Tier 1: Existing Data

Data: SPARC (175 galaxies; 141 with Cosmicflows-4 environment in the executed run)

Prediction: Rotation curve residuals correlate with local galaxy density

Kill: No correlation between residuals and environment at 2σ — met by the 2026-07-14 run (per-galaxy SPARC RAR offsets vs Cosmicflows-4 density: r² = 0.0001, p = 0.89, N = 141)

Killed by the same run, not a separate failure: That run is this card's SPARC phase, so the SPARC phase is not open. TEST-05 carries the lever-magnitude adjudication of the same run. The verdict is filed once, on TEST-03s.

⚠ Status note: Scope note (corrected 2026-09-14): TEST-01, TEST-03s and TEST-05 all test one prediction, environment-dependent RAR, and all three were answered by one SPARC run. Read them as one test, not three. The large-sample phase has never been run: the registered TEST-03 on ALFALFA-SDSS (14,585 galaxies classified cluster/field/void). (See revision notes.)

Data: Gaia DR3

Prediction: AS REGISTERED (superseded in substance; read the status below): wide binary anomaly depends on local stellar density: systems in LOWER-density environments should show STRONGER coherence-driven deviation from Newtonian dynamics. WHAT IT ACTUALLY PREDICTS for the registered wide/close ratio: γ_g ≡ 1 identically under density keying (the boost is shared by both members and cancels), so no density dependence survives the statistic; the kill was rewritten on 2026-06-12, after Chae 2023 and Banik+2024 were public, so that text is post-data. Mechanism: g_eff = g_N/C(ρ); lower ρ → smaller C → larger boost above Newtonian. [Sign corrected 2026-06-06; see revision notes.]

Kill: READ FIRST: the criterion below is written for a calibration no other page uses. At every density-keyed calibration on file the branch already fails existing data before Gaia: at the published knee ρ_crit = 0.029·V² the boost at the Sun is ~3.5×10⁴ in g (Oort limit, that knee only); at the knees where the Gaia ratio is null it fails lunar laser ranging (68/74 laws, all 8 of this card's windows) and SPARC (ΔBIC +2843). The acceleration branch's wide-binary boost is TEST-25's physics (see the status note). So what TEST-02 can still deliver is a γ interval for the acceleration branch, not a kill of anything live. Whether the density-branch exclusion becomes its own ledger row is the project lead's call; the count stays 6. | REWRITTEN 2026-06-12 (see revision notes): 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 (γ_g ≡ 1 in the ratio; the older 0.05–0.4% figure is knee-conditional, see revision notes). A confirmed Newtonian null is consistent with C(ρ) but equally consistent with GR — survival without points, non-discriminating. | WHICH MODEL MAKES THE 0.05–0.4%: the DENSITY-keyed branch C(ρ/ρ_crit), but only at a knee between 3.8×10⁻⁵ and 3.2×10⁻⁴ M☉/pc³ (γ = 0.489), a window no other page uses. At the published knee ρ_crit = 0.029·V² the solar-neighbourhood density sits far below the knee, so C ≈ γx ≪ 1 and, with g_eff = g_N/C, the boost is maximal: about 3.5×10⁴ in g, excluded by the Oort limit at that published knee (a knee-specific statement: the site-wide "refuted at the solar Oort limit" was retired 2026-09-09, because at the knees the galaxy fits use the Sun does not close the sector) (arithmetic in the 2026-09-10 note under the alert). That is the same branch SPARC refutes head-to-head (ΔBIC +2843, archive 2026-08-24). The ACCELERATION-keyed branch that fits SPARC is μ_simple(x/2) at γ = ½ and predicts MOND's wide-binary boost, EFE included — on that branch TEST-02 was never a discriminator. And "MOND ~18%" is the EFE-INCLUDED figure (corrected 2026-09-24; until then this line called it EFE-free): with the Milky Way external field (~1.8 a₀), AQUAL/QUMOND + EFE give a 1.0–1.4× boost in g depending on treatment, i.e. up to ~18% in velocity (√1.4 ≈ 1.18), which is the entire Chae (2023–25) vs Banik et al. (2024) dispute. Without the EFE the boost would be several times larger. State the range, not the point.

⚠ Status note: The current wide-binary dispute, which decides what a DR4 result means for MOND and the acceleration-keyed compander alike (abstracts read 2026-10-29): Banik et al. 2024 (MNRAS 527, 4573; arXiv:2311.03436) find Gaia DR3 wide binaries "fully consistent with Newtonian gravity" and exclude MOND at 16σ; Chae 2024 (arXiv:2309.10404, accepted to ApJ) finds an observed-to-Newtonian acceleration ratio of 1.49 (+0.21/−0.19) below about 10⁻¹⁰ m/s². The disagreement is about sample purity and modelling, not about the framework. A Newtonian null would kill the compander and MOND together; a Chae-type boost near 1.4 pins γ ≲ 1, where Cassini already fails (2026-10-06 squeeze). — SMOOTHING SCALE (stated once, 2026-10-27): the identically-null density-branch ratio needs the ambient density smoothed on a length far above 10⁴ AU, and the Ġ/G rate kill below uses 1–10 pc; both hold at 1–10 pc, which is also the length the galaxy fits need. | READING USED: the acceleration-keyed C_g as a QUMOND interpolating function, with the Milky Way's external field included. The "EFE = 0 exactly" on other pages holds only for the algebraic density-keyed reading, which gives this card's identically null density-branch ratio, not its boost. | CURRENT STATUS (2026-10-06; corrects the 2026-09-27 "each outcome spares one branch", caught by a simulated-visitor researcher persona): neither branch is waiting on Gaia. (Scope, added 2026-10-30 from a simulated-visitor researcher persona: this covers the two branches analysed on this card, acceleration-keyed with the Galactic external field and the density branch. The external-field-free corner γ ≈ 0.87–0.95 that survives at galaxy level on the TEST-25 card is a third reading, and Gaia does bear on it. A maintainer estimate, not an execution (algebraic, isolated binary, a₀′/γ held at 1.1×10⁻¹⁰ m/s²; maintainer/scripts/efe_free_corner_boost_across_the_chae_bin.py) puts its boost in g at 2.70 / 2.12 / 1.88 / 1.67 / 1.49 for an internal Newtonian acceleration of 0.2 / 0.36 / 0.5 / 0.7 / 1.0 ×10⁻¹⁰ m/s². Chae 2024's 1.49 (+0.21/−0.19) is a value for the whole bin below about 10⁻¹⁰, so the offset runs from 0σ to +5.8σ depending on where in the bin the systems sit. Until 2026-11-09 this card quoted one point of that curve as "about 3σ"; a σ needs the bin's g_N distribution, which has not been used. The trend is a better observable than the level: this reading rises as g_N falls and external-field-dominated MOND levels off. It is far above the Newtonian null of Banik et al. 2024 at every point. It has not been run against binned wide-binary data. The same corner is disfavoured at ~3σ by globular clusters, conditional on the mass model (Δχ² = +54 ± 19); see the TEST-25 card.) ACCELERATION branch: at the γ SPARC prefers (≈ 0.489) it is already failed through TEST-25, and the wide-binary boost comes from the same physics — the same ν, the same QUMOND field equation, the same Milky Way external field (≈ 1.8 a₀). A Chae-type boost therefore rescues nothing; a Newtonian null would add a second failure, shared with MOND's simple μ. Within the one compander family the three data sets each pick a γ (order-of-magnitude bracket, quasi-1D external-field-dominated, not pre-registered): UPDATED 2026-11-06: the quasi-linear QUMOND point-mass solution gives the asymptotic boost as ν_e(1 + L_e/3): 1.38–1.53 at γ ≈ ½, 1.15–1.26 at γ = 1, 1.05–1.13 at γ = 2, 1.03–1.09 at γ = 3 (Galactic field 1.6–2.2×10⁻¹⁰). A Chae-type 1.4–1.5 maps to γ ≈ 0.4–0.64; a precise 1.1–1.2 to γ ≈ 0.8–2.7; a Newtonian null excludes only the γ whose boost exceeds 1 + 2σ. And no γ is Cassini-passing any more: with a₀ taken from SPARC at each γ, Cassini fails at 14.5–19.3σ for every γ from 0.3 to 3 (the earlier wording was "Cassini-passing γ ≈ 1.5–2", withdrawn: it came from a scan holding a₀ fixed). So the acceleration-keyed family is already closed by SPARC × Cassini whatever DR4 shows; DR4 can only say which closed member it resembles, and no outcome can move Bucket 0 (scripts: maintainer/scripts/wb_qumond_monopole_boost_vs_gamma.py, cassini_q2_at_sparc_profiled_a0_high_gamma.py; superseded bracket wb_boost_vs_gamma_efe_bracket.py; research proposal wide_binary_row_is_not_split_cassini_and_dr4_squeeze_one_gamma_20261006.md, gates on the project lead). DENSITY branch: the Gaia statistic γ_g is a ratio of wide to close binaries drawn from one volume, so the ambient boost 1/C cancels and γ_g ≡ 1 exactly — identically null, not "below reach". The branch is excluded by other routes: SPARC head-to-head (ΔBIC +2843) and lunar laser ranging (next note). The count stays at 6. Older notes that said "practically untestable", "0.05–0.4%", or "each outcome spares one branch" are kept below as revision history. | DENSITY BRANCH EXCLUDED BY A RATE, NOT THE AMPLITUDE (explorer 2026-09-23; pre-registered at site commit 80b8c9c before the script): the "practically untestable" below is true only of the static 0.05–0.4% amplitude. A boost shared by everything in one neighbourhood cancels in a same-instant ratio, but not in time: the Sun moves through the disc and past nearby stars, so G_eff = G/C(ρ) drifts today. At density smoothing ℓ = 1–10 pc (what the galaxy fits need), the density-keyed knee grid predicts Ġ/G ≈ 10⁻⁸ to 10⁻⁵ per year, and these very 0.05–0.4% windows 7×10⁻⁹ to 6×10⁻⁸, against lunar laser ranging's Ġ/G = (7.1 ± 7.6)×10⁻¹⁴ yr⁻¹ (Hofmann & Müller 2018; error convention as published, not re-read here; the exclusion was computed with the bound loosened 13×, so a 1σ-vs-3σ reading does not change it). 68 of 74 laws are excluded, all 8 of this card's windows among them. The survivors are Newtonian to 10⁻⁸ at the Sun. This holds under L2 and L3 alike: with the smoothing kernel inside the action the field equation is unchanged, so the bound carries over exactly (explorer 2026-10-19, pre-registered edb0108). What L3 adds is a striction force sourced by the Sun's own self-energy, which acts on the planets as a repulsive Λ-like term and closes the small-smoothing hole (ℓ below ~0.3 pc) for 21 of 32 γ = 0.489 laws. This is a second, SPARC-independent root for the existing density-keyed kill (ΔBIC +2843), not a seventh refutation; whether it becomes a ledger row is the project lead's call. It does not touch the acceleration-keyed branch. Finding: explorer/findings/density-keyed-C-is-a-moving-G-lunar-laser-ranging-excludes-it-at-pc-smoothing.md. | 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 (see the current status above for what it can and cannot move). 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.

Data: ALFALFA + SDSS (14,585 galaxies)

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

Kill: TFR residual explains <20% of scatter

Primary card for the 2026-07-14 environment run (FAILED, counted once): the substitute TEST-03s, 141 SPARC galaxies against Cosmicflows-4 density, gave r² = 0.0001 (p = 0.89) against Session 177's kill bar r² < 0.09. This is the one card that carries that verdict, matching Honest Assessment's ledger row. TEST-01 and TEST-05 were killed by the same run and point here, so count one failure, not three. The registered ALFALFA-SDSS TEST-03 is still never run.

⚠ Status note: NEVER RUN AS REGISTERED — metric conflation (corrected 2026-07-09; see revision notes). 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 result, not the 14% figure. It does not count toward Bucket 0 and is not a framework prediction: Session 593 itself finds the predictor "IS MOND's TFR in disguise" (the TFR residual used as a mass-to-light proxy), and the 51% comes from coefficients re-fitted on the same i-band data (in-sample; the SPARC-trained coefficients give 16%). Wording "already-passing" retired 2026-10-09 after a graduate-physics visitor read it beside the 0-confirmed headline (conflation corrected 2026-07-09; see revision notes). 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 lever-magnitude adjudication. PROTOCOL DEVIATION, NOW DECLARED: the executed run is NOT the registered test. 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. RECONCILIATION (2026-09-11; see revision notes): Honest Assessment's "run as registered" and this card's "never run" are both true, of different registrations. The 2026-07-14 run IS run-as-registered against the Session 177 RAR-environment claim (environment explains >20% of RAR scatter; kill bar r² < 0.09), and is a substitute (TEST-03s) against this card's ALFALFA TEST-03. The claim and the kill bar bracket an undecided band, 0.09 ≤ r² < 0.20, where neither verdict fires; the old R² = 0.138 would sit inside it, and the measured 0.0001 is below both. The research ledger files this run as "TEST-08"; on this site TEST-08 is the Freeman-law card. That ID collision is routed to the operator; this card keeps TEST-03s.

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 ShapeFit+BAO, LRG1 row (ratio 1.09 +0.12/−0.14); Table 11 fiducial (0.4733); Table 10 σ₈

Prediction: fσ₈(z=0.51) ≈ 0.418 — a ~12% suppression below ΛCDM (0.473, DESI DR1 Table 11 fiducial). 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. [Provenance, added 2026-09-14: the 0.418 comes from Session 107's G_local/G_global = C_cosmic/C_galactic growth suppression, with σ₈(z=0) = 0.76 calibrated to S₈ in Session 102. The background-only dark-energy sector now on /dark-energy does not produce it. That sector's own growth forecast is ≈ −0.22% (0.10σ, ΛCDM-like), so this card tests a mechanism the current framework no longer contains. Three readings of how C enters growth give 0.418 (this card), ≈ 0.473 (dark-energy fluid) and 0.575 (uniform G/C, which enhances growth), so the sign is a modelling choice: /dark-energy#growth-readings (2026-10-07). The uniform reading is excluded by existing ISW, lensing and S₈ data (explorer 2026-10-07), so no live growth reading differs from ΛCDM at DR2 precision; retiring this card as a discriminating test gates on the project lead.]

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: disfavored 2.4σ on σ₈ (a different, GR-conditioned statistic). On the REGISTERED fσ₈ statistic the prediction sits ~1.5σ from the data and the data clear the 0.46 threshold by ~0.9σ (numbers corrected 2026-10-10), against the >3σ the kill criterion demands, so the threshold is crossed on the point estimate but not at the registered significance (see the three numbers above).

⚠ Status note: READ THIS FIRST (2026-10-12): the predicted 0.418 rests on Session 107's C_cosmic/C_galactic growth suppression, a mechanism WITHDRAWN in the archive on 2026-08-11. Put that next to two facts already on this card: the adopted DR2 kill (branch B) fires with under 1% probability if ΛCDM is true, and no live growth reading of the current framework differs from ΛCDM at DR2 precision (the uniform G/C reading, 0.575, is already excluded by ISW, lensing and S₈; the fluid reading is ΛCDM to 0.2%). Together: DR2 cannot test the current framework through this card. It can only retire the row (branch C) or embarrass a withdrawn mechanism. "The program's first genuinely prospective test" below describes the 2026-07-17 registration act, not a live test of anything the framework now contains. Retiring the card as discriminating gates on the project lead (routed 2026-10-07). Current verdict: NOT FAILED AS REGISTERED. The prediction misses on σ₈ only: disfavored 2.4σ on σ₈ AMPLITUDE (a GR-conditioned statistic, not the registered one); on the registered fσ₈(z=0.51) the prediction sits ~1.5σ below the data and the data exceed the 0.46 threshold by ~0.9σ (bar: 3σ); UNDERPOWERED AS REGISTERED; post-hoc retrodiction either way; not counted as a refutation. The adopted DR2 kill (branch B) fires with under 1% probability if ΛCDM is true (2026-09-21, below). LRG1 fσ₈ = (fσ₈)_fid × ratio = 0.4733 × 1.09 (+0.12/−0.14) = 0.516 (+0.057/−0.066), DESI DR1 Table 9 (ShapeFit+BAO) and Table 11, read verbatim 2026-10-10; the three numbers above are computed from this. CORRECTED 2026-10-10: from 2026-05-26 until today this card and eight other pages used a ratio of 1.16 ± 0.13, which is Table 9's QSO row (z = 1.49), not LRG1. A researcher simulated-visitor persona asked to see the table value quoted directly, which exposed it. Every σ on this card shrank; the verdict (underpowered as registered, not counted) did not change in kind, and the weaker "> 0.45 disfavors at > 2σ" clause is no longer met either. The "Kill Criterion Triggered" claim of the 2026-07-02 reframe (revision notes) 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: 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. 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 = 1.09 (+0.12/−0.14) "enhancement" (corrected 2026-10-10 from the QSO-row 1.16 ± 0.13) is a single ~0.6σ 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. DR2 full-shape growth constraints remain unpublished (~Spring 2027). PROSPECTIVE REGISTRATION ADOPTED (project lead, 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.) BRANCH B AS ADOPTED CANNOT FIRE UNLESS ΛCDM ALSO FAILS (maintainer 2026-09-21, from a simulated-visitor researcher persona; arithmetic in maintainer/scripts/test04a_dr2_branch_power.py): 0.46 is already the prediction plus 3σ of a forecast error (0.418 + 3 × 0.014), and branch B then asks for another 3σ at the measured error, i.e. obs > 0.46 + 3σ_DR2 ≈ 0.55–0.57, which puts ΛCDM (0.473) itself ~2.5σ low. If ΛCDM is true, branch B fires with under 1% probability at any σ_DR2 between 0.025 and 0.045, while branch A (≤ 0.46, the framework-friendly wording) fires 30–38% of the time. The clean reading, (obs − 0.418)/σ > 3, would fire 4–22% of the time; a single bin needs σ ≈ 0.015 to separate 0.418 from 0.473 with real power, so Session 107's own five-bin table is the statistic worth co-registering. The source forecast σ at this bin is 0.018, not 0.014. DR2 galaxy full-shape is still unpublished, so re-registering is still prospective. Changing a registration the project lead adopted GATES ON THE PROJECT LEAD (proposal test04a_dr2_branch_b_cannot_fire_reregister_before_data_20260921.md). Until it changes, read branch C as the near-certain outcome, and do not read branch A as support. 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. 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 at the registered amplitude: Session 177 says environment explains > 20% of RAR scatter, with a kill bar of r² < 0.09. [Corrected 2026-09-14; see revision notes.]

Kill: RAR scatter independent of Hubble type / environment

Killed by the same run, not a separate failure: r² = 0.0001 (N = 141, 2026-07-14). The kill bar fires, but this card is not a second environment failure. The status note below keeps the lever-magnitude adjudication. The verdict is filed once, on TEST-03s.

⚠ 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 (r = +0.012, p = 0.89), with a 95% upper limit of r² ≈ 0.03: about 3× under the kill bar (r² < 0.09) and about 6× under the framework's registered ">20% of scatter" claim; the kill fires. The registration does not say which scatter. Read against total scatter, as the bar is, that margin stands. Read against intrinsic scatter (~0.057 of ~0.13 dex), a 20% share is only ≈ 0.04 of total variance, and the upper limit excludes it narrowly; the r² < 0.09 bar would then be the wrong bar. (Rough: per-galaxy offsets have their own noise budget.) The weak non-significant secondaries are OPPOSITE-signed (EFE-like, not Synchronism-like; Chae's detection uses a different estimator, and this statistic has no power against it: MOND+EFE predicts r² ≈ 0.001 here). 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. (Earlier 2026-07-09 classification: see revision notes.) Script: explorer/scripts/test05_environment_lever_magnitudes.py. | WHERE THIS NULL SITS IN THE LITERATURE: the r² = 0.0001 environment null lands directly on the Rodrigues, Marra, del Popolo & Davari (2018, Nature Astronomy) claim that a₀ varies across SPARC galaxies, and on the rebuttals by McGaugh, Li, Lelli & Schombert (2018) and Kroupa et al. (2018) arguing the apparent variation is a fitting/uncertainty artifact. This null is consistent with the rebuttals — a universal a₀, no environmental modulation at the 10⁻⁴ level — which makes it the nearest thing on this site to a positive contribution: a bound on a density-tracked environment effect, not a framework confirmation. It is not a test of MOND's external field: propagated through this same estimator and proxy, full-strength MOND+EFE predicts r² ≈ 0.001, and only r² ≈ 0.036 through a perfect acceleration proxy, against this run's 95% upper limit of about 0.03 (explorer 2026-09-05; a persona's rough estimate of 0.014–0.14 on 2026-11-09 ran higher because 90% of the effect's variance goes into a channel degenerate with luminosity). Read against an acceleration proxy, the same offsets carry the external field's sign at amplitude 0.6 ± 0.3 of its prediction: 2σ from zero, not a detection.

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: WHAT 0.086 IS (2026-10-24, explorer 2026-10-23): σ_int = 0.086 is not a BTFR scatter. It is the residual of an in-sample photometric mass model and is independent of V: shuffling the rotation velocities across galaxies leaves it at 0.0870 against 0.0864, so velocity adds 0.0006 dex. The quantity this card registers therefore does not test the baryonic Tully–Fisher relation, and the CDM comparison it was downstream of is withdrawn on /cdm-discrimination. Like for like, the plain inverse BTFR on the same sample gives 0.073 dex in log V (an upper bound) against abundance matching's 0.064 (Desmond 2017, log V). | 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 CDM comparison this test was downstream of (its 2026-07 "CDM-consistent, z = +0.5" verdict was suspended 2026-10-09 and the statistic is not a BTFR scatter, 2026-10-24).

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 — EXPLORATORY, NOT YET FALSIFIABLE (a readiness label, not a cost tier: this stays a $0 item and is not on the Tier 2 pilots page; relabelled 2026-09-11, see revision notes) (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, see revision notes) 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. [Read this as the slope of the capped law through the radii SPARC actually sampled, not as an asymptotic prediction: the capped law has a Keplerian deep limit and no BTFR of its own, so the number depends on where SPARC stopped observing, and the ± 0.07 is the fit error at that sampling. Which acceleration, stated 2026-09-14: the TEST-09 and TEST-10 scripts evaluate C explicitly at the baryonic acceleration, with x = (g_bar/a₀)^(1/φ), a₀ = 1.05×10⁻¹⁰ m/s², and g_obs = g_bar/C(g_bar). There is no implicit solve in g_obs. The RAR-shape fits on /galaxy-rotation are the ones solved implicitly in g_obs. The 3.17 cap holds under either keying, because C ≥ Ω_m for every x ≥ 0.] 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 Keplerian, with rotation curves that fall as 1/√r where MOND's stay flat. MOND's n = 4 comes precisely from the √(a₀/g_bar) divergence a bounded boost cannot follow. [Precision, 2026-09-25, simulated-visitor graduate-physics persona: the older wording here, "deep limit n → 2 (verified numerically: 2.01)", holds only for a sample measured at one common radius. A Keplerian law has no radius-independent BTFR slope: for measurement radii R ∝ M^α it gives n = 2/(1−α), so n ≈ 3 for real disc radii (α ≈ 0.3–0.4), and n = 4 if each galaxy is read where g_bar falls to a fixed value (α = ½). What is radius-independent is the declining curve shape. The verdict does not move: the 3.35 above was computed at each SPARC galaxy's real measured radii.]

Kill: A single sample produces a BTFR slope inconsistent with its regime-mix prediction by > 0.3 — FIRED at B_max = 1/Ω_m: deviation 0.41 (convention-dependent: the 2026-09-18 ceiling sweep finds it does not fire at (Ω_m−Ω_b)/Ω_b, |Δn| = 0.297 against a strict > 0.3, or at Ω_m/Ω_b, 0.26, so it does not survive its own pre-fixed rule; convention-free, a bounded-boost law with B_max ≲ 5.3 is excluded by the SPARC BTFR slope; whether it stays in the count of 6 is pending the project lead; see the status note) (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: AS σ-DISTANCES: the registered rule (> 0.3) has no error term, so each candidate is also given as (n_obs − n_pred)/σ, with n_obs = 3.75 ± 0.10 and errors combined in quadrature: 1/Ω_m 0.406/0.124 ≈ 3.3σ; (Ω_m−Ω_b)/Ω_b 0.297/0.118 ≈ 2.5σ; Ω_m/Ω_b 0.260/0.116 ≈ 2.2σ (unrounded script output, re-run 2026-10-30; these read 3.4σ / 2.6σ until then, from a σ rounded to 0.12). Both slopes come from the same galaxies, so quadrature is an approximation. MEASURED 2026-11-05 (explorer, pre-registered at c9ff6ab): resampling the 123 galaxies once per draw and refitting both slopes gives a correlation of only +0.14, a paired σ 7% smaller than quadrature, and 3.6σ / 2.8σ / 2.5σ (σ 0.112 / 0.106 / 0.105). The 3.3 / 2.5 / 2.2 above are the quadrature reading. These answer a different question from the registered one: they test whether the prediction differs from the data at all, not whether it differs by more than 0.3. Under a zero-tolerance 2σ separation (a different rule from the one the count uses, which asks whether the 0.3 threshold itself is excluded at 2σ: margin 0.95σ paired, so it drops TEST-09) all three candidates fire; under 3σ only 1/Ω_m does (paired or quadrature); under the registered rule the kill is convention-dependent. The verdict below is the registered one, and which rule the count uses is pending the project lead. | CEILING-CONVENTION SWEEP EXECUTED (2026-09-18, site maintainer; closes the TEST-09 half of the registered Branch 1 of Research/proposals/boost_ceiling_provenance_and_class_exclusion.md, unrun since 2026-07-27). THIS KILL IS CONVENTION-DEPENDENT, like TEST-10's. The ceiling enters as the floor of C(a) = C_min + (1−C_min)x/(1+x); the site sets C_min = Ω_m, i.e. B_max = 1/Ω_m = 3.175, which no archive document derives. Re-running TEST-09's own pipeline — same cuts, same V_flat estimator, same bootstrap, identity control reproducing the published n = 3.35 ± 0.07 exactly — across the registered candidate ceilings: B_max = 3.175 (1/Ω_m) gives n = 3.35, |Δn| = 0.41, FIRES; B_max = 5.389 ((Ω_m−Ω_b)/Ω_b) gives n = 3.456, |Δn| = 0.297, DOES NOT FIRE (the registered threshold is a strict >0.3; this misses it by 0.003, so the verdict is decided at the third decimal; the |Δn| = 0.300 edge falls at B_max ≈ 5.31); B_max = 6.389 (Ω_m/Ω_b, the baryon budget) gives n = 3.49, |Δn| = 0.26, DOES NOT FIRE. Per the pre-fixed verdict rule (the kill stands iff it fires under every candidate), TEST-09's kill does NOT survive the sweep. Both discriminating galaxy-sector kills are therefore convention-dependent on the same undefended number, and the honest statement of this one is a class exclusion: a bounded-boost law with B_max ≲ 5.3 is excluded by the SPARC BTFR slope, which is the TEST-09 analogue of TEST-10's class bound from SPARC dwarfs (caps to ≈ 7.5 excluded at 3σ per disc). COUNT UNCHANGED PENDING REVIEW — whether a convention-dependent kill still counts in the "6 refutations" headline is the recount question the proposal gates on the project lead (open question 4), and this run supplies the number, not the decision. Pre-registered at site commit 89e0467 before the script was written; maintainer/scripts/which_C_carries_the_floor.py (+ _PREREG.md, _output.txt). | THE "FLOOR BINDS EVERYWHERE, SO THIS TEST IS ALGEBRA" READING IS REFUTED (same run). A 2026-09-18 simulated-visitor researcher pass argued from /galaxy-plotter's "max C on this disk: 0.001" that the Ω_m floor binds at every radius on every disc, so the galaxy sector applies a constant 3.17, so TEST-09's slope was forced before execution (a constant boost shifts a BTFR intercept, never a slope). The persona flagged it as needing a source check first. It fails on the premise: the plotter draws the DENSITY-keyed C_ρ = tanh(γ ln(1+ρ/ρ_crit)), which carries no floor, while TEST-09/TEST-10 evaluate the ACCELERATION-keyed C_a, whose floor is part of its functional form. On 123 real SPARC discs C_ρ's per-disc maximum is indeed tiny (median 1.2×10⁻³ at γ = 2; 0/123 reach Ω_m) — so the plotter's number generalises — but C_a C_a itself runs 0.329–0.954 over the same 2,856 radii (123 discs; per-radius median 0.515), with 0.00% of them within 1% of the floor and an applied boost of 1.05×–3.04× that never reaches the ceiling. The corollaries fail with the premise: the predicted f_DM is not a delta at 0.685 (one value per disc at its outermost radius, N = 123: median 0.585, s.d. 0.062, no galaxy within 0.01 of the cap; a different sample from the per-radius C_a median, which is why 1 − 0.515 ≠ 0.585), and the slope is not ceiling-independent (it moves 0.62 across B_max ∈ [2, 100] — which is exactly why the convention sweep above has a result at all). Logged here at the same prominence a confirmed finding would get: the over-refutation share of corrections rose from 1/20 to 9/24 between May and August 2026, and visitor-supplied refutations are inside that denominator. | EXPONENT CHECK: at the registered a₀ = 1.05×10⁻¹⁰ it does not. Exponent 1 gives n = 3.348 against 3.346 for 1/φ, and the kill fires the same way. At exponent 1 with its own cH₀·Ω_m a₀ = 2.06×10⁻¹⁰, n = 3.285. But with a₀ retuned freely, exponent 1 reaches n = 3.50 at a₀ ≈ 1.6×10⁻¹¹, a deviation of 0.25, under the 0.3 threshold. So the "no rescue for any φ ∈ [1.2, 4]" scan does not extend to φ = 1 with a₀ free, although that a₀ sits 6.5× below the registered value. The ceiling root (B ≤ 1/Ω_m) does not depend on the exponent. Script: maintainer/scripts/test09_exponent_one_instead_of_inverse_phi.py. | 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: the predicted slope is excluded at 3.3σ from the data; the registered criterion |Δn| > 0.3 is met on the point estimate (0.41), ~1σ above threshold under V_flat alone (P = 0.11), and robust under V_max (P ≤ 0.001). The three numbers above give the detail. 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. 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(g_bar) ≤ 1 − Ω_m = 68.5% (C evaluated explicitly at g_bar; see TEST-09), 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 (restated 2026-09-11): the 68.5% figure is fixed by Ω_m = 0.315 once the normalization B_max = 1/Ω_m is chosen — but that normalization is itself underived (Ω_m/Ω_b ≈ 6.4 is the other candidate), so it is a choice. What does NOT depend on the choice: the most dark-matter-dominated SPARC disc (f_DM = 0.927) needs B = 1/(1 − 0.927) = 13.7, above both 3.17 and 6.4 — the refutation survives either convention. What does depend on it: under 6.4, with SPARC's distance, inclination and M/L errors propagated (profiled, one-sided, all radii; explorer 2026-10-29), 6 of the 28 face-value exceeders stay above the cap at 2σ and 3 at ≥ 3σ (NGC 2915, NGC 3741, UGC 06667). ESO 444-G084, listed with NGC 3741 as the M/L-free pair until 2026-10-30, drops to 1.65σ once its 32 ± 6° inclination is propagated. The surviving exclusion is conditional on the gas census: multiplying the gas by 2.0 removes NGC 3741 and by 3.1 removes NGC 2915 (dark-gas proposals reach ×2–3; Pfenniger & Revaz 2005). A uniform factor that large is disfavoured, because BTFR residuals stay independent of gas fraction only for c ≤ 1.25 at Υ* = 0.5 (≤ 1.75 at 0.7; galaxy bootstrap, 95%). Gas that is hidden differently in each galaxy is not excluded. So lead with the tail, not the percentage.

⚠ Status note: LENSING, THE STRONGER FORM (added 2026-09-25; first set out by the explorer 2026-09-02 and left off this card until now; conditions added 2026-11-10). Two conditions travel with the lensing leg. (1) It assumes light follows the same effective potential that moves stars, as it does by construction in AeST and TeVeS; this framework has no light-deflection rule (see For Researchers), so the leg is a statement about completions that have one. (2) The "×5 on the baryons" is this site's own allowance for every cosmic baryon inside the lensing radius, not a number from Brouwer et al. 2021, whose fiducial g_bar "only takes into account the stellar and cold gas mass" (their footnote 3); their own footnote allows hot gas, dust and missing baryons to raise g_bar by up to about an order of magnitude at the outer edge, and at ×10 the most permissive cap (6.39) passes at 10⁻¹⁴ and fails only at 10⁻¹⁵, where the isolation criterion is least reliable. So the leg settles the TEST-09 convention question only under (1), and the census condition recorded on 2026-10-04 is the paper's own. Galaxy–galaxy weak lensing reaches accelerations rotation curves cannot. The KiDS-1000 lensing RAR (Brouwer et al. 2021, A&A 650, A113) follows the extrapolated MOND branch to g_bar ≈ 10⁻¹⁵ m/s², where the required boost is ~110 at 10⁻¹⁴ and ~350 at 10⁻¹⁵. Even with a 0.3 dex allowance below that branch and every cosmic baryon hidden inside the lensing radius (×5 on the baryons), the requirement at 10⁻¹⁴ is 11, which is 1.7× the most permissive candidate cap (Ω_m/Ω_b = 6.39) and 3.5× the site's 3.17. The kill rests on the two lowest bins, 0.4–4 Mpc from the lens, where isolation cuts and neighbouring haloes are the live caveats. A mass-dependent ceiling does not help: the explorer's best ε₀(M) relation gives B_max = 4–18 across 10⁹–10¹¹ M☉, 6–87× short. Script: maintainer/scripts/lensing_ceiling_every_convention.py. The six refutations in one table: /honest-assessment#refutation-ledger. | FAILED (executed 2026-07-15 on SPARC outer points; MOND-shared flag RETRACTED). The kill, stated in the form that survives every convention on SPARC alone: SPARC's MAXIMUM observed outer f_DM = 0.927 requires a boost B ≥ 1/(1−0.927) = 13.7, and no ratio built from Ω_m (1/Ω_b = 20.3 clears it on SPARC and is excluded by the weak-lensing RAR at 10⁻¹⁵ m/s², 2026-09-25) supplies it — a class exclusion: at face value caps up to 13.7 are exceeded, and with nuisances propagated caps up to ≈ 7.5 are excluded at 3σ for one disc (≈ 5.7 after a 153-disc trials correction). 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 simulated-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. 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 (Υ frozen at 0.5, points unweighted) 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 [empty only with the points treated as independent; see the convention note], not a boundary artifact. | CONVENTION NOTE (2026-09-29): every recorded BIC convention treated the 2,807 points as independent; with the galaxy as the replication unit (measured N_eff ≈ 150) the ΔBIC ≤ 10 retained interval is γ = 0.3–1.7, and the compander passes Cassini post-hoc at γ ≳ 1.5–2, so the in-house intersection is empty only under point independence. [Withdrawn 2026-11-06: that pass held a₀ fixed at 1.03×10⁻¹⁰; with a₀ from SPARC at each γ Cassini fails at 14.5–19.3σ for every γ from 0.3 to 3, so the intersection is empty at galaxy level too.] The defensible content is the published, marginalized 8.7σ (Desmond, Hees & Famaey 2024), which marginalizes the per-galaxy nuisances this pipeline holds fixed. | TWO GALAXY-LEVEL γ INTERVALS, TWO STATISTICS: γ = 0.3–1.7 is the registered statistic, the ΔBIC ≤ 10 retained band recomputed with N = N_gal = 166 and the nuisances (Υ, D, i) frozen. The γ̂ ≈ 0.6 [0.43, 0.95] on /galaxy-rotation is a different object: a 95% galaxy-bootstrap interval on the free-fit γ̂, with Υ, D and i profiled per galaxy (explorer gamma2_pin_nuisance_refit, the σ_int = 0.034 arm). [Corrected 2026-11-06: the next three sentences are withdrawn. With a₀ taken from SPARC at each γ, Cassini fails at 14.5–19.3σ for every γ from 0.3 to 3, so the galaxy-level intersection is empty too and TEST-25 does not depend on the convention.] Under the registered rule at galaxy level the intersection with the (withdrawn) Cassini-passing γ ≳ 1.5 is not empty (about γ = 1.5–1.7), so the in-house kill fires only with points as independent. The published 8.7σ (and Park et al. 2026, 3–15σ) covers this family near γ ≈ ½, not the 1.5–1.7 tail. So TEST-25 depends on the same convention as the γ = 2 pin, and the count range on /honest-assessment#count-rule now lists it (−1 at galaxy level).

⚠ Status note: TEST-25 status (2026-11-08). Published, for MOND's own slowly-transitioning functions: 1.9–15σ depending on mass model and sample (Desmond, Hees & Famaey 2024: 8.7σ fiducial, 1.9σ with M/L freedom and bulge galaxies removed; Park et al. 2026: 3–15σ). In-house, for this compander with a₀ refit to SPARC: 14.5–19.3σ for every γ from 0.3 to 3 with M/L pinned at Υ = 0.5/0.7 (13–18σ without bulges; the γ = 0.3 row is solver-limited to about ±6σ). Those σ values track the M/L prior (at γ = 3, about 10σ with Υ free per galaxy at 0.1 dex and about 7σ at 0.2 dex), so the number that travels is the M/L each family needs in order to pass. MOND's sharpest member tested (δ = 6, no bulges) passes at Υ_d ≈ 0.54, near stellar-population values, at about 1.8σ on SPARC. The compander needs Υ_d ≈ 1.2–1.4, more than twice that, which makes 36–42% of discs over-maximal and costs 2.9σ on SPARC at γ = 3; at γ ≤ 1 it does not pass for any Υ_d up to 1.5, and neither does McGaugh's RAR function. So the root is shared with MOND at δ = 1 / γ ≈ ½, and the family-wide failure is the compander's own. Earlier "2σ edge" and "narrow, not empty" statements compared against a Cassini pass that held a₀ fixed; both were superseded on 2026-11-06. READING USED: the acceleration-keyed C_g as a QUMOND interpolating function, with the Milky Way's external field included. The "EFE = 0 exactly" on other pages holds only for the algebraic density-keyed reading, which this card does not use. | FAILED, INHERITED FROM MOND, CONDITIONAL ON A MODIFIED-POISSON COMPLETION. The number this site stands behind is the published, marginalized 8.7σ (Desmond, Hees & Famaey 2024); the 2026 update with the newer Cassini value gives 3–15σ depending on the galaxy mass model (Park, Hees, Famaey, Desmond & Durakovic 2026, PRD 114, 024066). That bound is computed for QUMOND/AQUAL-type modified-Poisson theories; modified-inertia MOND evades it, and the framework has not fixed its own force law (see the wiring note on /coherence-function). The framework's only written field equation, ∇·[C∇Φ] = 4πGρ, is of the modified-Poisson type, so the inheritance holds for it; it would not bind a modified-inertia reading nobody has written. WHICH γ: the published 8.7σ is for the RAR-preferred interpolating functions, i.e. this family near γ ≈ ½. The family's fast-return tail (q = 2γ > 1) was said to pass Cassini post-hoc at γ ≳ 1.5–2; that held a₀ fixed. With a₀ taken from SPARC at each γ it fails at 14.5–19.3σ for every γ from 0.3 to 3 (2026-11-06), with M/L pinned; see the status line at the top of this card for what happens when M/L is freed. WHICH KEYING: the squeeze applies to the acceleration-keyed C_g only. The density-keyed C_ρ has no Cassini quadrupole of this kind; it meets its own Solar-System problem in the interplanetary-medium test (GM☉ from Earth and Saturn differ at O(1), 2026-09-15). (Executed 2026-07-23, re-verified 2026-07-24; propagated to this site 2026-07-28, see revision notes.) WHICH CHANNEL: the Cassini quantity is the external-field-induced quadrupole Q₂ of QUMOND (predicted: Blanchet & Novak 2011; measured: Hees et al. 2014, updated Park et al. 2026). The in-house instrument computes it as Desmond, Hees & Famaey 2024 do (their Eq. 12, the phantom-density integral with the Galactic external field), not from the function's asymptotics. Q₂ is set by the interpolating function's shape through the transition region, near the Sun's MOND radius (~7,000 AU, where g ~ a₀ ~ g_ext), not by its far tail at Saturn's orbit. McGaugh's ν, whose far tail is exponentially Newtonian, fails the same pipeline by +15.9 to +20.9σ, which shows the far tail is not the channel. Why the inheritance is a family property: in this compander one γ fixes the shape everywhere, so the γ SPARC prefers (≈ ½, the simple μ) also fixes the transition-region shape Cassini measures, and any one-parameter family with that tie is squeezed. Families with a separate transition-sharpness parameter (Hees et al. 2016) can escape. q = 2γ is the asymptotic label of that same γ, not the mechanism. (Until 2026-10-13 this paragraph credited the high-acceleration return exponent q = 2γ as the channel.) DIRECT TAIL, A SECOND SOLAR-SYSTEM LEG (computed by the explorer 2026-10-15): the compander's power-law return to Newton adds an anomalous pull at the planets themselves, independent of the external field. On EPM2011 supplementary perihelion precessions (Pitjeva & Pitjev 2013; values in mas/cy, the paper prints mas/yr) it excludes γ < 0.87 at 3σ (Saturn binds: γ = 0.489 predicts −9,576 against −0.32 ± 0.47 mas/cy); INPOP15a's conservative full-refit interval gives 0.78. Reading × test: acceleration-keyed with EFE fails Q₂ at every γ from 0.3 to 3 once a₀ comes from SPARC (the γ ≳ 1.5 pass held a₀ fixed), and needs γ ≳ 0.87 for the tail; a reading with EFE = 0 has no Q₂ test but still needs γ ≳ 0.87. The EFE-free corner, one status (2026-11-09): alive, disfavoured, not novel. It is the acceleration-keyed compander at γ ≈ 0.87–0.95, read algebraically with no external field effect. Cassini's quadrupole test does not reach it, because Q₂ is the external field's effect; the direct perihelion tail sets its floor of γ ≳ 0.87. It costs about 1.2σ on SPARC at galaxy level and about 3σ on globular clusters (Δχ² = +54 ± 19 against Newton, conditional on the mass model). It has no field equation: it is an algebraic fit, and a modified-inertia reading would have to be non-local in time. It differs from MOND with its external field only the way MOND without one does, so keeping or losing it cannot move Bucket 0. Gaia DR4 can kill it: its boost keeps rising as the internal acceleration falls (estimate: 1.49 at 1.0×10⁻¹⁰ m/s², 2.70 at 0.2×10⁻¹⁰), where external-field-dominated MOND levels off. Not yet run against binned wide-binary data. Its next adjudicators are the SPARC EFE detection (Chae et al. 2020) and binned wide binaries, not Cassini. GLOBULAR-CLUSTER DETAIL (explorer 2026-10-30, pre-registered at site 012ca7c; corrected here 2026-10-31): refit per law (tidal radius, anisotropy and mass free, 0.25 dex prior on the photometric tidal radius; 28 clusters), the external-field-free compander at γ = 0.9 costs Δχ² = +54 ± 19 against Newton (2.9σ; +93 ± 32 with β ≤ 0), and simple μ without EFE +71 ± 23. The statistic cannot see γ: cluster outskirts sit in the deep regime, where only a₀′/γ enters. So this is the disfavouring of MOND without an external field, inherited, not a test of the compander's shape. (The 2026-10-30 version of this sentence said "closed", 10.6σ behind MOND+EFE and 10.8σ behind Newton. Those were paired differences of residuals, in which the observed slope cancels exactly: they measured model separation, not data preference.) Caveats as for the GC table: L2/algebraic, isolated, Newton-fitted mass models, no escapers or anisotropy. Script: maintainer/scripts/gc_row_differences_cluster_bootstrap.py (+ _PREREG.md, _output.txt). | INHERITED FROM MOND: the defensible headline is the published, marginalized 8.7σ for the RAR-preferred interpolating functions (Desmond, Hees & Famaey 2024), which belongs to the function family MOND also uses, not to this framework alone; McGaugh's ν fails this site's pipeline by +15.9 to +20.9σ. This site's own run is unmarginalized: 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), all scored with points as independent. The framework's own fixed γ = 2 is separately disfavoured by SPARC (ΔBIC = +184 with the 2,807 points as independent; ≈ +11 scored by galaxy, 1.6–2.2σ, 2026-09-29: at the threshold, not decisive). So "γ = 2 cannot rescue the joint fit" holds only under point independence; at galaxy level the γ ≳ 1.5–2 tail is not a rescue either: with SPARC's a₀ it fails Cassini (2026-11-06; see WHICH γ above). (Sentence corrected 2026-10-14; until then it read "separately excluded by SPARC alone", which the 2026-09-29 galaxy-level run had already withdrawn. Simulated-visitor researcher persona.) 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 <0.22% radial / <0.006% angular on every accepted row. Scope, stated as narrowly as the result supports: 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 (simulated-visitor Pass 4; see revision notes): this result is, to within the choice of interpolating-function family, Desmond, Hees & Famaey (2024), MNRAS 530, 1781, who found the RAR–Cassini quadrupole tension at 8.7σ 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) It is not a Synchronism-specific refutation. 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) It is therefore non-discriminating between MOND and Synchronism, 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. (2b) MOND's own functions fail on this same instrument (pre-registered maintainer run, maintainer/scripts/cassini_q2_mond_interpolating_functions.py): McGaugh's RAR ν = 1/(1−e^−√y), the δ = 1 member of the δ-family, fails by +15.9σ to +20.9σ; Milgrom's simple ν by +15.3σ to +20.1σ; the compander at the SPARC fit, +17.95σ. The grid is a₀ ∈ {1.128, 1.20}×10⁻¹⁰ with the three registered external fields. With a₀ held at McGaugh’s value, no δ-family member enters the Cassini 95% interval below δ = 4. With a₀ refit to SPARC at each δ, none up to δ = 6 enters (δ = 4: +9.2σ, at a SPARC cost of ΔBIC +466, about 3σ at galaxy level); without bulge-dominated galaxies δ = 6 reaches +3.0σ at +164 (explorer, 2026-11-06). The compander falls only to 13–18σ on that cut (2026-11-07). So the inheritance is literal: the function MOND fits the RAR with is excluded as hard as the compander. (3) The magnitude is ~2× the published figure (+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 “8σ”. Note the same paper also pre-empts TEST-02 (wide binaries). Related literature this squeeze operationalizes: Blanchet & Novak (2011) computed the QUMOND prediction for the quadrupole channel; the measured bound Q₂ = (3 ± 3)×10⁻²⁷ s⁻² is from Cassini radio tracking (Hees, Folkner, Jacobson & Park 2014, PRD 89, 102002; citation corrected 2026-10-15 after a simulated-visitor researcher persona flagged it), updated to (1.6 ± 1.8)×10⁻²⁷ s⁻² with DE440 by Park, Hees, Famaey, Desmond & Durakovic (2026, PRD 114, 024066), who put the rotation-curve tension at 3–15σ depending on mass modelling; the in-house squeeze already scores against the 2026 value (sparc_cassini_joint.py carries both); 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: DESI DR3 BAO + CMB distance priors + supernovae (not yet released)

Prediction: The framework's dark-energy sector (a Cardassian-class modified Friedmann equation, H² = 8πGρ_m/(3C)) runs monotonically from w = −2γ toward −1, so sign(w₀+1) = sign(wₐ). On DESI DR2 the fit sits at ΛCDM's corner: γ = 0.487 (−0.021/+0.024), Δχ² = −0.3 for one extra parameter. It lands there by construction: the region DR2 prefers (w₀ > −1, wₐ < 0; 3.1σ for DESI + CMB, 2.8–4.2σ adding supernovae) is the one the sign lock forbids, so the best fit pays ΛCDM's own price, Δχ² ≈ +11 behind w₀wₐCDM. "At ΛCDM's corner" means "no better than ΛCDM", not "consistent with DR2's preferred region".

Kill: Fires if DR3 robustly requires thawing or crossing behaviour (the region the sign lock forbids). Because the family contains ΛCDM exactly at γ = ½, that outcome also excludes ΛCDM, so the kill is shared with ΛCDM. The one non-Λ outcome (freezing away from Λ) is Cardassian-class prior art (Freese & Lewis 2002), so no branch moves the confirmed-novel count off zero.

⚠ Status note: How close DR2 already is (DESI DR2 Results II, arXiv:2503.14738, abstract read 2026-10-29): the w₀wₐ fit favours the quadrant w₀ > −1, wₐ < 0, preferred over ΛCDM at 3.1σ for DESI BAO + CMB and at 2.8–4.2σ when supernovae are added, depending on the sample. That quadrant is the region the sign lock forbids (thawing, and crossing if w₀ + wₐ < −1). Central (w₀, wₐ) values are in the paper's tables and were not re-read here. A DR3 that holds this preference at higher significance fires the kill, and ΛCDM falls with it. — PROPOSED, NOT REGISTERED. Listed here because the Test Roadmap numbers it in the Tier 1 namespace; it is outside the 24 original tests and outside every tally on this page. Full card, branches and history on Top Decisive Tests.

Full TEST-26 card on Top Decisive Tests →

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; see revision notes): 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(<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(<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.