Research Roadmap

Status: Terminal analytical saturation — consolidation + watch-mode (clock-gated; iteration 16 advanced the hedge to R7; iterations 17–20 attacked the residual (E_O) through reduction, construction, computation, and proof — the E=0 half is now a theorem, and the entire remaining free-field gate is the corner lemma LEM-A1′; the no-go rests on {n₁, (E_O)}; hedge held at R7 throughout). Last updated: 2026-07-11

Update (post-iteration-5): the analytical program is saturated — five iterations converged on a stable PARTIAL / encodes-not-generates / not-yet-physics verdict, and the one designated verdict-flipping lever (OP-46 Lorentzian non-CKV readout) was executed and did not flip. The standing verdict is consolidated in CONCLUSION.md. Active effort now shifts from analysis to lightweight experiment-tracking (EXPERIMENT_WATCHLIST.md). The Tier-1/2 analytical items below are retained as a record of what was attacked and closed; the only genuinely-open analytical lever is OP-44/OP-CP1 (nonperturbative crossed-product fate, regime boundary $N_\ast$ ), plus the standing "what would reopen the analysis" trigger in CONCLUSION.md §8.

Update (post-iterations-6–7) — saturation held under new input and lever execution. Iteration 6 injected two years of new external literature (10 refereed tracks); iteration 7 executed the four named decidable levers. The verdict is unchanged for the sixth consecutive iteration, but the frontier sharpened to a single object. The compressed verdict-flipper has been re-compressed twice: from "derive geometry from algebra" → "derive an indefinite pairing from modular data" (iter 6) → executed and found geometry-void (iter 7: $\eta_0=\mathrm{sgn}(\ln\Delta)$ exists, smuggle-free, but is unitarily universal / algebra-incompatible / non-localizable) → the now-current target: derive an algebra-compatible, localized (n,n) pairing from modular data — the carrier problem (HYPOTHESES.md HYP-FACTORIZATION-IS-GEOMETRY), where five independent closure routes converge. The OP-46 hedge hardened MEDIUM → MEDIUM-HIGH. Iteration 8 (in flight) attacks the carrier problem via net/relative modular data plus three named residues (OP-44 R1/R2; OP-49 junction additivity (c′); OP-48c exit X1).

The current live agenda, by leverage:

The carrier problem (HYP-FACTORIZATION-IS-GEOMETRY) — the single analytical development that would flip "encodes" to "generates". Attacked in iteration 8; if it survives there, the next inputs are net-cohomological / modular-Berry-curvature constructions and any 2024–2026 result deriving localization (not just a pairing) from modular data.

The distinguishing-test sweep — the binding blocker per CONCLUSION.md §7 is not the algebra but the absence of any experiment that separates the wager from a geometry-first description (HYP-ENCODING-SCREEN). A standing iteration should sweep the live experimental literature for a candidate distinguishing test, refereed against the screen (write the chain wager → observable, mark each link). Seeded lead (held, unrefereed): Sharmila–Vermeulen–Datta, "Signatures of correlation of spacetime fluctuations in laser interferometers," Nat. Commun. 2025, arXiv:2505.22892 — a mechanism-agnostic, correlator-based fluctuation classification; expected to reinforce §7 (a correlator cannot separate fundamental from emergent metric) rather than threaten it.

The named residues — OP-44 R1 (distributional clock sources vs FMM/AMM linearization stability) and R2 (κ³ cubic-charge horizon non-splittability); OP-49 (c′) junction additivity; OP-48c X1/X2 framework exits. Each is decidable by a stated computation.

Empirical anchors (EXPERIMENT_WATCHLIST.md) — the 2027 DESI 5-yr $w(z)$ verdict (nearest dated event), GQuEST results, the CQ-gravity squeeze. None tests the wager; all test its gate/cores/target.

Update (post-iterations-8–12) — TERMINAL ANALYTICAL SATURATION; the agenda above is now a record, not a live list. Iterations 8–12 (plus a distinguishing-test hunt and a dedicated frontier scout) executed every named lever above and a dedicated terminal-saturation meta-audit. The verdict is unchanged for the eleventh consecutive iteration (iteration 12, 2026-06-19); the principal hedge has not moved in grade or condition since iteration 9. The carrier problem (≡ reverse-Weinberg–Witten ≡ the net-naturality theorem; HYPOTHESES.md HYP-FACTORIZATION-IS-GEOMETRY) is the single open analytical gate, and every reasoning-decidable approach to it is now closed or retired:

the commutant-to-generated gap (iter 10) does not close, and contains no carrier;

the bicentralizer re-grounding (iter 11) is a loose structural connection, not a reduction, to Connes' (genuinely open) bicentralizer problem; the physics-net relative-bicentralizer lever (iter 12) is non-load-bearing (trivial bicentralizer is the carrier-friendly condition);

the indefinite-metric / PT-symmetric / Krein carrier route (iter 12 scout; iter-11 A1 subquestion #3) is closed-negative — it collapses to encode-not-generate by a gauge-artifact / installed-not-derived / $\eta_0$ -equivalent trichotomy;

all three of iteration 11's open subquestions are discharged; a web-verified 2023–2026 external-math sweep found no result touching the residual.

Conclusion (referee-upheld A3 audit, iteration 11; re-confirmed iteration 12): every verdict-bearing residual is now decidable only by external input — a genuinely new operator-algebra / AQFT theorem (the net-naturality theorem / a reverse-WW witness / an external resolution of Connes' bicentralizer problem), or the 2027 DESI five-year $w(z)$ experiment (which bears on the target, not the wager). No purely-reasoning iteration can move the verdict. Active mode is therefore consolidation + lightweight watch, on exactly two clocks: (1) the carrier / net-naturality / bicentralizer / GMA-reconstruction mathematics (2025–2027), and (2) the 2027 DESI $w(z)$ verdict (nearest dated external event; the DR2 dynamical-dark-energy preference reduces to < 2σ under low-z SN-calibration systematics). New analytical iterations are not launched unless one of those clocks delivers a genuinely new input. The standing deliverable — the maximally-sharp reasoned account of why-not-yet — is the README-sanctioned obtained-outcome.

Update (2026-07-03, iteration 16) — clock (1) fired; the iteration ran; the hedge advanced; watch-mode resumes on a sharper state. Watch-sweep #1's clock-(1) input (Marrakchi arXiv:2606.23636) sanctioned the first post-saturation analytical iteration (G1–G4, referees binding; synthesis). Outcome: verdict unchanged (15th consecutive), but HYP-CKV-VACUITY advances R6 → R7 — the first hedge movement since iteration 9. The commutant-to-generated gap is now classified (not closed) by the referee-verified LEM-NET-NATURALITY-G (localized branch: dead, proof-grade; fully-natural non-localized branch: gauge gradings, Δ_geo = 0, proof-grade); the entire no-go now rests on {n₁ AND (E_O)} where (E_O) = vacuum ergodicity on massive double-cone algebras [OPEN]. The active watch state (supersedes sweep-#1's target, which iteration 16 showed ill-posed): clock (1) = (α) new definitions/theorems for expectation-free relative-bicentralizer-type invariants; (β) bicentralizer triviality; (γ) expectation-free relative T-invariant computations (adjacent conjecture T(M(O) ⊂ M(W)) = {0}); (δ) any resolution of (E_O) — the principal item; (ε) the DCNG definability lever (needs an operator-algebra/continuous-logic collaborator). Clock (2) unchanged: 2027 DESI five-year w(z) (Euclid cosmology co-timed mid-2027). New analytical iterations remain gated on a genuinely new clock input.

Update (2026-07-07, iteration 17) — the (E_O) assault ran; verdict unchanged 16th; hedge STAYS R7; watch-mode resumes. The principal watch item (δ) = (E_O) received a dedicated five-lens assault (E1–E5, three binding referees; synthesis), and watch-sweep #2 confirmed zero in-window strong findings. Outcome: (E_O) neither proved nor disproved — HYP-CKV-VACUITY stays at R7 (no R8, no retreat). New refereed content: (i) free-field (E_O) sharply reduced to a one-particle spectral question (purely continuous spectrum of ln δ_O / weak mixing ⟹ M(O)_ω = ℂ1; the naive "no-eigenvalue-0" reading refuted; the spectral fact numerical-only, leaning-true — Bostelmann–Cadamuro–Minz arXiv:2209.04681, Cadamuro arXiv:2312.08525, no closed form per Longo–Morsella arXiv:2012.00565); (ii) all three structure-theory routes for general (H) provably fail; (iii) the adversarial disproof fails on eight candidate mechanisms (no carrier; bare OPEN). The five-item clock-(1) watch state (α)–(ε) persists with (δ) (E_O) principal, now carrying the free-field spectral sub-target as the sharpest decidable lever (a proof of purely-continuous one-particle massive double-cone modular spectrum ⟹ (E_O) on the free subclass ⟹ R7 → R8 there). Clock (2) unchanged: 2027 DESI five-year w(z). New analytical iterations remain gated on a genuinely new clock input.

Update (2026-07-07, iteration 18) — the user-demanded generative assault + the first numerics; NO FLIP; verdict unchanged 17th. At the user's explicit instruction to try to devise the generative step, the strongest positive assault yet ran on two fronts (synthesis): (A) four construction angles — build the carrier on a ¬(E_O) mode (C1); relative/multi-state modular data (C2); AdS/CFT-as-generation (C3); derive the causal order n₁ (C4) — each adversarially refereed, both referees FLIP_REFUTED; every attempt either fails smuggle-free or is caught installing the signature/causal-order by hand. (B) the first numerical computation in the project — the free massive scalar double-cone modular spectrum (Peschel method, validated) obeys ε_min → π²/ln(L) with no isolated mode ⟹ a continuous spectrum with no eigenvalue at 0 ⟹ (E_O) holds for free d=2; no zero-mode, no carrier entry-ticket (scripts/eo-modular-numerics.py). Reasoning, construction, and computation now converge. Hedge stays R7; count FIVE; the (E_O) gate gains numerical support and a commutant-side reformulation. The verdict is not movable by reasoning or by the one numerically-decidable free-field probe; only external input (a continuum proof of (E_O), or the 2027 DESI w(z)) remains.

Update (2026-07-10, iteration 19) — proving the numerics; the E=0 half lands as a theorem; hedge stays R7; verdict unchanged 18th. The analytic follow-through (synthesis): LEM-K0 refereed CONFIRMED — for the factorial K_O, 1 ∉ σ_p(δ_O), so the E=0 / fixed-Weyl half of free-field (E_O) is [ESTABLISHED] (attribution: Figliolini–Guido 1989 already proved it via antilocality — primary source read; the iter-17 [unverified] tag retired; LEM-K0 is an independent second proof). Massless (3+1) case now theorem-grade a.c. The λ≠1 exclusion is the entire remaining free-field residual: [OPEN], provably undecidable at invariant level, bounded by conditional Mourre to finite-per-interval, observed ZERO by the pinning scan (no embedded eigenvalue at any energy/mass). The (δ) watch item sharpens to the named best-lead: extend FG's antilocality argument from μ = ±1 to all real μ (FG Thm 3.6 converts λ≠1 eigenvalues to real eigenvalues of their operator B) — a single-mechanism, externally-attackable question; if closed, free-field (E_O) closes entirely and R7 → R8 fires on the free subclass. Clock (2) unchanged: 2027 DESI five-year w(z).

Update (2026-07-11, iteration 20) — the antilocality extension attacked; no closure; the missing piece weakens to LEM-A1′; hedge HELD at R7; verdict unchanged 19th. Three refereed lenses + assembling referee (synthesis). The λ≠1 question is now exactly a bilateral-antilocality statement about ω = (m²−Δ)^{1/2} with coupling c = μ²/(μ²−1) > 1 (FG-1989 = the degenerate boundary case) — zero operator-algebra content remains. Two new unconditional rigidity theorems (eigenfunctions ∈ H¹₀(I); nowhere-locally-zero); exact O(m²) virial bulk (explains massless a.c.); a proved no-soft-theorem obstruction (embedded eigenvalues occur in the finite-interval-convolution family — Bertola–Katsevich–Tovbis, live-verified). Watch item (δ) now points at LEM-A1′: for every c > 1, ωF = 0 on I + ω(χ_E F + cχ_I F) = 0 on E + χ_I F ∈ H¹₀(I) ⟹ F ≡ 0 — a coupled Zaremba corner-indicial problem via Caffarelli–Silvestre extension, checkable cold by a fractional-UCP specialist (Fall–Felli/Rüland toolset); LEM-A1′ ⟹ (E_O) free-field ⟹ R7 → R8. Secondary: BKT-style Riemann–Hilbert steepest descent on the Casini–Huerta Painlevé-V resolvent. Numerics: third independent a.c. signature (fixed-energy edge-divergence probe), no bulk-normalizable candidate. Clock (2) unchanged.

Update (2026-07-11, iteration 21) — LEM-A1′ attempted; the c-collapse lands; the gate is now ONE spectral question (LEM-A1″); hedge HELD at R7; verdict unchanged 20th. The proof attempt (synthesis) produced three [ESTABLISHED] results: the Corner Indicial Theorem (cos²(πs) = c; complete simple roots n ± iτ₀; τ₀ = ε/2π exactly — the Bisognano–Wichmann relation from a corner computation; no local kill possible; lattice-verified twice); the strip geometrization (closed-form Q = m²R²(cosh ξ − cos η)⁻², exterior-dilation-analytic, e^{−2|ξ|} decay both ends; plus the Krein-symmetrizer no-go explaining why naive complex scaling resists); and the c-collapse — LEM-A1′ ⟺ σ_p(A) ∩ (1,∞) = ∅ for the single fixed self-adjoint operator A = S_I^{1/2}R_I S_I^{1/2} (the exact operator scripts/eo-modular-numerics.py diagonalizes; three clean numerical signatures already concern this very object). Watch item (δ) now points at LEM-A1″: prove the Mourre estimate for A with conjugate operator D = the Hislop–Longo Möbius-flow generator (the exact massless symmetry; the mass term has precisely the decay/analyticity profile Mourre theory wants; post-collapse the classical virial theorem applies — no Krein obstruction). Fallback: Feshbach n=0 channel + nonlocal subordinacy. LEM-A1″ ⟹ (E_O) free-field ⟹ R7 → R8. Clock (2) unchanged: 2027 DESI five-year w(z).

Update (2026-07-11, iteration 22) — the Mourre/Feshbach execution; a methods-no-go and a conditional theorem; the residue is LEM-A1‴; hedge HELD at R7; verdict unchanged 21st. Both LEM-A1″ routes executed (synthesis). Proved strategy-boundary: the Gaussian rank-one BIC counterexample [ESTABLISHED, cold-checked] — no decay/analyticity-class theorem can close the gate (nonlocal kernels inside every exponential class, dilation-entire, can host embedded eigenvalues); together with iteration 20's BKT no-soft-theorem, all remaining routes are forced through the structural origin of the specific operator. Conditional Mourre theorem: with the explicit conjugate D_g (i[A₀,D_g] = 1; A₀ := coth²(πD), definitional in 1+1D), under (H1) K = A − A₀ compact and (H2) K ∈ C^{1,1}(D_g): finite point spectrum per window, σ_sc = ∅, small-mR absence per window. Watch item (δ) now points at LEM-A1‴: crux (b′) on-shell nondegeneracy via V_eff's origin (Schur-complement/energy-monotonicity, or Froese–Herbst with D_g past the nonlocal rate ceiling); prerequisites cheap-first — (a′) the Birkhoff strong-regularity determinant, a single unperformed finite computation; (H1); (H2). Watch-sweep #3 (07-07 → 07-11): 0 strong. Clock (2) unchanged.

Update (2026-07-11, iteration 23) — (a′) established; the definitizability no-go; one retraction; the residual is LEM-A1‴-T → LEM-A1⁗; hedge HELD at R7; verdict unchanged 22nd. (synthesis) The (a′) computation is [ESTABLISHED] (distinct roots e^{±2πτ₀} ∀c>1, machine-verified twice) — but no off-the-shelf Riesz-basis theorem covers the pencil's repeated-root structure; the applicable chain is sine-type/Levin–Golovin + LEM-A1‴-T (a concrete, numerically-probeable Gram bound — the single upstream bottleneck feeding every live route). A fourth methods-no-go: global Krein definitizability fails ∀c>1; locally, conditional type-π₋ Pontryagin structure with the open channel at constant negative Krein density −(c−1) [ESTABLISHED]. One honest retraction (G1's z-slot monotonicity, struck in assembly). Watch item (δ) → LEM-A1‴-T first (numerical Gram probe, then the analytic bound), then LEM-A1⁗ (Pontryagin-channel on-shell transversality). Clock (2) unchanged.

Update (2026-07-11, iteration 24) — LEM-A1‴-T FALLS; the gate hangs on LEM-A1⁗ alone; hedge HELD at R7; verdict unchanged 23rd. The transfer lemma is proved for every fixed c > 1 (synthesis): the elementary three-step transfer (constant Im s_n ⟹ weighted-Fourier Riesz basis; unitary folding with n-independent q = e^{−2πτ₀}; constant intertwiner with det M ≠ 0), assembly stance PROOF_ASSEMBLES, explicit frame bounds bracketing every measured Gram point. Watch item (δ) → LEM-A1⁗, the single remaining blocker of (E_O)-free-field and R7 → R8. Iteration-25 first move: determine whether quadprime needs c-uniformity (NOT available) or per-fixed-c bounds (available); then push the transversality pairing through the folding coordinates. Secondary: the Bari supplement. Clock (2) unchanged.

Update (2026-07-12, iteration 25) — THE NORMAL FORM; the crux relocated to LEM-SEAM; hedge HELD at R7; verdict unchanged 24th. The scope question resolved (compact-window uniformity suffices — quantifier audit [ESTABLISHED]); P1-NF proved (synthesis): the gate is now a scalar imaginary-flux zero-mode exclusion. The Bari conditionality is discharged; the a = 2 ceiling is retracted as an artifact; the fifth methods-negative closes plain Konno–Kuroda. Watch item (δ) → LEM-SEAM ≡ {LEM-A1⁗-N}, with the S5 lemma (n-uniform weighted-Volterra bound) the designated first move of iteration 26, then the corner-trace lemma + the seam attack. Numerics: the transversality mechanism observed directly (support [INFERENCE, medium]). Clock (2) unchanged.

Update (2026-07-12, iteration 26) — S5 discharged; the equivalence established; LEM-TRACE established; the seam graded; hedge HELD at R7; verdict unchanged 25th. S5 landed in the repaired slacked form (synthesis) — the channel-family equivalence {LEM-A1⁗-N} ⟺ LEM-A1⁗ is now [ESTABLISHED], and LEM-TRACE discharged the resonant-log caveat. The seam chain is graded (B0/B1-free established; B2/B3 inference) but no exclusion theorem exists: the residual is exactly {LEM-SEAM-SC (sign-changing case), branch-(b) rate promotion, CH-26(iii) (the b → 0 channel closure via A₀-LAP + transversality), T1, SEAM-ESS + the B1 write-up}. Watch item (δ) → LEM-SEAM-SC + CH-26(iii). Iteration-27 first moves: SEAM-ESS + the B1 Hopf write-up, then branch-(b) rates, then T1, then CH-26(iii). Clock (2) unchanged.

Update (2026-07-12, iteration 27) — the seam groundwork; the crux compresses to the off-band bound (B); hedge HELD at R7; verdict unchanged 26th. CH-26(iii)'s two easy parts are [ESTABLISHED] (synthesis): the shell-channel A0-LAP and the on-band collapse O(√b) — the vanishing on-shell amplitude IS the collapse. The entire gate now compresses to (B), the uniform-in-b off-band bound sr(K^b_off) ≤ σ < 1 — "the whole ballgame," LEM-A1⁗'s sharpest reformulation, whose route is the ξ-locality of q (the exact hypothesis the Gaussian rank-one BIC violates). Branch-(b) core rates + dichotomy hardened to [INFERENCE, high]; the branch-(b) on-shell input ŵ = 0 was self-refuted at half-line and re-tagged (entangled with the open seam corner); T1-a hardened; SEAM-ESS (the dead lens) revealed heavier than framed and one problem with T1. Watch item (δ) → the off-band bound (B) + SEAM-ESS/T1 (together). Iteration-28 first moves: SEAM-ESS + T1 together, then (B) via ξ-locality + a uniform Grushin/Schur, then the branch-(b)(iii) whole-line repair. Clock (2) unchanged.

What to work on next, and why. Items are framed as questions to resolve or artifacts to produce, prioritized by leverage — how much a credible answer would move the central question of whether a universal theory is possible. Cross-references point to where the work lands.

Selection principle: prefer questions that are (a) load-bearing for unification, (b) at least partly decidable by existing or near-term evidence or by rigorous math, and (c) currently under-served in this wiki. De-prioritize questions whose answers would change nothing downstream.

Tier 0 — Maintenance & integrity (every iteration)

Lint pass per AGENTS.md: contradictions across pages, stale numbers, orphan pages, missing links, overclaiming, ID integrity.
Bibliography verification: replace every [unverified] in BIBLIOGRAPHY.md with a checked reference, or remove it.
Quantitative refresh: re-check measured values and tensions (e.g. $H_0$ , $S_8$ , muon $g\!-\!2$ after lattice/experiment updates) and re-tag in CONSTANTS_AND_SCALES.md.

Tier 1 — Highest leverage (drive the central question)

Sharpen the GR↔QFT interface. Make precise, in GAPS_AND_CONTRADICTIONS.md, exactly which incompatibilities are logical vs domain-of-validity. Treat gravity as an effective field theory and document what is actually known to fail (and at what scale) vs assumed to fail.
The black-hole information problem as a decisive test bed. Track the status of unitarity, the Page curve, island/replica-wormhole results, and what they do and do not establish. This is the cleanest arena where quantum theory and gravity must be reconciled.
The measurement problem, operationalized. Catalogue what each resolution (decoherence + branching, objective collapse, hidden variables, epistemic/QBist) costs and which make distinguishable predictions (e.g. collapse-model bounds from interferometry). Promote anything testable from [CONTESTED] toward decidability.
Cosmological-constant problem, stated without folklore. A careful, regularization-aware account (see CONSTANTS_AND_SCALES.md) of what is genuinely puzzling vs an artifact of naive cutoff estimates.

Tier 2 — Structural / mathematical

Assumption demotion program. For each fundamental/plausibly-fundamental entry in ASSUMPTIONS_LEDGER.md, ask: is there a derivation that would demote it? Highest-value targets: smooth-continuum spacetime, exact linearity of QM, the Born rule, locality, 3+1 dimensions.
Rigor gap in interacting QFT. Document the constructive-QFT frontier and the Yang–Mills mass-gap problem; clarify what "the Standard Model exists mathematically" would even require.
Information-theoretic reconstructions of QM. Evaluate how far axiomatic reconstructions (Hardy; entropic; CBH) actually explain the Hilbert-space formalism vs re-encode it.

Tier 3 — Candidate-framework development (gated by the verification protocol)

Emergent-spacetime program. Stress-test the entanglement→geometry claim (Ryu–Takayanagi, Jacobson's derivation, tensor networks): what would count as evidence outside AdS, and is there a falsifiable prediction? See HYPOTHESES.md, UNIFICATION_LANDSCAPE.md.
Distinguishing predictions audit. For every program in UNIFICATION_LANDSCAPE.md, record the single most plausible near-term distinguishing observation. Programs with none are flagged accordingly.

Tier 4 — Empirical anchors to monitor

Gravitational-wave catalogues (strong-field GR, possible deviations).
CMB / large-scale-structure surveys (dark sector, inflationary predictions, tensions).
Precision tests: equivalence-principle, Lorentz-invariance, and constancy-of-constants bounds (each tightens an entry in ASSUMPTIONS_LEDGER.md).
Collider / flavor / neutrino results bearing on beyond-Standard-Model structure.
Tabletop quantum-gravity proposals (gravitationally-induced entanglement) and collapse-model bounds.

Method for each iteration

Pick a small number of Tier-1/2 items.
Fan out reading; write structured findings; verify adversarially before promoting any claim (see AGENTS.md §4).
Update the affected pages in place; reconcile FINDINGS.md; log in CHANGELOG.md.
Re-ask the central question: did anything move the case for/against a universal theory? Record the delta in FINDINGS.md.