Dark Energy & DESI
Reparametrization — ΛCDM where it fits (direct DESI DR2 fit 2026-08-12: γ = 0.487, Δχ² = −0.3, mean-density reading only; read at local density as a fluid, P(k) pins γ = ½ to 5e-6, |2γ−1| < 1e-5); covariant completions fail the fit — proposed TEST-26 is a consistency check at DESI DR3, not a discriminatorThe question: the DESI survey (2024–25) reported hints that dark energy may be weakening over cosmic time — the dominant live anomaly in cosmology. Does the coherence framework say anything about it?
The answer, in one sentence: the framework has a dark-energy sector — derived in December 2025, arithmetically corrected in August 2026 — and every consistent version of it misses the specific behaviour DESI prefers, but the family contains ΛCDM at γ = ½, so it can only be killed by data that kill ΛCDM too. Status: Reparametrization. It nests ΛCDM, so no data can refute it without refuting ΛCDM, and it has no win branch (below). It is not a discriminating position. Only the dark-energy-fluid reading survives: read as modified gravity, Geff = G/C(ρ̄) drifts as the cosmic density falls, and lunar laser ranging excludes that by about 2,000× (box below). Read at the local density (the framework's own postulate), existing galaxy clustering data already pin γ to ½ (box below), so there is nothing left for DR3 to decide. On the mean-density reading: at DESI DR3 it is killed if DR3 excludes Λ in the thawing or crossing direction (w₀ > −1 with wa < 0, whether or not w = −1 is crossed) and tied if the data sit at ΛCDM (γ = ½). It has no win branch at DR3 either (executed 2026-10-08, pre-registered f3e045e): if the data move into the freezing quadrant it allows, the 2002 constant-w Cardassian (wCDM, same parameter count) fits the framework's curve to Δχ² ≤ 0.42 at every DR2-allowed γ. Telling the two apart at 2σ would need a 9.3σ departure from Λ, i.e. γ ≈ 0.30, which DR2 already excludes at Δχ² = 137. A freezing detection would select “freezing dark energy”, not this family. This page shows the construction, what it predicts, how the covariant check sharpened the verdict, and exactly what evidence would change it.
(This URL returned 404 until 2026-08-12, while the sector lived in prose inside the Honest Assessment — two expert simulated-visitor passes independently hit the gap. The fragmentation was the friction; this page is the fix.)
The construction (Session 100, 2025-12-08)
Substitute Geff = G/C(ρ̄) into the Friedmann equation:
Everything the coherence function C fails to “pass through” is read as an effective dark-energy density. The calibration C₀ = Ωm is forced (it is the definition of Ωm, not a fit — which is also why the archive's “derived ΩΛ = 1−Ωm” is an identity, not a prediction), leaving γ as the single parameter. Note the honest caveat carried from the galaxy sector: ρcrit is calibrated per sector (A·V²flat galactically; C₀ = Ωm cosmologically), and the two calibrations are unanchored against each other by ~10¹⁰ — the “one equation” carries sector-dependent constants, stated here where the sector is introduced.
Two things the construction is, stated plainly (added 2026-09-14). First, inverting the definition gives C = ρm/(ρm + ρDE): cosmological “coherence” is the model's matter fraction Ωm(a), identically, at every epoch and every γ. That is why C₀ = Ωm is forced — and the identity holds for any dark-energy model written this way, so it carries no content of its own; the content is only the functional form C(ρm). Carrying that same Ωm over to the galaxy sector's boost cap 1/Ωm is an added identification, not a consequence of this one. Second, H² ∝ ρm/C(ρm) is a modified Friedmann equation with no new degree of freedom — the Cardassian class (Freese & Lewis 2002, Phys. Lett. B 540, 1; modified-polytropic form, Gondolo & Freese 2002–03). Exactly: at γ = ½ it is 1/C = 1 + 2ρcrit/ρm, i.e. ΛCDM (notation warning, added 2026-10-08 for cosmologists: on this page ρcrit is the framework's coherence knee, a free parameter, not the critical density 3H²/8πG. Calibrated so that C0 = Ωm, it equals ρΛ/2, so “ρDE = 2ρcrit” means ρDE = ρΛ, not ΩDE = 2); at high density it tends to the modified-polytropic Cardassian with q = 1 and n = 1−2γ at low density it tends to a constant ρDE = ρcrit/γ (a Λ-like future, which the Cardassian family does not have unless n = 0). At DR3 precision it is observationally indistinguishable from the original constant-w Cardassian (Δχ² ≤ 0.42, explorer 2026-10-08), which makes the prior-art claim stronger than “same class”. The γ > ½ branch is also emergent dark energy (density falling into the past, phantom throughout). At γ = 1 the form is exact: C = tanh(ln(1+x)) gives ρDE ∝ 1/(x+2), the tanh-of-log form of Li & Shafieloo's GEDE (2020) with Δ = (3/2) ln 10 and the transition at x = 2. The match is in the function, not the model: GEDE fixes its transition by ρDE = ρm (z ≈ 0.24 in this family), and the form matches at z ≈ 0.73. That literature's motive is the H₀ tension, and this page's fit (γ = 0.487 −0.021/+0.024) is about 20σ from γ = 1 at face value, so a phantom H₀ route is closed for this family (algebra rechecked 2026-11-09; the paper's equation was read by a simulated-visitor persona, not re-read here). Neither the archive nor this site cited that literature before a simulated-reader review pass (researcher persona) pointed it out on 2026-09-14; it matters because Cardassian models given fluctuations were already found to over-produce the late integrated Sachs–Wolfe effect everywhere except a small neighbourhood of ΛCDM (Koivisto, Kurki-Suonio & Ravndal 2005, PRD 71, 064027). Checks: maintainer/scripts/de_sector_is_cardassian.py.
Does ρm include dark matter? Yes, and the sector can't work without it. The Ωm = 0.315 in C₀ = Ωm is Planck's, and about 0.27 of it is cold dark matter. The DESI fit's CMB distance priors carry it too. Yet the archive also says “no dark matter particles; coherence explains both dark sectors” (Sessions 241 and 277). So we asked whether the construction could be the dark matter and the dark energy, with ρm = baryons only (C₀ = Ωb = 0.049). It can't. Recombination needs about 5.4 times as much dark matter as baryons, and today needs accelerating expansion. The best any γ manages while still accelerating today is 1.5 (0.8 if C is keyed on the total density). The γ values that do give 5.4 at recombination decelerate today (q₀ ≈ +0.33). The log-argument tanh changes too slowly to do both jobs. This result uses only the expansion history; no perturbations, CMB peaks or fluid reading are needed. The check was pre-registered before the script existed: maintainer/scripts/de_sector_without_cdm.py. So this is a dark-energy sector that needs cold dark matter put in by hand. That fits the SPINE reading of dark matter as real patterns that interact only gravitationally, and it doesn't fit the reading where a coherence boost replaces dark matter. Open question: which dark-matter story does the framework keep? If both, galaxies get a real halo and a boost on top of it, which double counts. (This is an internal inconsistency on standard numbers, not a new refutation; the count stays at 6.)
Which density is C read at? The answer decides whether γ is free. The DESI fit below uses the mean matter density ρ̄m(a) — a background-only reading. The framework's own postulate is that C is read at the local density. Read locally, the sector is a single fluid whose sound speed is cs² ≈ 0.22 (2γ−1) today (Gondolo & Freese's fluid Cardassian): negative below γ = ½ (clumps blow up), positive above it (clumps are smoothed out). That pressure term enters growth multiplied by (k/aH)², which is 10⁴–10⁵ on the scales where the matter power spectrum P(k) is measured. Executed (explorer 2026-09-14, rule pre-registered before computing): existing P(k) requires |2γ−1| ≲ 10⁻⁵, i.e. γ = ½ to within ~5×10⁻⁶ — about 5,000× narrower than the DESI fit's 1σ. The two sides of that bound are different in kind: below γ = ½, cs² < 0 is a gradient instability: in linear theory every scale smaller than about (aH)/√|cs²| grows exponentially, so on the adiabatic reading the γ < ½ side has no stable member at any distance from ½, and 10⁻⁵ only marks where the blow-up reaches the scales P(k) measures. Above ½ the pressure smooths clumps out (Jeans suppression), and 10⁻⁵ is an amplitude bound. The DESI mean-density fit, γ = 0.487, sits on the unstable side. (The galaxy fit's γ ≈ 0.49 is a different function, keyed on acceleration, so it is not on this axis.) The escape is the same on both sides: a non-adiabatic sound speed (cs² = 0, or an entropy-carrying second field), which the archive does not write down. The order of magnitude in one line: the gradient term enters growth as cs²(k/aH)², and (k/aH)² ≈ 9×10⁴ at k = 0.1 h/Mpc today, so a mode changes by order unity over the matter era once |2γ−1| ~ 10⁻⁵; the executed run gives a power ratio of 1.2 at k = 0.2 h/Mpc for |2γ−1| = 2×10⁻⁵ and 2.7×10²² at k = 0.1 for the DESI-fit 0.026. At the DESI best fit γ = 0.487 the matter power is already ~10× ΛCDM's at k = 0.01 h/Mpc. This is the known result for the class: fluid Cardassian models are inconsistent with galaxy P(k) (Amarzguioui, Elgarøy & Multamäki 2005, JCAP 01, 008), as is generalized Chaplygin gas away from ΛCDM (Sandvik, Tegmark, Zaldarriaga & Waga 2004, PRD 69, 123524). Two-sided, and why the (1+w) suppression does not apply: for a separate dark-energy fluid the pressure perturbation is sourced in proportion to (1+w), so a small cs² near w = −1 is nearly invisible. Here ρDE = f(ρm) moves with the matter, so matter and dark energy are one fluid and the pressure acts on the matter perturbation itself. The explorer's run shows both sides: at γ = 0.4999 the matter power at k = 0.1 h/Mpc is 6× ΛCDM's (blow-up), and at γ = 0.5005 it is 0.007× (Jeans suppression). That is the Sandvik et al. pair, one failure on each side. Which reading this bound belongs to: the fluid one. Under the modified-G reading of the same substitution there is no pressure term at all; its growth number (+21 % in fσ₈(0.51)) is at growth readings and is excluded by the ISW sign and lensing (explorer 2026-10-07). Labelled 2026-10-10. Which sound speed (added 2026-09-23): the pin uses the adiabatic cs² = dP/dρ that a barotropic ρDE = f(ρm) forces. It does not hold under the other two conventions an EFT-of-dark-energy reader will ask about. With cs² = 0 there is no pressure term and the pin disappears (the 2026-08-18 no-Jeans analysis is that case). With a rest-frame cs² = 1 the dark energy stops clustering below the horizon and the pin also disappears; for the Chaplygin class this is the known “silent quartessence” escape via entropy perturbations (Reis, Waga, Calvão & Jorás 2003, PRD 68, 061302). Both escapes need something the postulate does not supply: dropping the pressure, or a second degree of freedom that carries entropy. So the pin binds the local reading as stated, not every completion of it.
So the sector has three readings, and none keeps everything: local + fluid ⇒ γ is ½ (ΛCDM) to 10⁻⁵; local + modified gravity ⇒ no covariant theory exists, and Koivisto+2005's modified-gravity branch also over-produces ISW (imported, not executed here); mean density only ⇒ γ is free and the DESI fit stands, but coherence is no longer evaluated locally. Open question: which reading does the framework actually hold? Script: explorer/findings/scripts/de_horn_l_as_a_fluid_jeans_term.py. No registered prediction is refuted; the refutation count stays 6.
Arithmetic provenance: the archive's published w(z) table was wrong twice — a sign error in the continuity relation and a dropped −1 term (its formula returns w = −2 for ordinary matter, where the correct answer is 0). Corrected 2026-08-10; dated errata are in the research repo (Sessions 100/101). The corrected w(0) at γ = 2 is −1.26 at the site-standard Ωm = 0.315, not the “> 0” the archive reported — eight months of downstream reasoning had followed the uncorrected branch.
What the substituted model predicts: a sign lock
The corrected equation of state runs monotonically from w = −2γ in the far past to exactly w = −1 in the far future, for every γ. It approaches the cosmological-constant value from one side and can never cross it. In the (w₀, wₐ) language cosmologists use, that forces sign(w₀ + 1) = sign(wₐ). DESI DR2 (arXiv:2503.14738) prefers precisely the forbidden combination — w₀ > −1 with wₐ < 0 — in all four of its data combinations (DESI's own reported preference for w₀wₐCDM over ΛCDM: 3.1σ for DESI BAO + CMB, and 2.8σ, 3.8σ and 4.2σ adding Pantheon+, Union3 and DESY5 supernovae respectively; DES's own recalibration, DES-Dovekie, lowers the 4.2σ to 3.2σ, with w₀ = −0.803 ± 0.054 and wₐ = −0.72 ± 0.21, Popovic et al., arXiv:2511.07517, which calls this “only a weak preference”; the fit further down this page uses Dovekie). That quadrant is wider than “crossing”: in CPL the early-time value is w₀ + wₐ, so a crossing of w = −1 needs w₀ + wₐ < −1 (DESI's central values do cross). The rest of the quadrant is ordinary thawing dark energy (w starts near −1 and rises), which never crosses. In Caldwell & Linder's (2005) classification the lock allows only evolution toward −1: freezing from above for γ < ½ (w₀ > −1, wₐ > 0), or its phantom mirror from below for γ > ½ (w₀ < −1, wₐ < 0). It excludes thawing and crossing in either direction. That is a wider forbidden region than “forbids crossing”. It is not a discriminating kill, because the family contains Λ. At γ = ½ the modelis ΛCDM, so data that prefer thawing over freezing only push the fit to γ = ½. The family dies only when Λ itself is excluded in the thawing or crossing direction, and then ΛCDM dies with it. The framework's dark-energy sector is a superset of ΛCDM, so it cannot lose a test that ΛCDM passes. Its only branch that differs from ΛCDM is a win branch (freezing away from Λ at significance), and that branch is Cardassian-class prior art (Freese & Lewis 2002). (Restated 2026-09-23 from “a crossing of w = −1”, after a simulated-visitor researcher persona pointed out the thawing sub-quadrant. Corrected 2026-09-27: the 09-23 wording called this “a cleaner kill: it fails as soon as the data prefer thawing over freezing”. That was wrong for the reason above, and a later simulated-visitor researcher persona caught it. The 2026-08-12 direct fit had already said TEST-26 is ΛCDM-degenerate on every surviving branch. The TEST-26 registration gates on the project lead.) Scanning γ: zero values reach that quadrant; forcing w₀ to match compels a wrong-sign wₐ (offsets 3.4–5.4σ across the combinations, sign-and-scale statement only — no covariance is claimed). Those σ figures did not survive a direct fit — see “The direct fit” below: forcing w₀ to DESI's central value prices a point the likelihood never visits. The sign lock is real; its cost is ΛCDM's cost.
The covariant check (2026-08-11): the lock dies, the no-go hardens
The substitution above is not a solution of any covariant theory — its two assumptions (H² = 8πGρm/(3C) and ρm ∝ a⁻³) jointly violate the Bianchi identity of the framework's own field equation (Appendix D: Gμν = 8πG Tμν/C). One assumption has to give, and the two minimal repairs bracket the completion space:
Completion A — keep the field equation as written
The Bianchi identity forces ρ/C ∝ a⁻³, so the background is exactly Einstein–de Sitter for every γ and every calibration (verified numerically to 10⁻¹³). The dark-energy sector vanishes identically — Session 100's “dark energy emerges naturally” was its conservation assumption read back. Bonus pathology: the vacuum floor closes the FRW constraint at finite scale factor — under Session 100's own calibration the equation has no FRW solution beyond a ≈ 1.04, about 4% more expansion from today.
Completion B — promote C to a Brans-Dicke-type scalar
The Ċ-terms destroy the w = −1 attractor: every γ now ends in a finite-scale-factor singularity, the γ = 1/2 = ΛCDM degeneracy is broken (no member of the completed family is ΛCDM), and the literal sign lock dies — mixed-sign (w₀, wₐ) pairs exist. But 0 of 192 γ values reach the DESI quadrant, at every Brans-Dicke ω tested (0, 1, 5, 50): the completed family crosses the phantom divide in the anti-DESI direction. Forcing w₀ to DESI's value forces wₐ = +0.23…+0.60 — wrong sign in all four combinations (3.4–6.3σ, sign-and-scale only). Re-priced by the direct fit below: B does not merely miss the quadrant, it fails the fit (Δχ² ≥ +79 vs ΛCDM at every ω), and at the Cassini-allowed ω ≥ 4×10⁴ the no-go hardens (w₀ = −3.18).
Why every road ends the same way — one identity. For any model whose dark energy is algebraically slaved to the matter density (ρDE = ρm·F(x), x = ρ̄/ρcrit, any F), the continuity equation collapses to wDE(z) = dlnF/dlnx. The whole expansion history is one static curve read from high density to low. DESI's preferred crossing then requires ρDE(x) to have an interior maximum — and no completion of C = tanh(γ ln(1+x)) produces one: the family yields monotone ρDE (the sign lock), identically zero (completion A), or minimum-type (completion B's anti-DESI crossing). Never a maximum.
Which force law generates this sector?
The framework's galaxy sector runs on the algebraic law g = gbar/C (with a post-hoc field-equation patch ∇·[C∇Φ] = 4πGρ for momentum conservation); its only covariant equation is Appendix D's. The answer to “which one generates the cosmology” is: neither, exactly. Appendix D's equation on FRW gives Einstein–de Sitter (no dark energy, completion A above); the substitution Geff = G/C is a third, independent construction that solves no covariant theory and is only trustworthy as the far-past limit of completion B. The fork-amplitude diagnostic the site applies to the galaxy sector applies here with the same verdict: the sectors are connected by notation, not by a single derivation. (See Relation to MOND for the galaxy-sector fork.)
The direct fit (2026-08-12): the quadrant rhetoric dissolves, the covariant no-go hardens
Every DESI statement above was made in CPL (w₀, wₐ) space, a parameterization the family does not live in. The family was then fit directly to DESI DR2 BAO (13 points, per-tracer correlations) + Planck 2018 distance priors + the Dovekie SN recalibration (1,820 SNe, full covariance), with the pipeline first reproducing DESI's published w₀wₐCDM posture. Three results:
- The substituted family is not “3.4–6.3σ excluded” — it is ΛCDM. Best γ = 0.487 (−0.021/+0.024; on the mean-density background; read at local density, P(k) pins |2γ−1| ≲ 10⁻⁵), Δχ² = −0.3 vs ΛCDM with one extra parameter; its best member projects to (w₀, wₐ) = (−0.993, +0.023). (Not the same object as the +0.23…+0.60 above: that is completion B with w₀ forced to DESI's value; this is the free best fit of the non-covariant substituted family.) It cannot reach the crossing, and the data-level price of that is exactly ΛCDM's own: +11.0 behind w₀wₐCDM (~2.9σ for two parameters), no more. (Data combination: DESI DR2 BAO + compressed CMB + one SN sample, DES Dovekie. On BAO + compressed CMB alone the in-house gap is 8.3, against DESI's ~12.5 from the full CMB likelihood: compression recovers about two-thirds of it. Named 2026-10-18 after a simulated-visitor researcher persona could not reconcile 11.0 with DESI+CMB's 3.1σ.) The forced-w₀ σ figures were the fifth instance of an exclusion-flavoured number that did not survive execution.
- Both covariant completions fail the fit outright. Completion A is exact Einstein–de Sitter: χ² ≈ 9,900. Completion B is Δχ² = +79 to +187 worse than ΛCDM for every ω tested — and (2026-08-19) the published ω grid topped out 800× inside the region Cassini excludes for an unscreened scalar (ω ≥ 4×10⁴); at the allowed ω the no-go hardens to w₀ = −3.18. The sector survives current data only in its non-covariant form, and only by being ΛCDM.
- The first executed cross-sector γ test — and it has no power to fail. γcosmo = 0.487 vs γgalaxy = 0.489 “agree at 0.1σ” — but γ = ½ is exactly Λ and exactly MOND's simple μ, so the two sectors' standard models sit at the same point by construction. Agreement between the two fits is the agreement of Λ with the simple μ, inherited, with no power to fail. Both reductions are one line of algebra (at γ = ½, ρm/C = ρm + 2ρcrit; and any C = ρ/(ρ+K) gives ρm/C = ρm + K, exact Λ, so landing on Λ is a property of the simplest saturating rational function, which tanh-log becomes at γ = ½, not of tanh-log), and the scale is fitted separately in each sector, in different variables (mean density here, gobs in galaxies), so both datasets landing on the γ where tanh(γ ln(1+x)) becomes a known function carries no evidential weight. The 0.011 is SPARC's fitted offset from ½ (a slightly McGaugh-like RAR shape), consistent with zero at σγ = 0.11 (galaxy-limited, 2026-08-14). Telling that offset from zero would need σγ ≈ 0.004, and it would answer a different question (does SPARC prefer the simple μ exactly?), not a cross-sector one. (Until 2026-09-23 this item said “γ = 0.489 is exactly MOND's simple μ … 0.011 apart by construction”. That was wrong: the simple-μ point is γ = ½, as the box above says. A simulated-visitor researcher persona caught it; the archive ledger carried the same sentence and is corrected too.)
Status after this: Reparametrization (badge definitions; the research archive's ledger files it in its “reparametrizations” bucket) — ΛCDM where it lives, excluded where it would differ; no novel dark-energy prediction; refutation count unchanged. A researcher persona (2026-09-06) asked for a seventh refutation row on the strength of the σ figures above; the honest answer is the opposite — the sector is less refuted than this page said, because it is not distinct. Script and inputs: explorer/findings/scripts/fit_gamma_family_to_desi_dr2.py; finding gamma-family-direct-fit-desi-dr2-substituted-is-lcdm-covariant-excluded.md. (This section was missing from 2026-08-12 to 2026-09-06 while the archive ledger already carried the result; the page under-reported its own deflation.)
Honest bounds on the DESI comparison
- The comparison is quadrant-level in CPL space, not a fit. Projecting a monotone non-CPL w(z) onto (w₀, wₐ) has known biases, and whether DESI's crossing preference survives the parameterization is actively debated (Shlivko & Steinhardt 2024; Cortês & Liddle 2024; Wolf, García-García & Ferreira 2024–25). That literature is the framework's best available defense and is cited here in both directions: it could rescue the framework from a premature kill, and it could equally let a real crossing be dismissed as artifact. The honest adjudication — fitting the actual one-parameter w(z; γ) family to the data — was done on 2026-08-12 (section above); this bullet read “has not been done” until 2026-09-06. The CPL-projection debate is now moot for the substituted family: it sits at ΛCDM's corner regardless of parameterization.
- The sector has one perturbation theory, and it pins γ. The locality fork (research repo 2026-08-18: δDE/δm = 1 + wDE) forecast an fσ₈ shift of about −0.22% — ΛCDM-like, 0.10σ — but that is the pressure-free local reading. Its growth equation omitted the fluid's pressure (Jeans) term, which dominates by (k/aH)²; with it, P(k) forces |2γ−1| ≲ 10⁻⁵ (box above). The −0.22% / 0.10σ figure and “power, not data, is the blocker” hold only for the mean-density (background-only) reading. The −0.22% channel is also not the source of TEST-04a's fσ₈ ≈ 0.418, which came from Session 107's separate Glocal/Gglobal mechanism (see Tier 1). Beyond that channel, the CMB-anchored contours the σ figures borrow assume a perturbation model the framework does not have. The quadrant statement needs only the signs, which are DESI's headline result; the σ numbers are sign-and-scale contexts, not likelihood statements.
- Completion B's pinning is an ansatz. C is held to its algebraic trajectory C(ρ̄(a)); a true scalar obeys its own equation of motion, and an enforcing sector with non-negligible stress is unconstrained by anything in the archive. What is closed is the completion the archive's own structure implies, not every conceivable dynamical extension.
- DESI DR2 (w₀, wₐ), read from the paper's Table 5 (DESI DR2 Results II, arXiv:2503.14738 v3, w₀wₐCDM rows; read 2026-10-13): DESI+CMB w₀ = −0.42 ± 0.21, wₐ = −1.75 ± 0.58; +Pantheon+ −0.838 ± 0.055, −0.62+0.22−0.19; +Union3 −0.667 ± 0.088, −1.09+0.31−0.27; +DESY5 −0.752 ± 0.057, −0.86+0.23−0.20. Every combination has w₀ > −1 and wₐ < 0, the quadrant the sign lock forbids. The preference over ΛCDM is 3.1σ (DESI+CMB) and 2.8–4.2σ with supernovae (abstract).
- Nothing on this page is a new counted refutation. The refutation count stays at its audited value; this sector's status is Reparametrization (it nests ΛCDM and has no win branch), and the readings excluded on this page are excluded readings, not counted kills. Completion A's Einstein–de Sitter exclusion rests on the 1998 dark-energy discovery, not on new statistics.
One observable, three readings: growth fσ₈ at z = 0.51
The root cause first: the background is defined, the perturbations are not. The substitution G → G/C fixes the expansion history, but without an action there is no unique rule for how C enters the growth of structure, so there is no unique growth prediction. The three numbers below are three choices of that rule, not three measurements of one prediction.
A researcher visitor (2026-10-07) found two incompatible growth numbers on this site, −0.22% here and 0.418 (12% suppression) on TEST-04a, and asked the obvious question: if gravity is G/C with C ≤ 1, why would growth ever be suppressed? The answer is that the archive contains three different ways of putting C into the growth equation, and they disagree on the sign.
| Reading | How C enters the growth source | fσ₈(0.51) | Status |
|---|---|---|---|
| Session 107 ratio | Glocal/Gglobal = Ccosmic/Cgalactic < 1 | 0.418 (−12%) | The number TEST-04a carries. Rests on a Ccosmic ≠ Cgalactic distinction withdrawn in the archive 2026-08-11; the current framework does not contain it. |
| Dark-energy fluid (background-only) | δDE/δm = 1 + wDE; gravity unmodified | ≈ 0.473 (−0.22%) | ΛCDM-like. With the fluid's pressure term, P(k) pins γ = ½ to ~10−5 (box above). |
| Uniform G/C | The same G → G/C that builds H² = 8πGρm/(3C) also sources perturbations. Since C ≡ Ωm(a) on this background, the boost is 1/Ωm(a): 1.6 at z = 0.51, 3.2 today, for any γ | 0.575 (+21%); σ₈(0) = 0.916 | Computed 2026-10-07 (estimate; ΛCDM background, CMB-era amplitude held fixed). Enhances growth. Sits +1.0σ from DESI DR1's LRG1 bin (0.516 +0.057/−0.066; corrected 2026-10-10, it read +0.4σ against a value derived from the QSO row), but that bin was already published, so this is a retrodiction. Its σ₈ is 2.2σ above DESI's 0.841 ± 0.034 (a GR-conditioned number). No covariant theory exists for it, and Cardassian modified-gravity branches over-produce the ISW effect (Koivisto et al. 2005). Excluded by existing data (explorer 2026-10-07): ISW sign flip and Σ1 ≈ 1.6 without slip; S8 +4.7σ with lensing unmodified (see below). Not a prediction. |
So the sign is a modelling choice, not a prediction. The framework's own G/C, applied uniformly, enhances growth; the suppression came from a ratio of two C's that the framework no longer has. Any DESI DR2/DR3 growth registration has to say which row it tests before the data arrive. As adopted, TEST-04a tests the first row. The uniform reading has since been checked against existing data, and it is excluded (explorer 2026-10-07, pre-registered at site be3ecba). How C enters light deflection is not specified anywhere in the archive, so both options were run. If lensing feels the same G/C (no slip, the plain reading), the lensing potential grows 2.7× from z = 3 to today. The ISW–galaxy cross-correlation then flips sign (proxy A ≈ −8.5 against the observed ≈ +1.0 ± 0.2), which is the same categorical test that ruled out the cubic Galileon. Σ1 ≈ 1.6 sits about 20σ from DESI DR1's 1.021 ± 0.029. If lensing is left unmodified, which needs a slip mechanism the framework does not supply, S8 = 0.890 is +4.7σ from KiDS-Legacy, and the lensing-free DESI+CMB μ0 sits about 3.5σ off. The ISW proxy is a Limber kernel ratio, not a Boltzmann-code Cℓ; the sign is robust, the size indicative. With row 1 withdrawn, row 3 excluded and row 2 equal to ΛCDM to 0.2%, no live growth reading differs from ΛCDM at DESI DR2 precision. The explorer recommends retiring TEST-04a as a discriminating test; that decision gates on the project lead. Finding: explorer/findings/uniform-g-over-c-growth-is-excluded-isw-sign-flips-...md. The researcher visitor who expected the +21% reading to be in trouble with ISW and S8 (2026-10-08) was right. Script: maintainer/scripts/growth_under_uniform_G_over_C.py (+ _output.txt; two of its three written predictions failed: the enhancement is late-time-limited, so smaller than expected).
The modified-G reading also fails locally, with no growth model needed (added 2026-11-05). If Geff = G/C(ρ̄m) is the G that binds the Earth and the Moon, it drifts as the mean density falls: Ġ/G = 3H0 · d ln C/d ln ρ. With C0 = Ωm, at γ = ½ this is exactly 3(1 − Ωm)H0 = 1.4×10−10 per year. Lunar laser ranging measures (7.1 ± 7.6)×10−14 per year (Hofmann & Müller 2018), so the reading is out by about 2,000×, and by at least 527× against LLR's 2σ upper edge for every γ from 0.3 to 3. The same Geff is what the uniform growth row applies, so that row is now excluded twice, once by ISW and once by the Moon. The dark-energy-fluid reading, with gravity unmodified, has Ġ = 0 and is untouched; it is ordinary Cardassian-class dark energy. The local-density version of G/C is the separate LLR exclusion on For Researchers (item 6). A researcher simulated-visitor persona raised this on 2026-11-05; script maintainer/scripts/de_modified_g_reading_vs_llr.py (predictions in its header before it ran; 3/3 held; the identity d ln C/d ln ρ = 1 − Ωm at γ = ½ reproduces to 10−10). Not a counted refutation: no archive document asserted that the cosmic G/C governs local dynamics.
The test: TEST-26 (proposed; State: Self-Eliminating-or-Tie)
“Self-Eliminating-or-Tie” is an operational state, not a badge: no outcome selects the framework. Here the kill is shared with ΛCDM and the win with constant-w Cardassian.
Read this first (2026-09-27): TEST-26 cannot single out the framework. Its kill fires only when DR3 excludes Λ in the thawing or crossing direction, and that outcome refutes ΛCDM equally. On the local-fluid reading, existing P(k) already pins |2γ−1| ≲ 10−5 (and every γ < ½ is gradient-unstable), so the sector is Λ there. On the mean-density reading γ is free, and the only non-Λ outcome is freezing, which is a win branch for a known model class. The win side is shared too (explorer 2026-10-08, pre-registered f3e045e): on DR3-like Asimov data the 2002 constant-w Cardassian fits any DR2-allowed point on the framework's curve to Δχ² ≤ 0.42, in all 11 precision arms. Resolving the curve's shape at 2σ needs a ≥ 9.3σ departure from Λ, which needs γ ≈ 0.30, and DR2 excludes that at Δχ² = 137. No TEST-26 outcome singles out the framework: it is a test of ΛCDM with the framework attached. It is kept on record so that a tie cannot later be read as a success. It is not a decisive test of Synchronism.
A prospective registration against DESI DR3 (~2027–28) is drafted on Top Decisive Tests: the kill fires if DR3 excludes Λ in the thawing or crossing direction (w₀ > −1 with wa < 0, whether or not w = −1 is crossed), the region the sign lock forbids, with a pre-committed projection-robustness check; the “confirming” branch is a tie (the substituted γ = 1/2 branch is ΛCDM — though that identity is itself substitution-conditional, since completion B has no ΛCDM member). Recorded now so a later tie cannot be read as a success. Adoption gates on the operator.
Provenance chain: sector derived 2025-12-08 (Session 100) · this site falsely declared “no dark-energy sector exists” 2026-07-22–08-10 (negative existence claim verified against compilation docs only — the standing rule adopted from that failure is that compilation documents can prove presence, never absence) · w(z) arithmetic corrected and sign lock derived 2026-08-10 · covariant completions derived, lock killed, no-go hardened to model class 2026-08-11 · independently re-verified in the research repo 2026-08-12. Full audit trail: Honest Assessment.
Revision notes (history; not the current claim). Dated corrections moved here from the running text on 2026-11-08, verbatim, in page order.
- corrected 2026-09-27 from “the framework's one live falsifiable position”; until 2026-11-05 this page also called it “a live position” here and “a currently-disfavoured falsifiable position” further down, three statuses for one sector
- Corrected 2026-10-09; this sentence previously read “wins only if the data move into the quadrant it allows… not impossible by construction”, 2026-09-14. That sentence was right that a tie-on-fit can win on selection in principle, and wrong that the shape could be resolved: it is a level difference, not a shape difference, at DR3 precision.
- −1.24 at Ωm = 0.30, the value this sentence quoted until 2026-10-21 without naming its Ωm
- Corrected 2026-09-24: this box used to say “one algebraic fact with two faces” and “both sectors independently pin the framework” (retired wording). That contradicted the notation-not-derivation paragraph further down this page.
- Until 2026-10-13 this item said the centrals were carried from the abstract and “should be re-verified”; a simulated-visitor researcher persona noted it was one lookup.
- worded “requires the crossing” until 2026-10-26; a thawing-only result would have killed the family without firing that text