PUH Theorem 395 — The Skeleton Cluster: Thousands of Seeds Packed Within a Parsec and at Rest Would Deepen Their Cloud's Well but Not Gather Its Gas, and Each Star Must Still Catch Its Own

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. T394 found that a single skeleton solar system (T196) — a stellar seed with its satellite cores — weighs 1.0014 seeds by Earth's core fraction, short of every threshold at which a well at rest draws in its own mass of dense cold gas in one free fall. The author answered: 'Seeds don't act alone.' The Sun formed with some 6,000 to 10,000 stars (Desch and Miret-Roig 2024), so, if each star had a skeleton, the Sun's came in a crowd, and 'this amount of skeleton solar systems could create a larger gravity well. Enough material for all stars within it.' T196 already pictured neighbouring cores of equal mass bound together as 'stellar nurseries'. This paper calculates whether such a crowd gathers its cluster's gas, whether each star then holds a seed, and how long a crowd lasts, with T291's seed (1.6 × 10²⁷ kg) and standard physics. RESULT 395.1 — A CROWD SPREAD LIKE ITS GAS DEEPENS NO WELL. 6,000 to 10,000 skeletons weigh 4.835 to 8.058 solar masses; the gas that makes that many stars (0.4 M☉ each, efficiency 10 to 30 per cent; Lada 2010) weighs 8,000 to 40,000 and already carries 1.77 to 5.3 seeds per star at T291's count. Spread like the gas, the seeds add at most 0.11 per cent to its pull. RESULT 395.2 — PACKED TOGETHER AND AT REST, A CROWD DEEPENS ITS CLOUD'S WELL BUT DOES NOT GATHER ITS GAS. Packed within its Bondi radius at 10 K — 0.5873 and 0.9788 pc, 926.2 and 333.4 times more tightly than seeds spread like gas of 100 per cm³ — a crowd is one well, 3.753 to 6.254 times T394's threshold there (1,601 seeds' mass). But that threshold is also gravity's ceiling: cold gas falling from rest brings in exactly a mass's own mass in one free fall, whatever the mass, so no well gathers faster than its gas collapses; and the gas inside these crowds' Bondi radii already weighs 1.011 and 2.809 times the crowd. Settled in the crowd's potential, that gas and the crowd weigh 21.21 and 83.85 solar masses against a Jeans mass of 15.7: by a rough measure a crowd at rest tips the gas within its reach into collapse at its place above 4,489 to 5,317 skeletons, in about the time the gas takes to collapse by itself, and only while it moves through the gas slower than about 55 to 158 m/s. The cluster's 8,000 to 40,000 solar masses collapse on their own. The author's larger well would be real on these two conditions; the material for all the stars is the cloud's. RESULT 395.3 — THE GAS STILL MAKES THE STARS. Gas breaks into stars on its own Jeans scale, 1,128 to 3,566 seeds' mass at 10⁵ to 10⁴ molecules per cm³, so a crowd at most marks where its part of the cloud's collapse begins; each skeleton is again a passenger. RESULT 395.4 — EACH STAR MUST STILL CATCH ITS SEED, AND THE COUNT IS FINELY BALANCED. With the forming cores at rest among a crowd's seeds, Liouville's theorem (T375's method) allows up to 2.831 to 22.24 seeds per star through a 100-AU disk that keeps every bound seed crossing it (T394). Dense cores move against their gas with line-of-sight spreads of 0.18 and 0.33 km/s (Kirk et al. 2010): with the cores spread at 0.33 km/s, 0.0427 to 0.119 seeds per star for crowds filling their Bondi radii, 0.313 to 0.868 packed within half of them, and 0.758 to 0.935 at their most durable sizes — estimates, not bounds, since a core forms in about the time a seed takes to cross it. One per star needs the cores to move with the seeds to within about 0.08 to 0.3 km/s, depending on the packing. RESULT 395.5 — HOW LONG A CROWD LASTS. Passing molecular clouds break a crowd filling its Bondi radius in 0.181 to 0.503 billion years (Gieles et al. 2006); with relaxation and the clouds combined, a crowd at its most durable size lasts 1.16 to 1.77 billion years if limited by the Galaxy's tide, 4.19 to 5.65 if it evaporates as if isolated. To last 9.2 billion years, from the Rebound to the Sun's birth, a crowd needs more than 2.28 × 10⁴ to 1.93 × 10⁵ skeletons, depending on the model. A crowd moving with the Galaxy's seeds gathers nothing. A CORRECTION TO T394. T394 described its threshold as the mass above which a core gathers its cloud faster than the cloud collapses, becoming 'a gatherer rather than a passenger' (Result 394.7). The threshold marks instead where a well's growth stops being limited by the gas's pressure and becomes limited by gravity — no faster than the gas collapses by itself; tipping the gas within its reach into collapse needs about 2.81 to 3.33 times the threshold for a crowd at 100 per cm³. The values stand. T394's version 1.1 carries the corrected wording. NOT CLAIMED: that a crowd gathers its cluster's gas; that the Sun formed around a crowd; that crowds exist; that crowds set the sizes of birth clusters; anything about crowds in the first clouds; how a seed kept by a disk moves inward. KILL-CONDITIONS: dense cores shown to move with a crowd's seeds to within about 0.08 to 0.3 km/s; molecular clouds shown to break clusters far more slowly than Gieles et al. find; a mechanism shown to pack seeds within a parsec, at rest with their gas; seeds far more numerous than T291's count; a young cluster shown to have formed around a dark mass of thousands of objects of about 10²⁷ kg within its central parsec. OPEN: how thousands of seeds came to sit within about a parsec, at rest with their gas, within a few billion years of their cluster; how the gas within their reach could be quieter than about 0.06 to 0.16 km/s against them when the gas around dense cores moves at about 0.85 km/s; and how each forming star's core moves with the seeds — a mechanism not yet found.