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 M_min <= 4e-14 Solar Masses (8e16 kg); 22 Decades of Mass Floor Open Only to Non-Evaporating Cores

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 & Veermae (PRD 96, 023514 (2017)), applied PER EXPERIMENT; 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 M_min in [m_Planck, 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 [M_min, M_max] (T287), normalized to the comoving dark-matter budget: psi(m) = (1/2) M_min^(1/2) m^(-3/2). The mass is light-end dominated (alpha > 2, exactly what T285's kill-condition demanded), so M_max is irrelevant and the mass fraction above any scale a is (M_min/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 f0^2 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 I_E = INT psi/f_max,E dm <= 1 PER EXPERIMENT (PRD 96, 023514). Lens population assumed virialised — forced by boundedness (an unbound population could not BE the halo mass). Constraint values VERIFIED this session, not recalled. THE LANDSCAPE. Binding: Subaru-HSC M31 — Niikura et al. (Nat. Astron. 3, 524 (2019); arXiv:1701.02151), corrected for finite source sizes by Smyth et al. (PRD 101, 063005 (2020); floor ~1e-10 Msun), updated by the 39.5-hour campaign (12 candidates): f < 2% for m > 1e-10 Msun, as reported in arXiv:2605.19332 (2026). Also: Kepler (compiled, arXiv:2211.05767), EROS-2 (Tisserand et al., A&A 469, 387 (2007)), OGLE (Wyrzykowski et al., MNRAS 413, 493 (2011)), MACHO (Alcock et al., ApJ 542, 281 (2000)). NS-capture bounds: disputed, non-credited, run as sensitivity only (would tighten the ceiling to ~5e12 kg; 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 [m_Planck, 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): M_min <= 4.1e-14 Msun = 8.1e16 kg = 8.1e19 g. The free-core mass floor must sit at or below the mass of a ~35 km rocky body. The framework's informal "trillions of TINY primordial Planck cores" is promoted from a choice of words to a data-forced requirement, with the number attached. THE DIVIDEND — 22 DECADES OPEN ONLY TO NON-EVAPORATING CORES. A STANDARD PBH population with the identical spectrum is confined to [3.5e-17, 4.1e-14] Msun — 3.1 decades — because evaporation eats everything lighter. PUH cores never evaporate (P287.1, grounded in T288: the reverse Snap ascends an infinite barrier; T156 Corollary 1; T206 irreversibility), so their floor extends to the Planck mass: 24.6 decades. The no-Hawking prediction converts from a liability check into ~22 DECADES of mass territory PERMANENTLY CLOSED to every standard compact object — the quantified escape from the CDM-indistinguishability trap: PUH's dark matter can be seated where a standard compact-object population CANNOT EXIST AT ALL, licensed by a falsifiable prediction no PBH model can imitate without ceasing to be a PBH model. Recorded without weight: Carr et al.'s own 2017 analysis identified a surviving all-dark-matter window near 2e-14 Msun — essentially where this ceiling lands. CONSEQUENCES AT THE CEILING: mean free-core mass <= 2.4e17 kg (exact tau = 5/2 identity: <m> = 3 M_min); 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).