compatible with \(\pi/3\) plus running | FORWARD — awaiting DUNE / Hyper-K | /observables/delta-cp/ | DCT-SM-01 |
| Muon \(g\!-\!2\) anomaly — FNAL/BNL world average vs SM | Open; \(\sim\!5\sigma\) tension vs WP 2020 SM, smaller vs BMW lattice | DCT mass-coupling \(\Delta a = \varepsilon (m/M_{\rm Pl})^2 f(\alpha)\); \(\varepsilon\) is calibrated against the muon anomaly itself, then projected onto electron and tau channels as zero-additional-parameter cross-checks. | \(a_e\), \(a_\tau\) consistency given calibrated \(\varepsilon\) | PASS (SOFT, calibrated) — electron g-2 cross-check consistent; \(\varepsilon\) first-principles derivation is OPEN | /observables/muon-g-2/ · /electron-g-2/ | DCT-SM-01 |
| Inverse fine-structure constant \(1/\alpha\) | Empirical 137.0359990…; no SM-internal derivation | Polytope-derived ansatz \(\varphi^5 \cdot 4\pi \cdot (1 - \mu^2/2) = 136.82\) (post-hoc; first-principles route is OPEN, see E4). | \(1/\alpha \approx 136.82\); CODATA \(137.036\) | PASS (SOFT, post-hoc) — 0.16\(\%\) gap; flagged OPEN derivation | /observables/one-over-alpha/ | DCT-SM-01 |
| Periodic-table structure — why exactly the rows and columns we observe? | Open; periodicity emerges from \(n,\ell,m,s\) but not from a deeper structural principle | The 600-cell vertex partition gives \(\Sigma d_j^2 = 120\), the same count that organises the periodic-table rows; planned in the upcoming DCT-ATOM-01 cluster paper. | Period structure 2-8-8-18-18-32-32 from polytope | OPEN — derivation in progress (DCT-ATOM-01 planned) | /observables/periodic-table/ | DCT-ATOM-01 (planned) |
Strong gravity and quantum gravity
| Outstanding problem | Mainstream status | DCT mechanism | Predicted observable | Empirical status | Sub-page | Cluster paper |
|---|---|---|---|---|---|---|
| Black-hole information paradox | Open; remains the central conceptual problem in semi-classical gravity | Information-density (IDD) theorem: information accumulated in the boundary layer is recovered through the conformal-wall as the BH evaporates; planned cluster paper DCT-IDD-01. | Information-recovery curve in BH evaporation | OPEN — theorem stated; full publication forthcoming (DCT-IDD-01 planned) | /observables/bh-information/ | DCT-IDD-01 (planned) |
| Hawking ratio \(T_\theta / T_H\) — thermal vs derived BH temperature | Open; conformal-anomaly “factor of 2” problem | Polytope identity: the 600-cell binary icosahedral phase set fixes \(T_\theta/T_H = 2\) structurally. | \(T_\theta/T_H = 2\) structurally | PASS — structural identity | /observables/hawking-ratio/ | DCT-SBD-01 |
| Wald entropy \(S_{BH}\) — deviation from Bekenstein–Hawking? | Open; corrections from higher-curvature terms unconstrained | Polytope identity: \(P_0 \cdot S_{BH}\) is invariant under the conformal-wall map. | \(P_0 \cdot S_{BH}\) invariance | PASS — structural identity | /observables/wald-entropy/ | DCT-SBD-01 |
| PPN \(\beta\) deviation — how big is the post-Newtonian \(\beta\) deviation in scalar–tensor gravity? | Open / FORWARD; current LLR bound \(|\beta - 1| < 1.1 \times 10^{-4}\) | Closed form \(\beta - 1 = 1/[(2\omega_0+3)(2\omega_0+4)]\) with \(\omega_0 = 50{,}037\) gives a direct numerical prediction. | \(\beta - 1 = +1.0 \times 10^{-10}\) | FORWARD — below LLR; BepiColombo MORE 2028 first realistic test | /observables/beta-ppn/ | DCT-PPN-01 |
| PPN \(\gamma\) deviation (Cassini-style precision tests) | Cassini bound \(|\gamma - 1| < 2.3 \times 10^{-5}\); BepiColombo MORE will reach \(10^{-6}\) | Closed form \(\gamma - 1 = -2/(2\omega_0+3)\) with the canonical \(\omega_0\). | \(\gamma - 1 = -4.0 \times 10^{-5}\) | FORWARD — near current Cassini precision; BepiColombo MORE will discriminate | /observables/gamma-ppn/ | DCT-PPN-01 |
| Brans–Dicke stiffness backreaction | Open / structural; standard BD theorems leave the pulsar-timing window underdetermined | SBD theorem (DCT-SBD-01): closed-form bound on \(\dot\omega_b\) from BD scalar oscillations during the inspiral. | NANOGrav 15-yr binary-pulsar period derivative | PASS — structural bound consistent with NANOGrav 15-yr | /observables/sbd-pulsar/ | DCT-SBD-01 |
| Gravitational-wave luminal speed \(c_T = c\) — LIGO/Virgo GW170817 | Constrained to \(|\delta c_T/c| < 10^{-15}\) by GW170817–GRB170817A | The DCT action propagates GWs in the Einstein frame at exactly \(c\); no disformal \(c_T\) deviation. | \(\delta c_T / c = 0\) structurally | PASS — consistent with GW170817 | /observables/gw170817-c-t/ | DCT-PPN-01 |
Structural identities and mathematical foundations
| Outstanding problem | Mainstream status | DCT mechanism | Predicted observable | Empirical status | Sub-page | Cluster paper |
|---|---|---|---|---|---|---|
| Spectral identity master \(2\omega_0+3 = c_{BD} \cdot P_0^2\) | Not in mainstream physics; structural relation new to DCT | The same \(\omega_0 = 50{,}037\), \(c_{BD} = 138{,}189\), \(P_0 = 0.850651\) cluster appears across PPN, BAO, SBD, and SM derivations — a single closed identity ties them. | \(2\omega_0+3 = c_{BD} \cdot P_0^2 = 100{,}077\) | PASS — exact algebraic identity | /observables/master-identity/ | DCT-SPI-01 |
| 12 spectral identities on the 600-cell | Not in mainstream physics; new structural-identity programme | Twelve algebraic identities relating polytope invariants (Casimirs 31 and 154, the LHY constant \(G_{LHY} = 3701/6300\), spectral gap, vertex sum \(\Sigma d_j^2 = 120\), McKay 2I \(\to\) \(E_8\), conformal-wall map, Hawking ratio, Wald-entropy invariance, SBD theorem) to physical observables. | \(\log_{10}\)BF over the 12-identity panel | PASS — \(\log_{10}\)BF \(= +27.5\); LEE-corrected \(>9\sigma\) | /observables/master-identity/ | DCT-SPI-01 |
How this list is curated
The 22 rows above are the long-standing problems where DCT supplies a corpus-canonical mechanism. They are chosen against three criteria:
- The problem is widely recognised as open in mainstream physics literature.
- The DCT mechanism is in a published or in-preparation cluster paper, and reduces to a single closed expression in canonical constants (\(P_0\), \(\omega_0\), \(c_{BD}\), \(\varphi\), \(z = 12\)) with no per-observable free parameter.
- There is at least one observable that adjudicates the prediction — either now, or in a forward experiment named on this site under /predictions/#forward.
Rows with status FAIL or tension are kept on this list rather than buried — the scientific value of the page depends on honesty about where DCT does not yet match data. Background BAO is not a graded MISS after the May 2026 null-geometry revision (homogeneous \(P(t)\) cancels in \(\chi_{\rm null}\); see /observables/bao/). The headline 33-facet FAIL under constant-\(P_0\) is \(S_8\) vs KiDS-Legacy 2025; globular-cluster ages remain a sharp tension on the same branch. Cross-refs: scorecard, audit_fails.py.