Primordial Black Holes as Incomplete Crystallization:
Seeds Without a Formation Model
Raghu Kulkarni
SSMTheory Group, IDrive Inc., Calabasas, CA 91302, USA raghu@idrive.com
August 30, 2026
Abstract
JWST has found a ∼ 10
5
M
⊙
black hole accreting inside a dense gas envelope 660 million years
after the Big Bang, and the population it belongs to — the little red dots — is abundant.
In the Selection–Stitch Model the vacuum is a crystallized lattice, matter is its incomplete
crystallization at the Planck scale, and a black hole is a region without lattice. The published
definition reaches that state by collapse, and, for primordial holes, conjectures a second origin:
relic pockets of the crystallization transition, never assembled, proposed for holes light enough
to have evaporated since. This note takes that conjecture above the survival cutoff. A region
the crystallization never reached is a black hole from the start, with no collapse and no history.
If crystallization was imperfect at any scale, its macroscopic imperfections are primordial black
holes: the particle spectrum and the primordial population are one defect spectrum, divided by
the published cutoff at 10
16.5
g. Four consequences follow without a formation model: seeds
exist before gas; they are born naked and cocooned later; no growth time is required; and the
mass function is not predicted but measured — the little-red-dot census counts the Big Bang’s
large-scale defects. The unknown dynamics of why regions were missed becomes an observable:
missed regions are uncorrelated with primordial density, wall breaches sit at its peaks, and
the clustering of little red dots decides between them. The note is falsifiable only in the weak
direction.
1 The observation and the question it sharpens
On 12 August 2026 Naidu et al. reported MoM-BH*-1: a black hole of roughly 10
5
solar masses
at redshift 7.76, enshrouded in gas so dense that the system radiates like a star — a “black hole
star” [1]. They argued that such objects are the engines of the little red dots found throughout
JWST’s deep fields [2]. The population is abundant at cosmic dawn and gone by low redshift. Two
caveats travel with the result: the masses of the population may be overestimated where resonant
scattering broadens the lines [1], and supermassive-star alternatives remain in play. The robust
claim, which this note builds on, is narrower: black holes of at least 10
4
–10
5
M
⊙
exist, accrete, and
are common at 660 million years.
The standard question is how they got so massive so fast. Light seeds must grow at or above the
Eddington rate for the entire available time; heavy seeds require direct collapse of atomic-cooling
halos [3, 4]; and primordial black holes have been proposed as seeds that skip the growth problem [5].
This note is a contribution to the last category from a framework in which the primordial option is
built into the definition of a black hole: the same vacancy that collapse produces, reached without
collapse.
1
2 The framework, for readers outside it
The Selection–Stitch Model is a research program, not an established theory, and this note uses
only its published parts. Each paragraph below states one published result and the paper that
established it.
The vacuum is a crystal running a code [6]. Space is not a continuum but a face-centered-
cubic lattice of Planck-scale bonds, each node joined to twelve neighbors (K = 12), on which a
quantum error-correcting code runs. The code is a fixed set of parity checks that continuously
verify the lattice’s state; “stitching” is the act of forming a bond that the checks then maintain.
The crystal formed by a phase transition, and imperfectly [8]. The universe was not born
as a lattice. It crystallized into one from a frustrated tetrahedral foam — a K = 4 → K = 12 phase
transition, verified computationally in Ref. [8],
§
2.3 — the lattice growing outward as a stitching
front. The crystallization was imperfect, and the imperfections are matter. Where an extra node
of the old phase was caught inside the closing lattice, it bonded to its four surrounding vertices and
became a trapped defect: the proton. Its mass emerges as a count of the lattice operations required
to keep verifying it, and that count reproduces the proton-to-electron mass ratio 1836 from the
geometry with no adjustable parameter. The electron is a different defect class, a dislocation loop.
Mass is the cost of verification [7]. A particle persists because the code checks it every cycle,
and the cycle rate is the Compton frequency. Mass is the energy of that verification, and the particle
spectrum is derived from the lattice’s error-correction structure. Gravity enters as the strain field
the defects impose on the lattice.
A black hole is a region without lattice [9]. It is a hole in the crystal, called a K = 0 vacancy
because its nodes have no bonds at all. The published paper reaches this state by collapse: when
the strain that matter imposes exceeds what the bonds can carry — the lattice’s metric wall —
the lattice un-stitches, leaving a vacancy. At linear order the lattice’s metric reproduces general
relativity’s. The vacancy’s entropy is a count of the bonds severed at its boundary, and fixing one
length — the bond length, L
0
= 1.843 ℓ
P
— against the Bekenstein–Hawking coefficient reproduces
S = A/4ℓ
2
P
with nothing further adjusted.
Black holes evaporate geometrically, with a cutoff [9]. The same paper derives a second
evaporation channel from lattice surface tension, with a lifetime scaling as M
2
. A classical terrace-
nucleation barrier at the faceted boundary then produces an exponential freeze-out once the horizon
exceeds a scale of about one fermi. The result is a survival cutoff near 10
16.5
g: holes below it
evaporated in the early Universe, each at an epoch fixed by its mass — the paper’s epoch map —
and holes above it are permanent.
Two disciplines of the series. Every claim carries a status tag — [derived], [conjectured], and
so on — so the reader can see what rests on published mathematics and what is interpretation.
And what the framework has not done is stated as clearly as what it has: it has no derivation
of the crystallization dynamics, no nonlinear gravity, and no account of why crystallization was
imperfect. This note lives entirely within those limits.
2
3 The corollary
Three published statements from
§
2 are needed: the vacuum is a crystallized lattice [6]; matter is
its incomplete crystallization [8]; and a black hole is a region without lattice, a K = 0 vacancy
with entropy equal to a count of the bonds at its boundary [9]. The published paper reaches that
state by collapse across the metric wall (
§
2). Every hole formed since the first stars is of this kind.
So is the primordial population of the published black-hole paper [9] (hereafter the companion): it
adopts the standard formation picture, a hole forming at the horizon mass at t
form
∼ GM/c
3
. It
then follows the sub-cutoff members onto the epoch map, where the lightest evaporate before one
second [9]. That population is below the cutoff and is not the subject here.
The published paper itself conjectures a second origin for primordial holes (its
§
14): relic pockets
of the vacuum’s crystallization transition — never assembled, hence never barrier-gated — with
trapped voids of radius 1–50 fm mapping onto its 10
14.8
–10
16.5
g band, and no mass function
derived [9]. This note takes that conjecture above the cutoff. The corollary is one sentence. A
region that crystallization did not reach is a K = 0 vacancy from the start — a primordial black
hole by definition, whatever its size and whatever the reason it was missed. Collapse un-stitches
lattice that existed; a primordial hole never had any. The end state is identical — the same
boundary count, the same evaporation channel — and only the origin differs. At the Planck scale,
incompleteness leaves particles; at macroscopic scale, it leaves black holes. There is one defect
spectrum (Fig. 1), and the published survival cutoff divides it [9]: uncrystallized regions below
M
cut
≃ 10
16.5
g evaporated on the companion’s epoch map, before or around recombination; those
above it survive forever. The survivors are the primordial black-hole population, present from the
crystallization epoch itself. [the relic-void origin is the companion’s conjecture; its extension above
the cutoff, and the existence of macroscopic uncrystallized regions, are this note’s]
20 10 0 10 20 30 40
log
10
mass [g] one incompleteness, forty orders of magnitude
particles
(paper 2)
uncrystallized regions below the cutoff:
evaporated on the epoch map (companion, §8)
uncrystallized regions above the cutoff:
survive; the primordial black-hole population
M
cut
10
16.5
g
MoM-BH*-1, 10
5
M
proton
Figure 1: One incompleteness, forty orders of magnitude. Particles are the Planck-scale defects
of crystallization; uncrystallized regions above the published survival cutoff are its macroscopic
defects and persist as black holes. MoM-BH*-1 sits in the surviving band.
4 What follows without a formation model
The dynamics of crystallization — why a region was missed — is not known, and this note does
not pretend to it. The following hold regardless.
3
Seeds before gas. An uncrystallized region exists at the end of crystallization, before any baryon
has cooled. The seed question — how a hole reached 10
5
M
⊙
by 660 million years — does not
get answered; it dissolves. The hole predates its own gas. This much is shared with the standard
primordial route, which also forms such a hole within the first second; what the relic-void origin
adds is that no primordial overdensity and no formation threshold are required. [follows from the
corollary; the timing is common to both primordial routes]
Born naked, cocooned later. A primordial vacancy has no envelope when it forms. The black-
hole-star phase is the first infall of gas onto an old hole, and the population’s disappearance at
lower redshift is its cocoons clearing. The observed demography — abundant at cosmic dawn, gone
by the present — is what an old population being briefly dressed would look like. [conjectured
reading, consistent with the observed demography]
No growth-time problem at any mass. Whatever the mass function of uncrystallized regions,
each member has had the entire age of the Universe. Super-Eddington growth in a cocoon, which
the observation supports [1], is then a mechanism for the envelope’s luminosity, not a requirement
on the seed. [follows from the corollary]
Survival. Every region above the cutoff survives; nothing about this population is threatened
by the companion’s evaporation channel. [derived]
5 The mass function as a measurement
The one quantity the framework cannot supply is the number of uncrystallized regions per unit
mass. The dynamics that would set it — grain structure of the crystallization, energy densities at
the metric wall, the reach of the stitching front — are not estimable. The note therefore inverts the
usual relation between theory and data. The little-red-dot census is not a test that the framework
must predict; it is a measurement of the Big Bang’s large-scale defect spectrum. Each black-hole
star counted is one region the crystallization missed, and the mass function JWST assembles is the
first data on how the lattice failed at scales it has never been probed at. [framing; no prediction
claimed]
6 Turning the unknown dynamics into an observable
The two candidate reasons a region could be missed make opposite spatial predictions. If regions
were missed — the stitching front never arrived, a grain-scale lapse in the crystallization — their
positions carry no memory of the primordial density field: black-hole stars scattered through the
field, uncorrelated with the peaks that become the nodes of the cosmic web. If regions were
wall breaches — strain or energy above the stitching limit — they sit at the primordial peaks by
construction, and black-hole stars occupy the future nodes of the cosmic web from birth, before
any merger history could have delivered them there. This branch coincides spatially with standard
primordial formation from overdensities; the missed branch is the one no standard route produces.
Standard seeding models place supermassive holes at nodes only after billions of years of hierarchical
assembly. The clustering of little red dots relative to their protocluster environment is therefore
a test of crystallization dynamics that no calculation can perform: the framework says one of the
two, names the observable that decides, and declines to guess. [the dichotomy is derived from the
two candidate dynamics; neither dynamics is claimed]
4
7 What would count against this
The note is falsifiable only in the weak direction. A demonstration that every high-redshift hole is
consistent with stellar-mass seeds plus cocooned super-Eddington growth would remove the need
for primordial regions without excluding them. Two results would count more directly. A black-
hole star whose age, environment, and mass jointly require a seed older than any possible stellar
progenitor supports the corollary. A measured clustering that is neither field-like nor peak-like —
holes tied to the positions of the first star-forming halos rather than to the primordial density —
would indicate that the population is astrophysical after all. The resonant-scattering caveat on
masses [1] affects the shape of the measured defect spectrum, not the existence argument.
8 Limitations
(L1) The central idea — that some primordial black holes are regions the crystallization never
reached — is a conjecture. The companion proposes it for holes light enough to have evaporated by
now, and derives neither how many such regions formed nor with what masses. This note extends
the same conjecture to the larger regions that survive to the present. Black holes formed later,
by the collapse of stars or gas, arise by a different process and are not discussed here. (L2) No
account of the crystallization dynamics is offered, and none of the note’s consequences depends on
one. In particular, the number of uncrystallized regions per unit mass is taken from observation,
not predicted. (L3) The clustering test requires environment measurements for little red dots that
are only now becoming possible, and its two branches — missed regions and wall breaches — are
idealizations that real dynamics could mix. (L4) The survival cutoff near 10
16.5
g, which separates
regions that evaporated from regions that persist, is taken from the companion and carries the
order-of-magnitude uncertainty stated there.
Declarations
Funding. Not applicable.
Availability of data and material. The figure is produced by one script, archived with the
series’ verification suites in the public repository (incomplete crystallization seeds.py).
Competing interests. The author declares no competing interests.
Authors’ contributions. Not applicable (single author).
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5
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