PUH Theorem 297 (Positioning and Discriminator) — The Loop Quantum Gravity Bouncing-Black-Hole Programme as PUH's Nearest Independent Rival: Convergence on Non-Singular Cores and Long Bounce Times, Divergence on Evaporation, and the Sign of the Low-Mass Spectrum as the Test

Photonic Universe Hypothesis (PUH) — Positioning and Discriminator. THE OMISSION. A search of the full PUH corpus returns ZERO engagement with Rovelli, Vidotto, or the loop-quantum-gravity bouncing-black-hole programme — the one active mainstream research effort independently proposing a non-singular Planck-density core in place of the singularity. This note corrects that omission. It contains no new derivation; its contribution is accurate positioning, and the positioning sharpens an existing PUH prediction rather than softening it. THE CONVERGENCE. Rovelli and Vidotto (2014) proposed Planck stars: quantum-gravitational pressure halts collapse at Planckian density, no singularity forms, the object subsequently rebounds. PUH reaches the same terminal picture from lattice structure — the E8 condensate admits only finite folding, the Planck Shell is where the fold saturates (T156), and the core is a fully degenerate fixed point of the E8 Lie-Poisson structure (T172). Two programmes, no shared machinery, one conclusion. Recorded as independent convergence on a contested claim; unconfirmed in both cases. THE TIMESCALE CONVERGENCE. The LQG bounce time is contested within that literature. Haggard–Rovelli estimated order M² — shorter than Hawking's M³ — and suggested evaporation could be neglected; this is the version predicting lunar-mass holes exploding today. Frolov–Vilkovisky estimated M·eM, far exceeding evaporation. Christodoulou–D'Ambrosio, in spinfoams, obtained M·e^ (ξM²), reinforcing that evaporation cannot be neglected; the current consensus has Hawking radiation dominating throughout with tunnelling only at the Planck scale. PUH, via extreme time dilation between core rate and external rate, places the rebound at trillions upon trillions of years externally — landing with the long-bounce camp, independently. CORRESPONDENCE CAVEAT STATED: identifying PUH's core rebound with the LQG black-to-white transition is a correspondence PROPOSED here for comparison, not derived. THE DIVERGENCE, ABSOLUTE. In every LQG version Hawking radiation operates; they differ only on whether it dominates. In PUH it does not operate at all — and this is a THEOREM, not a postulate. In the Lie-Poisson formulation (T172), two Casimir leaves merging into one is topologically allowed and one leaf splitting into two is topologically forbidden: cores amalgamate, cores cannot evaporate. The Planck Shell reinforces this at transport level by reflecting rather than absorbing (T156), which is also how PUH preserves information (T214). The frameworks therefore drive the population in OPPOSITE DIRECTIONS — LQG grinds every core downward, PUH drives every core upward. Self-consistency: if larger cores rebound later, amalgamation continually pushes the population toward longer waiting times, reinforcing the absence of observed rebounds. THE DISCRIMINATOR. Evaporation drives populations whose remaining lifetime is short toward dn/dM ∝ M^ (+2) — the low-mass end swept clean, density rising with mass, with the presently-expiring scale near 5×10¹1 kg (10¹5 g). PUH's amalgamation cascade gives the Smoluchowski gel-point spectrum dN/dm ∝ m^ (−5/2) (T287. 3) — the low-mass end dominant, density falling with mass. OPPOSITE SIGNS, four and a half powers apart. The permitted mass WINDOW divides them equally: evaporating populations admit a floor band of about 3. 1 decades because everything lighter is gone, while PUH's floor may extend to the Planck mass across 24. 6 decades — the roughly 22 decades open only to non-evaporating cores, registered in T289 before this comparison existed. THE NEW KILL-CONDITION (P297. 1, ARMED). PUH predicts the primordial-black-hole explosion rate is IDENTICALLY ZERO — not suppressed, zero, because the process is topologically forbidden. Directly searched: HAWC excludes above 3400 pc^-3 yr^-1 at 99% confidence (strongest existing direct electromagnetic limit) ; H. E. S. S. of order 10³ for 10–100 s windows; VERITAS 2. 2×10⁴. Indirect extragalactic-background limits are tighter but assumption-laden: ~10 pc^-3 yr^-1 if clustered in haloes, 10^-6 if uniform, with Galactic gamma-ray ~0. 06 and antiproton ~0. 02. CTAO is projected near 36 pc^-3 yr^-1. FALSIFIER: one confirmed primordial-black-hole explosion, which would end T172's theorem, the amalgamation-only picture, T289's dividend, and the non-evaporating core identification of dark matter. No margin is claimed — the prediction is exactly zero, so the commitment is armed at whatever sensitivity comes next. THE LIMITATION, AT FULL STRENGTH. Non-detection does NOT confirm PUH. An empty sky is equally explained by there being no primordial black holes in the range at all — the mainstream reading. The test is ASYMMETRIC: a detection kills PUH; continued silence supports it not at all. Existing null results are NOT presented here as favouring this framework; they do not. What they establish is that the kill-condition is live and continuously tested by running instruments. Breaking the degeneracy requires the POPULATION, not its silence: a detected population where evaporation forbids survivors would favour PUH strongly; a demonstration that the range is empty at the required abundance would count heavily against it — the gauntlet T289 already runs. NOT CLAIMED: that LQG supports PUH (it is a rival, and on evaporation incompatible) ; that null explosion searches are evidence for PUH; that the core rebound and the black-to-white transition are the same process; that any new derivation appears here; that the timescale convergence confirms either framework; or that the Section 5 discriminator has been executed — it is identified, not run.