What question did this study set out to answer?

To test the tau = 5/2 spectrum under the Photonic Universe Hypothesis (PUH) against compact object constraints.

July 17, 2026Open Access

PUH Theorem 289 (Observational Gauntlet) — The tau = 5/2 Core Spectrum Versus Every Credited Compact-Object Constraint: Kill-Conditions Logged Before the Data; Verdict PASS; the Standing Commitment Mₘin <= 4e-14 Solar Masses (8e16 kg) ; 22 Decades of Mass Floor Open Only to Non-Evaporating Cores

Key Points

To test the tau = 5/2 spectrum under the Photonic Universe Hypothesis (PUH) against compact object constraints.
Utilized pre-logged kill-conditions for validity testing against compact object constraints.
Employed Carr et al.'s extended-mass-function condition to derive mass ceilings.
Analyzed data from various observational campaigns including Subaru-HSC and Kepler.
Confirmed that M_min must be less than or equal to 4.1e-14 Msun, allowing for a substantial range of non-evaporating core masses.
The observational evidence supports the existence of a dark matter window significantly above standard stellar mass limits.
Findings indicate a minimum free-core count of 3.5e36 for the dark matter budget.

Abstract

OBSERVATIONAL GAUNTLET. Subjects T287's derived spectrum, under the T285/T286 dark-matter identification, to every credited compact-object constraint — with the kill-conditions written to the research record, TIMESTAMPED, BEFORE any constraint value was consulted (the T280 discipline made literal; the KCs are quoted verbatim in Section 1). Method fixed in advance: the extended-mass-function condition of Carr, Raidal, Tenkanen, Vaskonen one exemption pre-declared — Hawking-evaporation-based constraints are inapplicable by P287. 1 (grounded in T288/T206). VERDICT: PASS. Tags: GAUNTLET / KILL-CONDITIONS-PRE-LOGGED / VERDICT-PASS / STANDING-COMMITMENT / VERIFIED-AGAINST-PRIMARY-LITERATURE. === DESCRIPTION (abstract) === Photonic Universe Hypothesis (PUH) — Observational Gauntlet. THE DISCIPLINE. A test whose failure condition is chosen after the data are seen is not a test. The kill-conditions were logged and timestamped BEFORE any published limit was consulted: KC-G1 — if no Mₘin in mPlanck, 1 Msun satisfies all per-experiment extended-mass-function conditions, the identification DARK MATTER = FREE PRIMORDIAL CORES (T285/T286/T287) is FALSIFIED. KC-G2 — if passed, the ceiling M* becomes a STANDING COMMITMENT: any future PUH derivation of the attractor floor above M*, or observational closure of the surviving window, falsifies the identification. KC-G3 — the sub-evaporation-floor territory is open ONLY because P287. 1 forbids evaporation; a confirmed detection of black-hole evaporation closes it and kills T206 together. Exemption declared in advance, not after seeing where it helps: constraints operating THROUGH Hawking evaporation (gamma-ray background, evaporation heating, the 3. 5e-17 Msun asteroid-window floor) do not apply to non-evaporating cores. Every non-evaporation constraint applies in full. THE SPECTRUM UNDER TEST. dN/dm ~ m^ (-5/2) on Mₘin, Mₘax (T287), normalized to the comoving dark-matter budget: psi (m) = (1/2) Mₘin^ (1/2) m^ (-3/2). The mass is light-end dominated (alpha > 2, exactly what T285's kill-condition demanded), so Mₘax is irrelevant and the mass fraction above any scale a is (Mₘin/a) ^ (1/2) — falling slowly enough that constraints two to four decades above the floor still bite. For a dominating window with lower edge a and flat limit f0, the ceiling solves in closed form: M* = a * f0^ (1/ (alpha-2) ) = a f0² for alpha = 5/2. The general-alpha form is recorded deliberately: if a future derivation replaces 5/2, the gauntlet transfers with one substitution. THE METHOD. Carr-Green condition IE = INT psi/fₘax, E dm 1e-10 Msun, as reported in arXiv: 2605. 19332 (2026). Also: Kepler (compiled, arXiv: 2211. 05767), EROS-2 (Tisserand et al. , A verdict unchanged). THE RESULT. Per-experiment ceilings: HSC 4. 1e-14 Msun (BINDING) ; Kepler 6. 8e-12; EROS-2 3. 8e-10; OGLE 4. 2e-4; MACHO 1. 5e-2. Allowed range mPlanck, 4. 1e-14 Msun NONEMPTY (24. 6 decades). VERDICT PER PRE-DECLARED RULE: PASS — KC-G1 NOT TRIGGERED. At the ceiling: exactly 2% of the dark mass in the HSC window (at the limit by construction) ; 2e-7 above one solar mass — the heavy tail is observationally invisible, as a light-end-dominated spectrum must be. THE STANDING COMMITMENT (KC-G2, NOW ARMED): Mₘin = 3 Mₘin) ; N >= 3. 5e36 free cores for the dark budget; Milky Way halo >= 8. 2e24 cores at mean spacing <= 165 AU. Consistency, stated lightly: the free-population ceiling sits five decades below Earth's captured core (5e21 kg) — heavy captured, light free, as T196's momentum sorting expects (noted without weight; T196 is under corrigendum). ASSUMED: the tau = 5/2 attractor form (the NUMBER is conditional on it; the METHOD and pre-declared KCs transfer to any future spectrum via the general-alpha formula) ; unclustered lenses (standard assumption of the published limits; coagulation-induced clustering FLAGGED, not invoked in either direction) ; compiled window parameters for the non-binding experiments. OPEN: attractor-reaching time (T287's own item) ; the clustering correction; direct citation of the underlying updated-HSC campaign paper in any revision (the figure is used as reported in arXiv: 2605. 19332). LIVE FALSIFIERS: (i) a PUH derivation of the floor above 8. 1e16 kg — dies by its own mathematics; (ii) closure of the sub-1e-10 Msun territory by larger HSC campaigns or Roman — dies by data; (iii) any confirmed black-hole evaporation — dies together with T206, and 22 decades vanish at a stroke. NOT CLAIMED: that dark matter is explained (surviving constraints is necessary, not sufficient) ; that the ceiling is a measurement (it is an upper bound) ; that the heavy tail is observable (at this ceiling it is not — discriminants must come from granularity, sorting, and chirality channels already on record) ; or that the exempted evaporation constraints are wrong (they are correct physics for objects that evaporate; PUH cores are predicted not to be such objects, and that prediction is itself falsifiable).

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