Every typed node

Work-energy theorem

The net work done on a particle equals its change in translational kinetic energy.

W_net = integral F_net . d r

Newton's second law

The net external force equals the time rate of change of momentum; for constant mass this reduces to F_net = m a.

F_net = d p / d t

Conservation of linear momentum

The total linear momentum of an isolated system is constant.

P = sum_i p_i

Maxwell equations in SI form

The classical electromagnetic field equations relating electric and magnetic fields to charge and current.

div E = rho / epsilon_0

HYPExamples

Eight-hertz organizing-frequency hypothesis

Early test proposal; 8 Hz is not asserted to be a universal constant.

N_8HZ

Time-dependent Schroedinger equation

The nonrelativistic quantum state evolves unitarily under its Hamiltonian according to the Schroedinger equation.

i hbar partial psi / partial t = H psi

Planck-Einstein energy-frequency relation

A photon of frequency f has energy E = h f; more generally quantum stationary-state phases evolve with angular frequency E/hbar.

E = h f

Lorentz-invariant spacetime interval

The Minkowski interval is invariant under Lorentz transformations between inertial frames.

Delta s^2 = c^2 Delta t^2 - Delta x^2 - Delta y^2 - Delta z^2

Mass-energy equivalence

Rest energy relation in special relativity.

E = m c^2

Agent circulation and immune-review architecture

Symbolic mapping for bounded transport, review, quarantine and coordination roles.

CIRCULATION_IMMUNITY

Information-theoretic ToE blueprint sketch (example only)

Non-authoritative conceptual scaffold that maps information-layer bookkeeping ideas onto familiar physics vocabulary. Status is SYM: illustrative sketch only — not an established theory, not peer-reviewed, and not a claim of experimental verification. Do not treat as UPI core physics identity.

UNIFIED_BLUEPRINT_SKETCH

Quadralith symbolic control graph

Optional conceptual graph; it is not an accepted physical model.

AUM <-> alpha <-> Omega <-> Phi <-> AUM

Vortex-DNA functional architecture

Transparent collaboration and boundary-control model; DNA is metaphorical.

FUNCTIONAL_ARCHITECTURE

Intentionally invalid symbolic promotion

A negative test fixture.

N_PROMOTION

First and second laws of thermodynamics

Energy is conserved in thermodynamic processes, while entropy production is nonnegative for an isolated macroscopic system.

Delta U = Q - W

Equal Temperament Musical Notes and Pitch Frequency Mapping

Mathematical and physical mapping of Western 12-tone equal temperament (12-TET) musical notes to acoustic fundamental frequencies, pitch notation, staff clefs (G-klav and F-klav), and duration ratios.

f(n) = f_0 * 2^(n / 12)

DERExamples

DNA Nucleotide Sequence Bio-Acoustic Frequency Mapping

Sonification mapping translating DNA nucleotide bases (Adenine, Cytosine, Guanine, Thymine) into acoustic pitch frequencies, musical notes, and dimensionless 8 Hz reference indices N8.

f(base) = note_frequency(base)

HYPBiology

Biological homochirality and symmetry-breaking amplification

A bounded node separating observed biological handedness, demonstrated asymmetric autocatalysis, and unresolved origin mechanisms.

ee = abs(x-y)/(x+y)

ESTCoding theory

Extended binary Golay code G24

The unique (up to equivalence) binary linear [24, 12, 8] code. It is perfect, self-dual, and has 759 weight-8 codewords (octads). This index ships a software encoder and nearest-codeword decoder.

n = 24, k = 12, d = 8, t = 3

ESTCoding theory

E8 root lattice

The unique even unimodular lattice in 8 dimensions. Its 240 roots are the vertices of the 4_21 polytope. This is a theorem in lattice theory, not a model of spacetime.

||v||^2 = 2 for every root v

ESTCoding theory

Leech lattice Λ24

The unique even unimodular lattice in 24 dimensions with no vectors of norm 2. It realises the densest known sphere packing in 24 dimensions (proved optimal).

min { ||x||^2 : x in Λ24, x ≠ 0 } = 4

DERComputational

Classical state-vector simulation resource boundary

Derived computational boundary for software that explicitly stores and updates every amplitude of an N-dimensional quantum state. Such a simulator can reproduce ideal finite-dimensional linear algebra but uses classical resources proportional to the represented basis size.

memory_dense_state = O(N)

Schumann resonances of the Earth–ionosphere cavity

The Earth and the ionosphere form a spherical electromagnetic cavity whose fundamental is near 7.8 Hz, with harmonics near 14, 20, 26 Hz. This is geophysics. It is not a human operator lock and not a universal organizing frequency.

f_n ≈ (c / 2 π R_E) * sqrt(n(n+1))

Bekenstein–Hawking horizon entropy

Geometric entropy of a semiclassical event horizon: S = k A / (4 ℓ_P²). This is the purest gravitational entropy we have — an area law, not a named gas. It applies to horizons, not to an arbitrary frequency quantum.

S = k A / (4 ℓ_P^2)

Anti-de Sitter spacetime

Maximally symmetric Lorentzian geometry of constant negative curvature: Einstein's equation with Λ < 0. It has a conformal boundary. This is a solution, not a claim that we live in AdS.

R_μν - (1/2) R g_μν + Λ g_μν = 0

ESTTheories

AdS/CFT correspondence

Maldacena's duality: quantum gravity in anti-de Sitter space is equivalent to a conformal field theory on the conformal boundary. Established as a dictionary for specific compactifications (AdS5×S5/N=4 SYM, AdS3/CFT2, AdS4×S7/ABJM). Not a model of our cosmology, which is closer to de Sitter.

Z_gravity[φ_0] = < exp(∫ O φ_0) >_CFT

ESTTheories

Ryu–Takayanagi entanglement entropy

In AdS/CFT the entanglement entropy of a boundary region A equals the area of a bulk extremal surface γ_A homologous to A, in Planck units. This is the in-domain holographic entropy: information on the boundary, area in the bulk. It is not the Schwarzschild area of a lab mass m_I.

S_A = Area(γ_A) / (4 G_N)

DERTheories

AdS4 × S7 / ABJM

The 11-dimensional instance of AdS/CFT: M-theory on AdS4 × S7 is dual to the ABJM 3d N=6 Chern–Simons-matter theory (M2-branes). This is how an 11D brane enters holography — as a named pair, not as a picture of the lab.

AdS4 × S7 ↔ ABJM_{N,k}

DERInformation physics

Mass equivalent of a frequency quantum

Compose the Planck–Einstein relation E = h f with the inertia of energy E = m c². The same kind of step Einstein took with Planck: a derived identification, not a new independent axiom. m here is the mass equivalent of energy h f — not photon rest mass, and not the rest mass of an arbitrary oscillator.

E = h f

HYPInformation physics

Information mass

T€@X (2026) identification: when information is physically instantiated as a frequency quantum, its inertial mass is m_I = h f / c². This is a named reading of the derived mass equivalent, not a second formula and not a photon rest mass.

m_I = h f / c^2

Landauer’s principle for bit erasure

Erasing one bit of information in a physical computer at temperature T dissipates at least kT ln 2 of heat. This is a thermodynamic bound on logically irreversible operations, not a political slogan and not a local entropy reset.

Q >= k T ln 2 per erased bit

STOPInformation physics

Sub-Planck horizon of a frequency quantum

For laboratory frequencies the Schwarzschild radius of m_I = h f / c² is far below ℓ_P. Geometric entropy is then being asked of a horizon that does not exist in the semiclassical theory. The loop STOPS at this station.

R_s(f) = 2 G h f / c^4

HYPInformation physics

Universal information measure

A proposed closed measure: every physical encoding with frequency f is assigned the number m_I = h f / c², dual to geometric entropy S = k A(m_I)/(4 ℓ_P²), dual to 11D brane degrees of freedom, returning to the encoding. That is what a measure is — a number on every measurable. The loop is HYP. The 11D closure is SYM. The geometric-entropy step STOPS when the Schwarzschild radius of m_I falls below ℓ_P.

m_I = h f / c^2

DERInformation physics

Digital multi-torus qudit search simulator

A classical state-vector implementation of finite-dimensional qudits, local Fourier duality, phase oracles, diffusion and amplitude amplification. Each declared torus is a cyclic mixed-radix coordinate with d basis states, allowing registers with more than three states per search axis. The implementation is software and does not claim quantum hardware or speedup.

H = tensor_i C^(d_i)

DERInformation physics

Dual-observer trace and invariant mapping

A traceable model connecting two observer-dependent representations through a translation operator, a preserved invariant, forward generation, backward reconstruction, conflict scoring, and evidence-sensitive status control. The implemented physical reference profile uses 1+1 dimensional Lorentz transformations.

X_B = D_A_to_B(X_A)

HYPInformation physics

Information-to-dark-sector bridge candidate

Research hypothesis testing whether declared information or horizon inputs can non-circularly constrain a shift-symmetric P(X) effective field model with dark-matter-like and acceleration-like regimes. This is not established physics.

E = h*f

Indaleko abstract payload 160 TB is not the body used figure

Audit STOP for arXiv:2602.20507. The abstract claims a 31-million file dataset spanning 160TB across eight storage platforms. Chapters 5–6 report 31.9 million files, 35.1 TB capacity, 16.2 TB used, and 78.6 GB of ArangoDB metadata. The two number sets are not identified as the same quantity.

log10(160e12) - log10(16.2e12) ≈ 0.995

m = hf/c² does not close the Standard Model

A public X claim that the photon rewrite closes the Standard Model. CKM, the Higgs vacuum expectation, and three generations are not generated by m=hf/c². STOP until a residual to a measured SM parameter exists.

m = h f / c^2

LOOP 201: unresolved information-to-P(X) parameter map

Audit STOP for the current dark-sector bridge: no non-circular derivation has yet fixed rho_0, X_0, and P_2 from information or horizon inputs while preserving correct bulk/horizon energy accounting.

P(X) = -rho_0 + P_2*(X-X_0)^2

ESTTheories

Newtonian Mechanics

Classical mechanics based on Newton's laws of motion and universal gravitation. Applies to macroscopic objects at non-relativistic speeds.

F = ma (Second Law)

ESTConstants

Planck Constant

Fundamental quantum constant relating energy and frequency. h = 6.62607015×10⁻³⁴ J·s (exact by 2019 SI definition).

E = h × f

Dark Matter

Unseen matter comprising ~85% of matter in the universe. Inferred from gravitational effects on galaxies and large-scale structure.

dark_matter

ESTMechanics

Helical motion, screw conversion, and coupled-rotor balance

Established classical mechanics and differential geometry for motion combining translation along an axis with rotation around it. The node indexes helix position, velocity, acceleration, pitch, curvature, torsion, force, kinetic energy, angular momentum, power, ideal screw conversion, and two-rotor angular-momentum balance.

theta(t) = omega t + phi_0

ESTQuantum algorithms

Phase-oracle amplitude amplification

Established ideal quantum-search mechanism in which a phase oracle marks target states and a reflection about the initial state rotates amplitude toward the marked subspace. Grover search is the uniform-state special case.

O_f |x> = (-1)^(f(x)) |x>

Conformal field theory

A quantum field theory invariant under conformal transformations (and, in the holographic setting, typically a large-N gauge theory). In two dimensions the symmetry algebra is Virasoro.

T^μ_μ = 0

Quantum error correction as syndrome measurement

A stabilizer code detects errors by measuring commuting Pauli checks. The syndrome names a coset; a decoder proposes a recovery. Classical codes such as G24 enter as CSS ingredients — they are not themselves quantum memories.

s_i = ±1 from measuring generator g_i

Finite-dimensional Hilbert state space

Established mathematical state-space framework for a finite d-level quantum system. Pure states are normalized rays in the complex vector space C^d, observables are represented by Hermitian operators, and valid closed-system basis changes are unitary.

H_d = C^d

Born probability rule for finite basis measurements

Established quantum-mechanical probability rule. For a normalized state expanded in an orthonormal measurement basis, the ideal probability of outcome j is the squared magnitude of its complex amplitude.

alpha_j = <j|psi>

Multi-qudit tensor-product register

Established composition rule for multiple finite-dimensional quantum systems. Local state spaces combine through a tensor product, producing a register dimension equal to the product of the local dimensions.

H = tensor_(i=1)^n C^(d_i)

Qudit Fourier-dual basis

Established normalized discrete Fourier transform on a d-level quantum system. It maps computational-basis states to a mutually unbiased Fourier basis and is inverted by the conjugate transform.

F_d |j> = (1/sqrt(d)) sum_(k=0)^(d-1) exp(2 pi i j k / d) |k>

Generalized qudit shift and phase gates

Established d-level generalization of the Pauli shift and phase operators. The cyclic shift X_d permutes computational-basis labels modulo d, while Z_d changes their relative phases using d-th roots of unity.

omega_d = exp(2 pi i / d)