Glossary

Milgrom's acceleration constant: a₀ = cH₀/(2π) ≈ 1.08×10⁻¹⁰ m/s².

In MOND, this is a fundamental constant. In Synchronism, it EMERGES from cosmology — it's the Hubble acceleration divided by 2π. This is one of Synchronism's strongest results.

Protocol where AI agents stress-test each other's claims.

One agent defends a claim, another demands operational definitions and falsification criteria. Produces falsifiable test cards and forces precision.

Currently in active research focus; being extended or revised.

MRH-relationship badges describe how a claim sits in the current research inventory, preferred for in-flight work. Active-MRH means the claim is under live investigation. At the current stewardship stage nothing is honestly characterizable as "established," so verdict-shaped tags like Validated are avoided.

A model-selection score balancing fit quality against the number of parameters. Lower AIC = better model.

AIC = 2k − 2·ln(L), where k is the number of free parameters and L is the maximum likelihood. Unlike BIC, AIC does not penalize parameters as strongly (uses 2k not k·ln(n)). AIC favors models that fit well; BIC also penalizes complexity more. In the Synchronism context, running AIC across the compander family (tanh, Hill/Naka-Rushton, logistic, erf, μ-law) would determine whether the tanh choice is informative or arbitrary. This comparison has not yet been run.

A cross-matched catalog of ~15,000 galaxies combining 21-cm HI gas masses (ALFALFA) with optical properties and environment metrics (SDSS).

ALFALFA (Arecibo Legacy Fast ALFA) mapped HI 21-cm radio emission from nearby galaxies, providing gas masses and rotation widths. Cross-matching with SDSS gives stellar masses, star formation rates, and large-scale environment metrics. The combined ALFALFA-SDSS catalog was used to test Synchronism's environment-dependent RAR scatter prediction (TEST-03). Result: R² = 0.14, below the pre-registered kill criterion of R² > 0.20 — the test failed.

Closed audit finding on a historical track; durable negative result; does not move.

Audited-Negative is the strongest closure badge. It means an explicit audit found the claim false, contradicted by data, or internally inconsistent — and this finding is a permanent part of the record. Examples: A-from-Jeans (closed 2026-06-07: Session 66 script gives A≈4.6×10⁻⁵, 600× off under the framework's own scaling); RAR γ=2 (ΔBIC=+184, rejected).

A characteristic spacing (~150 Mpc) imprinted in galaxy distributions by sound waves in the early universe.

Before the universe cooled enough for atoms to form, matter and light were coupled in a hot plasma. Sound waves propagated through this plasma, and when atoms formed (at "recombination"), these waves froze in place. Today, galaxies are preferentially spaced ~150 Mpc apart — a "standard ruler" used to measure the universe's expansion history. Synchronism's TEST-04 predicts a ~10⁻⁴ shift in this spacing between high- and low-density environments.

Protons, neutrons, and everything made of them — the ordinary matter you can touch.

"Baryonic matter" means ordinary matter (atoms, stars, gas, dust) as opposed to dark matter or dark energy. About 5% of the universe's total energy content is baryonic. When galaxy rotation pages mention "baryonic mass" or "baryon density," they mean the mass of ordinary visible matter — the stars, gas, and dust you can actually observe.

The standard theory of conventional superconductivity: electrons form Cooper pairs and condense into a macroscopic quantum state.

BCS theory (Bardeen, Cooper, Schrieffer 1957) explains how phonon-mediated attraction causes electrons to form bound pairs (Cooper pairs) below a critical temperature T_c. Above T_c, electrons behave independently (low coherence). Below T_c, they condense into a macroscopic quantum state with high coherence. In Synchronism's γ Calculator, BCS superconductors are placed in the "Collective" regime with N_corr ≈ 10⁷ (pairs per coherence volume) — but this is a back-fit, not a forward prediction from BCS theory itself.

A state of matter where bosons occupy the same quantum ground state below a critical temperature, forming a macroscopic quantum object.

A Bose-Einstein Condensate (BEC) forms when bosons (integer-spin particles: photons, He-4 atoms, Cooper pairs) are cooled below a critical temperature T_c. Unlike fermions, bosons can occupy the same quantum state, allowing a macroscopic fraction to condense into the ground state. BEC is highly coherent — N_corr is the entire condensate (10⁶–10⁹ atoms). In Synchronism's γ Calculator, BEC is placed in the "Collective" regime, which is correct (high N_corr, classical in Synchronism's non-standard usage). Note: Synchronism uses "Classical" to mean high-coherence collective behavior — the opposite of the standard physics usage.

A model-selection score that penalizes free parameters. Lower BIC = better model given data. ΔBIC > 10 is strong evidence against the weaker model.

BIC = k·ln(n) − 2·ln(L), where k is the number of free parameters, n is the number of data points, and L is the maximum likelihood. The ΔBIC between two models quantifies the evidence in favor of the model with lower BIC. By convention: |ΔBIC| < 2 = negligible evidence, 2–6 = positive evidence, 6–10 = strong evidence, >10 = very strong evidence. In the Synchronism context, the unanswered question is: does C(ρ) achieve a lower BIC than (a) a polynomial of similar order, (b) the MOND RAR interpolating function, or (c) other sigmoid companders (logistic, Hill, erf)? This comparison has not yet been run.

The quantum mechanics rule that measurement probabilities equal |ψ|² — the squared amplitude of the wave function.

Standard quantum mechanics: if a system is in state ψ = α|0⟩ + β|1⟩, the probability of measuring outcome "0" is |α|² and "1" is |β|². The Born rule is an axiom of standard QM — it cannot be derived from the Schrödinger equation alone without additional assumptions. Synchronism's /born-rule page attempts to derive it from coherence conservation, but the page's own verdict: "no worse than Zurek's envariance, no better" — the derivation is a Reparametrization. No experimental deviation from |ψ|² is predicted.

The standard formula describing a particle resonance: probability amplitude ∝ 1/[(E−M)² + (Γ/2)²], where M is the rest mass and Γ is the decay width.

The Breit-Wigner distribution gives the probability that a particle resonance is observed at energy E, given a true mass M and total decay width Γ. The narrow-width approximation (Γ ≪ M) is the standard condition for a stable resonance appearing as a sharp peak in cross-section data — equivalent to the Källén-Lehmann spectral condition in QFT. Synchronism's entity criterion (Γ < m) is this narrow-width condition. The connection to the PDG resonance catalog: real resonances satisfying Γ < m appear as sharp peaks; borderline cases (σ/f₀(500), ρ(770)) sit at Γ ≈ M. The entity criterion adds an ontological interpretation (entities "exist" only when Γ < m) rather than a new mathematical condition.

Empirical power-law between a galaxy's total baryonic mass and its flat rotation velocity: M_bar ∝ V_flat^n.

The BTFR is one of the tightest empirical relations in galaxy dynamics: baryonic mass (stars + gas) scales as a power law of the asymptotic flat rotation velocity. The slope n depends on the sample regime: n → 4 in deep-MOND galaxies (SPARC-dominated), n ≈ 2.75 for transition-regime full samples (Synchronism Session 193), n → 2 near-Newtonian. Lelli et al. 2019 found n = 3.85 ± 0.09 for the SPARC deep-MOND-dominated sample — consistent with the regime-dependent prediction. The BTFR is a textbook MOND signature; a positive result would be consistent with both MOND and Synchronism.

Maps presence to coherence: C(ρ) = tanh(γ ln(ρ/ρ_crit + 1)). A sigmoid/compander function, not an order parameter.

The central equation of Synchronism. Takes presence (ρ) — the density of compatible structural elements within a Markov Relevancy Horizon — and returns a coherence value between 0 and 1. Physical density (g/cm³) is one form of presence, but presence also encompasses temperature, energy levels, catalytic surfaces, and other factors that support emergence.

Note: ⚠ Physicist note: C is NOT quantum phase coherence. Quantum-coherent systems (BEC, BCS, superconductors) sit at LOW C because they have large N_corr → small γ. C measures density-driven collective ordering, the opposite of the standard CM usage.

How collectively a group of elements behaves, from sparse/independent (0) to dense/collective (1).

Low coherence (C→0): elements act independently — sparse matter, individual particles. High coherence (C→1): extremely dense, tightly packed systems — neutron stars, not superconductors. ⚠ Terminology note for physicists: Synchronism uses "coherence" to mean density-driven classical ordering, NOT quantum phase coherence. Quantum-coherent systems (BEC, BCS superconductors) have large N_corr → small γ → LOW C in this framework. C=0 does not mean "incoherent" in the quantum sense; it means sparsely interacting. The key physics is density and collective behavior, not quantum-vs-classical character.

Note: ⚠ Physicist terminology note: Synchronism "coherence" is NOT quantum phase coherence. In condensed matter, quantum-coherent systems (BEC, BCS superconductors) are maximally quantum-coherent — but they have large N_corr → small γ → LOW C in this framework. C=0 does not mean "incoherent" in the CM sense; it means sparsely interacting. C measures density-driven collective behavior, the opposite of the standard quantum-coherence usage. See also: C(ρ) entry, Mean-Field Theory entry.

A sigmoidal function that maps a wide dynamic range onto a bounded output — the mathematical class C(ρ) belongs to.

A compander (compressing + expanding) maps a large input range to a bounded output via a smooth sigmoidal curve. The name comes from audio compression: μ-law companding (telephone networks) uses tanh to compress loud signals without clipping quiet ones. The same class appears across disciplines: Hill function (biochemistry: oxygen binding to hemoglobin), Naka-Rushton equation (retinal response to light intensity), Kubo susceptibility (statistical mechanics near criticality). C(ρ) = tanh(γ·ln(ρ/ρ_crit + 1)) is a compander in this class — it maps density across 80+ orders of magnitude to a bounded coherence value [0,1]. Key consequence: companders are purely evaluative (input → output), not self-consistency equations. They cannot encode universality classes, critical exponents, or spontaneous symmetry breaking — these require a feedback loop (e.g., m = tanh(βJzm) in Ising mean-field). The site's /parameter-derivations page explicitly uses the term compander; this is the settled self-identification of C(ρ).

An electron beam scans so fast it appears everywhere at once. Measurement = sampling at different sync rates.

A CRT display’s electron beam creates different perceptions depending on sampling rate: a stable image (slow), flickering bands (medium), or a single dot (fast). Nothing about the screen changes — only synchronization timing. Synchronism claims quantum phenomena work the same way: superposition is temporal scanning, collapse is catching the dot, and entanglement is two synchronized screens.

The process by which quantum superpositions break down and systems start behaving classically.

In standard physics, decoherence occurs through interaction with the environment. In Synchronism, decoherence IS the MRH crossing — when correlations extend beyond the Markov Relevancy Horizon, quantum behavior transitions to classical.

A large-scale sky survey at Kitt Peak Observatory measuring galaxy spectra to map cosmic expansion.

DESI (Dark Energy Spectroscopic Instrument) is a spectroscopic survey that measures the redshifts of ~40 million galaxies and quasars to map the universe's large-scale structure. DESI Data Release 1 (DR1, 2024) provided the most precise measurements to date of fσ₈ (the combined growth-rate parameter) across multiple redshift bins. Synchronism's TEST-04a predicted fσ₈(z=0.51) ≈ 0.418, below ΛCDM; DESI DR1 observed ≈ 0.55 ± 0.06, above ΛCDM. This 2.4σ disagreement is the framework's first adjudication by external data.

In MOND, a system embedded in an external gravitational field can be affected even if the internal acceleration is above the MOND threshold.

The External Field Effect (EFE) is a feature of MOND theories (Bekenstein-Milgrom 1984) with no Newtonian analog. In Newtonian gravity, external uniform fields cancel out internally (equivalence principle). In MOND, a system's internal dynamics depend on the total (internal + external) acceleration relative to a₀. This means a wide binary star system in a high-density environment (high external field) behaves more Newtonian than the same system in a low-density void. The EFE is observationally relevant for the Synchronism TEST-02 (wide binary density dependence): MOND+EFE also predicts environment-dependent dynamics, making TEST-02 potentially degenerate with MOND unless the amplitude prediction differs.

Prediction was tested and contradicted by data, with a specific error documented.

Failed predictions are not removed — they are documented with the exact error. Examples: YBCO T_c predicted 607K (observed 93K, 6.5× error); Bullet Cluster dark matter viscosity sign wrong. Failures stay visible.

A prediction is falsifiable if there exists an observation that would disprove it.

Every Synchronism prediction has a defined "kill criterion" — a specific outcome that would falsify it. This is what separates testable science from unfalsifiable speculation. The site documents both successful and failed predictions.

The product of the growth rate f(z) and the matter fluctuation amplitude σ₈ — a key observable for structure growth.

fσ₈(z) combines two cosmological measurements: f(z) = d(ln D)/d(ln a), the logarithmic growth rate of structure (how fast overdensities grow), and σ₈(z), the amplitude of matter fluctuations at redshift z. Together they quantify how rapidly large-scale structure is building up. Higher fσ₈ = faster growth = more clustering. Synchronism Session 107 predicted fσ₈(z=0.51) ≈ 0.418, below ΛCDM (≈0.474). DESI DR1 measured ≈0.55 ± 0.06, above ΛCDM — a 2.4σ disagreement with Synchronism, and a sign reversal relative to the prediction.

A specific, pre-registered outcome that would falsify a prediction if observed.

Each Tier-1 test has a kill criterion: a numerical threshold that, if crossed, means the framework's prediction is wrong. Example: TEST-02 kill is "wide-binary anomaly is independent of local stellar density." Kill criteria are stated before the data is analyzed, not after — this is what makes them falsifying rather than rationalizing. The set of kill criteria is the framework's most important methodological contribution.

A pre-registered numerical threshold has been crossed; the test is treated as failed unless a revised pre-registration is made.

A Kill Criterion is a pre-registered falsification threshold: before the test is run, a specific numerical value is set such that if the result crosses it, the prediction is treated as failed. "Kill Criterion Triggered" means that threshold was crossed. It is a stronger statement than "Failed" alone because it means the failure was anticipated and quantified in advance. In Synchronism's test catalog, TEST-03 (RAR environment scatter) has kill criterion R² < 0.20 — observed R² = 0.14, criterion triggered. TEST-04a has kill criterion fσ₈(z=0.5) > 0.46 — DESI DR1 measures ≈ 0.55, criterion triggered. Note: "Kill Criterion Triggered" and "Speculative" are mutually exclusive — Speculative means no quantitative test has been defined; Kill Triggered means one was defined and crossed.

The logarithm base e (≈ 2.718). Compresses very large ranges into manageable numbers.

ln(x) answers: "what power must I raise e to, to get x?" For example, ln(1) = 0, ln(e) = 1, ln(100) ≈ 4.6. In the coherence function C(ρ) = tanh(γ · ln(ρ/ρ_crit + 1)), the natural log compresses the enormous density range of physical systems (interstellar gas to neutron stars spans 80+ orders of magnitude) into a range that tanh can differentiate. The "+1" inside the log ensures the argument is always ≥ 1, so ln ≥ 0 and C ≥ 0.

A physics approach where each particle feels the average effect of all others, not individual interactions.

Simplifies many-body problems by replacing complex particle-by-particle interactions with a single "mean field." In the Ising model, the self-consistency condition m = tanh(βJz·m) is a fixed-point equation — m appears on both sides, tanh is the self-consistent solution, and the result is genuine spontaneous symmetry breaking with critical exponents. C(ρ) borrows the tanh *form* but is not derived this way: its argument is ρ (external density), not the order parameter itself. There is no fixed-point equation, no free energy minimized, no SSB, and no critical exponents — the Honest Assessment labels this a "Category Error." C(ρ) belongs to the compander family (μ-law/Hill/Naka–Rushton), not the mean-field class.

An alternative to dark matter: gravity behaves differently at very low accelerations (below a₀ ≈ 1.2×10⁻¹⁰ m/s²).

Proposed by Milgrom in 1983. Successfully predicts galaxy rotation curves without dark matter. Synchronism claims to derive MOND's acceleration constant a₀ from cosmological parameters, making it emergent rather than fundamental.

Synchronism and MOND make identical predictions for this test; the outcome cannot discriminate between them.

Some Tier-1 tests cannot distinguish Synchronism from MOND regardless of outcome, because both frameworks make the same prediction in that regime. These are labeled "MOND-shared." Examples: TEST-09 (BTFR slope variation with regime) — Milgrom (1983) and McGaugh (2012) already predict the same regime-dependent slope; TEST-10 (dwarf galaxy dark matter dominance) — standard MOND predicts the same pattern. A MOND-shared test is not useless — it tests both frameworks against data — but it cannot provide evidence for Synchronism over MOND. The site uses this badge on /tier-1-existing to distinguish tests that discriminate (potentially) from tests that do not.

An "event horizon for influence" — the bubble of nearest neighbors that matter. Everything outside it can be ignored without losing predictive accuracy.

Think of an atom: Andromeda exists, but its gravitational and electromagnetic influence on a single atom is below the noise floor. The MRH is the minimal neighborhood such that removing anything inside degrades prediction, and adding anything outside does not improve it. Formally: the minimal set of interacting degrees of freedom whose state transitions materially influence coherence evolution. In quantum mechanics, crossing the MRH IS measurement/decoherence. Presence (ρ) is defined relative to an MRH: change the MRH, presence changes.

Number of particles moving as a correlated unit.

The fundamental input to γ = 2/√N_corr. A single electron has N_corr = 1 (γ = 2, quantum). A crystal lattice might have N_corr = 10²⁴ (γ ≈ 10⁻¹², classical).

Synchronism's prediction that RAR scatter depends on environment.

Standard models predict RAR scatter is constant. Synchronism predicts it varies with local density. Statistical test: p = 5×10⁻⁶, strongly supported.

In the framework's parallel hypothesis space; not currently in active focus but not abandoned.

Parallel-Paths means the claim is on the shelf — not being actively investigated but not disowned. The framework maintains multiple parallel research tracks simultaneously; Parallel-Paths marks a track that is not the current priority.

A sudden shift in how a system behaves, like water freezing or a magnet losing its magnetism.

In Synchronism, the quantum-to-classical transition is modeled as a phase transition controlled by γ. At γ ≈ 1, systems sit right at the boundary — where chemistry, biology, and the most interesting physics occur.

Formula or derivation produced after the confirming experiment was already published.

A post-diction matches known data but was not a forward prediction — the experiment's result was already in the literature when the formula was derived. Epistemically weaker than "Validated" (genuine pre-registered prediction confirmed) but distinct from "Reparametrization" (notation change). Post-dictions can be valuable as consistency checks and can motivate forward predictions, but they do not independently confirm a framework.

How much compatible stuff is nearby — "density" but generalized. A single word for "the right kind of neighbors within your MRH."

Why not just call it density? Physical density (g/cm³) is one form of presence, but the framework applies the same equation to chemistry (presence = compatible molecular configurations), neural tissue (presence = coupled neurons), and galaxies (presence = baryonic density). A single word covers all these cases. Presence is not merely quantity — it encodes compatibility, configuration, and environmental suitability: ρ = f(compatibility vector), the scalar projection of a multidimensional compatibility space onto a single number. Must be quantifiable, domain-transparent, MRH-dependent, and falsifiable.

The "what it's like" of conscious experience — the redness of red, the pain of pain.

In Synchronism, qualia are modeled as coherence resonance patterns that emerge when C crosses ≈ 0.50. This is speculative and untested. The site marks all consciousness claims with appropriate caveats.

Note: All consciousness predictions are untested. This is the most speculative part of the framework.

Tight correlation between observed and baryonic acceleration in galaxies.

Discovered in SPARC data: what you see (baryonic matter) predicts what you get (total gravitational acceleration) with very small scatter. Synchronism predicts the scatter should be environment-dependent.

Two patterns cycling in perfect sync show identical behavior regardless of distance. No information travels between them.

Like two CRT screens displaying identical pictures from synchronized electron beams: sample either screen at any rate, and both show the same thing simultaneously. Not because information traveled, but because their cycles were correlated from the start. Synchronism’s explanation for quantum entanglement.

When a result turns out to be equivalent to existing physics expressed in different variables.

Several Synchronism results (e.g., the η reachability factor = Abrikosov-Gor’kov pair-breaking) are reparametrizations. The site marks these honestly with orange badges. The novelty is in unification, not in each individual result.

Note: Not a failure — reparametrizations confirm the framework is consistent with known physics, but they don’t count as new predictions.

The result is mathematically equivalent to existing physics expressed in different variables.

A reparametrization is not a failure — it shows the framework is consistent with known physics. But it is not a new prediction. Example: the η reachability factor = Abrikosov-Gor’kov pair-breaking (1960). The honest assessment tracks reparametrizations separately from genuinely novel predictions.

One autonomous AI research exchange in the Synchronism archive — a claim worked, challenged, and resolved. Sessions are numbered (e.g. "Session 107") and roughly chronological.

The research archive was produced by 3,308 autonomous AI sessions. Each session is one unit of work: a derivation attempted, a claim stress-tested, a dataset analyzed. Site citations like "Session 107" point to the archive document with that number. Session count measures activity, not validity — the site's own audit found the number of sessions has no bearing on whether a result is correct (several headline numbers propagated for hundreds of sessions before anyone re-ran the underlying computation).

Was in active focus; currently not pursued; reasons documented; reactivation condition specified.

Sidelined differs from Parallel-Paths: the claim was actively worked and then explicitly deprioritized for documented reasons. To reactivate a Sidelined claim, the specified condition must be met (e.g., new data, resolution of a prior contradiction).

Database of 175 galaxies with precise rotation curves and mass models.

The gold-standard dataset for testing galaxy rotation theories. Synchronism was tested against all 175 galaxies.

A conceptual proposal without a specific quantitative test defined.

Speculative claims are ideas the framework motivates but has not turned into falsifiable predictions. They may become testable with more development. Higher epistemic risk than Untested, which has a defined test.

⚠ Deprecated — conflicts with current stewardship discipline. Use Reparametrization, Untested, or Active-MRH instead.

⚠ This badge is deprecated. It conflicts with the stewardship principle that nothing is honestly characterizable as "established" at the current stage. Historical meaning: the data supported the claim with high significance but with caveats (prior art, limited R², non-independent explanation). Existing usages are being migrated to the current badge system (Reparametrization, Failed, Untested, Speculative, Active-MRH). See Honest Assessment for the canonical badge definitions.

Replaced by a later formulation; pointer to successor.

A Superseded claim was not wrong per se — it was absorbed into a more general or more precise successor. The pointer to the successor is part of the badge.

A mathematical function that smoothly maps any input to a value between −1 and +1 (or 0 and 1 when shifted).

In Ising mean-field theory, tanh arises naturally from the self-consistency loop m = tanh(βJz·m). In Synchronism, there is no such self-consistency — the tanh shape is a phenomenological choice motivated by Landau-universality. Any sigmoid (logistic, erf, arctan, Hill) satisfying the same boundary conditions would be an equally valid choice. See /parameter-derivations for the explicit disclaimer.

Tier 1: falsification tests runnable against existing public data (Gaia, SPARC, DESI). Tier 2: exploratory hypotheses lacking a derived amplitude or mechanism — not yet falsifiable as stated.

The tier system classifies proposed tests by readiness, not importance. Tier 1 means existing data could in principle decide the test now: a stated prediction, a stated kill criterion, and a public dataset. Tier 2 means the idea is exploratory — no derived amplitude, no specified mechanism, or no meaningful kill criterion yet (e.g. TEST-07 cosmic interference, recommended for demotion to Tier 2 by the site's own audit). There is no Tier 3. The only Tier-1 listing is on the Tier 1: Existing Data page.

A specific prediction exists, but the relevant data or experiment has not been run.

"Untested" is not a failure — it means nobody has looked yet. Many Synchronism predictions in astrophysics and quantum measurement are Untested because this lab cannot run experiments and the specific test has not been done by others.

The constant speed at which stars orbit in the outer parts of a galaxy.

Galaxy rotation curves show that stars far from the center orbit at roughly constant speed instead of slowing down (as Newton predicts). This "flat" velocity is the key observable that reveals the dark matter problem.

⚠ Deprecated — no claim currently holds this badge. See Honest Assessment for the current badge system (Reparametrization, Failed, Untested, Speculative).

⚠ This badge is deprecated. The 0 of 6 "Validated" claims that survived expert audit were all demoted to Reparametrization or Failed. "Validated" conflicts with the current stewardship discipline (nothing is honestly characterizable as established at this stage). In new content, use Active-MRH, Reparametrization, or the appropriate descriptive tag instead. Historical note: "Validated" meant the numbers agreed quantitatively with data — but agreement alone does not establish novelty; reparametrizations of known physics can "validate" without adding new physics.

A prediction or test has been voluntarily retired because it was found to be contradicted by the framework itself, physically unmotivated, or replaced by a better formulation.

A Withdrawn prediction means the framework itself has disowned the test — not because external data refuted it, but because internal analysis showed it was either (a) contradicted by another part of the framework, (b) unmotivated (no derivation of the predicted amplitude), or (c) superseded by a more precise test. In Synchronism's test catalog: TEST-04 (BAO coherence modulation) was withdrawn because (1) Session 107 contradicts it internally, (2) the predicted effect (10⁻⁴) is 600× below standard nonlinear BAO shifts and thus unmotivated, and (3) the kill criterion of 10⁻⁵ is smaller than current measurement precision. Withdrawn differs from Failed: failure comes from data; withdrawal comes from the framework itself.

Transition-sharpness coefficient (dial): γ = 2/√N_corr. A motivated ansatz, not a derivation. (γ multiplies the log; it is not an exponent.)

Large γ (few correlated units — a single electron: N_corr = 1, γ = 2) gives a sharp C(ρ) transition; small γ (many correlated units — a crystal: γ ≈ 10⁻¹²) gives a flat one. γ ≈ 1 marks the sparse/collective boundary where chemistry clusters. Note the inversion: the most collective systems get the FLATTEST curves — BCS superconductors land at C ≈ 0. (This entry previously stated the regimes backwards — "γ << 1 quantum, γ >> 1 classical" — corrected 2026-06-12.) Structurally, γ is claimed to encode MRH coupling density (γ ∝ λ·K/D, where λ = interaction strength, K = connectivity, D = dimensionality), but no protocol independently measures N_corr in any system.

The BIC difference between two models. ΔBIC > 10 = very strong evidence against the worse model; ΔBIC=+184 (point estimate) or ≥+33 (conservative) both far exceed this threshold.

ΔBIC = BIC_model1 − BIC_model2. Positive ΔBIC means model 2 is better. Convention: ΔBIC > 10 is "very strong evidence." In the Synchronism RAR shape test (2026-05-21): γ=2 compander vs free-γ on 2807 SPARC points gave ΔBIC=+184 (point estimate) or ≥+33 under conservative intra-galaxy correlation correction. Both values far exceed the >10 threshold — the γ=2 form is categorically rejected regardless of which figure is used. The free-γ form collapses to MOND (γ≈0.49), so either result closes the discriminating test.

Superconductivity parameter equivalent to Abrikosov-Gor'kov pair-breaking efficiency.

Synchronism independently derived this factor, which turned out to match a known 1960 result. An honest reparametrization, not a new discovery.

Note: Marked as reparametrization — this is known physics in new notation.

The standard model of cosmology: the universe is ~68% dark energy (Λ), ~27% cold dark matter, ~5% ordinary matter.

The mainstream cosmological framework that explains the universe's expansion, galaxy formation, and cosmic microwave background. Synchronism doesn't replace ΛCDM — it proposes an alternative interpretation of what "dark matter" represents (coherence effects rather than invisible particles).

Alternative formulation: ξ = topology + geometry + dynamics.

The compression action variable unifies matter (topology), gravity (geometry), and quantum mechanics (dynamics) into a single parameter that feeds into the coherence function.

Reference density — a saturation knee, not a critical point. C(ρ_crit, γ=2) = 0.88; the midpoint C=0.5 sits at ρ ≈ 0.32×ρ_crit. ρ_crit = A × V_flat² (astrophysical case).

ρ_crit sets the scale at which the coherence function enters saturation — NOT a phase-transition critical density. At γ=2, C(ρ_crit) = tanh(2·ln 2) = 0.88; the actual C=0.5 midpoint is at ρ ≈ 0.32×ρ_crit. The "+1" regulator in ln(ρ/ρ_crit + 1) makes the function asymmetric. "Critical density" or "transition density" are misleading terms for this parameter — the correct description is saturation knee or reference density.

A number like "2.4σ" means the result is 2.4 standard deviations from the expected value — roughly a 1-in-60 chance if the model is correct.

In statistics, σ (sigma) is the standard deviation — a measure of how spread out a distribution is. When scientists say a result is "2.4σ away" from a prediction, they mean: if the prediction were exactly correct, there is about a 1.6% chance of seeing a discrepancy this large by random chance. The conventional thresholds in physics are: 2σ = "interesting" (~2% chance), 3σ = "evidence" (~0.3% chance), 5σ = "discovery" (~0.00003% chance). A 2.4σ disagreement (like DESI DR1 vs Synchronism's fσ₈ prediction) is taken seriously but is not by itself a definitive refutation.

Measures how "lumpy" the universe is on 8 Mpc/h scales. A key cosmological parameter.

σ₈ (sigma-8) quantifies the amplitude of matter density fluctuations on scales of 8 Megaparsecs per h (where h is the dimensionless Hubble constant). A higher σ₈ means galaxies clump more strongly; a lower σ₈ means smoother distribution. Planck CMB data gives σ₈ ≈ 0.83; weak-lensing surveys (KiDS, DES) give σ₈ ≈ 0.77–0.80. This "S₈ tension" is an active area of cosmology. Synchronism Session 107 predicted σ₈ ≈ 0.76; DESI DR1 measures σ₈ = 0.841 ± 0.034, disfavoring the prediction at 2.4σ.