Honest Assessment

This page audits the claims listed in Key Claims. It documents what works, what failed, what we got wrong, and what remains untested. Updated as new results come in.

Validation badge definitions (canonical reference)

How to read a badge (contract, 2026-07-08): every badge has two parts. The color and leading word(s) are the formal status, drawn only from the two families below (plus deprecated back-compat tags). Any text after the dash is a free-text finding descriptor specific to that result — e.g. “Wrong Category,” “Wrong Direction,” “Dimensional Identity,” “Naturalness Gap,” “Refuted by Execution,” “Ontological Reframe.” Descriptors are not additional badge types; the epistemic verdict is always the formal status. Three negative-outcome words, one relationship (added 2026-07-18): a Failed badge is the formal status of any data-contradicted prediction; a refutation (the footer count) is the narrower subset of Failed results executed on external data against a registered criterion; “Refuted by Execution” is the descriptor marking that a specific run — not an argument — did the killing. Every refutation carries a Failed badge; not every Failed badge counts as a refutation. Not every defined tag has a current instance — tags exist to cover the claim lifecycle, not to guarantee one of each. (The “Model Explainer” tag on the Tools page is a content grouping, not a validation badge — it means “shows how the equation works,” with no verdict content.)

MRH-relationship tags (MRH = Markov Relevancy Horizon — the framework's term for the bounded context something is currently relevant within) describe how a claim sits in the current research inventory. Preferred for in-flight work. Rationale: at the current stewardship stage, nothing is honestly characterizable as “established” — the framework is being stewarded along many parallel paths, and verdict-shaped tags promote substantive content out of that parallel space prematurely.

Active-MRHCurrently in active research focus; being extended or revisedParallel-PathsIn the framework's parallel hypothesis space; not currently in active focus but not abandonedSidelinedWas in active focus, currently not pursued; reasons documented; reactivation condition specifiedSupersededReplaced by a later formulation; pointer to successorAudited-NegativeClosed audit finding on a historical track; durable record; does not move

Descriptive tags describe an empirical relationship rather than a verdict on truth-status. These remain useful at the current stewardship stage:

UntestedPrediction exists, no data yetSpeculativeConceptual proposal without quantitative testReparametrizationEquivalent to existing physics in different notationFailedPrediction contradicted by data (with specific error)

Deprecated (kept for back-compat with existing usages; do not appear in new content):

ValidatedVerdict-shaped; conflicts with stewardship discipline. Use Active-MRH or Reparametrization as appropriate.Strongly SupportedSame; existing usages being migrated incrementally by the daily maintainer track.

Operational states (not badges; describe prediction lifecycle):

Kill Criterion TriggeredA pre-registered falsification threshold was crossed. Carries Failed badge. Stronger than “Failed” alone because failure was quantified in advance.MOND-sharedRETIRED (class audited 2026-07-14/15). Asserted “a positive result confirms Synchronism AND MOND equally.” All three carriers dissolved when executed or adjudicated: TEST-09 (BTFR — kill fired, 3.3σ), TEST-10 (dwarf DM fractions — 69% of SPARC exceeds the framework's 68.5% ceiling), TEST-05 (environment levers differ by ~50–5,000×). A tie badge was the site's only unfalsifiable label — it carried no execution burden and sounded modest. New rule: a claimed tie carries the same execution burden as a claimed kill (both predictions computed, agreement shown within the data's discriminating power).WithdrawnFramework disowned the test — not from data refutation, but from internal contradiction, unmotivated amplitude, or supersession. Carries no badge (never adjudicated). TEST-04 (BAO).Self-Eliminating-or-TieNo measurement outcome selects Synchronism over the standard alternatives — either the signal is below systematics reach, or both outcomes (null and confirmed anomaly) are covered by Newton or MOND respectively. TEST-02 (wide binaries).Sign CorrectionAnnotation marking that the prediction direction on this page was corrected after initial publication. Not a verdict badge — a correction provenance marker. TEST-02 (2026-06-06).Null-ClassThe result achieves the same or better fit using a structurally simpler null model (e.g., polynomial in atomic number Z). The match is evidence of monotonicity in the target variable, not framework-specific physics. Chemistry correlation explorer.Artifact LessonAdded to this legend 2026-08-05 (it was in use on three tool cards and defined in no legend). Marks an interactive tool, not a prediction: the tool animates a relation the audit found wrong, kept deliberately so a reader can watch it fail rather than read that it failed. Applies to the phase-boundary visualizer (γ = 2/√N_corr, audited-negative), and to tools whose displayed law is superseded. Companion label “Model Explainer” means the tool shows how the equation works and is not itself a verdict on whether the equation is correct. Both are tool-card labels; neither is a validation badge.89% Boundary-ConsistentFraction of natural phenomena in the gamma-boundary catalog whose gamma parameter falls within the regime boundaries defined by the visualizer. Descriptive only — not a prediction or a test. Carries Template Bias Caveat.Template Bias CaveatThe 89% consistency figure is derived from a catalog that was populated using the framework's regime boundaries as a guide — boundary-consistent framing is baked into the collection method. The fraction should not be read as independent confirmation.

Status lifecycle verbs (added 2026-07-23 — this vocabulary was used with precision across test cards but documented nowhere; four independent reviews flagged the gap). These are the capitalized verbs that appear in headings and status notes. They are distinct on purpose:

EXECUTEDThe registered computation was actually run on real data, with scripts cited — as opposed to asserted, estimated, or argued. Always date-stamped. The strongest provenance word on the site.ADJUDICATEDA verdict was rendered by structural argument or by analysis of already-published results, without a new run (e.g. TEST-05's lever-magnitude comparison). Weaker provenance than EXECUTED; the distinction is preserved so readers can tell which verdicts rest on runs.CLOSEDApplies to a research question, not a prediction: the question is resolved (sometimes as a null) and no further work is planned. E.g. “EFE gap — CLOSED,” “form selection closed as a null.”WITHDRAWNApplies to a test: retracted by the framework before execution because of internal contradiction, underivable amplitude, or supersession. Never adjudicated, carries no verdict badge. E.g. TEST-04 (BAO).RETIREDApplies to vocabulary or framing, not to data verdicts: a label or badge class removed from service after audit showed it defective. E.g. the “MOND-shared” tie-badge class (retired 2026-07-15 when all three carriers dissolved on execution). “MOND-shared / RETIRED” therefore means: this label used to sit here, and the label itself — not the test — was withdrawn from the site's vocabulary.RECLASSIFIEDMoved between categories (e.g. Tier 1 → Tier 2, prediction → exploratory hypothesis) after audit showed the original category's entry requirements were never met. The row is kept in place, demoted visibly, so the demotion is not silent.NEVER RUN AS REGISTEREDA different dataset, sample, or statistic was substituted and adjudicated in the registered test's place — the substitute has its own verdict, but the test as originally pre-registered remains unrun and still runnable. Distinct from WITHDRAWN (which is retracted, not substituted). E.g. TEST-03 (the ALFALFA-SDSS run was executed as TEST-03s instead).UNDERPOWERED AS REGISTEREDThe registered kill threshold sits inside the measurement's own known systematics or pipeline-dependence range, so neither outcome (threshold crossed or not) can adjudicate anything until the registration is tightened. Marked before the data arrives where possible, not as a post-hoc excuse. E.g. TEST-06 (BTFR σ_int threshold vs. ~3× velocity-definition-dependent scatter), TEST-04a (fσ₈ criterion met at ~1.5σ against a >3σ demand).Ceiling ExceededA structural failure mode specific to this framework: the data demands more than the framework's built-in maximum (the bounded boost 1/Ω_m = 3.17), so no parameter choice can rescue the fit. Needs no threshold registration — the ceiling is algebraic.[Brackets]Text in brackets inside a quoted prediction (e.g. “[Withdrawn]”) marks that the surrounding wording is preserved verbatim for the record but is no longer asserted.

Transitions: statuses move in one direction. Untested → Executed/Adjudicated → Failed (or survives); Failed never softens back. A retirement or reclassification is itself a dated, logged event with the audit that forced it linked from the card. Adjudication authority: the daily explorer track runs executions; the maintainer track propagates verdicts to pages; contested calls are gated on the human operator and marked as such. If a status note seems to contradict its heading, the most recent dated entry wins — cards accumulate their history deliberately rather than rewriting it.

Full discipline: Research Philosophy. Migration plan: forum post 2026-05-28.

Why read an audit of a theory that didn't pan out? Because the honest map of what failed — and why — is the actual product. Knowing what a density-based coherence function structurally cannot do is genuinely useful: it eliminates a class of modified-gravity ideas in one stroke, explains why galaxy fits can't extend to clusters, and documents a rare case of a self-audited theory reaching its own null verdict. The methodology that produced this audit is the contribution; the physics just provided the test case.

CORRECTED 2026-08-09 — the sentence that stood here from 2026-07-23 was false. It read: “there is no field equation anywhere in this framework's galaxy sector — no action, no Lagrangian, no covariant formulation, no dynamics.” The archive has had one since 2025-12-01: manuscripts/Appendix_D_Synchronism_in_General_Relativistic_Form.md§D.2 states a modified Poisson equation, §D.3 effective Einstein equations, §D.5 a worldline action. The site asserted their non-existence for seven months without grepping for them. The accurate statement is narrower and still damaging: the field equation is postulated, not derived — and the one the archive actually states is eliminated. Appendix D writes ∇²Φ = 4πGρ/C (call it L1) and g = gbar/C (L3) as if they were one law. They are not: L3 is the spherical solution of ∇·[C∇Φ] = 4πGρ (L2), so L2 ≡ L3, while L1 is a different theory — 0.57–1.42 dex away in g on the site's own five galaxies, and γ-invariant, so no choice of the framework's one free parameter closes the gap. L1 dies with no data at all: as ρ→0, C→γρ/ρcrit, so the source ρ/C→ρcrit/γ, a uniform density floor filling all space ⇒ every isolated galaxy gets 10¹⁷–10¹⁸ M inside 100 kpc and a curve rising forever, for every γ and every ρcrit. Every test on this page uses L2 ≡ L3. None of the refutations below change — they are driven by the shape of C and the B ≤ 3.17 ceiling, not by the presence or absence of a Lagrangian. (Full statement ↓)

What failed, in one paragraph — no jargon (added 2026-07-24 for readers on the beginner path): This project proposed one equation meant to describe how things hold together at every scale, from atoms to galaxies. When its galaxy predictions were tested against real telescope measurements, it failed every decisive test. It predicted a specific relationship between a galaxy's mass and its rotation speed — the measured relationship landed far enough away to cross the line the project itself had drawn in advance as “this would kill the theory.” It puts a hard cap on how much “missing gravity” a galaxy can display — and about two-thirds of real galaxies display more than that cap allows. And an environmental effect it predicted turned out, when measured, not to exist at all. Where the equation does fit galaxies, it fits only by imitating MOND — a 40-year-old rival theory that tweaks gravity instead of adding dark matter — and never fits better than it. How fatal is this? As a theory of galaxies: fatal, by its own scoreboard — zero confirmed predictions, six executed refutations resting on three to four independent roots. (This sentence read “four executed refutations” until 2026-08-09 — the pre-recount number, left stale on the page while the header of the same page said six. One count, one place: six executed, 3–4 roots, classified by kind in the table below.) Why does the site still exist? Because a few of the framework's core ideas have never been testable with existing instruments (untested is not the same as failed), and because this record — a theory testing itself in public and publishing every failure — is itself the point. The paragraph below says the same thing with the actual numbers.

The same, with the numbers: The sharpest failure is now the galaxy mass–speed relation (the BTFR, TEST-09, run 2026-07-14): the framework's built-in ceiling on how much it can boost gravity forces a prediction that genuinely differs from the rival theory MOND — and the real data (123 SPARC galaxies) fired the pre-stated kill criterion at 3.3σ. The same ceiling caps how dark-matter-dominated a galaxy can appear at 68.5% — a convention-dependent figure (see the Verdict section below); the number that survives regardless of convention is the tail: SPARC's maximum observed DM fraction (0.927) requires a boost of at least 13.7, which no candidate cosmic ratio supplies (TEST-10, 2026-07-15). The framework's registered environment effect was also run (2026-07-14): no trace (r² = 0.0001 against a >20% claim). The earlier cosmology test (DESI growth suppression) isdisfavored but not counted as a refutation — the test as registered lacked the power to discriminate (corrected 2026-07-14). The galaxy transition-shape test — run on 2,807 SPARC data points (175 galaxies) in May 2026 — collapsed the framework onto MOND (ΔBIC=+184 against the γ=2 version; free-γ = MOND). The predictions we thought were novel turned out to already exist in physics under different names. Zero predictions have been independently confirmed. Zero parameters have an independent first-principles derivation — the last surviving candidate (A-from-Jeans) was closed as audited-negative on 2026-06-07: the Session 66 script produces A ≈ 4.6×10⁻⁵ (600× off the stated 0.029) under the framework's own ρcrit ∝ V² scaling. Scoreboard: 0 confirmed, 0 prospective predictions tested, 6 refutations executed on external data, 5 reparametrizations, 0 independently-derived parameters (recounted 2026-07-30; the BTFR slope moved from the reparametrization list to an executed refutation on 2026-07-14, and the Cassini/SPARC squeeze and Bell/CHSH substrate test were added to the count on 2026-07-30 — both were already executed and badged Failed/Refuted elsewhere on the site).

What a non-physicist should take away:
  • The one equation fits galaxy rotation — but only as well as MOND, an existing 40-year-old idea, and never better.
  • Its one genuinely distinguishing galaxy prediction (the mass–speed relation, TEST-09) was run against real data in July 2026 and failed its own pre-stated kill criterion at 3.3σ; its cosmology prediction (slower growth of cosmic structure) is disfavored but that test turned out to lack the power to decide.
  • None of its numbers come from first principles — every parameter is fitted to data or simply asserted.
  • No currently proposed experiment can tell it apart from existing physics.
  • The real product is this audit itself: every failure documented, with the numbers, by the same project that made the claims.

The Verdict (Updated July 2026)

After 3,308 sessions + 13 adversarial stress tests: 0 confirmed predictions, 0 prospective predictions tested, 6 refutations executed on external data (astronomical, ephemeris, and laboratory). The sharpest events, in order of decisiveness:

Read “6” as executed runs, not independent roots (qualified 2026-08-08). Two of the six (TEST-09, TEST-10) are corollaries of the same bounded-boost ceiling B ≤ 1/Ωm, which Parameter Derivations badges Asserted, Not Derived — so strictly they refute the assertion, and the honest figure for independent empirical roots is 3–4, not 6 (worked through on Tier 1). Three expert visitor passes have now flagged the footer's bare “6” against that body text; the footer now carries the qualifier. The two failures that depend on no convention and no data are the mass-cancellation no-go and the vacuum divergence — see Key Claims.

(0) The boost-ceiling pair (TEST-09/TEST-10 — executed 2026-07-14/15): The bounded boost C(a) caps gravitational amplification at 1/Ωm = 3.17 — the framework's only structural difference from MOND. That ceiling forces a BTFR slope prediction (n = 3.35) that genuinely differs from MOND's (3.81); observed n = 3.75 ± 0.10 fired the registered kill criterion at 3.3σ, and no parameter choice rescues it. Read as a dark-matter-fraction cap, the same ceiling limits apparent fDM to 68.5% under the 1−Ωm convention — the headline “69% of SPARC exceeds it” figure is convention-dependent: under the alternative baryon-budget convention (Ωmb ≈ 6.40, giving fDM,max ≈ 0.844) the reported median (0.755) actually passes, and the 69% figure does not hold. What survives under either convention is the tail: SPARC's maximum observed DM fraction is 0.927, which requires a boost of at least 13.7 — no candidate cosmic ratio supplies that, a class exclusion regardless of which convention sets the ceiling. The framework's registered environment effect (>20% of RAR scatter) was also run as registered: r² = 0.0001 — refuted by execution. These, plus the RAR shape test and the Cassini/SPARC squeeze and Bell/CHSH substrate test below, are the six executed refutations in the footer count.

(1) DESI fσ₈ (TEST-04a — corrected 2026-07-14): The framework predicted suppressed growth: σ₈ ≈ 0.76 (fσ₈(z=0.51) ≈ 0.418, 12% below ΛCDM's 0.474).What DESI DR1 full-shape actually shows (arXiv:2411.12021): combined σ₈ = 0.841 ± 0.034 (Table 10) → 2.4σ tension — the predicted suppression is absent. But that amplitude is a GR-conditioned statistic; the registered criterion (fσ₈(z=0.51) > 0.46 at >3σ) was met at only ~1.5σ — the test as registered lacked the power to discriminate, and is not counted as a refutation. Verdict: post-hoc retrodiction — disfavored on σ₈ amplitude; underpowered on the registered statistic. The LRG1 (z=0.51) bin at fσ₈/(fσ₈)_fid = 1.16 ± 0.13 (“enhancement”) is a single ~1.2σ fluctuation, not the ensemble signal — the DR1 ensemble growth index γ_growth ≈ 0.58 ± 0.11 actually leans mildly toward suppression, the framework's own direction. Pinning the kill on “wrong direction” would be fragile against DR2 (growth results unpublished, ~Spring 2027); the amplitude statistic is the defensible one. Note: a 2026-05-25 “correction” that claimed fσ₈ ≈ 0.45 was itself an error — that value belongs to arXiv:2512.03230 (DESI Peculiar Velocity Survey, z≈0.07), misattributed to the z=0.51 full-shape slot. The “mechanism-class transferable contribution” characterization is not restored — it was an overstatement of a post-hoc test.

(2) RAR Transition Shape (2026-05-21): The one non-degenerate galaxy-scale discriminating test — whether the compander's transition curve (γ=2) differs from McGaugh's MOND interpolating function — was run on 2807 real SPARC points. γ=2 is refuted at ΔBIC=+184 (conservative: ≈33). Free-γ converges to γ≈0.49 = MOND, with RMS identical to McGaugh.

How to read the ΔBIC ladder (sharpened 2026-07-27, external-reviewer point). The two numbers do different work and should not be read as one scale. The γ=2 result is a pure likelihood verdict (Δk = 0): ΔBIC = +184 is decisive misfit. The free-γ result is almost pure parameter charge: with N = 2807, ln N = 7.94, so one added free parameter costs +7.94 in BIC before any likelihood is considered. The observed ΔBIC = +7.1 therefore implies Δχ² ≈ −0.84 — the free-γ compander fits the data marginally better than McGaugh's ν and loses on BIC solely as a complexity charge for carrying a knob MOND does not need. The honest statement is not “collapses to MOND equivalence” but the stronger one: the compander is a strictly worse-parameterized reparametrization of the RAR, buying Δχ² < 1 for one added degree of freedom. (Open bookkeeping item: whether a₀ was floated in both arms, i.e. whether Δk = 1 or 2. At Δk = 2 the penalty is 15.9 and the compander fits better by Δχ² ≈ 8.8 — a different number, the same conclusion. The fit record should state which.)

Discrimination, stated precisely (corrected 2026-07-27). This page previously read “net discriminating galaxy tests vs MOND: 0, by execution.” That sentence was written on 2026-05-21, before TEST-09 and TEST-10 executed, and it is false as written — it also contradicted Tier 1, which says of TEST-10 “this observable discriminates, and the framework loses it.” The claim splits in two, and both halves are worth stating:

The RAR transition-shape test is the one that genuinely cannot discriminate: at free γ the curves coincide. Discrimination is absent there, not across the executed ledger.

(3) Cassini/SPARC joint squeeze (TEST-25 — executed 2026-07-23, propagated to site 2026-07-28): the framework's single scale-universal compander cannot be used asboth the SPARC-fitting galaxy function and a QUMOND-style Solar System interpolation function — at the SPARC-preferred γ ≈ 0.489, the Cassini quadrupole discrepancy is +17.95σ, and every point in the retained ΔBIC ≤ 10 grid (γ = 0.425–0.600) fails Cassini by +17.7σ to +18.0σ — a robust empty intersection, not a boundary artifact. This is by far the sharpest number on the site. See Tier 1 for the full scope statement (it closes the joint realization, not modified inertia or a multi-scale function).

(4) Bell/CHSH substrate test (Bet B1): the framework's single-observer substrate was tested directly against Bell's inequality and refuted on both no-signaling arms — see below for detail. The only executed lab-data refutation on the site.

Added 2026-07-30: (3) and (4) were both executed and badged Failed/Refuted elsewhere on the site (Tier 1, Bell/CHSH section below) but were silently absent from the footer's “4 refutations” count and from this page's “sharpest events” list — the count's scope word (“astronomical”) filtered out the one ephemeris result and the one laboratory result without saying so, and both happen to be failures. Two visitor personas independently caught this the same day. The footer count is now 6, spanning astronomical, ephemeris, and laboratory data.

The entity criterion Γ < m, previously labeled the sole surviving novel prediction, was reclassified as a Reparametrization (2026-05-20): it is the standard narrow-width condition Γ ≪ m from QFT — known since Breit-Wigner (1936) and formalized in the Källén-Lehmann spectral representation. Synchronism's contribution is an ontological interpretation, not the condition. Novel-survivor count: 0. The framework produced 47 internal contributions across ~3,308 sessions — well-posed questions and methodology outputs, zero confirmed novel results. “Unconfirmed” ≠ “wrong” — but the evidence now includes six executed refutations on external data (astronomical, ephemeris, and laboratory) and zero surviving novel predictions.

What “Coherence” Does and Doesn't Mean Here

This page audits parameters, tests, and symmetry constraints — so it should also audit the framework's central variable by name. C(ρ) runs from 0 (sparse, independent constituents) to 1 (dense, collective behavior). That is not the physicist's “quantum coherence” — it is closer to a classicality or collectivity measure along the density axis. The naming is close to inverted relative to standard usage: BCS superconductors and Bose–Einstein condensates — the most quantum-phase-coherent systems known — score low and flat on C(ρ) at all physically accessible densities (their enormous Ncorr makes γ tiny, flattening the curve). A condensed-matter reader who imports the standard meaning of “coherence” will read several pages backwards.

Why not rename it? A rename was adjudicated and rejected (2026-06): retrofitting a new name across a historical research corpus would assert that the corpus said something it didn't. The honest fix is stating the collision wherever it can mislead — the glossary carries the ⚠ warning on every coherence-adjacent entry, and it is stated here because this is the page that claims to audit everything.

What Was Tested

Analyses run with results. A kill-criterion-triggered result appears here, not under “What Works” — the heading reflects what was attempted, not what succeeded. The site-wide footer count (“0 confirmed; 6 refutations executed on external data”, recounted 2026-07-30) covers executed refutations across three data types — astronomical: the RAR transition shape (γ=2 pinned, ΔBIC=+184), the BTFR slope (TEST-09, registered kill fired at 3.3σ, 2026-07-14), dwarf DM fractions (TEST-10 — class exclusion via SPARC's max observed DM fraction, 2026-07-15; the “69% exceeds ceiling” headline is convention-dependent, see the Verdict section above), and the registered environment run (r² = 0.0001 vs the registered >20% claim, 2026-07-14); ephemeris: the Cassini/SPARC joint squeeze (TEST-25, +17.95σ, 2026-07-23); and laboratory: the Bell/CHSH substrate test (Bet B1, refuted on both no-signaling arms). Through 2026-07-29 the count and its stated scope (“external astronomical data”) silently excluded the last two, both of which were already executed and badged Failed/Refuted elsewhere on the site — a scope word that happens to filter out only failures understates the audit rather than strengthening it, which is the opposite of this page's purpose. DESI TEST-04a is still deliberately not counted — the test as registered lacked the power to discriminate (corrected 2026-07-14). Note what the count is not: none of these tests is prospective — every adjudication used data that existed before the criterion. The program's prospective-registration count remains 0.

What the six actually refute — classification added 2026-08-09

Every visitor persona in the 2026-08-09 pass independently hit the same defect: the count is quoted everywhere and auditable nowhere. Two separate problems. (a) The inclusion rule was never written down. It is: a row counts if it was executed against a registered criterion on data the framework did not fit, and carries one of the operational labels Kill Criterion Triggered, Failed, Ceiling Exceeded, or Empty Intersection. Three of those four labels are absent from the badge legend readers are pointed to — so the number could not be reconstructed from the site's own vocabulary. That vocabulary gap is real and is not fixed by this table (it is queued as its own sweep). (b) The six are not six of a kind.

EntryWhat it refutesClass
TEST-09 BTFR slope 3.35 vs 3.75±0.10 (3.3σ)The asserted ceiling BmaxFramework-specific
TEST-10 dwarf fDM ceilingThe same asserted Bmax — corollary, not an independent rootFramework-specific
RAR shape, ΔBIC = +184 at γ=2The asserted γ=2 pin. Free-γ → 0.489 recovers MOND, so this refutes a pin, not a mechanismFramework-specific
Environment scatter, r² = 0.0001A genuinely framework-specific prediction. The cleanest kill on the listFramework-specific
TEST-25 Cassini/SPARC, +17.95σThe RAR-preferred interpolating-function family — which MOND also uses. Published as Desmond, Hees & Famaey 2024 at 8.7σInherited from MOND
Bell/CHSH substrate (Bet B1), S ≤ 2.00Bell's theorem. A proof, not an experiment — this page calls it a “pedagogical corollary” elsewhereTheorem

Read the column, not the total. Four entries are about this framework and they test two asserted constants (Bmax, the γ=2 pin) plus one real prediction — which is what the existing “3–4 independent roots” figure already says, and that is the number to quote. One entry is a published MOND constraint the framework inherits by being in the same IF family; it does not discriminate between the two. One is a theorem, and a theorem is not “external data.”

Why the total is still 6 and not 4. The 2026-07-30 recount raised it from 4 precisely because a scope word (“astronomical”) was filtering out the site's two sharpest failures. Dropping them again on a different technicality would re-commit that error in the opposite direction. Both are executed, both are badged Failed, both stay counted — and both are now labelled for what they are, which is what the count was missing. The honest one-line summary: everything that distinguishes this framework from MOND is a single asserted constant, and two of the six refutations test it.

Galaxy Rotation: ALFALFA-SDSS

Untested — TEST-03 Never Run As Registered

σint = 0.086 ± 0.003 dex — CDM-consistent (z = +0.5 in the definitive run), not below CDM. Sample correction (2026-07-10): the 0.086 figure belongs to the source session's optimal quality cut, N = 677 (SNR > 15, eW50 < 10, b/a < 0.65, V > 80 km/s), not to the full ALFALFA–SDSS cross-match — the full sample (N = 14,435 in the definitive session) gives σint = 0.118 ± 0.001. This card previously paired the headline N with the optimal-cut statistic — the same numerator/denominator splice class as the TEST-03 correction below, caught by walking the number to Session 610's own table.

Correction (2026-07-09): this card previously reported “environment-dependent RAR scatter at p = 5×10−6, R² = 0.14” as the ALFALFA-SDSS (N = 14,585) result and said its kill criterion fired. That pairing is mathematically impossible at N = 14,585 (R² = 0.14 there implies p of order 10−500, not 10−6) — the (R², p) pair is only self-consistent at SPARC scale (N ≈ 130–175), which is TEST-05's sample, not this one. TEST-03's actual environment-density result on the 14,585-galaxy cross-match was never computed as registered. See the corrected TEST-03 and TEST-05 cards for the full provenance trace.

Verdict correction (2026-07-04): an intermediate session had read σint as −6.2σ below the CDM prediction; that reading was retracted in-archive once distance-noise modeling was added — the source session's own definitive run reports CDM-consistent at z = +0.5, and the verdict is itself modeling-choice-dependent (z ranges +0.5 to +64 across choices). The retracted “below CDM” framing had propagated to this page, Galaxy Rotation, and CDM Discrimination — all three now carry the corrected verdict.

MOND (Modified Newtonian Dynamics) Unification: a₀ = cH₀/(2π)

Reparametrization — Dimensional Analysis

MOND's acceleration constant a₀ related to cosmological parameters via a₀ = cH₀/(2π). 13% error at H₀ = 67.4 vs observed value. This numerical coincidence has been noted since Milgrom (1983), and other frameworks (McCulloch 2007, Verlinde 2017, Smolin 2017) derive the same relation with the same geometric factor. The quantities c, H₀, and G are the only dimensionally relevant cosmological constants, and cH₀ naturally has units of acceleration. Best classified as dimensional analysis, not a unique derivation.

Chemistry: γ ≈ 1 Boundary

Reparametrization — Null Model RUN (2026-05-10) — Null-Class

1,703 chemical phenomena. Sound velocity r = 0.982, electronegativity r = 0.979. Top correlations are strong — and the relevant null has been computed: it matches them.

Null model result (run 2026-05-10; this row previously said “not yet run” — that was stale): Sound velocity, electronegativity, and atomic volume are all near-monotonic functions of atomic number Z, so the relevant null is r(polynomial in Z), not r = 0. A 2-parameter degree-2 polynomial in Z was fit to the same targets, analytically and numerically: |Δr| ≤ 0.07 on essentially all density-monotonic targets, and the polynomial sometimes outperforms Synchronism (r ≈ 0.99 vs ≈ 0.87 on linear-in-Z and generic smooth-monotonic targets). Verdict: the chemistry correlations are null-class — they demonstrate density-monotonicity (known physics), not anything specific to C(ρ).

Additional caveats: ~11% failure rate. Era 2 chemistry (sessions 134-2660) identified as template-based. 1,703 phenomena include statistically dependent samples (sound velocity, electronegativity, and atomic volume co-vary for well-known bonding reasons). See Chemistry Limitations.

Freeman's Law: Σ₀ from First Principles

Reparametrization — Dimensional Identity — Same Class as a₀

Surface density Σ₀ = cH₀/(4π²G) ≈ 119 M☉/pc². ≈4% error vs Freeman's observed value (124 M☉/pc²) — corrected 2026-07-09 from a previously stated 110 / 12% arithmetic error (two visitor personas independently caught it the same day).

Like a₀ ~ cH₀, this is the only surface-density scale buildable from the available cosmological constants (c, H₀, G). Any framework that imports these constants will recover the same dimensional relation. It is also not independent evidence from a₀: Σ₀ = a₀/(2πG) exactly, so the ≈4% Freeman match is the same ≈13% a₀-vs-Milgrom gap propagated through a fixed linear relation, not a second derivation. Reclassified from “Validated” to Reparametrization alongside a₀ on the same grounds.

Caveats (updated 2026-07-17): the H₀ inconsistency with Parameter Derivations' former 123.3/0.5% figure is resolved — the split was an undisclosed Hubble-constant switch (119.0 at H₀ = 67.4, 123.6 at H₀ = 70; identified by a visitor physics persona). Site standard is now H₀ = 67.4 km/s/Mpc (Planck 2018), giving the ≈119 shown here. Separately, Freeman's (1970) value is a surface brightness; converting to surface density needs M/LB ≈ 1–3, so the target is uncertain by a factor of ∼2 — neither page's percentage is meaningful standing alone.

What Failed

Critical Exponents — Category Error (Corrected 2026-05-25)

Failed — Wrong Category — Not a Critical Phenomenon

An explicit, everywhere-analytic sigmoid has no critical point — no fixed point, no diverging susceptibility, no diverging correlation length. C(ρ) is not a critical phenomenon: ρ is an external input evaluated directly, not solved self-consistently (unlike Ising's m = tanh(βJzm), where m appears on both sides — that's what generates criticality). Comparing “predicted critical exponents” to renormalization-group exponents presupposes the very criticality C(ρ) does not have. The prior framing (“exponents 2× off”) was a fossil from the phase-transition era of the project — retained too long alongside the (correct) compander reframe. Corrected verdict: the Landau-universality argument fails not because the exponents are wrong by a factor, but because the category does not apply.C(ρ) belongs to the compander family (μ-law / Hill / Naka–Rushton class). No critical exponents exist to compare.

Melting Point Predictions

Failed — 53% Error

Average error 53%. Crystal structure dominates melting behavior, and C(ρ) has no crystal-specific parameters.

Superconductor Tc

Failed — 6.5× Wrong

Tc = Δ/(1.76kBη) predicts 607K for YBCO (yttrium barium copper oxide). Actual: 93K. Off by 6.5×.

η Reachability Factor

Reparametrization

Independently derived, then found to be identical to Abrikosov-Gor'kov pair-breaking efficiency (1960). All 23 superconductor predictions are standard condensed matter in different notation.

Fractal Coherence Bridge

Failed — Negative Verdict

C(ρ) was proposed to explain cross-scale hierarchy boundaries. 36/36 tests: 0/7 boundaries predicted. The tanh form is generic (Landau theory). C(ρ) is description, not explanation.

TEST-03: ALFALFA-SDSS TFR Scatter — REMOVED FROM “WHAT FAILED” (2026-07-09)

Untested — Never Run As Registered

In plain terms: this card previously said the framework failed its own pre-registered environment test. It didn't — the number reported as the failing result belongs to a different test on a different, smaller sample. The environment test on the 14,585-galaxy sample was never actually run. That's a gap, not a failure, and it's a more embarrassing kind of error to have made on the site's own self-audit page than the failure it was reporting. Glossary →

R² = 0.14 with p = 5×10−6 and N = 14,585 is internally impossible: at that N, R² = 0.14 implies t ≈ 48.7 (p of order 10−500). The pair is self-consistent only at N ≈ 130–175 (SPARC scale) — TEST-05's sample. Archive tracing confirms it: 0.14 is a Hubble-type/morphology term from Session 377 on N ≈ 171, misattributed to the ALFALFA-SDSS cross-match. The registered TEST-03 environment-density correlation on 14,585 galaxies was never computed.

Independently found three ways: archive Session 639 (2026-04-30) first traced the metric conflation; the explorer track's 2026-07-08 citation-walk closed the provenance chain (registered threshold was r² < 0.09, which R² = 0.138 passes, and the catalog postdates the measurement by 15 days); two visitor personas independently re-derived the (N, p) inconsistency on 2026-07-09. See the corrected TEST-03 and TEST-05 cards for the full trace. TEST-05, which does own the (R²=0.14, p=5×10−6) result on its registered terms, was reclassified MOND-shared on 2026-07-09 — a verdict re-adjudicated 2026-07-15: the tie dissolves on lever magnitude (MOND+EFE's external-acceleration lever moves outer g_obs by ~0.09 dex; C(ρ)'s ambient-density lever by ≤2×10−3 dex — and the C(a) law predicts exactly zero). The registered environment-density run now exists (research repo, 2026-07-14: SPARC RAR offsets vs Cosmicflows-4 density, r² = 0.0001 vs the registered >20% claim — refuted by execution; weak secondaries are opposite-signed, EFE-like). See the TEST-05 card.

RAR Transition Shape — SPARC ΔBIC=+184, γ=2 Refuted, γfree=MOND (2026-05-21)

Failed — Kill Criterion Triggered — CLOSED

In plain terms: across 175 galaxies analyzed together, the framework's preferred curve-shape fits measurably worse than MOND's (ΔBIC is a fit-quality penalty; +184 is decisive, and even the conservative estimate ≥ +33 is). If you let the framework's shape parameter float freely, it simply turns into MOND's curve — so it is either worse than MOND or identical to it, never better. Glossary →

The only non-degenerate galaxy-scale discriminating test between the Synchronism compander (μSyn = tanh(γ ln(1+x)), γ=2) and MOND's RAR interpolating function was executed on 2807 real SPARC points. Kill criterion: ΔBIC > 10 favoring McGaugh refutes γ=2. Actual result: ΔBIC = +184 (conservative intra-galaxy correlation correction: ΔBIC ≈ 33 — still decisive).

The residual is a coherent S-shaped ≈0.05–0.10 dex signature at the RAR transition (gbar ≈ a₀), significant at ~8σ per bin. Free-γ fit converges to γ≈0.49 = MOND, with RMS identical to McGaugh to four digits. ΔBIC = +7 for free-γ is entirely the BIC parameter penalty, not a fit difference — the compander at its best-fit γ is MOND. Net discriminating galaxy tests vs MOND: 0, by execution.Script: explorer/scripts/rar_transition_shape_real_sparc.py. See also Galaxy Rotation: RAR Transition Shape.

“Converges to MOND” is not a coincidence — it is an identity, and here it is (added 2026-08-08). The free fit could not have landed anywhere else. Using this page's own Hill form, tanh(γ ln(1+x)) = [(1+x)−1]/[(1+x)+1], set γ = 1/2 exactly. Then 2γ = 1 and it collapses to C(x) = x/(x+2) = μsimple(x/2) — MOND's simple interpolating function, with the factor of 2 absorbed entirely into the fitted ρcrit. SPARC's 0.489 is 2.2% from that exact point. So the four-digit RMS agreement with McGaugh is the only possible outcome once the fit is free to find γ = 1/2: the functional form was never a difference from MOND at all. The only difference that ever existed is the argument (local ρ in place of gbar) — which is exactly what For Researchers isolates and refutes. Corollary: the Hill index at the preferred fit is n = 2γ = 0.978 ≈ 1, and n = 1 is the non-cooperative limit of a Hill function. The framework's distinctive content is that density drives a collective transition; the data set the cooperativity parameter to the value meaning there is no collective transition — the same fact as the criticality retraction on The Core Idea, arriving through the fit rather than through the math.

TEST-04a: DESI RSD fσ₈ — Post-hoc Retrodiction, Disfavored on σ₈ but Underpowered on the Registered Statistic (Corrected 2026-07-14)

Failed — Disfavored 2.4σ on σ₈ — ~1.5σ on Registered fσ₈ — Post-hoc — Test Underpowered to Discriminate

In plain terms: the framework predicted the universe's large-scale structure should be about 10% “smoother” (less clumpy) than standard cosmology expects. The DESI galaxy survey measured the clumpiness (that's σ₈): the prediction misses by 2.4 standard deviations — unlikely to be luck — and it was written down only after earlier hints pointed that way, which makes it weaker still. Glossary →

The load-bearing constraint is amplitude, not direction. Session 107 (Dec 2025) predicted σ₈ ≈ 0.76 (calibrated to the then-live S₈ lensing tension). DESI DR1 full-shape (arXiv:2411.12021) combined σ₈ = 0.841 ± 0.034 (Table 10) — a 2.4σ tension. That tension is robust regardless of which single bin is inspected.

The single-bin “enhancement” reading is a qualified, not load-bearing, finding. LRG1 (z_eff=0.51) fσ₈/(fσ₈)fid = 1.16 ± 0.13 — growth above the ΛCDM fiducial in that one bin (~1.2σ). But the DESI DR1 full-shape RSD ensemble growth index γgrowth ≈ 0.58 ± 0.11, above GR's 0.545 — which leans mildly toward suppression, the framework's own predicted direction. Reading LRG1 alone as “sign-wrong regardless of which bin” over-reads a single ~1.2σ bin against an ensemble that trends the other way. (Corrected 2026-07-02: a 2026-07-01 explorer re-execution and an independent 2026-07-02 visitor Pass 4 researcher read both flagged the same overclaim.)

Correction (2026-07-14): the registered kill criterion and the delivered verdict use different statistics, and the substitution is not innocent. The kill criterion below is registered on fσ₈(z=0.51) > 0.46 for a >3σ ruling-out. Computed directly from this page's own numbers — LRG1 fσ₈ = (fσ₈)fid × 1.16 ± 0.13  = 0.474 × 1.16 ± 0.062 = 0.550 ± 0.062 — the 0.46 threshold is exceeded by only ~1.5σ, well short of the >3σ the criterion demands for a ruling-out (it does clear the weaker >2σ “disfavors” clause at 0.45). The 2.4σ figure that formerly carried a “Kill Criterion Triggered” label on this page (last instance removed from the Verdict section 2026-07-17) is instead a comparison on σ₈, a different parameter inferred from a full-shape EFTofLSS fit whose perturbation kernels assume GR growth — using a GR-conditioned amplitude to falsify a modified-growth model risks circularity, a point this page's own EFTofLSS citation below already half-concedes (1–2σ theory systematic). DESI's own purpose-built modified-gravity analysis — Ishak et al., “Modified Gravity Constraints from the Full-Shape Modeling of Clustering Measurements from DESI 2024,” arXiv:2411.12026 (JCAP 09 (2025) 053), previously uncited on this site — constrains exactly the parameter a growth-suppression mechanism lives on: μ₀ = 0.11 (+0.45/−0.54) from DESI FS+BAO+BBN+ns alone, tightening to μ₀ = 0.05 ± 0.22 with CMB+DES-SN. A ~12% fσ₈ suppression maps to a substantially negative μ₀, which sits inside DESI-alone's 1σ band (the exact mapping needs the assumed time-dependence worked out — not yet run on this site; seeded as an explorer topic).Honest reading: the test as registered lacks the statistical power to discriminate this framework from GR — a more useful negative result than a manufactured kill, but materially weaker than “Kill Criterion Triggered” implied. The framework's cosmology sector is not rescued by this correction: the growth suppression was never derived— it was calibrated. (Corrected 2026-08-09: this read “it still has no field equation to source a growth suppression from in the first place.” Appendix D §D.3 does state effective Einstein equations Gμν = 8πG Tμν/C(ρ), which are cosmology-capable; nobody has ever solved them for the growth history and compared. The gap is an unrun calculation, not a missing object — which makes it a task rather than an excuse.) The σ₈ discrepancy on its own predicted value (0.76 vs. 0.841) remains a real, if GR-conditioned, 2.4σ miss. (Found and verified: 2026-07-14 visitor Pass 3 and Pass 4, cross-checked against this page's own cited numbers before editing.)

Two aspects of the honest verdict: (1) Post-hoc origin — doubly so — Session 107 was committed 2025-12-10 after DESI DR1 was published April 2024; σ₈ calibrated to the lensing S₈ tension (KiDS/DES era), then propagated to DESI. No prospective prediction registered. Additional layer: the S₈ tension itself is receding — DES Y3 6×2pt and KiDS-Legacy (2024–2025) reanalyses have pulled S₈ back toward Planck, so the calibration anchor was a transient observational state, not a stable target. This makes TEST-04a post-hoc against a moving baseline. (2) Disfavored 2.4σ on amplitude— the σ₈≈0.76 prediction sits 2.4σ below the DESI DR1 combined fit; this is the durable disfavor (a GR-conditioned statistic, not the registered kill — see the 2026-07-14 correction above). A 2026-05-25 “correction” that claimed kill not triggered was itself an error: 0.4497 ± 0.0548 belongs to arXiv:2512.03230 (DESI Peculiar Velocity Survey, z≈0.07) misattributed to the z=0.51 full-shape slot. The “mechanism-class transferable contribution” is NOT restored — it was an overstatement.Context (2026-05-23): EFTofLSS analyses (Cabass, Simonović, Zaldarriaga et al. 2024-2025) explain DESI DR1 fσ₈ within ΛCDM at 1-2σ via one-loop counterterms.Calibration note (2026-06-24): the kill fires on LRG1 alone at ~2.15σ if read as a single-bin sign test — standard practice treats that as sub-threshold. The amplitude tension (2.4σ, ensemble σ₈) is what previously carried the “Kill Criterion Triggered” label (label retired 2026-07-14; see correction above), not the single-bin direction.Currency (2026-07-02): DESI DR2 full-shape growth (fσ₈) constraints are not yet published (expected ~Spring 2027); this verdict is frozen at DR1. The re-open policy below is unaffected — no DR2 growth datum exists yet to trigger it.

What this rules out beyond Synchronism: DESI DR1 full-shape (arXiv:2411.12021) finds LRG1 fσ₈/(fσ₈)fid = 1.16±0.13 — growth above ΛCDM, opposite the predicted suppression. This constrains Synchronism-form uniform, scale-independent late-time growth suppression: any framework that predicts a uniform coherence-damping of structure growth across all scales sits in the same disfavored direction.Scope note: this does not exclude massive neutrinos, warm dark matter, or f(R) gravity — those mechanisms are k-dependent and scale-localized, fundamentally distinct from a uniform coherence suppression; DESI+CMB joint analyses treat them as fully live. The constraint applies specifically to the uniform scale-independent class, not to suppression mechanisms in general.

Quantum Arc — Zero Confirmed Predictions (Session #581 Audit)

Reparametrization — 0 Confirmed, 1 Refuted — 2026-02-08

Session #581 (2026-02-08) conducted an 8-test quantum audit. Overall verdict: zero confirmed predictions, 4 reparametrizations, 1 refutation, 1 post-hoc fit, 1 not-preferred.

Key refutation — boost ceiling Bmax = 3.17: The framework predicts a maximum gravitational boost ratio B = gobs/gbar of Bmax ≈ 3.17 (from SPARC — Spitzer Photometry & Accurate Rotation Curves — calibration). The deepest SPARC bin shows ⟨B⟩ = 10.82, with 579 individual SPARC data points exceeding Bmax (corrected 2026-08-07: this page previously read “579 galaxies,” but SPARC contains 175 galaxies — the 579 counts rotation-curve points, as key claims states correctly). This is the strongest direct refutation in the framework's own internal audit. It was not previously visible on this page. Its corollaries were executed 2026-07-14/15 and both fail: a bounded boost has no deep-MOND regime, forcing the wrong BTFR slope (TEST-09 — kill fired at 3.3σ), and caps the apparent DM fraction at 1 − Ω_m = 68.5% under one convention — the “69% of SPARC exceeds it” headline doesn't survive the alternative baryon-budget convention (see Verdict, above); the class exclusion via SPARC's max observed fraction (TEST-10) does. Everything gravitational on this page that differs from MOND is downstream of this one bound. (Notation note 2026-06-12: the source audit called this quantity “γ”, colliding with the transition-sharpness parameter γ = 2/√Ncorr used everywhere else on this page — including the separate “γ = 2 refuted at ΔBIC = +184” result. They are different quantities; we use B here to keep them apart.)

The two “literature-consistent” quantum results (Γ = γ²(1−c) and Bell-freezing c(d)) are both reparametrizations: the decoherence formula is the textbook correlated-dephasing variance (Palma–Suominen–Ekert 1996); the Bell-freezing functional form was imported from waveguide QED (Session #235 admission). Audit finding propagated to site 2026-05-16.

Bell/CHSH Substrate Test (Bet B1) — Refuted, Both No-Signaling Arms

Failed — Executed 2026-06-21 / 2026-07-06 — S ≤ 2 Without Signaling

In plain terms: Bell tests give quantum mechanics a distinctive score: real experiments reach about 2.83, while any classical, local mechanism can score at most 2. Simulations built from this framework's own machinery score 1.85–2.00 — classical territory — and only beat 2 when allowed to cheat with faster-than-light signaling. So the framework doesn't sidestep the famous quantum weirdness; it fails the same test classical physics fails. Glossary →

The framework's single-observer substrate was tested directly against Bell: CHSH simulations with freely chosen settings, measured only through observer-pattern phase-lock. Local construction: S = 1.98. Nonlocal-grid construction: S ≡ 2.00 at every coupling strength (gauge-equivalent to relabeling the measurement angles — a local model in disguise). Global-clock construction: S up to 2.67, but only by introducing signaling. No construction reaches the Tsirelson bound (2√2 ≈ 2.83) without signaling.

Substrate-independence (run 2026-07-06): the same cap holds on the framework's own saturation-gated Intent-density substrate (S = 1.85 ≤ 2, no signaling) — the S ≤ 2 bound is Bell's structure theorem for any real-valued local-realist model, not an artifact of the borrowed phase substrate. The Born-rule cos² projection law reaches 2√2 exactly, but only by importing Hilbert-space structure wholesale. This is the framework's cleanest self-executed negative result; full construction detail on Two Reframes. The substrate's Bell behavior is not an untested protocol: it was tested, by execution, and capped at the classical bound.

BTFR Slope (TEST-09) — FAILED, Kill Criterion Triggered (Executed 2026-07-14)

Failed — Kill Criterion Triggered — 3.3σ, deviation 0.41 > 0.3

In plain terms: the heavier a galaxy, the faster its outer edge spins — and the exact mathematical relationship between mass and speed (the “slope”) is measured precisely. MOND's prediction matches it. This framework's gravity boost has a built-in maximum, and a maxed-out boost behaves like ordinary Newtonian gravity — which forces the wrong slope. Run on 123 real galaxies, the framework misses by more than its own pre-registered failure threshold. Glossary →

Executed 2026-07-14 on real SPARC (same V_flat estimator applied to observation, MOND, and Synchronism): observed n = 3.75 ± 0.10 (reproduces Lelli 2019's 3.85 ± 0.09); MOND n = 3.81 ± 0.04 (passes, 0.6σ); Synchronism n = 3.35 ± 0.07 (fails, 3.3σ; registered kill criterion > 0.3 fires at 0.41). No parameters rescue it — reaching 3.75 requires Ω_m → 0.001 and φ → 2, where the law degenerates algebraically into MOND.

Why the old “MOND-shared / cannot discriminate” badge was wrong in structure: the framework's boost is bounded (B ≤ 1/Ω_m = 3.17 — the ceiling in the boost-ceiling entry above), so it has no deep-MOND regime: its deep limit is Newtonian-times-constant, slope n → 2, not MOND's n → 4 (which requires the divergent √(a₀/g) boost). The previously listed “n → 4 deep-MOND” limb was asserted (S193, synthetic 9-galaxy ladder), never derivable from the bounded formula; archive S58 had recorded the discrepancy honestly and was overwritten. The BTFR is exactly an asymptotic-boost observable — this failure is a corollary of the boost ceiling, as is TEST-10's (dwarf DM fractions — the class exclusion via SPARC's max observed fraction, not the convention-dependent 69%/68.5% headline; see Verdict above; executed 2026-07-15). Full trace on Tier 1 — TEST-09.

Structural Tensions (March 2026 Stress Tests)

Eight adversarial stress-test sessions probed the CFD reframing for genuine novel predictions. Results: one candidate prediction, four forced choices, and several structural failures.

Structural No-go: Local Density vs Non-local Acceleration (Milgrom 2005 instance)

Failed — Wrong Variable (2026-06-01)

In plain terms: the framework computes its gravity boost from how dense matter is right at each point. But real galaxy data organize by the total pull of everything enclosed within your orbit — a fundamentally different quantity. No single density threshold can bridge the two across systems (it misses clusters by factors of thousands), which is why the galaxy fits can't extend anywhere else. Glossary →

C(ρ) is a function of local density ρ. The RAR/MOND relation it mimics in galaxies is a function of gbar — the enclosed-mass acceleration, a non-local, geometry-dependent quantity. A pointwise intensive variable cannot reproduce an acceleration-space relation across systems with different mass geometries except by per-system calibration.

The failure surfaces exactly where the two variables decouple: clusters require ρcrit,cluster 104–106× smaller than the galaxy value — destroying universality. Four natural ansätze tested on Coma: A1/A4 overshoot by 104; A2 collapses to Newtonian; A3 is structurally impossible (C ∈ [0,1) bounds velocity at ≤2, observed dispersion requires ~4.6).

Transferable finding — scope demoted 2026-07-27: This no-go applies to modified-gravity ansätze that key on local volumetric density ρ(r) and modulate the force algebraically (a C(ρ) multiplier on g), which is the class C(ρ) belongs to. It does not apply to all local-ρ schemes: the earlier wording said “any,” and a walk of the screening literature found a published counterexample — Burrage, Copeland & Millington, PRD 95, 064050 (2017) reproduce the RAR on 153 SPARC galaxies with a symmetron keyed on ρ(r) and universal Lagrangian parameters, because their extra force is the gradient of a function of ρ rather than a multiplier on it. Detail and the corrected citable form on For Researchers. It also does not apply to frameworks using non-local state variables — Verlinde (enclosed baryonic mass MB(<r)), MOG/STVG (enclosed mass scalar), or MOND surface-density formulations (column-integrated Σ) all escape it. The discriminating axis is thelocality of the state variable, not whether the framework is “density-based.” The root obstruction is Milgrom's non-locality theorem (astro-ph/0510117): a MOND-type modification must be strongly non-local in space/trajectory to produce the acceleration-keyed RAR (Lelli et al. 2017). C(ρ) is the quantified local-density instance of that obstruction, not a new theorem. Note: MOND also has one acceleration scale (a0) and fails at clusters by a residual factor of ~2 — so scale-count alone is not the discriminator; the variable (local ρ vs non-local gbar) is.

The no-go on the velocity axis (2026-07-02): the same obstruction as a sign statement — for the density knee to track MOND's acceleration threshold, the BTFR forces ρcrit ∝ a₀²/(GV²) ∝ V−2 (profile-independent); the framework asserts ρcrit = A·V+2. The exponent is inverted, the magnitude is 240×–300,000× too high, and with the framework's own values the entire luminous disk sits at C ≲ 0.28 — the knee is never crossed inside a galaxy. No recalibration of A repairs a sign. Full derivation on Parameter Derivations.

Dark Matter Viscosity Sign Error

Failed — Wrong Direction

CFD mapping: C = 1/μeff. Dark matter (low C) should mean high viscosity = more sticky. But the Bullet Cluster shows dark matter passes through itself — LESS sticky than baryons. The viscosity interpretation predicts the wrong direction. The deeper structural failure (local ρ vs non-local gbar variable mismatch) is described in the box above.

Lorentz Invariance: Preferred-Frame + Dim-4 Naturalness Gap (Added 2026-07-02)

Audited-Negative — Naturalness Gap: 16–28 OOM; custodial escapes unexhibited

In plain terms: the framework needs a universal “absolute clock,” which physics-wise means a preferred frame of reference. Coupling that to known particle physics generically produces effects that experiments have already excluded at 16–28 orders of magnitude below the expected size. Other theories have known escape mechanisms; this framework implements none of them. Not a data refutation — a severe “why don't we see it?” problem. Glossary →

The framework's defining commitment — a discrete substrate with absolute time — generates a preferred rest frame. Two computed consequences: (1) no discrete 3D lattice has continuous rotational symmetry SO(3); “no preferred scan-axis” does not imply “full Lorentz invariance,” and grid geometry is unspecified. (2) The sharper result (2026-06-26 computation): the dim-4 SME Lorentz-violating coefficient cμν is not Planck-suppressed here — tree-level cμν = 0 by single-substrate universality, but the one-loop radiative correction is UV-dominated and Planck-cutoff-independent: cμν ~ α/π ~ 10−2. Existing cavity and nucleon-comagnetometer bounds reach 10−18–10−30 — a 16–28 order-of-magnitude fine-tuning gap (a CPSU 2004 naturalness problem, not a data-driven refutation). Two standard perturbative escapes exist in the literature (SUSY — Groot Nibbelink & Pospelov 2005; anisotropic scale-hierarchy — Pospelov & Shang 2012, demonstrated for Hořava-class absolute-time gravity) but neither is exhibited in this framework; single-substrate universality is itself the obstacle to adopting the scale-hierarchy route. Status: open custodial-mechanism gap, not a closed refutation — this is the framework's most severe naturalness constraint and its only non-MOND, non-Zurek falsification channel.

A separate, structurally protected LIV channel (time-of-flight dispersion, dim≥5) is notaffected by this gap — even-k lattice symmetry forbids the linear term, and the surviving quadratic term sits ~107 below current LHAASO reach and is non-unique to this framework (shared with LQG/causal-set models). Full three-lock argument and both LIV faces: For Researchers →.

R(I) Correction Unobservable

Failed — ~10⁻⁸⁰ at Neutron Stars

The only genuine novel prediction path (R(I) viscosity correction to quantum pressure) gives corrections of ~10−80 at the densest accessible physics. Lives at Planck-scale densities. Not accessible to any foreseeable experiment.

Entity Criterion: Γ < m — Reclassified (2026-05-20)

Reparametrization — Ontological Reframe — Not a Novel Prediction

Previously labeled the sole surviving novel prediction. The condition Γ < m is the standard narrow-resonance / narrow-width condition from QFT — required for a Breit-Wigner pole to be well-defined. Synchronism's contribution is an ontological interpretation (“coherence cycle completion”), not the condition itself. QFT already classifies broad resonances as poor quasiparticles and narrow ones as well-defined particles. Novel-survivor count after external expert audit: 0 of 6 (0 of 47 internal-consistency candidates pending audit, out of 3,308 total sessions — see the A2ACW methodology for the full chain).

What's Untested

Consciousness Threshold (C ≈ 0.50)

Untested

34 predictions, contingent on a C-axis calibration protocol that does not yet exist. The EEG (electroencephalography) experiment sketch ($150K, 12 months) cannot run as stated: per Key Claims, no procedure maps any measurement (EEG phase coherence, fMRI, Φ) onto the C-axis — the claim is currently unrunnable, which is the stronger verdict. Calling these “falsifiable” without the calibration step would contradict that verdict. Consistent with that: the one internal test ever cited against the 0.50 value (gnosis-research Session 63) measured SNARC salience — a different variable with no mapping to C — so no threshold value has actually been tested. (A prior version of this page said both 0.50 and 0.64 were “rejected at p < 0.0001”; the 0.64 rejection had no source in any repository and was removed 2026-07-08.)

Quantum Predictions

Untested

6 testable protocols for MRH-based (Markov Relevancy Horizon) measurement theory. Requires dedicated experiments.

BAO (Baryon Acoustic Oscillation) Modulation — Withdrawn

Superseded — Withdrawn 2026-05-04 (TEST-04)

Formerly listed here as “testable with existing survey data.” That was stale: TEST-04 (BAO peak-shift modulation) was withdrawn 2026-05-04 by internal contradiction — the framework's own Session 107 forecasts BAO matching ΛCDM at 0.0% in all five DESI redshift bins (the sound horizon is set at z~1100 when C ≈ 1 everywhere), so no modulation is predicted. The growth sector moved to RSD fσ₈ (TEST-04a, adjudicated above). See test catalog.

H₀ Tension — Not Addressed

Speculative — No prediction

The Hubble tension — a ~5σ discrepancy between early-universe (CMB) and late-universe (distance-ladder) measurements of H₀ — is the dominant open problem in cosmology (2018–2026). Synchronism makes no statement on H₀. If C(ρ) couples to expansion-rate physics via ρ_crit ↔ Λ, there should be a prediction about how coherence modifies recombination (early-time fix) or late-time acceleration (late-time fix). Neither has been worked out. A framework claiming cosmological scope that does not address H₀ tension is leaving the most-cited empirical opening in cosmology off the table.

Correction (2026-07-27): “makes no statement on H₀” is too strong, and this page was the one over-claiming its own silence. The framework carries a₀ = cH₀/(2π) as Claim 3's key equation. That relation is invertible: with the measured a₀ = 1.2 × 10⁻¹⁰ m/s² it returns H₀ = 2πa₀/c ≈ 77.6 km/s/Mpc — above SH0ES by several σ and far above the CMB value. So there is an H₀ consequence; it is simply unflattering, and it was being booked as no statement at all. What remains true is the substantive point above: no mechanism for the tension has been worked out, neither an early-time nor a late-time fix. The correct badge is a failing soft constraint, not silence — and it is one more reading on which a₀ ≈ cH₀/2π looks like numerology rather than a derivation. Flagged by the graduate-physics visitor pass; the same inversion had been noted internally 2026-07-26 without reaching this page, which is the propagation break rather than the physics.

Research Outputs (Not Discoveries)

Reparametrization — Top-3 Swept 2026-07-03 — 0/3 Novel

Session #615 (final accounting) inventoried all outputs across ~3,308 sessions: 47 research contributions at a 1.4% session yield. Novel-surviving yield after domain-expert audit: 0. Every output that a domain expert examined resolved as a reparametrization of known physics, an internal consistency finding, or a null result. The 47 outputs are genuine — well-posed questions, characterized failures, methodology results — but none constitutes a confirmed novel prediction.

Top results: 6-variable MOND offset model (LOO R²=0.938), TFR residual as complete M/L predictor (51.4% improvement on 14,437 galaxies — an analysis subset of the 14,585-galaxy ALFALFA-SDSS cross-match), σint = 0.086 ± 0.003 dex (BTFR intrinsic scatter). Status (updated 2026-07-04): these three were swept against prior art and the archive on 2026-07-03 — 0/3 survive. The offset model and the TFR-residual predictor are the same fact (the offset model is dominated by log-luminosity at t = −36, i.e. it is the Tully-Fisher residual), and both reduce to published work: Kannappan et al. 2002 (TF residuals carry M/L information), Li et al. 2018 (RAR offsets are the error budget of a constant-M/L assumption), and Stiskalek & Desmond 2023 (exhaustive regression null over galaxy features). The σint = 0.086 figure is addressed above — it inverted the source session's own retracted verdict. Demotion base rate across the whole program: 9 of 9 audited claims (the prior 6 “Validated” claims plus these 3) failed to survive. Given that record, the honest prior on any not-yet-swept contribution is near-certain demotion, not residual upside — and the research archive's own later sessions (#631–#691) have in fact already demoted the remainder in-archive (cosmology: zero novel items; C(ρ) → MOND + Curie-paramagnet identities verified by computer algebra; chemistry claims reduce to the Debye model; the “47” count itself is a flagged ~57% overcount against a canonical list of ~30). The site's citation-walk of those in-archive demotions is ongoing. Full list in the publication roadmap.

Methodology caveat: The 1.4% rate is an internal-consistency-survival rate, not a discovery rate. A2ACW adversarial agents share the same training distribution — they catch inconsistencies the corpus already knows, but cannot find errors systematic across the whole corpus, and cannot generate novelty that isn't already in the training distribution. The 47 contributions are exploration outputs and well-posed research questions, not confirmed results. Zero confirmed predictions means zero: no contribution in this list has been validated by independent experiment. See Research Philosophy for what “Validated” requires.

What the Program Demonstrates

Where This Sits in the Modified-Gravity Landscape

Several frameworks occupy the same phenomenological territory as Synchronism in the low-acceleration galaxy regime. All share the observation that a₀ ≈ cH₀/(2π) emerges from cosmological constants. Rival lineup last refreshed: 2026-07-23 — this table is date-stamped the same way refutations are, because a “0 discriminating tests” verdict is only as current as the rivals it is scored against.

MOND (Milgrom 1983)Empirical μ-function. No dynamics, no governing equation. Synchronism's compander collapses onto MOND at free-γ (SPARC RAR, ΔBIC=+7 vs ΔBIC=+184 for γ=2).
Verlinde Emergent Gravity (2016)Derives MOND-like rotation curves from entropy gradients in the Hubble volume. Tested by Brouwer et al. (2017) KiDS lensing — consistent at ~1σ. Key question: does C(ρ) reduce to Verlinde in the low-acceleration limit? Not yet shown.
TeVeS (Bekenstein 2004)Lorentz-covariant scalar-vector-tensor extension of MOND. Has galaxy-rotation and lensing predictions. Failed: requires dark matter for the Bullet Cluster; GW170817 constrains the tensor sector. No longer the benchmark relativistic completion — see AeST below.
AeST (Skordis & Złośnik 2021)Aether-scalar-tensor theory — the current benchmark relativistic MOND completion. Reproduces galaxy phenomenology, passes CMB power-spectrum tests where TeVeS failed, and GW speed equals c. Keyed on |∇Φ| — i.e. NON-local in density — which is exactly the escape class the locality no-go on this page identifies: the surviving relativistic MOND theory avoids the local-density trap that kills C(ρ). Caveat: post-2021 stability concerns are under active discussion; cite as "AeST-class," not AeST-final. (Added 2026-07-23 — an expert review correctly flagged that this table was frozen at TeVeS-2006 while the verdict "0 discriminating tests vs MOND+ΛCDM" was being scored against it.)
MOG / STVG (Moffat 2006)Running gravitational coupling with massive vector field. Makes post-Newtonian predictions beyond rotation curves. No direct comparison with Synchronism compander exists.

Current status: Synchronism's compander is curve-equivalent to MOND in the galaxy regime (free-γ = 0.49 ≡ MOND at SPARC precision) — not theory-equivalent (see caveat below). Relationship to Verlinde's entropic gravity is uncharted — whether C(ρ) is a sub-case, extension, or reparametrization of Verlinde in that regime has not been worked out. See Galaxy Rotation for the SPARC result.

CORRECTED 2026-08-09: this paragraph asserted “there is no field equation anywhere in this framework's galaxy sector.” That was false — Appendix D of the archive stated one on 2025-12-01, seven months before the assertion was written (see the correction at the top of this page for L1/L2/L3 and the a-priori elimination of L1). Two further facts make the old wording untenable rather than merely imprecise. (1) The completion was never hard: substituting C for μ in AQUAL (Bekenstein & Milgrom 1984) or QUMOND (Milgrom 2010) is mechanical, and AQUAL and QUMOND agree to <0.1 dex on realistic disks — for rotation curves the choice of completion is nearly a formality. (2) The site had already crossed the bridge it said did not exist: TEST-25 computes a solar-system quadrupole moment in QUMOND, which is not possible without dynamics. What survives, and is the honest claim: the framework's field equation is postulated, not derived; the archive's own version (L1) is eliminated a priori; and writing the surviving one down changes none of the refutations, because all of them are driven by the shape of C and the B ≤ 3.17 ceiling. That is a narrower claim than “no dynamics exist” and a stronger one — it says the missing Lagrangian was never what was wrong. The plotter's quadrature form v(r) = √(vb² + [Vflat·C(ρ(r))]²) remains a plotting stand-in with no field equation behind it, and is labelled as such there. (Original note 2026-07-14, visitor Pass 3 + Pass 4; corrected 2026-08-09 after explorer 2026-08-08 found Appendix D and visitor Pass 3 + Pass 4 independently flagged the AQUAL/TEST-25 contradiction.)

Cosmological Tensions We Don't Address

A framework claiming cosmological scope should say explicitly where it is silent. The following are open problems in cosmology (2024–2026) where Synchronism makes no prediction:

Evolving dark energy (DESI DR2 w₀wₐ) — removed from the silence list: the framework has a dark-energy sector, and it forbids the quadrant DESI prefers. The research archive derived the sector on 2025-12-08 (Session 100, Modified Friedmann): H² = 8πGρm/(3C) with ρDE = ρm(1−C)/C. With the archive's arithmetic corrected (its published w(z) table carried a sign error and a dropped −1 term; the corrected weff(z=0) for γ=2 is −1.24, not the “> 0” the archive reported), the sector is a strict one-parameter family: C₀ = Ωm is forced, γ is the only knob, and w(z) runs monotonically from −2γ in the far past to exactly −1 in the far future, for every γ. That fixes sign(w₀ + 1) = sign(wₐ): the model approaches w = −1 from one side and can never cross it.

DESI DR2 (arXiv:2503.14738) prefers exactly a crossing — w₀ > −1 with wₐ < 0 — in all four of its data combinations. The framework's locus never enters that quadrant for any γ; forcing w₀ to match compels a wₐ of the wrong sign (offsets 3.4–5.4σ across the four combinations). Two honest bounds on that statement: (1) the γ = 1/2 branch is exactly ΛCDM (C ≡ Ωm(z) identically — the same algebraic degeneracy that makes γ = 1/2 MOND's simple μ in the galaxy sector), so it inherits ΛCDM's 2.8–4.2σ DESI tension and no more — “refuted by DESI” would be an over-claim. (2) The sign lock holds for the model as specified (Geff = G/C substituted into the Friedmann equation); a covariant completion would generate Ċ-terms that could in principle move the locus — that derivation is open. The refutation count does not change: nothing here is a new executed kill. What changes is scope — the framework is not silent on the dominant live anomaly in cosmology; it forbids it, which is a falsifiable, currently-disfavoured position adjudicable at DESI DR3 (~2027–2028). A kill-or-tie pre-registration (proposed TEST-26, adoption gating on the operator) is drafted on Top Decisive Tests.

Provenance: this entry stated the opposite (“C(ρ) contains no dark-energy sector”) from 2026-07-22 to 2026-08-11. That was a negative existence claim verified against only the compilation layer (SPINE/FUNDAMENTALS/PREDICTIONS/STATUS) — the derivation had existed in Research/ since December 2025. Standing rule adopted from the failure: negative existence claims must be verified against the primary derivation layer; compilation documents can establish presence, never absence. Full audit: explorer finding 2026-08-10; PREDICTIONS.md retraction 2026-08-10.

Explicit silence is more honest than tacit omission: these are open problems for Synchronism, not just unaddressed topics.

Self-Audit on the Self-Audit Protocol (A2ACW)

The adversarial self-audit (A2ACW) produced the 47 contributions and maintained the honest assessment. Two retrospective tests of the protocol's own limits were run in May 2026:

Temporal-Asymmetry Test (2026-05-18)

0 / 6 caught

6 claims later demoted (Born rule, wide-binary EFE [External Field Effect — MOND], galaxy rotation, decoherence formula, chemistry r=0.98, dual-C). A2ACW retrospectively tested: would the adversarial protocol have caught these? Result: 0 of 6. Median prior-art year for the demoted claims: ~1996. Two models sharing the same training corpus share the same blind spots.

Vocabulary-Asymmetry Test (2026-05-19)

4 / 6 caught

Pre-translating claims into modern vocabulary before adversarial review caught 4 of the 6 demoted claims. The 6 demotions decompose into three failure-mode classes: (1) prior-art rediscovery — 4 claims (Born rule/Zurek 2003, wide-binary EFE/Bekenstein-Milgrom 1984, galaxy rotation/MOND 1983, Γ=γ²(1−c)/Palma-Suominen-Ekert 1996); (2) internal-consistency tension — 1 (dual-C); (3) null-baseline deficit — 1 (chemistry r=0.98). Vocabulary asymmetry catches 4/4 on the prior-art sub-class; the 2 misses are different failure modes, not vocabulary failures.

A2ACW v2 implication: A complete adversarial protocol needs three axes: (1) vocabulary translation (catches prior-art rediscovery), (2) symbol audit (catches notation collisions — e.g., γ used as three incompatible quantities across the framework), (3) null-baseline computation (catches absence-of-evidence claims presented as positive evidence — e.g., r=0.98 on density-monotonic targets). Combined: 6/6 theoretical catch rate (self-simulated upper bound). See A2ACW Protocol →

Bottom Line

Synchronism is not a theory of everything. It's a research tool that maps density to coherence and sometimes produces useful insights. The coherence function works well as a classification tool (what regime is a system in?) but poorly as a predictive tool (what exactly will happen?). Its best results come from cosmology; its worst from condensed matter.

“All models are wrong; some are useful.” — Research Philosophy

Related Concepts

Why Synchronism?The question before the answerChemistry LimitationsMelting points (53% error), critical exponents (2× off)Research Philosophy"All models are wrong; some are useful"What Synchronism Is NotScope boundaries: not a TOE, not peer-reviewed, not original physics