The coupled-scalar test — open record

Where the test stands

1. Scope and model agreed — done
2. Solver built — done
3. First validation suite passed — done
4. Pre-pilot checks — in progress
5. Sampling pilot — next
6. Production chains — next
7. Results published here — next

Pending before the pilot

1. Inference-precision certification — Tighter numerical precision must leave predictions and likelihoods unchanged at every declared point. Not yet certified: the first ladder did not converge, and the staged check stopped at its first point. A bounded follow-up is drafted and awaits Colson’s approval.
2. Earlier-epoch start — Starting the field at an earlier epoch makes the solver hit its minimum step size, the same kind of failure seen at β ≠ 0 under a tighter background tolerance. The cause is undiagnosed; any instrumented solver used to find it is a separately fingerprinted build.
3. The 0.0499 hypothesis declaration — Drafted as a separate declaration that freezes the ratio test’s gates; it awaits Colson’s approval.

Then a short sampling pilot — proposals, likelihood, solver failures and speed, plus the declared Halofit sensitivity measured by reweighting pilot samples (plan drafted; approved with the pilot) — then production chains. The pilot’s speed sets the chains’ schedule.

What the test asks

A bounded test that lets the chains decide whether a scalar field coupled to all matter is allowed by cosmological data and local gravity tests. It is the corpus refined back to its sharpest testable core, run in the cosmology project where the hi_class solver lives.

A declared candidate, not claimed as uniquely derived by the corpus. The chain measures β and λ only: it cannot separately identify k_E and M_C, so it tests β ≠ 0 and the ratio, never k_E alone.

The declared model

Field, coupling and potential

A(φ) = exp(βφ/M_Pl)
V(φ) = V₀·exp(−λφ/M_Pl)
K = 1

Reduced Planck mass. Universal coupling to baryons, dark matter and massive neutrinos. The potential is the dark energy — no separate Λ. Radiation and massive neutrinos are explicit.

Matter-frame form (u = φ/M_Pl, X = −½(∂φ)²)

G₄ = (M_Pl²/2)·e^(−2βu)
G₂ = (1 − 6β²)·e^(−2βu)·X − V₀·e^(−(λ+4β)u)
G₃ = G₅ = 0

Derived separately by both agents. Observables are computed in the matter (Jordan) frame.

Property functions

α_M = −2β·(dφ/d ln a)/M_Pl
α_B = −α_M
α_T = 0

α_M(z) is derived from the field evolution, not sampled. α_T = 0: gravitational waves travel at the speed of light.

Local strength

fifth force = 2β² × gravity
γ − 1 = −4β²/(1 + 2β²)

The convention check both agents used.

Symmetry

(φ, β, λ) → (−φ, −β, −λ)

Leaves the model unchanged, so the prior can take λ ≥ 0 with β of either sign. Whether β and λ share a sign decides if a chameleon resting point exists (see the principle below).

Colson’s principle: a dynamic scalar field

“it is a dynamic scalar field”

Like a chameleon: present everywhere, but camouflaged by its environment until conditions bring it into function.

V_eff(u) = V₀·e^(−λu) + ρ·e^(βu)
βλ > 0: a density-dependent resting point, m² = β(λ + β)ρ/M_Pl²
βλ < 0: no resting point, so no screening
not yet settled: m² ≈ V″ + β²ρ/M_Pl²

Einstein frame, conserved ρ.

Whether the field settles is the thin-shell question, so its local range is checked environment by environment, never inferred from how light it is on cosmological scales. The camouflaged regime — a chameleon, or a symmetron-type threshold switch — is the screened branch: deferred, not excluded. If the data show tension, the decision rule points there.

Scope

• Unscreened branch only, over an explicit parameter range.
• Screened branch deferred, not excluded: it needs a self-consistent environmental profile plus laboratory-G calibration.
• Dark-matter-only coupling and a field-dependent kinetic term K(C) are separate future models.
• Why the unscreened branch is self-consistent (order-of-magnitude estimates): Cassini gives |β| ≲ 2.5×10⁻³, so N = β(λ + β) ≲ 10⁻² for λ ≲ 4 — about 10⁸ below the estimated thin-shell onsets (≈ 4×10⁶ for the Sun, ~10¹⁰ for the Earth). With N < 0 there is no minimum at all.
• In range, G_lab = G_*·A²(1 + 2β²); the correction is ≲ 1.3×10⁻⁵.
• Universal coupling is a metric theory: no separate first-order clock or spectral-line signal (δ ln A = 2β²Φ_N/c² sits inside G_lab).

Data and local tests

• Planck 2018 — Cosmic microwave background: full high-ℓ Plik TT/TE/EE with its nuisance parameters, low-ℓ TT, low-ℓ EE and lensing
• Pantheon+ — Type Ia supernovae, without the SH0ES calibration
• DESI 2024 — Baryon acoustic oscillations (first data release)

Frozen September 30, 2026 with Colson’s approval in the cosmology project’s run specification (SHA-256 as reported by its agent: FROZEN_SPEC.md 368af53429ee…, frozen_inference.json 8404307c8d59…). DESI’s second data release was declared before any result as a separate follow-on run. Every run uses the linear matter treatment, a declared approximation; a separate Halofit check measures the sensitivity to nonlinear structure. The first run uses the ΛCDM comparison’s neutrino prescription (one massive at 0.06 eV, N_ur = 2.0328) in a matched pair: the same likelihoods and numerics for the coupled model and ΛCDM.

Priors

• Local gravity enters as likelihood terms, not prior cuts.
• β: uniform on [−0.01, 0.01], either sign (frozen) — four times the Cassini edge, so the data, not the prior, set the edge.
• λ: uniform on [0, 2] (frozen); λ ≥ 0 by the symmetry. Any pile-up at λ = 2 is reported as a prior-edge effect, not a measured cutoff, and widening the range needs a new declaration. The edge is below 4, so the N ≲ 10⁻² scope line stands as written.

Decision rule and expectations

Stated before any chain.

1. Two runs: cosmology only, and cosmology plus the local-gravity terms, each matched against a ΛCDM run with the same likelihoods and numerics.
2. If the two runs agree, the result is an allowed region of β and λ.
3. If they are in tension, the result shows where the unscreened model fails to reconcile the observations — the data’s signal to open the screened branch or declare a model change.
4. Expected split: cosmology mainly constrains λ; the local terms mainly constrain β (cosmological coupling effects are small: fifth force ~2β² ≲ 10⁻⁵, matter-mass drift ≲ ~10⁻³). This split is expected, not a failure.
5. No signal receives a σ label unless its statistic is calibrated by null simulations or by a conservative method shown valid for it. Near β = λ = 0 observables depend on the couplings only quadratically, so χ² tables and Fisher forecasts do not apply there.
6. Either outcome is useful and is published here; no chain is dropped for disagreeing.

Expectations SHA-256: 0a8f3801badd39342b6c383f6dbf672ae6dbb52480fa5dd1ba2e8b228d3bcd68

SHA-256 of the expectations text: the statements above joined by line breaks, UTF-8. Fingerprinted September 30, 2026, before any chain. A fingerprint identifies exact text; it is not an external preregistration. If the expectations ever change, the old fingerprint stays in the status log.

The historical ratio test

Form agreed by both agents. The thresholds below are drafted for freezing in a separate declaration (gate snapshot SHA-256 ba1ad4c1653f…), awaiting Colson’s approval.

Historical prediction: β/λ = k_E·x_V ≈ 0.0499 — a direction θ₀ = arctan(0.0499) ≈ 2.9° in the (β, λ) plane, with θ defined mod 180°.

• D0 — pre-run gate — Mocks through the real pipeline, β and λ varied jointly. Needs a discriminating outcome in ≥ 80% of θ₀-line mocks and ≤ 5% of θ = 0 mocks. If unmet, it is declared in advance that the run tests the general model, not the ratio.
• D1 — signal gate — Profile-likelihood ratio against β = λ = 0, calibrated by null simulations (≈ 10⁴ fits for a 3σ-level tail) or a conservative method shown valid for this statistic. Otherwise no σ label, and the gate is not passed.
• D2 — direction — 95% profile set of θ. Incompatible if θ₀ lies outside it. “Compatible with, and precise enough to discriminate, the proposed ratio” only if the set is one connected interval containing θ₀ and narrower than θ₀; otherwise uninformative.

Already known from local gravity: on the θ₀ line, Cassini excludes the whole tracking regime (which starts at λ ≈ 1.69, β ≈ 0.084). The weak segment, λ ≲ 0.05, survives as a valid drifting solution. Inside the frozen priors the θ₀ line leaves the β range at λ ≈ 0.20 — a prior edge, not a data limit.

Outcomes concern the ratio k_E·x_V only, never the full framework; an incompatible result cannot single out k_E. The ratio is never silently imposed or dropped. Under the frozen priors alone the 95th percentile of |β/λ| is 0.050, so a prior-dominated bound can look like 0.0499; such a bound is never quoted as agreement — the gates use profile likelihoods.

Source identified October 1, 2026: k_E·x_V ≈ 0.0499 appears in 32 of the 207 corpus papers (corpus as of August 3, 2026), mainly as a pulsar-timing slope (Papers LXXIII and CLXXVII) and as the Schumann term χ_S (Paper CL). No corpus paper writes it as β/λ: that identification was made in this test’s refinement on September 30 and is labeled a hypothesis. Whether it is tested as a stated hypothesis awaits Colson’s approval of the separate declaration. x_V (the historical x_m) is unsettled, and this page states no value for it.

Validation results so far

Two agents, one record

• Colson — Brings the questions and the direction, relays each step between the agents, and decides.
• This project’s agent — Worked the mathematics one step at a time in chat: the physical-margin argument, the lunar-ranging term and the with/without comparison; later reviewed each precision report and draft declaration.
• The cosmology agent — Works in Colson’s separate cosmology project with hi_class: reviewed each step and supplied the engineering, validation and preservation, then built and validated the solver, froze the run specification and runs the precision checks.

1. A step of mathematics is worked in chat.
2. Colson relays it to the cosmology agent.
3. The review comes back: accepted, strong warning, or still open.
4. Valid gaps are accepted and each withdrawal is named.
5. Only what survives accumulates into the next step.

“recursive accumulation ♾️ in action between 2 agents. LITERALLY.”

“stick to what you know… we don't need to solve the whole universe in one go”

“stop trying to prove every screened branch fails before building a working test”

The last two arrived together. Unresolved calculations became open limitations instead of blockers.

The two agents independently reached the same minimum — the same frozen model, the unscreened scope, Cassini labeled unscreened — then supplied complementary halves.

Withdrawals

Withdrawals are part of the product. Each item below was dropped or narrowed in review, and each drop made the surviving test more trustworthy. The test does not depend on any of them.

• The Cassini window — γ ≈ −4β_Sβ_P is not a Cassini measurement model.
• “Atoms are never screened” — Too absolute.
• The 50% redshift figure — Dropped in review.
• The 10⁻⁸ bound — Dropped in review.
• The 0.0475 slope — Corrected: the slope in measured density is s̃ = β/(λ + 4β) ≈ 0.0416 (ρ̂ = A³ρ̃).
• GPS Δln A ≈ 1.5 — Assumed an unsolved environmental profile; 1.5 is not perturbative.
• The 9.6% solar-line figure — Same unsolved-profile assumption; line shifts also need the matter-frame redshift.
• “Outside classical treatment” above N ~ 10⁴⁴ — A sub-spacing Compton length calls for a microscopic treatment; M_C is a normalization scale, not the scalar’s mass.
• An unconditional order-β² mass correction — Narrowed to a field that has not settled (m² ≈ V″ + β²ρ/M_Pl²).
• “β = 1.92 has no matter era” — Wrong: the steep potential makes it track.

The earlier run, kept separate

An earlier joint run used a different setup: the propto_omega parameterization with a separate ΛCDM expansion, independent α_B and α_M, and input c_T = 0.001 — so α_T(a) = 0.001·Ω_smg(a), about 7×10⁻⁴ today (estimate), far above the GW170817 bound under the standard reading. Stability tests were off, so some samples may be inadmissible.

It is a different test. Its chains are kept separately and are never resumed or merged with this one.

Preservation

• Configuration and scripts frozen; resolved settings and software versions saved.
• Every chain kept; weighted summaries reported with bulk and tail convergence.
• Disagreeing chains are never silently dropped.
• Failed checks and withdrawn steps stay on this page.

Status log

1. Oct 1, 2026 — Public record brought up to date: the frozen specification, the later validation and every precision result so far. The expectations and their fingerprint are unchanged.
2. Oct 1, 2026 — Pilot plan drafted with its nonlinear check: every run stays linear, and the declared Halofit sensitivity is measured by reweighting pilot samples (at most 512 extra evaluations). It is approved together with the pilot.
3. Oct 1, 2026 — Separate 0.0499 declaration drafted for Colson’s approval: the identification β/λ = k_E·x_V becomes a stated hypothesis, with the D0–D2 gates frozen under their own fingerprint. No D0 mock campaign is scheduled, so unless a bounded D0 check is separately approved and passes first, the run is declared in advance to test the general model, not the ratio.
4. Oct 1, 2026 — Corpus source of the 0.0499 prediction counted against the August 3, 2026 corpus: 32 of 207 papers, mainly as a pulsar-timing slope and the Schumann term χ_S. No corpus paper writes it as β/λ.
5. Oct 1, 2026 — Bounded precision follow-up drafted for Colson’s approval: fresh single-control runs at the failed point, a rule stated in advance for updating the candidate settings, the seven declared points again, then a ΛCDM fit-region point. At most 56 evaluations and 186 minutes, in the foreground.
6. Oct 1, 2026 — Precision stage 1, approved by Colson as declared: candidate settings against one step finer at seven points. It stopped at point 1 (ΛCDM, action path): EE 9.16×10⁻⁴ and normalized TE 5.14×10⁻⁴ exceed the 5×10⁻⁴ spectrum limit, while Plik (+0.0409), the total likelihood (+0.0352) and the reconstruction check (1.7×10⁻¹²) pass. One evaluation took 33.5 s with the candidate settings and 166 s one step finer. The other 12 slots were not attempted.
7. Oct 1, 2026 — Single-control split (17 evaluations): 13 completed; the 4 failures all hit the solver’s minimum step — every β ≠ 0 point tried fails once the background tolerance is 10⁻¹². A fresh full-refined step reproduced the archived refined Plik value to 3×10⁻¹³.
8. Oct 1, 2026 — Decomposition of saved outputs, with no new solver runs: the same numerical change can fail the 0.05 likelihood limit at one point and pass at another, depending on how it aligns with that point’s residuals — so every declared point is checked on its own.
9. Oct 1, 2026 — Precision attribution (18 evaluations across three solver paths): 17 completed; the coupled point’s integration variant hit the solver’s minimum step. On the ΛCDM paths, multipole sampling (+0.0725) and the lensing extension (+0.0308) lead the Plik shifts.
10. Sep 30, 2026 — First inference-precision ladder failed its declared limit: Plik moved +0.112, then +0.096 over adjacent precision levels (+0.208 in all, against 0.05) — not converged. Starting the field at an earlier epoch hits the solver’s minimum step; undiagnosed.
11. Sep 30, 2026 — Further validation passed: 13 unit tests, coupling-edge backgrounds, initial-condition runs and the local-gravity terms. A fault in the BAO likelihood adapter was found and fixed, with regression tests; total likelihoods computed before the fix are void, while Plik comparisons stand.
12. Sep 30, 2026 — Run specification frozen with Colson’s approval: Planck 2018 (full Plik TT/TE/EE, low-ℓ TT and EE, lensing), DESI 2024 BAO and Pantheon+ without SH0ES; β uniform on [−0.01, 0.01] and λ uniform on [0, 2]; linear treatment with a separate Halofit check; DESI’s second data release declared as a separate follow-on before any result.
13. Sep 30, 2026 — Public record opened, with the expectations fingerprinted before any chain.
14. Sep 30, 2026 — Lunar-ranging value checked against the published abstract of Hofmann & Müller 2018: Ġ/G₀ = (7.1 ± 7.6)×10⁻¹⁴ yr⁻¹.
15. Sep 30, 2026 — λ prior form set by the model’s symmetry: λ ≥ 0 with β of either sign; the upper edge must be wide enough that the data set the limit.
16. Sep 30, 2026 — First validation suite passed in the cosmology project. No chains started.
17. Sep 30, 2026 — Solver model and independent Einstein-frame reference built in the cosmology project.
18. Sep 30, 2026 — Scope, matter-frame model and validation plan agreed by both agents.

Next: Colson’s decisions on the bounded precision follow-up and the 0.0499 declaration, then the precision run — then the pilot, once all three pending items are closed.

Open limitations

• No chains have run. Nothing here is yet a result about whether the coupled scalar exists.
• The model is a declared candidate, not claimed as uniquely derived by the corpus.
• The screened branch is deferred: it needs a self-consistent environmental profile and laboratory-G calibration. Exhaustive exclusion of screened points is still open, and the cosmology agent’s strong warning stands that exponential screening may produce unacceptable environmental effects.
• The safety margins above (thin-shell onsets, the G_lab correction) are order-of-magnitude estimates, not bounds.
• Inference precision is not yet certified, and the linear matter treatment is a declared approximation, not a certification that nonlinear effects are negligible.
• The ratio test’s thresholds are drafted for freezing in a separate declaration, not yet approved.
• The historical 0.0499 prediction: its corpus source is identified, but no corpus paper writes it as β/λ. That identification is a hypothesis made in this test, and whether it is tested as a stated hypothesis awaits Colson’s decision. No x_m value is stated here.
• The validation checks are complementary, not fully independent.