Tier 1: Existing Data

Data: SPARC (175 galaxies)

Prediction: Rotation curve residuals correlate with local galaxy density

Kill: No correlation between residuals and environment at 2σ

⚠ Status note: Scope note: TEST-01 (SPARC residuals vs. density) and TEST-05 (RAR scatter vs. environment) test the same underlying prediction — environment-dependent RAR — on different samples. SPARC is higher-quality resolved curves (175 galaxies); ALFALFA-SDSS is larger statistical power (14,585 galaxies). These should be read as two phases of one test, not as two independent tests.

Data: Gaia DR3

Prediction: Wide binary anomaly depends on local stellar density: systems in LOWER-density environments should show STRONGER coherence-driven deviation from Newtonian dynamics. Mechanism: g_eff = g_N/C(ρ); lower ρ → smaller C → larger boost above Newtonian. [Sign corrected 2026-06-06; previous "higher-density → stronger deviation" was backwards.]

Kill: REWRITTEN 2026-06-12 (previous criterion predated the C(a)→C(ρ) fork and was inverted — it would have killed the framework for its own prediction coming true): a Gaia-confirmed MOND-scale wide-binary anomaly (~18% velocity deviation; Chae-type ~1.4× boost at low internal acceleration) in the clean sample REFUTES C(ρ), which predicts a Newtonian null (0.05–0.4%). A confirmed Newtonian null is consistent with C(ρ) but equally consistent with GR — survival without points, non-discriminating.

⚠ Status note: KILL BRANCH ADJUDICABLE NOW (2026-06-12): the refutation branch does not wait on future Gaia data — it waits on the published Gaia DR3 adjudication already in the literature: Chae (2023–2025) claims a MOND-like ~1.4× boost at low internal accelerations; Banik et al. (2024) claims Newtonian behavior excludes that boost at high significance, from the same data with different cuts. If the Chae side prevails, C(ρ) is refuted with existing data; if Banik holds, C(ρ) survives degenerately with Newton. Adjudication queued to the explorer track (proposal: test02_kill_branch_adjudicable_now.md). | SELF-ELIMINATING-OR-TIE (2026-06-07): This test has no outcome that favors Synchronism. If Gaia confirms the null (Banik 2024 / Pittordis & Sutherland 2023): that confirms Newton — Synchronism merely reproduces Newton here. If Gaia confirms ~18% anomaly (Chae 2023): that confirms MOND and refutes Synchronism-C(ρ) — Newton and Synchronism are refuted together. No measurement selects Synchronism over the standard alternatives. Additionally, 0.05–0.4% (C(ρ) prediction) is below current Gaia DR3 wide-binary systematics — practically untestable, not just difficult. | SIGN CORRECTION (2026-06-06): The prediction direction was reversed on this page from 2026-05-05 to 2026-06-06. The correct direction is lower density → stronger deviation (g_eff = g_N/C(ρ) gives low ρ → low C → larger boost). Both MOND+EFE and C(ρ) agree on this direction — direction is not a discriminator. The amplitude IS structurally distinct: C(ρ)-density form predicts ~0.05–0.4% velocity deviation (Newtonian null level) vs MOND ~18%; Gaia DR3 reach is ~80× insufficient. Substrate contingency: the anomaly's existence is actively disputed (Chae 2023 detects it; Banik 2024, Pittordis & Sutherland 2023, Saurabh 2024 do not). This is the third C(a)→C(ρ) fork: C(a) predicts the anomaly but is MOND-degenerate (refuted by SPARC RAR at ΔBIC=+184); C(ρ) is structurally distinct but predicts the Newtonian null. | DATA MILESTONE (2026-07-03): Gaia DR4 (~late 2026) will reset the wide-binary systematics floor and re-open the Chae/Banik adjudication on better data — the next scheduled event that could move this test. Clarifier: "adjudicable now" and "practically untestable" refer to different branches — the REFUTATION branch (Chae-type boost confirmed → C(ρ) dead) is adjudicable from published DR3 literature today; the CONFIRMATION branch (measuring the predicted 0.05–0.4% null as distinct from zero) is below systematics reach regardless. Adjudicable, but non-selecting.

Data: ALFALFA + SDSS (14,585 galaxies)

Prediction: TFR residual captures all intrinsic scatter (51% improvement)

Kill: TFR residual explains <20% of scatter

⚠ Status note: NEVER RUN AS REGISTERED — metric conflation (corrected 2026-07-09, closing the "presumptively failed" note below after independent citation-walks by the explorer track 2026-07-08 and two visitor personas 2026-07-09 converged on the same five errors). The R² = 0.14 figure previously shown here as TEST-03's result is not a valid measurement of the N = 14,585 ALFALFA-SDSS sample: at N = 14,585, R² = 0.14 implies t ≈ 48.7 (p of order 10⁻⁵⁰⁰), not the p = 5×10⁻⁶ quoted alongside it. The (R², p) pair is self-consistent only at N ≈ 130–175 — SPARC scale, i.e. the sample used by TEST-05, not TEST-03. Tracing the number further (archive S377/S381/S591): 0.14 is a Hubble-type/morphology term on N ≈ 171, not a measurement of environmental density on the 14,585-galaxy ALFALFA-SDSS cross-match; the registered environment-density correlation (classify by cluster/field/void, apply the <20% bar) was never executed. The 51% TFR-residual/BTFR prediction above (Session 593, N = 14,437) is a separate, already-passing result that this same card had been conflating with the failing 14% figure since 2026-04. Honest status update (2026-07-15): the registered environment-density test HAS NOW BEEN RUN (research repo, 2026-07-14, on SPARC RAR offsets vs Cosmicflows-4 densities): r² = 0.0001 — no environment dependence at the registered amplitude; the framework's environment prediction is refuted by execution, not by the old conflated statistic. See TEST-05 for the full adjudication. PROTOCOL DEVIATION, NOW DECLARED (2026-07-27, flagged independently by two expert visitor passes): the executed run is NOT the registered test, and this card has been carrying both statuses in one entry without saying which applies to what. The registered test was N = 14,585 ALFALFA-SDSS galaxies classified by cluster/field/void. What ran on 2026-07-14 was N = 141 SPARC galaxies against Cosmicflows-4 ambient density — a different dataset, a different density proxy, and a ~100× smaller sample. That substitution may well be the better measurement (Cosmicflows-4 gives a continuous distance-corrected density rather than a three-way classification), but on a program whose distinguishing methodological claim is pre-registration, swapping the sample and keeping the kill is exactly the move pre-registration exists to prevent. The substitute is therefore designated TEST-03s and adjudicated on its own terms; the registered TEST-03 remains NEVER RUN and is still runnable on ALFALFA-SDSS. The headline refutation census reads more honestly as 3 registered kills + 1 substituted-protocol kill. Both readings are shown rather than one being quietly chosen.

Data: DESI, SDSS DR17, Euclid

Prediction: [Withdrawn] BAO peak shifts ~10⁻⁴ between high/low-density regions

Kill: [Withdrawn] BAO identical everywhere to 10⁻⁵ precision

⚠ Status note: WITHDRAWN (2026-05-04) — Three converging failures: (1) The framework's own Session 107 (Dec 2025) explicitly forecasts BAO matches ΛCDM at 0.0% in all five DESI redshift bins — the sound horizon is set at z~1100 when C ≈ 1 everywhere, so no modification is possible. (2) The 10⁻⁴ number has no session-level derivation; it appeared only in compilation documents that drifted from the underlying sessions. (3) Standard nonlinear physics already produces ~6×10⁻² environment-dependent BAO shifts (600× larger); the kill criterion of 10⁻⁵ is 3000× below DESI Y3 precision. See /bao-coherence-modulation for full documentation. Replacement: TEST-04a (DESI RSD fσ8 suppression) — the test Session 107 actually predicts.

Derivation status →

Data: DESI DR1 (arXiv:2411.12021, Table 9 & 10)

Prediction: fσ₈(z=0.51) ≈ 0.418 — a ~12% suppression below ΛCDM (0.474). Mechanism: G_local/G_global = C_cosmic/C_galactic suppresses structure growth at late times. Session 107 forecasts 1.7σ–3.2σ discrimination per DESI LRG bin.

Kill: fσ₈(z=0.51) > 0.46 (rules out Synchronism at >3σ); fσ₈(z=0.51) > 0.45 disfavors at >2σ

Pre-registration status: Post-hoc retrodiction — σ₈ calibrated to lensing S₈ tension in Session 102; propagated to DESI fσ₈ in Session 107 (committed 2025-12-10); DESI DR1 published April 2024. Status (corrected 2026-07-14): disfavored 2.4σ on σ₈ (a different, GR-conditioned statistic); on the REGISTERED fσ₈ statistic the disfavor is only ~1.5σ against the >3σ the kill criterion demands — the criterion was not met as registered.

⚠ Status note: CORRECTED 2026-07-14: the kill criterion below is registered on fσ₈(z=0.51) > 0.46 for a >3σ ruling-out. Computed directly: LRG1 fσ₈ = (fσ₈)_fid × 1.16 ± 0.13 = 0.474 × 1.16 ± 0.062 = 0.550 ± 0.062 — exceeds 0.46 by only ~1.5σ, well short of the >3σ the criterion demands (it does clear the weaker >2σ "disfavors" clause at 0.45). The "Kill Criterion Triggered" claim in the 2026-07-02 reframe below was delivered on σ₈ = 0.841 ± 0.034, a DIFFERENT statistic inferred from a full-shape fit that assumes GR growth kernels — using a GR-conditioned amplitude to falsify a modified-growth model risks circularity (the EFTofLSS citation below already half-concedes a 1-2σ theory systematic on this exact number). DESI's own purpose-built modified-gravity analysis — Ishak et al., arXiv:2411.12026 (JCAP 09 (2025) 053) — gives μ0 = 0.11 (+0.45/-0.54) from DESI alone, tightening to 0.05 ± 0.22 with CMB+SN; a ~12% fσ₈ suppression maps to a μ0 inside DESI-alone's 1σ band (exact mapping not yet run — seeded as explorer topic). Honest reading: the test as registered lacked the power to discriminate this framework from GR. This does not rescue the framework's cosmology sector (the growth suppression was calibrated, never derived — CORRECTED 2026-08-09 from "no field equation sources a growth suppression": Appendix D §D.3 states effective Einstein equations G_μν = 8πG T_μν/C(ρ), committed 2025-12-01, which are cosmology-capable and have simply never been solved for the growth history; the gap is an unrun calculation, not a missing object. The σ₈≈0.76 vs 0.841 gap remains a real 2.4σ miss on that GR-conditioned parameter) — it corrects which statistic carries the kill and how confidently. PRIOR REFRAME (2026-07-02, superseded by the statistic correction above but the amplitude-vs-direction point still stands): post-hoc retrodiction — disfavored 2.4σ on σ₈ AMPLITUDE. DESI DR1 full-shape (arXiv:2411.12021) combined σ₈ = 0.841 ± 0.034 (Table 10) vs Synchronism's predicted σ₈ ≈ 0.76: the predicted suppression is absent; data ΛCDM-consistent. The load-bearing statistic is the ensemble amplitude, NOT direction: the LRG1 (z=0.51) fσ₈/(fσ₈)_fid = 1.16 ± 0.13 "enhancement" is a single ~1.2σ bin the DESI collaboration does not treat as robust, and the DR1 ensemble growth index γ_growth ≈ 0.58 ± 0.11 (above GR's 0.545) leans mildly toward suppression — the framework's own predicted direction. A "wrong direction" framing would be fragile against DR2; the amplitude framing is the defensible one. (Independently converged: 2026-06-24 explorer, 2026-07-01 explorer re-execution, 2026-07-02 + 2026-07-03 visitor Pass 4 researcher reads.) DR2 full-shape growth constraints remain unpublished (~Spring 2027). PROSPECTIVE REGISTRATION ADOPTED (dp, 2026-07-17 — the program's first genuinely prospective test; the pre-registration audit had found 0/10): all three DR2 outcomes are pre-committed IN WRITING before publication, adjudicated within 7 days, on the REGISTERED statistic (DR2 full-shape fσ₈ at z≈0.51, not σ₈): (A) fσ₈ ≤ 0.46 → registered criterion met by suppression direction, but the prediction remains post-hoc — confirmed-count stays 0; (B) fσ₈ > 0.46 at ≥3σ → the kill fires as registered, at registered power — the clean prospective refutation DR1 could not deliver; (C) between → "underpowered to discriminate" survives its own test and the row retires. No branch can be chosen after the data. (Research repo: PREDICTIONS.md, Bucket 1 registration block. This supersedes the narrower 2026-06-12 re-open policy below.) HISTORY — CORRECTED 2026-05-26 (previous 2026-05-25 "correction" was itself an error): LIKE-FOR-LIKE single-bin fσ₈ comparison: predicted fσ₈ ≈ 0.418; LRG1 observed fσ₈ ≈ 1.16 × 0.474 ≈ 0.55 — gap ~2σ (single-bin, qualified — see current verdict). SEPARATE σ₈ comparison: 2.4σ (ensemble, robust). These are two different observables — do not compare the 0.418 fσ₈ prediction to the 0.841 σ₈ observation directly. The 0.4497 ± 0.0548 figure cited in the 2026-05-25 edit belongs to arXiv:2512.03230 (DESI Peculiar Velocity Survey, z≈0.07) — a different survey misattributed to the z=0.51 full-shape slot. Note: the "mechanism-class sign reversal / transferable contribution" characterization is NOT restored — that was an overstatement; this is a post-hoc test. CONTEXT (2026-05-23): EFTofLSS analyses (Cabass, Simonović, Zaldarriaga et al. 2024-2025) explain DESI DR1 fσ₈ within ΛCDM at 1-2σ. CURRENCY (2026-06-11): this verdict is frozen at DR1 — DR2 growth has not been re-run against the kill criterion. RE-OPEN POLICY (2026-06-12): the verdict would unfreeze only if DR2 full-shape reported fσ₈(z≈0.5) ≤ 0.46 (back under the kill threshold). A DR2 value at or above DR1's would not change the verdict, only deepen it; no DR2 outcome can convert a post-hoc retrodiction into a prospective success. FRAMING: predicting σ₈ ≈ 0.76 in late 2025 was a bet that the S8 lensing tension (KiDS/DES) was physical; KiDS-Legacy and DESI full-shape have since moved against that camp. The failure is a documented bet on a tension that dissolved — which is what makes the mechanism-class reading (any coherence-damped growth-suppression framework sits in the same disfavored box) a statement about a real corner of the literature, not just this framework.

Data: SPARC + density catalogs

Prediction: RAR scatter shows NP2 environment dependence (p = 5×10⁻⁶)

Kill: RAR scatter independent of Hubble type / environment

⚠ Status note: RE-ADJUDICATED (2026-07-15): the "MOND-shared" tie assigned on 2026-07-09 dissolves on lever magnitude — the two frameworks' environment mechanisms couple to DIFFERENT variables, and their predicted effect sizes differ by orders of magnitude. MOND+EFE couples to external ACCELERATION (non-local): at SPARC outer radii (median g_bar/a₀ = 0.055) a typical external field (e_N ≈ 0.033, Chae 2020 median) modulates g_obs by ~0.09 dex — comparable to the full observed RAR scatter (~0.11 dex), which is why it is statistically detectable (Chae et al. 2020/2021, ~4σ, though disputed — Freundlich et al. 2022 and Paranjape & Sheth 2022 offer non-EFE readings in which ΛCDM-expected correlations mimic the signal). C(ρ) couples to ambient DENSITY added to local ρ (strictly local): even with the outer-disk density taken maximally low, the ambient contribution is a 4×10⁻⁵ (field) to 4×10⁻³ (δ~100 group) fractional perturbation, giving ~2×10⁻⁵ to 2×10⁻³ dex — roughly 50× smaller than MOND's lever at like-for-like environments and 2–4 orders of magnitude below the scatter. Undetectable. And the framework's OTHER galaxy law — C(a) on internal acceleration, the one TEST-09/10 actually use — predicts exactly ZERO environment dependence. Either law, a DETECTED environment dependence is specific evidence for the non-local coupling and unreachable by the framework's own mechanism: this is the locality no-go on the environment axis. AND THE REGISTERED RUN NOW EXISTS (research repo, 2026-07-14): per-galaxy SPARC RAR offsets vs distance-corrected Cosmicflows-4 ambient density (N = 141; instrument validated on 28 UMa cluster members) give r² = 0.0001 (p = 0.89) — ~900× under the framework's registered ">20% of scatter" claim; the kill bar (r² < 0.09) fires. The weak non-significant secondaries are OPPOSITE-signed (EFE-like, not Synchronism-like; Chae's detection uses a different estimator and is not contradicted). The execution and the structural adjudication agree: the framework registered an environment effect its own local mechanism cannot produce (predicted lever ~10⁻³ dex), and the data show none at its registered amplitude. S381's caveat resolved: the old R² = 0.14 signal was Hubble-type/morphology on N ≈ 171, not environment. HISTORY (2026-07-09): TEST-05's registered criterion is a null-independence test ("RAR scatter independent of Hubble type / environment"), and the p = 5×10⁻⁶ / R² = 0.14 result (N ≈ 130–175, SPARC scale — see the corrected TEST-03 note above) rejects that null on its own terms; the 07-09 pass reclassified it MOND-shared on the grounds that MOND+EFE predicts the same qualitative dependence — an argument that compared directions while neither side's amplitude had been computed. Script: explorer/scripts/test05_environment_lever_magnitudes.py.

Data: Future resolved rotation curves

Prediction: σ_int remains at 0.086 dex with larger sample

Kill: σ_int > 0.12 dex with N > 1000

⚠ Status note: UNDERPOWERED AS REGISTERED (marked 2026-07-17, before the data arrives, not after): the registered kill threshold (σ_int > 0.12 dex) sits inside the disclosed ~3× pipeline-dependence range below — either outcome would be attributable to velocity-definition choice, so the test cannot adjudicate anything until the registration fixes one velocity definition in advance. Pipeline-dependence caveat (2026-07-04): Lelli et al. 2019 (MNRAS 484, 3267) report BTFR orthogonal intrinsic scatter on the same galaxy population ranging 0.026–0.070 dex depending solely on which velocity definition is used (V_flat vs. W_P20 vs. V_max vs. V_2.2). A single-pipeline σ_int value is not a fixed target — the kill threshold should be read against that ~3× pipeline-dependent range, not as a precise number. See CDM Discrimination for the corrected CDM verdict (z = +0.5, CDM-consistent) this test is downstream of.

Data: SDSS, DES, DESI surveys

Prediction: [Exploratory] Galaxy cluster separations may show oscillatory modulation at λ ~ 500 Mpc

Kill: N/A — no amplitude derivation exists; no mechanism is specified; not falsifiable as stated

⚠ Status note: DEMOTED TO TIER-2 (executed 2026-07-07; flagged 2026-05-17): This does not qualify as a Tier 1 falsification test and no longer counts toward the Tier 1 inventory. The /cosmic-interference page itself states "Without a derivation, this is not a prediction in the scientific sense — it is an exploratory hypothesis." No amplitude has been derived from γ or ρ_crit. No mechanism is specified (sound-horizon shift? phase rotation? coherence interference?). No engagement with DESI 2024-2025 BAO results. No kill criterion is physically meaningful without an amplitude. The row is retained here, demoted in place, so the demotion is visible rather than silent — it is an exploratory hypothesis pending derivation, not a test.

Derivation status →

Data: SPARC surface brightness data

Prediction: Σ₀ emerges from first principles with <5% error

Kill: Derived Σ₀ differs from observed by >15%

⚠ Status note: RECLASSIFIED (see /honest-assessment): Σ₀ = cH₀/(4π²G) is the unique surface-density scale buildable from the cosmological constants c, H₀, G — the same dimensional identity class as a₀ = cH₀/(2π). Any framework that imports these constants recovers the same relation. The ≈4% agreement with Freeman's observed value (124 M☉/pc²) — corrected 2026-07-09 from a prior arithmetic error stating 110/12% — is consistent with dimensional analysis, not a framework-specific prediction, and is not independent of a₀'s own ~10% gap (Σ₀ = a₀/(2πG) exactly). Classified: Reparametrization — Dimensional Identity.

Data: SPARC (Lelli 2016 mass models, 123 galaxies after quality cuts)

Prediction: Computed from the framework's own formula (C(a) = Ω_m + (1−Ω_m)x/(1+x), boost capped at 1/Ω_m = 3.17): BTFR slope n = 3.35 ± 0.07. The previously listed "deep-MOND sample → n ≈ 4" limb is retracted — a bounded boost has NO deep-MOND regime. As g_bar → 0 the boost saturates at 3.17, a constant rescaling of G, which is Newtonian: the framework's deep limit is n → 2 (verified numerically: 2.01), the OPPOSITE end of the ladder from MOND's n = 4. MOND's n = 4 comes precisely from the √(a₀/g_bar) divergence a bounded boost cannot follow.

Kill: A single sample produces a BTFR slope inconsistent with its regime-mix prediction by > 0.3 — FIRED: deviation 0.41 (registered variable, same V_flat estimator applied to observation, MOND, and Synchronism alike). Threshold provenance: the >0.3 criterion in its operative wording was fixed 2026-04-24 (site commit 89825cf, restating the 2026-04-23 back-annotation) — eleven weeks before execution and before the bounded-boost analysis existed. Disclosed: that restatement changed the criterion's variable (band-universality → regime-mix deviation) while carrying the 0.3 magnitude over.

⚠ Status note: FAILED — KILL CRITERION FIRED (executed 2026-07-14 on real SPARC; MOND-shared flag RETRACTED). 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; deviation 0.41 > 0.3). Precision on the MOND comparison (added 2026-07-23, expert-review point): the 3.81 is MOND run through the same regime-mix fit pipeline as the other two slopes — a like-for-like differential, which is what the criterion adjudicates. MOND's PARAMETER-FREE deep-limit prediction is exactly n = 4 (M ∝ V⁴/Ga₀), and the observed 3.75 ± 0.10 sits ~2.5σ below that — mild tension with canonical MOND worth naming, and it sharpens rather than softens this card's verdict: Synchronism's 3.35 fails against both the fitted and the canonical MOND comparison. No parameters rescue it: at the framework's own Ω_m = 0.315 the best over all (φ, a₀) is 3.45 — the kill fires for every exponent; reaching 3.75 requires Ω_m → 0.001 and φ → 2, at which point the law degenerates algebraically to MOND. The honest parameter accounting (φ provenance audit, 2026-07-17): ONE derived ingredient (Ω_m, from cosmology) plus ONE fitted exponent dressed as a constant — φ is fitted-then-named (archive S45 adjudicated the first φ-sighting "intriguing coincidence, not significant"; the later "derivations" restate φ's defining identity x+x²=1 rather than derive it; see /parameter-derivations). A free exponent that still cannot reach the data is a deeper failure than a derived one — the no-rescue scan already covers every exponent value. OPEN ROBUSTNESS ITEM (flagged by two independent expert reviews 2026-07-18): the observed BTFR slope is velocity-definition dependent (Lelli 2019: V_flat vs W_P20 vs V_max spans roughly 3.0–4.1 — the same systematic this page cites on TEST-06), and the kill margin (0.41 vs 0.3) sits inside that range. The execution's defense is that the SAME V_flat estimator was applied to observation, MOND, and Synchronism — the adjudicated quantity is a differential under one consistent definition — but whether the differential stays above 0.3 under W_P20 and V_max has NOT been executed. RESOLVED — DEFINITION-ROBUST BY EXECUTION (2026-07-18, same-day run of the registered protocol under its pre-fixed verdict rule): all 11 adjudicated runs exceed 0.3 (minimum 0.32) — V_flat 0.44 ± 0.12; W_P20 across 8 generator/sample variants 0.32–0.61; V_max 0.56–0.72 with paired-bootstrap P(dev ≤ 0.3) ≤ 0.001. The observed arm reproduces Lelli 2019's per-definition slopes (V_max 3.47 vs 3.52; V_2.2 3.08 vs 3.06). Two disclosed caveats: (1) the point estimate is definition-robust but the SIGNIFICANCE is uneven — it is carried by V_max (P ≤ 0.001); V_flat alone is only ~1.2σ above threshold (P(≤0.3) = 0.11) and the W_P20 margin is thin (0.34 ± 0.10, P = 0.36); (2) exploratory inner-disc/single-point measures outside the registered outer-velocity scope (V_2.2, V_last: 0.25–0.28) sit under threshold — the kill is a statement about outer/flat rotation velocities, where the bounded boost binds. When citing this kill's strength, prefer the V_max form (0.72 ± 0.09) or pair it with TEST-10's definition-free ceiling violation (69% of galaxies exceed 3.17). MOND passes the same differential under every definition (max 0.20). Robustness script: explorer/scripts/test09_velocity_definition_robustness.py. The old "MOND-shared / cannot discriminate" badge was wrong in structure, not just in outcome: the BTFR is an asymptotic-boost observable, and boundedness — the framework's only feature distinguishing it from MOND — forces disagreement exactly there (this is a corollary of the boost-ceiling refutation on /honest-assessment). Provenance: archive S58 recorded the discrepancy honestly ("predicted n=2.75, observed n≈4"); S193 overwrote it with a synthetic 9-galaxy rescue asserting a deep-MOND limb the bounded formula cannot produce. S58 was right. Scripts: explorer/scripts/test09_btfr_bounded_boost_real_sparc.py, test09_parameter_scan_no_rescue.py.

Data: SPARC outer rotation-curve points (Q ≤ 2, i > 30°, N = 153)

Prediction: CORRECTED: the registered "DM fraction → 100% for M_bar < 10⁸ M☉" was never the framework's prediction — it is MOND's (unbounded ν). The framework's own bounded boost (B ≤ 1/Ω_m = 3.17) caps the apparent DM fraction at f_DM = 1 − C ≤ 1 − Ω_m = 68.5%, for every galaxy, at every radius, for every parameter choice.

Kill: As registered: "baryon-dominated dwarfs below 10⁸ M☉ exist." The kill fires in REVERSE: the framework dies at the DM-dominated tail its own ceiling forbids. Threshold provenance: the 68.5% ceiling needs no registration date because it is STRUCTURAL, not tuned — f_DM = 1 − C ≤ 1 − Ω_m = 0.685 (equivalently 1 − 1/3.17), fixed by the framework's own Ω_m = 0.315 with zero adjustable freedom. No choice made before or after the data could move it.

⚠ Status note: FAILED (executed 2026-07-15 on SPARC outer points; MOND-shared flag RETRACTED). LEAD REWRITTEN 2026-08-10 — this card previously led with the "69% exceed the ceiling" percentage while its own text, further down, said the surviving kill was "not the median-based percentage this card leads with." The page stated its lead was wrong and left the lead standing; a visitor Pass 4 then re-reported the convention-dependence as a new P0. The kill, stated in the form that survives every convention: SPARC's MAXIMUM observed outer f_DM = 0.927 requires a boost B ≥ 1/(1−0.927) = 13.7, and no candidate cosmic ratio supplies it — a class exclusion, B_max ≲ 14 is excluded by SPARC dwarfs. Everything below is the fuller accounting. Observed outer apparent DM fractions: median 0.755, max 0.927 — 106/153 = 69% of ALL SPARC galaxies exceed the framework's structural 68.5% ceiling ONLY under the underived convention B_max = 1/Ω_m (dwarfs below 10⁹ M☉: 67% exceed; the ten most DM-dominated galaxies are all impossible for the bounded boost while MOND matches them to a few percent — median residual f_obs − f_pred is +0.18 for Synchronism vs −0.03 for MOND). Beyond SPARC it is worse: pressure-supported dwarf spheroidals reach M_dyn/M_bar ~ 10²–10³ (Walker & Peñarrubia 2011 and subsequent dispersion-based mass modeling) against the framework's cap of 3.17. "A positive result confirms Synchronism and MOND equally" was wrong: MOND's boost is unbounded and accommodates near-100% fractions; the framework's cannot — this observable discriminates, and the framework loses it. Same structural root as TEST-09: both are corollaries of the boost ceiling. CEILING CONVENTION-DEPENDENCE (propagated from /parameter-derivations, flagged 2026-07-28 and independently re-confirmed by a 2026-07-29 visitor pass): B_max = 1/Ω_m has no derivation — no archive document connects it to the compander. A dynamical-to-baryonic boost more plausibly references the baryon budget Ω_m/Ω_b ≈ 6.40, giving f_DM,max ≈ 0.844, under which the reported MEDIAN (0.755) actually PASSES and the "69% of SPARC exceeds the ceiling" headline does not hold under this convention. The kill that survives regardless of convention is narrower and lives in the tail: SPARC's maximum observed f_DM = 0.927 requires B ≥ 13.7, which no candidate cosmic ratio supplies — a class exclusion (B_max ≲ 14 is excluded by SPARC dwarfs), not the median-based percentage this card leads with. Script: explorer/scripts/test10_dwarf_dm_fraction_ceiling.py.

Data: SPARC (2,807-point RAR, McGaugh 2016 pipeline) + Cassini spacecraft quadrupole bound on the Solar System

Prediction: The free-γ fit to SPARC converges to γ ≈ 0.489 (ΔBIC = +7.1 vs McGaugh, ΔBIC = +184.0 at the framework's fixed γ = 2). Applying the site's own Hill identity, tanh(γ·ln(1+x)) = [(1+x)^2γ − 1]/[(1+x)^2γ + 1], the fitted γ sets the compander's high-acceleration return exponent q = 2γ ≈ 0.98 — indistinguishable from MOND's SIMPLE interpolating function ν − 1 ∝ 1/y (q = 1). If the SAME scale-universal tanh-log compander is used as a QUMOND interpolation function for the Solar System, it makes a parameter-free prediction for the Cassini-bound post-Newtonian quadrupole.

Kill: Pre-registered (commit 9c77e7be): the SPARC-retained ΔBIC ≤ 10 grid interval (γ = 0.425–0.600) is incompatible with the signed, two-sided 95% Cassini quadrupole bound under every recorded BIC convention and external-field sensitivity — a robust empty intersection, not a boundary artifact.

⚠ Status note: FAILED — ROBUST EMPTY INTERSECTION (executed 2026-07-23, re-verified 2026-07-24; not yet on this site until today, though flagged independently by a 2026-07-28 visitor persona who thought it unregistered). At the SPARC optimum (γ = 0.489, profiled a₀ = 5.33×10⁻¹¹ m/s²) the Cassini discrepancy is +17.95σ; across the full ΔBIC ≤ 10 retained interval it spans +17.71σ to +18.00σ — the result is not an artifact of the best-fit point or a boundary. Zero survivors at every tested external-field strength (g_ext = 2.00×10⁻¹⁰ and 2.48×10⁻¹⁰ m/s², plus the legacy 2014 Cassini interval) and at every SPARC ΔBIC threshold (6, 10, 14). The framework's own fixed γ = 2 is separately excluded by SPARC alone (ΔBIC = +184) and cannot rescue the joint fit. Instrument self-validated: RAR checkpoints (γ = 0.489, ΔBIC values) reproduce the 2026-07-22 compander form-selection run exactly; mu-to-nu mapping error ≤1.4×10⁻¹⁰; quadrature convergence &lt;0.22% radial / &lt;0.006% angular on every accepted row. <strong>Scope, stated as narrowly as the result supports:</strong> this closes the realization "universal tanh-log interpolation used as a QUMOND modified-gravity function for both galaxies and the Solar System" — the SAME γ that fits SPARC cannot also satisfy planetary ephemerides. It does NOT directly test modified inertia, a non-gravitational engineering compander, system-dependent or multi-scale functions, dark-matter/hybrid models, or the Synchronism umbrella ontology — escaping requires changing the realization, not retuning γ inside it. PRIOR ART AND DISCRIMINATING POWER — ADDED 2026-08-09 (visitor Pass 4; this row previously cited only the two older papers below and never stated the consequence): this result is, to within the choice of interpolating-function family, <strong>Desmond, Hees &amp; Famaey (2024), MNRAS 530, 1781</strong>, who found the RAR&ndash;Cassini quadrupole tension at <strong>8.7σ</strong> for AQUAL and QUMOND with RAR-preferred interpolating functions (shape parameter δ ≈ 1; Cassini demands δ ≳ 2.5), and reported that the tension persists across all IF families they tested. Executed here 2026-07-23, two years later, without citing it. Three consequences the row must carry. (1) <strong>It is not a Synchronism-specific refutation.</strong> It excludes the RAR-preferred IF family in modified-gravity MOND; this framework inherits it by sitting in that family — at γ = 1/2 the compander is Milgrom's simple μ identically. (2) <strong>It is therefore non-discriminating between MOND and Synchronism</strong>, which is applied asymmetrically elsewhere on this site: TEST-09 and TEST-10 declare MOND the winner, while /galaxy-plotter draws its MOND reference curve with ν(y) = ½ + √(¼ + 1/y) — the simple-ν function, the exact object this test excludes. The squeeze applies to both or to neither. (3) <strong>The magnitude is ~2× the published figure</strong> (+17.95σ here vs 8.7σ there) because Desmond et al. marginalize over a₀, mass-to-light, and RAR-fit uncertainty while this computation fixes γ and profiles a₀ only — the same over-refutation signature as the ΔBIC = +184 effective-N inflation and the standalone a₀ &ldquo;8σ&rdquo;. Note the same paper also pre-empts TEST-02 (wide binaries). Related literature this squeeze operationalizes: Blanchet &amp; Novak (2011) supplies the quadrupole channel (Q₂ = (3±3)×10⁻²⁷ s⁻²) and Hees et al. (2016) previously showed MOND's simple-μ family is disfavored by planetary ephemerides for the same reason (slow high-acceleration return). Artifacts: Research/preregistrations/sparc_cassini_tanhlog/ (PREREGISTRATION.md, RESULT.md, joint_result.json), simulations/sparc_cassini_joint.py (Synchronism research repo).

Data: Coma cluster (X-ray gas + galaxy velocity dispersion mass estimates)

Prediction: [Closed] Four natural C(ρ)-to-apparent-mass ansätze were tried against Coma: A1 M_app/M_B = ⟨1/C⟩_vol; A2 M_app/M_B = 1/(1−⟨C⟩); A3 M_app/M_B = 1 + ∫Cρ dV/M_B; A4 M_app/M_B = 1/⟨C⟩_mass.

Kill: All four failed: A1 and A4 overshoot the observed mass ratio by 10⁴; A2 collapses to Newtonian (no boost at all); A3 is structurally bounded at ≤2 regardless of parameters, vs. the observed ratio of 4.6 — impossible by construction, not by fit.

⚠ Status note: CLOSED BY EXECUTION (2026-05-28, refined 2026-06-01 and 2026-06-09): the earlier framing here ("if [a bridge] exists in the archive, it is the last open door") is superseded — the bridge was built four ways and tested on Coma; all four fail. Root cause (2026-06-01): NOT one-scale insufficiency — MOND has exactly one scale (a₀) and only misses clusters by a factor ~2 (Sanders 2003). C(ρ) also has one scale (ρ_crit) and misses by 10⁴. The dominant cause is the WRONG VARIABLE: g_bar = G·M(&lt;r)/r² is non-local in ρ, so a function of local density cannot reproduce an acceleration-space law (the RAR) across systems of very different density profiles at matched acceleration. Novelty audit (2026-06-09): this is a quantified INSTANCE of Milgrom's non-locality theorem (astro-ph/0510117) — the discriminating axis is locality, not "density-based" per se, so non-local density constructions (Verlinde 2016's enclosed M_B(&lt;r), MOND-Σ) are not caught by this no-go. See /for-researchers and /honest-assessment for the full derivation; explorer/findings/cluster-bridge-impossibility-coma.md, cluster-bridge-wrong-variable-not-one-scale.md, and density-compander-nogo-is-milgrom-nonlocality-instance.md for the computation.