Contents lists available at ScienceDirect
Physics Open
journal homepage: www.elsevier.com/locate/physo
The Mass-Energy-Information Equivalence: A bottom-up identification of the
particle spectrum via FCC lattice error correction
Raghu Kulkarni
SSMTheory Group, IDrive Inc, Calabasas, CA 91302, USA
A R T I C L E I N F O
Handling Editor: William Barletta
Keywords:
Quantum error correction
FCC lattice
Mass-energy-information equivalence
A B S T R A C T
Does information possess physical mass? Modelling the physical vacuum as a substrate-free quantum error-
correcting code suggests that an elementary particle’s mass is simply its fault-tolerant verification cost. We test
this Mass-Energy-Information (M/E/I) equivalence on the Face-Centred Cubic (FCC) lattice, tracking defects
within a [[192, 130, 3]] CSS code. Through a bottom-up classification of all possible defect geometries, we
filter 25 candidate states through four strict thermodynamic and topological axioms — Minimum Topological
Dimension, Sector Completeness, Boundary Closure, and Kinematic Shedding — each derived from established
QEC theory or lattice gauge theory. Exactly 5 physically stable states survive this sieve. Their verification costs
— 1, 207, 273, 1836, and 1839 — match the empirical mass ratios of the electron, muon, pion, proton, and
neutron to within 0.12%. The rejected configurations violate specific physical constraints and match no known
particles. No parameters are fitted. This offers highly constrained macroscopic evidence that inertial rest mass
is the thermodynamic shadow of quantum error correction overhead.
1. Introduction
Landauer’s 1961 theorem [1] cemented the idea that information
has a physical footprint: erasing or manipulating one bit dissipates
at least ≥ ln 2 of energy. Coupling this with Einstein’s mass-
energy equivalence [2] implies a Mass-Energy-Information (M/E/I)
equivalence, where one bit carries a fundamental mass = ln 2∕
2
.
Measuring this mass in a laboratory remains practically impossible
— the Landauer mass near 10
−35
kg at room temperature is drowned
out by any material substrate [3]. We can instead investigate the M/E/I
equivalence in a system lacking an independent substrate: the physical
vacuum itself. If spacetime is modelled as a discrete quantum error-
correcting network — a CSS stabilizer code on the FCC lattice [4] —
particles emerge as localized syndrome patterns. Without a hardware
substrate, their informational verification cost is their only source of
mass.
An interactive 3D visualization of the FCC lattice code and the five
surviving defect structures is available at https://raghu91302.github.
io/ssmtheory/fcc_interactive_5.html.
This paper presents: (i) the physical motivation for vacuum QEC and
the mechanism of emergent Lorentz invariance (Section 2); (ii) a strict
mathematical definition of
grounded in QEC theory (Section 3); (iii)
physical derivations of all four axioms (Section 5); (iv) an enumeration
of 25 candidate defect geometries (Section 6); (v) step-by-step deriva-
tions of all five surviving particles (Section 7); (vi) connections to the
broader Standard Model (Section 9).
E-mail address: raghu@idrive.com.
2. Physical motivation: Why does the vacuum perform QEC?
2.1. Error source and stability
The FCC lattice is the unique densest sphere packing in three dimen-
sions [5]. A ground state of maximum packing density is also maximally
stable: any deviation from perfect close packing costs energy propor-
tional to the local density defect. We interpret this stability requirement
as continuous quantum error correction. The error source is not an
external thermal bath or vacuum fluctuations in the conventional QFT
sense, but the intrinsic discretization of spacetime: any departure from
exact FCC coordination constitutes a topological mismatch — a logical
error — that costs energy
× ln 2 to detect and restore. The FCC
geometry is simultaneously the ground state and the error-correcting
code.
2.2. Emergent Lorentz invariance
A common concern about discrete lattice models is conflict with
special relativity. We establish emergent Lorentz invariance in two
steps: (i) exact spatial isotropy from the structure tensor, and (ii)
emergent Lorentz boosts in the continuum limit.
Step 1: Spatial isotropy. The = 12 FCC nearest-neighbour bond
vectors are
𝐧
∈
(±1, ±1, 0), (±1, 0, ±1), (0, ±1, ±1)
2, = 1, … , 12. (1)
https://doi.org/10.1016/j.physo.2026.100414
Received 27 March 2026; Received in revised form 15 April 2026; Accepted 23 April 2026
Physics Open 27 (2026) 100414
Available online 27 April 2026
2666-0326/© 2026 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-
nc-nd/4.0/ ).
R. Kulkarni
Define the rank-2 structure tensor
≡
12
=1
. We compute each
component explicitly:
=
(
)
2
= 4 ×
1
2
bonds (±1,±1,0)
+ 4 ×
1
2
bonds (±1,0,±1)
+ 0
bonds (0,±1,±1)
= 4,
=
=
1
2
(+1)(+1) + (+1)(−1) + (−1)(+1) + (−1)(−1)
+ 0 + 0 = 0.
By the three-fold permutation symmetry of the bond set,
=
= 4
and all off-diagonal components vanish. Therefore:
= 4
. [exact, by enumeration] (2)
This guarantees equal propagation speed in every spatial direction.
The odd-rank tensor
≡
vanishes exactly: every bond
𝐧
has a partner −𝐧
(the FCC lattice is centrosymmetric), so every
odd-power sum cancels:
= 0. [exact, by inversion symmetry] (3)
Eq. (3) ensures (𝐤) = (−𝐤): there is no preferred direction and no
linear () term in the dispersion.
Step 2: Isotropy of the dispersion relation. For a scalar field on the FCC
lattice, the dispersion relation is (𝐤)
2
=
12
=1
[1−cos(𝐤 ⋅ 𝐧
)]. At long
wavelengths (𝐤 1), expand the cosine:
(𝐤)
2
≈
2
2
12
=1
(𝐤 ⋅ 𝐧
)
2
=
2
2
=
2
2
⋅ 4 𝐤
2
= 2
2
𝐤
2
, (4)
so =
lat
𝐤 with
lat
=
2. The dispersion is exactly isotropic at all
orders in for which the Taylor expansion is valid — the isotropy is
a direct algebraic consequence of
= 4
, not an approximation.
Corrections appear only at (
4
4
) from higher terms in the cosine
expansion, suppressed by (𝐤)
4
∼ (∕
)
4
for Planck-scale lattice
spacing ∼ 𝓁
.
Step 3: Lorentz boosts. The two tensor identities (2)–(3) and the
isotropic linear dispersion (4) are sufficient for Lorentz boosts to
emerge in the standard continuum limit [6]. At all energies below
the lattice cutoff 1∕ (taken to be the Planck scale
∼ 10
19
GeV),
these corrections are negligible and the dispersion is exactly isotropic.
Lorentz boosts then emerge in the standard way: a lattice Hamiltonian
whose dispersion is isotropic and linear in (at long wavelengths) gives
rise to a relativistic effective field theory in the continuum limit [6].
The lattice does break Lorentz symmetry at the cutoff scale 1∕, but
these violations are suppressed by (∕
)
2
and are consistent with
all current experimental bounds [7], which constrain Lorentz violation
below 10
−20
–10
−40
of the Planck scale.
3. Thermodynamic cost in a substrate-free vacuum
3.1. Strict definition of
Definition 1 (Fault-Tolerant Verification Cost). Let
sector
∈ {0, 1}
×
be the coupling sub-matrix for defect , where
is the number of phys-
ical qubits (edges) in the defect’s geometric footprint,
is the total
number of stabilizer constraints capable of detecting the defect (vertex
stabilizers plus face stabilizers), and
= 1 if qubit participates in
constraint . The fault-tolerant verification cost is
≡ dim(
sector
) =
×
. (5)
This is the classical bit overhead of the syndrome extraction circuit.
is the classical bit overhead of the syndrome extraction circuit: not the
number of stabilizer measurements (= nnz(), which counts only active
entries) nor the gate count (which scales with circuit depth). It is the
full dimension of the coupling matrix.
Why dim(), not nnz()? In fault-tolerant syndrome extraction [8,9],
both active pairs (
= 1, verified via CNOT gates) and inactive pairs
(
= 0) must be verified. The reason is hook errors: errors introduced
by the extraction circuit itself can corrupt qubits outside a stabilizer’s
support [9]. If an inactive pair is left unchecked, a hook error propagat-
ing through it may go undetected, breaking fault tolerance. Therefore
the total classical bit overhead is dim() =
×
, not nnz() = (the
number of physical qubits). For the proton:
= 36,
=
0
+
2
=
13 + 38 = 51,
= 36 × 51 = 1836. For the electron:
= 1,
= 1,
= 1.
3.2. Landauer-Einstein mass formula
The connection between
and mass follows from two established
results:
1. Information has energy. By Landauer’s principle, generating
classical bits through an irreversible process requires at least
× ln 2 of energy [1,3]. Syndrome extraction is thermody-
namically irreversible: it collapses the quantum syndrome state
into a classical bit string, dissipating energy
× ln 2.
2. Energy has mass. By =
2
[2], this energy corresponds to
mass
=
× ln 2∕
2
.
3. The vacuum has no substrate. For a hard drive, the Lan-
dauer mass (∼10
−35
kg/bit) is negligible beside the substrate
mass (∼0.1 kg). But if the vacuum is the code state, there is no
independent substrate. The information content of a localized
excitation is its only mass.
Therefore:
=
×
ln 2
2
. (6)
3.3. Temperature independence of mass ratios
Landauer’s principle was originally formulated for classical bits at
finite temperature, whereas the present system is a vacuum quantum
error-correcting code. We address this in two parts.
Applicability to QEC. Fault-tolerant syndrome extraction is thermo-
dynamically irreversible: measuring a stabilizer collapses a quantum
superposition to a classical outcome, a process that cannot be undone
without additional energy expenditure. This irreversible generation of
a classical bit is precisely the process to which Landauer’s principle
applies [3]. The bound ln 2 per bit holds for any irreversible classical
bit generation, regardless of whether the bit originates from a quantum
or classical source.
Temperature cancels in the ratio. The paper’s central claim is a dimen-
sionless mass ratio, not an absolute mass. Substituting Eq. (6) for two
particles and :
=
× ln 2∕
2
× ln 2∕
2
=
. (7)
The temperature , Boltzmann constant , and speed of light cancel
exactly. This cancellation holds for any temperature and requires no
assumption about the value of — whether it is the Planck temperature
=
5
∕
2
≈ 1.4 × 10
32
K, the CMB temperature, or any other
value.
Same temperature for all particles. Different particles inhabit the same
vacuum code state. Since they are excitations of the same FCC lattice
at the same Planck-scale energy, they experience the same vacuum
temperature . This is identical to all phonons in a crystal sharing the
same lattice temperature: the medium is common, so is the same
for all excitations. The assumption
proton
=
electron
is therefore not
an independent axiom but a direct consequence of the single-vacuum
hypothesis.
The mass ratio
∕
=
∕
= 1836∕1 is a pure topological
invariant of the FCC coordination cluster, independent of temperature,
energy scale, or cosmological epoch.
Physics Open 27 (2026) 100414
2
R. Kulkarni
Fig. 1. The architectural sub-structures of the FCC coordination cluster
13
. Left: 1-sheet (1D topology) — a star graph
1,4
with no faces ( = 0); the electron
defect. Centre: 2-sheet (2D topology) — two coupled sheets with triangular (
▵
) and square (
□
) faces; the pion defect. Right: 3-sheet (3D volume) — the full
cuboctahedral cluster with = 12 bonds; the muon, proton, and neutron defects.
Table 1
-vectors of the FCC coordination sub-structures.
Sub-structure
0
(V)
1
(E)
▵
□
2
(F) Euler
1-sheet (1D) 5 4 0 0 0 1
2-sheet (2D) 9 16 8 2 10 3
3-sheet (3D) 13 36 32 6 38 15
4. Topology of the FCC vacuum code
The FCC lattice supports a highly efficient CSS code [4]. Its repeat-
ing unit is the 13-node coordination cluster
13
(origin plus = 12
nearest neighbours). The = 12 coordination decomposes uniquely
into three orthogonal 2D sheets of 4 neighbours each. Topological sub-
structures and their -vectors (
0
,
1
,
2
) are given in Table 1 (see Fig.
1).
The coupling matrix for the full 3-sheet cluster is ∈ {0, 1}
36×51
with nnz() = 192 = (the number of physical qubits),
=
1
(the
edge Hodge Laplacian), and dim() = 36 × 51 = 1836.
5. The axioms: Physical derivations
To determine which mathematical sub-matrices constitute physi-
cally viable particles, we apply a strict topological sieve. Each axiom is
derived from established physics in QEC theory or lattice gauge theory.
Axiom 1 (Minimum Topological Dimension). The extraction circuit scales
from 1D to 2D to 3D strictly based on the defect’s structural footprint.
Physical derivation. In QEC, a stabilizer can detect a Pauli error
only if the stabilizer’s support and the error’s support have non-trivial
overlap [10]. A stabilizer with zero support overlap with the defect
commutes with it unconditionally — it returns the same syndrome
outcome whether the defect is present or absent. Such a measurement is
information-theoretically inert: its outcome carries zero mutual infor-
mation about the defect’s location or type, and therefore contributes
zero bits to
. Including zero-overlap stabilizers in the syndrome
extraction circuit would inflate
without improving detection capa-
bility, violating the definition of
as the fault-tolerant verification
cost. Consequently, only stabilizers with non-zero support overlap con-
tribute to
, which forces the circuit to scale strictly with the defect’s
topological footprint. For the FCC cluster: a 1D footprint (single edge)
shares support with no face stabilizer, so
= 1; a 2D footprint shares
support with the 2-sheet sub-structure, giving
= 16; a 3D footprint
engages the full cluster with
= 36.
Axiom 2 (Sector Completeness). The active sub-matrix must cover all
stabilizers capable of detecting the defect.
Physical derivation. This is the standard fault-tolerance requirement
of Shor [8] and Chao–Reichardt [9]. If any stabilizer capable of de-
tecting the defect is omitted, hook errors introduced by the extraction
circuit may propagate through the omitted stabilizer and go unde-
tected. A baryon spanning all three sheets must therefore trigger all
+ = 51 constraints; it cannot selectively ignore the 6 square faces
(
□
) to save cost, because those faces can detect hook errors from the
colour-flux tubes.
Axiom 3 (Boundary Closure). The active sub-matrix must form a closed
gauge boundary.
Physical derivation. In lattice gauge theory [11,12], gauge invariance
requires ∇⋅𝐄 = at every vertex (Gauss’s law on the lattice). A confined
quark–antiquark pair on two sheets has an open colour-flux boundary;
the colour charge leaks unless a 1D string connects the pair and carries
the compensating flux. Without the closing string, the state is not
gauge-invariant and immediately decays. The closing string is a 1D
object — a single edge connecting the two colour sources — with trivial
sector (no face stabilizers active on a 1D link), giving
string
= 1× 1 = 1
by the same formula as the electron (
= 1). Hence
= 272+1 = 273.
Axiom 4 (Kinematic Shedding for Rest Mass). A deconfined, spatially
extended state subtracts
2
trajectory checks to isolate rest mass.
Physical derivation. Rest mass is the verification cost at rest. A de-
confined particle moving through the lattice generates trajectory cor-
relations across = 3 extraction rounds in = 3 spatial directions:
2
= 9 redundant syndrome bits each round measure the same fact
(the particle has moved to a new location) rather than the particle’s
internal structure. These 9 kinematic checks are subtracted to isolate
the internal (rest-mass) cost. This is the lattice analogue of isolating
rest mass via
2
=
2
2
+
2
4
: subtracting the kinematic momentum
contribution leaves the rest-mass term. Only states with dim(
sector
) >
2
can shed kinematics; a minimal weight-1 defect (electron) has no
extended footprint.
6. The 25-candidate defect sieve
We enumerate all permutations of footprint (1/2/3-sheet), sector
(trivial, vertex, EM
□
, confined, full + ), and dynamic state
(static/moving/string-closed). This yields 25 mathematically distinct
configurations; Table 2 presents the complete sieve.
The seven 1-sheet candidates (rows 1–7), eight 2-sheet candidates
(rows 8–15), and ten 3-sheet candidates (rows 16–25) are each filtered
by the axioms; 20 are rejected and do not correspond to any known
particle.
Physics Open 27 (2026) 100414
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R. Kulkarni
Table 2
The 25 candidate configurations filtered by the four axioms. Five physically closed, minimal states survive.
Footprint Sector Dynamics dim()
Verdict
✓ 1-sheet Trivial Minimal 1 1 Electron
× 1-sheet Full Minimal 20 20 Ax1: 1D cannot bound faces
× 1-sheet Full Moving 20 11 Ax1/4: no extended footprint
× 1-sheet EM
□
Static – – Ax1:
□
= 0 on 1 sheet
× 1-sheet EM
□
Moving – – Ax1: same
× 1-sheet Confined Static – – Ax1: confinement needs 2+ sheets
× 1-sheet Confined Moving – – Ax1: same
✓ 2-sheet Confined String 272 273 Pion
±
× 2-sheet Full Static 304 304 Ax1: baryon requires 3 sheets
× 2-sheet Full Moving 304 295 Ax1: same
× 2-sheet EM
□
Moving 32 23 Ax1: deconfined leptons spread
× 2-sheet EM
□
Static 32 32 Ax3: no closure on 2 sheets
× 2-sheet Confined Static 272 272 Ax3: open boundary without string
× 2-sheet Confined Moving 272 263 Ax4: colour-confined states pinned
× 2-sheet Vertex Static 18 18 Ax3: open boundary, no faces
✓ 3-sheet Full Static (+) 1836 1836 Proton
✓ 3-sheet Full Static (0) 1836 1839 Neutron
✓ 3-sheet EM
□
Moving 216 207 Muon
× 3-sheet Confined Static 1620 1620 Ax2: incomplete without
□
× 3-sheet Confined Moving 1620 1611 Ax4: confined 3D cannot move
× 3-sheet Vertex Static 468 468 Ax3: unclosed boundary
× 3-sheet Vertex Moving 468 459 Ax3/4: unclosed + kinematic
× 3-sheet Full Moving 1836 1827 Ax4: confined 3D cannot move freely
× 3-sheet EM
□
Static 216 216 Ax4: colourless must shed kinematics
× 3-sheet EM
□
Static(0) 216 219 Ax4: colourless must move
a
a
The neutral static EM state inherits the internal probe of the neutral baryon (+ = 3), giving
= 216 + 3 = 219, but is still rejected:
Axiom 4 requires colourless deconfined states to be moving.
Table 3
Derived topological costs vs. empirical mass ratios [13].
Particle Predicted
Formula Experimental
∕
Deviation
Electron 1
×
= 1 × 1 1.000 0.000%
Muon 207 36 × 6 − 9 206.768 0.11%
Pion
±
273 16 × 17 + 1 273.132 0.05%
Proton 1836 36 × 51 1836.153 0.008%
Neutron 1839 36 × 51 + 3 1838.684 0.017%
Rejected configurations and BSM particles. The 20 rejected configu-
rations do not predict particles beyond the Standard Model. Each
rejection is caused by internal mathematical inconsistency under the
four axioms — dimensional mismatch, open gauge boundary, sector
incompleteness, or kinematic inconsistency — not by the physical
absence of a corresponding particle. No topologically stable state exists
in the FCC code with the geometry of any rejected configuration. The
framework therefore makes no prediction of new stable particles at
energies accessible to current collider experiments, and is consistent
with all experimental exclusion limits from the LHC [14].
7. The physical particle spectrum: Step-by-step derivations
7.1. Electron (
= 1)
Footprint: 1-sheet, 1D (single edge error)
Sub-structure:
= 1, = 2, = 0 (
= 0: no faces on
one sheet)
Sector: trivial (no face stabilizers active; Axiom
1)
Dynamics: minimal (no extended footprint; Axiom 4
does not apply)
=
×
= 1 × 1 = 𝟏.
The electron is the minimal excitation of the code. Since
= 0 on
a single sheet, there are no cross-sheet hook error propagation paths,
confirming that
= 1 (only the single syndrome change).
7.2. Muon (
= 207)
The muon spans the full 3-sheet cluster (
= 36) but is colourless
and deconfined, so only the
□
= 6 square faces of the EM sector are
active (
= 6). Because the muon moves freely through the lattice,
Axiom 4 applies:
= 36 × 6 −
2
= 216 − 9 = 𝟐𝟎𝟕.
7.3. Pion
±
(
= 273)
Footprint: 2-sheet (quark-antiquark pair)
Sub-structure:
= 16, = 9,
▵
= 8,
□
= 2
Sector: confined (
□
decoupled; active
= +
▵
= 9 + 8 = 17)
Dynamics: string-closed (Axiom 3 requires gauge
closure)
Base:
×
= 16 × 17 = 272.
Boundary closure (Axiom 3):
= 272 + 1 = 𝟐𝟕𝟑.
The +1 is the verification cost of the closing string: a 1D object with
trivial sector and no extended footprint, identical in structure to the
electron (
= 1 × 1 = 1).
7.4. Proton (
= 1836)
Footprint: 3-sheet (Y-junction [15]; full FCC cluster)
Sub-structure:
= 36, = 13, = 38 ⇒
=
0
+
2
= 51
Sector: full + (charged; Axiom 2 requires all
constraints)
Dynamics: static (colour-confined; Axiom 3 satisfied
by bounding cage)
Physics Open 27 (2026) 100414
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R. Kulkarni
=
×
= 36 × 51 = 𝟏𝟖𝟑𝟔.
This is also the dimension of the full coupling matrix : dim() =
1
× (
0
+
2
) = 36 × 51 = 1836 [4].
7.5. Neutron (
= 1839)
Footprint: 3-sheet (same as proton)
Sub-structure:
= 36,
= 51 (same base cost as
proton)
Sector: full + ; but neutral (no global
bounding flux)
Dynamics: static; neutral boundary mimics vacuum
The proton carries electric charge and emits a global topological flux,
which itself satisfies Boundary Closure (Axiom 3) — the bounding cage
closes the gauge boundary without additional probes. The neutron has
no such global flux: its boundary is electrically neutral and is indis-
tinguishable from the surrounding vacuum code state. To distinguish
the neutron from an empty site, the extraction circuit must actively
probe the = 3 internal colour-flux arms of the Y-junction, one per
spatial dimension. This internal probe is mandatory for the neutral case
and absent for the charged case — the asymmetry follows from gauge
structure, not from fitting (see Table 3):
= 36 × 51 + = 1836 + 3 = 𝟏𝟖𝟑𝟗.
8. Comparison with experiment
Proton–neutron mass difference. The model gives
−
= 3
; the
measured value is 2.531
, an 18.5% discrepancy on the splitting. This
gap is expected: discrete topological costs set the integer baseline, while
electromagnetic self-energy and bare quark masses produce sub-integer
QFT corrections that lie outside the framework.
9. Extension to the broader standard model
9.1. Scope of the first-shell enumeration
The 25 candidates in Table 2 span all defect geometries within the
first coordination shell of the FCC lattice ( = 12 nearest neighbours).
This shell accommodates the five lightest non-strange particles. Par-
ticles requiring a second-shell description, a condensate description,
or a sub-threshold (near-vacuum) description lie outside the present
enumeration.
9.2. Gauge bosons
The = 12 FCC bonds partition exactly as =
TOR
+
TR
= 8+4 =
12, where
TOR
= 8 triangular-plaquette bonds host the SU(3) sector (8
gluons) and
TR
= 4 square-plaquette bonds host the electroweak sector
(
+
,
−
, , ). This partition exactly reproduces the Standard Model
gauge boson count at the structural level. The gauge boson masses
involve the Higgs mechanism and lie outside the topological defect
classification of the present framework.
9.3. Neutrinos
All five first-shell stable states have verification cost
≥ 1. The
electron (
= 1) is the minimum stable defect. Neutrino masses,
suppressed by seven orders of magnitude below the electron, would
correspond to
1 — strictly below the first topological threshold
of the M/E/I framework. Within the M/E/I picture this is consistent: the
sieve finds no stable first-shell defect with 0 <
< 1, which is why
neutrinos do not appear in Table 2 as massive topological defects. A
derivation of neutrino masses and PMNS mixing angles within the FCC
vacuum framework requires an extended sub-threshold analysis beyond
the scope of the present work.
9.4. Heavier leptons and strange hadrons
The tauon, kaons, lambda baryons, and sigma baryons are not
matched by any first-shell configuration. This is a scope boundary of the
present framework: the five surviving states account for the five lightest
non-strange particles; no first-shell defect geometry corresponds to
these heavier particles.
9.5. Higgs boson
The Higgs boson is the vacuum condensate mode of the FCC lat-
tice, not a topological defect. Its mass scale (125 GeV) far exceeds
the first-shell defect energies, placing it outside the topological defect
classification of the present framework.
9.6. Excluded configurations and BSM physics
All 20 rejected configurations in Table 2 are eliminated by inter-
nal topological inconsistency — dimensional mismatch, open gauge
boundary, or kinematic contradiction — not by the physical absence
of a corresponding particle. The framework predicts no stable non-
SM particle within the first coordination shell, consistent with all LHC
exclusion limits [14].
10. Conclusions
Discarding the continuous geometric vacuum in favour of a discrete
topological CSS code allows a bottom-up identification of five consis-
tent defect states whose verification costs exactly match fundamental
particle masses. The mass ratio
∕
=
∕
is a pure topological
invariant: , , and cancel exactly, leaving integer predictions from
the FCC -vectors alone. Applying strict axioms grounded in QEC
theory and lattice gauge theory filters 25 candidate geometries down
to exactly 5 physically viable states. Their precise alignment with the
empirical Standard Model mass spectrum provides robust, falsifiable
evidence that inertial mass is the thermodynamic shadow of quantum
error correction overhead.
CRediT authorship contribution statement
Raghu Kulkarni: Writing – review & editing, Writing – original
draft, Visualization, Validation, Methodology, Conceptualization.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared to
influence the work reported in this paper.
Data availability
Data will be made available on request.
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