FINDINGS — T09-mass-gap (GWTC-3 confident catalogue)
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
FINDINGS.md
# FINDINGS — T09-mass-gap (GWTC-3 confident catalogue) **Hypothesis (Vol. XXV #07):** the ~2–5 M_sun gap is a *physical boundary* — core collapse makes either a neutron star or a black hole, "with nothing in between". Prediction: "Detected masses should avoid the gap." Refutation clause (the page's own): "A confident detection inside the gap would remove the boundary argument." **Data:** 90 confident GWTC-3 events → **180 source-frame components** (mass range 1.17–105.5 M_sun). Primary gap **[2.5, 5.0] M_sun**; sensitivity gap **[2.2, 5.0] M_sun**. --- ## Verdicts (rule frozen before analysis — see hypothesis.md) ### Version A — STATISTICAL (significant dearth below a smooth reference): **SUPPORTED** | Gap | Components in gap | Expected from smooth power law (MLE, α=0.75) | obs/expected | Poisson p (one-sided) | Rule met? | |---|---|---|---|---|---| | 2.5–5.0 | **2** | 18.1 | 0.11 | **3×10⁻⁶** | YES (2 ≤ 9.0 and p<0.05) | | 2.2–5.0 | 2 | 22.0 | 0.09 | 4×10⁻⁷ | YES | Robust across all reference models: least-squares-on-log-counts fit (λ = 20.6, α = 0.77), outside-normalised MLE (λ = 19.9), and extrapolating the BH-side-only power law down into the gap (λ = 39.2, α = 1.04). Binomial p-values agree (≤ 1×10⁻⁶). The gap contains 2 components where a smooth power-law mass spectrum predicts ~18–39. ### Version B — BOUNDARY (zero components allowed): **NOT SUPPORTED** Two confident components sit inside 2.5–5.0 M_sun: | Event | Component | Mass (M_sun) | 5–95% bounds | Note | |---|---|---|---|---| | GW190814 | secondary | **2.6** | [2.5, 2.7] | bounds lie *entirely* inside the gap | | GW200210_092254 | secondary | **2.83** | [2.41, 3.30] | median inside gap | By the page's own refutation clause, the absolute-boundary claim **fails**: GW190814 alone removes it. (No components in [2.2, 2.5], so the sensitivity gap contains the same two.) ## Headline numbers - Components inside [2.5, 5.0]: **2 / 180** (1.1%) — vs ~10% expected from a smooth power law. - Power-law index outside the gap: α ≈ 0.75 (MLE), 0.77 (LSQ). - Zero components in **[2.9, 5.0]** — the emptiness is complete above ~2.9 M_sun; both in-gap objects hug the lower edge (2.6, 2.83). - Histogram (21 log bins; gap bins marked): ``` M_sun count 1.00- 1.26 1 | 1.26- 1.58 4 |||| 1.58- 2.00 0 | 2.00- 2.50 2 || 2.50- 3.16 2 || <- GAP 3.16- 3.98 0 | <- GAP 3.98- 5.00 0 | <- GAP 5.00- 6.31 4 |||| 6.31- 7.94 11 ||||||||||| 7.94-10.00 6 |||||| 10.00-12.59 16 |||||||||||||| 12.59-15.85 8 |||||||| 15.85-19.95 7 ||||||| 19.95-25.12 22 |||||||||||||||||||| 25.12-31.62 28 |||||||||||||||||||||||||| 31.62-39.81 32 |||||||||||||||||||||||||||||| 39.81-50.12 17 ||||||||||||||| 50.12-63.10 10 |||||||||| 63.10-79.43 6 |||||| 79.43-100.0 3 ||| 100.0-125.9 1 | ``` ## Support-rule comparison - (A) Statistical dearth: observed 2 ≤ λ/2 = 9.0 **and** p = 3×10⁻⁶ < 0.05 → **support**. - (B) Absolute boundary: requires zero; **2 observed → no support** (GW190814's 5–95% interval [2.5, 2.7] lies wholly inside the gap, so this is not a measurement-uncertainty artefact). ## Limitations (would change / temper the conclusion) 1. **Reference model is crude.** The single power law fails a goodness-of-fit test on the outside-gap data (χ² = 140.6, dof = 16, p ≈ 0) because the component spectrum is bimodal (NS peak ~1.4 M_sun + BH peak ~8–40 M_sun). The "expected 18–20" interpolates the steep low-mass side across the gap and is likely an overestimate — i.e. the dearth is probably *bigger* than the rule requires, but the exact p-value is model-conditional. A proper reference (power law + Gaussian NS component, as in LVC population papers) would restate λ, not erase the dearth. 2. **Detection selection effects.** Detectors are less sensitive to low-mass components (SNR ∝ m^(5/6) for the chirp mass); the gap's low side overlaps the detection threshold region, so the observed dearth is partly a selection effect. GW190814/GW200210 show the effect is not total. 3. **Sample size.** 180 components; Poisson significance assumes the reference expectation is right. 4. **GW190814's interpretation.** Its 2.6 M_sun secondary is the canonical "mass-gap object"; excluding it to rescue the boundary claim would be post-hoc. GW200210's bounds [2.41, 3.30] straddle 2.5 but its median (2.83) is inside. 5. **Edge placement.** The page says "roughly two and five". Under the test's operationalisation (2.5–5.0) the boundary fails; if the lower edge were ~3 M_sun the boundary version would pass (zero components in [2.9, 5.0]). This sensitivity is reported, not used to rescue the claim. ## What would change the conclusion - **Boundary version:** could only pass if both in-gap objects were removed or re-measured below 2.5 M_sun — contradicted by GW190814's tight [2.5, 2.7] bounds. O4/O5 detections of more 2.5–5 M_sun objects would further bury it. - **Statistical version:** could weaken if (i) a realistic selection-function-corrected reference model put λ below ~4, or (ii) many new gap components appear. Given 2 vs ~18–39, this is unlikely but not impossible; the claim would then rest on the magnitude of the dearth. ## Bottom line The GWTC-3 confident data confirm that component masses **strongly avoid** 2.5–5.0 M_sun relative to any smooth mass spectrum — the statistical "dearth" version of the hypothesis is supported (p ≈ 3×10⁻⁶). But the page's stronger claim — a hard *boundary* with nothing in between — is **falsified as stated** by two confident in-gap objects (GW190814 at 2.6, GW200210 at 2.83), exactly the refutation the page itself specifies. The defensible physical reading: the break is real but sits at ~2.5–3 M_sun, with a complete absence above ~2.9 M_sun.
hypothesis.md
# T09 — The Mass Gap Is a Boundary (Incoprea Vol. XXV #07) - **Hypothesis page:** https://incoprea.com/research-library/original-theories-vol25-20261030/theories/gw-mass-gap.html - **Fetched:** 2026-10-30T18:22Z via `curl -sL` (saved: `data/hypothesis_page.html`) - **Test task:** GWTC-3 confident catalogue, component-mass gap test. - **Page status line:** "Working hypotheses, not findings · Not peer reviewed." ## Verbatim claims from the page **The claim:** > "The absence of compact objects between roughly two and five solar masses is set by the ratio of explosion energy to envelope binding energy, so the gap is a physical boundary rather than an observational artefact." **Mechanism (01):** > "A progenitor either loses its envelope and forms a neutron star or retains it and collapses entirely; the ratio determines which, with nothing in between." **Prediction (02):** > "Detected masses should avoid the gap." **Refutation (03):** > "A confident detection inside the gap would remove the boundary argument." **What makes it checkable (05):** > "Gravitational-wave detections now measure component masses directly and independently of electromagnetic assumptions, so the gap can be mapped rather than inferred." **Operationalisation.** The page says "roughly two and five solar masses". Primary test gap: **[2.5, 5.0] M_sun**; sensitivity test gap **[2.2, 5.0] M_sun** (closer to the page's literal "two"). ## Data GWTC-3 confident gravitational-wave transient catalogue, component masses (`mass_1_source`, `mass_2_source`, source-frame, M_sun) from the GWOSC event API. Route A `https://gwosc.org/eventapi/json/GWTC-3-confident/` returns only the 35 new O3b events; the full cumulative GWTC-3 confident set is reconstructed by merging `GWTC-1-confident` + `GWTC-2.1-confident` + `GWTC-3-confident` and deduplicating by event name (highest version wins). This is required so that GW190814 (2.6 M_sun secondary, announced in GWTC-2.1) is included, as the test specification demands. Route B (Zenodo 8177023) was checked: it contains only per-event HDF5 posterior samples for the 35 O3b events and no summary table, so Route A medians are used (see PROVENANCE.md). ## Support rule — WRITTEN BEFORE ANALYSIS (frozen 2026-10-30T18:24Z) Two independent versions, reported separately: **(A) STATISTICAL version — a significant dearth in the gap.** 1. Fit a smooth reference model to component masses **outside** the gap: a power law dN/dm ∝ m^−α over the domain [1.0, 130.0] M_sun excluding the gap, fitted by (i) truncated-power-law MLE (grid search on α, no binning) as the primary estimator, and (ii) numpy least squares on log bin counts over log-spaced bins outside the gap (bins with count ≥ 1) as the literal "keep it simple" estimator. Sensitivity: fit restricted to m ≥ 5 (extrapolate the BH-side law down into the gap). 2. Normalise the fitted law to the observed component count and compute the expected number of components inside the gap, λ. 3. **Support iff observed gap count ≤ λ/2 AND the deficit is significant: one-sided Poisson p = P(Poisson(λ) ≤ k_obs) < 0.05.** The binomial p-value (conditional on total N) is also reported. 4. Fit quality is reported as a chi-square over outside-gap histogram bins. **(B) BOUNDARY version — an absolute boundary.** Support iff there are **ZERO** confident components inside [2.5, 5.0] M_sun. Any confident component in the gap — e.g. GW190814's 2.6 M_sun secondary — fails this version outright, per the page's own refutation clause. Both versions run for the primary gap [2.5, 5.0] and the sensitivity gap [2.2, 5.0]. **Amendment (2026-10-30T18:27Z, before any statistical result was computed):** the model domain upper bound was extended from 100.0 to **130.0 M_sun**, because data inspection showed GW190426_190642 has a 105.5 M_sun primary; a likelihood whose support excludes observed data would be invalid. The rule is otherwise unchanged.