Recognition Physics is a parameter‑free, meter‑native framework. From a small set of fixed equations and constants, it derives the numbers we measure—without tunable knobs. The structure is over‑constrained and falsifiable: if any mapped equality fails, the framework does too.
The mathematics is straightforward and checkable by any physicist. What is posted here already reproduces the core results; we are expanding details continuously.
E_coh is the minimal, universal quantum of energetic “weight” the ledger assigns to one coherent unit of recognition. It is not an adjustable parameter: its φ‑scaling is fixed by the derivation layer and its SI magnitude is anchored by the single bridge choice of units. Formally,
E_coh = E_0 · φ^{-5}
where φ = (1+√5)/2 is the unique self‑similar fixed point and E_0 is the bridge’s base energy unit. Under the standard meter‑native landing used on this site, we display E_coh ≈ 0.090169943 eV.
The ledger calculus forces a unique symmetric cost functional J(x)=½(x+1/x) and a minimal eight‑tick cycle in 3D space. A single coherent recognition must span the minimal structure that supports stability and dual balance. The irreducible recognition degrees are:
Self‑similar recognition steps scale on the φ‑ladder; counting the five independent recognizer constraints yields the φ^{-5} factor. Thus E_coh inherits the same geometrically forced scaling observed throughout the framework (masses, rates, gaps).
Either way, φ^{-5} is invariant; only the label (units) changes.
All on‑shell particle masses share one base unit and one scaling grammar:
m = B · E_coh · φ^{r + f}
Because E_coh is fixed, there is no freedom to “re‑scale” a single particle: changing E_coh would uniformly distort the entire spectrum and break cross‑sector ratios.
With the time‑first landing and exact ħ, u(E_coh)=u(τ_0). In length‑first, E_coh shares the ½·u(G) contribution through τ_0 inferred from λ_rec. Either way, publishing u(τ_0) or equivalently the consistency check with G closes the metrology loop.
τ_rec is the minimal duration of a single recognition hand‑off — the shortest possible time to post one debit/credit pair on the ledger and advance a state. No physical process can complete one recognition step in less than τ_rec.
Time‑first: u(τ_rec)=u(τ_0). Length‑first: u(τ_rec)=½·u(G). Publish u(τ_0) (or the consistency check against G) to close the metrology loop — there is no adjustable scale beyond these anchors.
λ_rec is the minimal spatial stride for a single recognition hand‑off — the shortest distance a null exchange traverses in one atomic tick. It plays the role of a meter‑native anchor for displays while leaving all dimensionless derivations unchanged.
λ_rec = √(ħ G / c³)
Optional documented convention: a π‑normalized display variant λ_rec(π) = λ_rec / √π; the two are linked by an explicit lemma in the artifact and represent conventions, not new physics.
In SI (post‑2019), ħ and c are exact by definition. Therefore the relative standard uncertainty is u(λ_rec) = ½ · u(G).
Under a time‑first landing, the kinematic hop per tick (λ_kin = c·τ_rec) must agree with the Planck‑form λ_rec within the combined uncertainty of (τ_0, G).
A_L = {−4, −3, −2, −1, 0, +1, +2, +3, +4} is the minimal signed alphabet used to post discrete recognition costs on the ledger. Each symbol represents one indivisible increment of cost (positive or negative), with 0 denoting a null posting.
This alphabet is dimensionless and fixed at the proof layer; it does not introduce any tunable parameter.
Together these constraints eliminate all smaller alphabets (insufficient span) and all larger ones (instability/overhead), leaving the nine‑state set as unique and minimal.
A_L underlies the LNAL instruction set by providing the allowed per‑tick cost quanta that operations may emit or absorb. Programs are sequences of LNAL instructions whose underlying symbol stream over A_L respects dual balance and the eight‑beat scheduler.
B_i counts the number of independent recognition channels that contribute linearly to a state’s mass at the structure‑only level. It is a dimensionless integer fixed by sector definitions and combinatorics — not a tunable constant.
Examples of minimal sectors used on this site: leptons B_e=1, quarks B_q=3 (color triplet), gauge sector exemplar B_W=12 (aggregate multiplicity in the gauge block used for the spectra demonstrator).
Result: B_i is fixed by counting (e.g., 3 for quark color), not by fitting. Changing B_i would violate either channel independence or sector minimality.
m = B_i · E_coh · φ^{r + f}
The ledger gap is the positive dimensionless constant δ_gap = ln φ, where φ=(1+√5)/2. It quantifies a minimal, unavoidable surplus in the discrete recognition calculus arising from self‑similar recursion and dual balance — the “price” of maintaining consistent recognition.
The gap arises from the undecidability series with generating functional
F(z) = Σ_{m≥1} (-1)^{m+1} / (m φ^{m}) · z^{m} = ln(1 + z/φ), |z|≤1
Evaluating at z=1 gives the ledger gap δ_gap = F(1) = ln φ.
δ_gap is pure number — no SI units, no bridge dependence. Its value is exact given φ’s algebraic definition; there is no experimental uncertainty attached to δ_gap itself.
Any recognition structure satisfying Meta‑Principle (MP: ¬(∅▷∅)), Composability, and Finiteness admits a unique (up to order‑isomorphism) positive, double‑entry ledger with an immutable generator δ > 0. For every finite closed chain the posted sum telescopes to 0 (local conservation).
Reality keeps receipts. Every change has a matching counter‑change; you can’t mint credits from nowhere or change the coin size mid‑story. Under the minimal assumptions (no miracles, composable changes, no infinite rabbit‑holes), a two‑column ledger isn’t optional—it’s forced.
Let the self‑similar update be x_{n+1}=1+\tfrac{k}{x_n} with k>0 and x_0>1, interpreted as k indivisible sub‑recognitions per tick. Countability enforces k∈\mathbb N; cost minimization over k selects k=1. The fixed‑point equation x=1+1/x has the unique positive solution φ=(1+√5)/2. Thus φ is the universal scaling constant.
When you repair an imbalance by splitting it into equal, indivisible steps, the cheapest allowed split is into exactly one step per tick. That constraint forces the golden ratio to govern the scale‑by‑scale pattern.
Let dual‑balance decompose a voxel recognition into two edge‑disjoint closed cycles (potential/realised). A non‑trivial link between these cycles is necessary to prevent erasure of dual cost by isotopy. In d=2 no independent cycles exist (Jordan), in d≥4 links are unlinked by ambient isotopy (Alexander duality). Hence d=3 is minimal and necessary. A strict global tick order provides the temporal dimension, yielding 3+1 spacetime.
You need exactly three directions to tie—even once—the simplest knot that keeps dual costs from canceling. In fewer, knots collapse; in more, they untie. Time is the universal ordering of ticks.
On the cube graph Q_3 with vertices V=\{0,1\}^3, a ledger‑compatible recognition walk ρ:ℤ→V that (i) steps along edges each tick, (ii) is periodic with minimal period T, and (iii) visits all 8 vertices in one period, must have T=8. A Hamiltonian Gray cycle realises T=8; no T<8 walk satisfies (i)–(iii).
To fully “touch” every corner of the smallest 3D voxel exactly once per cycle, you need eight beats—no fewer, no more.
In the discrete ledger on Q_3, a null exchange is a recognition hop that carries no net ledger imbalance across a tick. Ledger atomicity (one edge per tick) bounds the spatial advance per tick by the single‑hop length λ_rec; therefore the maximal signal speed is c := λ_rec/τ_rec. Under the Reality Bridge, this displays as the universal speed of light.
Light is just the fastest possible hand‑off of recognition: one voxel hop in one tick. Nothing can beat one hop per tick, so c is the speed limit.
There exists a factorization of pole masses into a structure‑only piece and a finite dressing: m_i = B_i · E_coh · φ^{r_i + f_i}, where: B_i ∈ \{1,3,12,...\} counts independent recognition channels (sector factor), r_i∈\mathbb Z is the unique minimal ledger path length consistent with the field’s gauge charges, and f_i is the dimensionless RG residue defined by a definite integral of the SM anomalous dimension between a universal matching scale and the pole scale. No per‑species knobs enter.
A particle’s mass is (channels) × (one universal energy coin) × (a φ‑ladder step). The integer step r is fixed by its charges; the small extra f is the standard finite quantum dressing—computed, not fitted.
Under coarse‑graining of the ledger on a 3D voxel lattice and bridge continuity assumptions, the effective continuum action density depends on a scalar curvature functional whose regulator is the second variation of ledger entropy with respect to geometric deformations: κ := ∂²S/∂R². This identification preserves conservation, gauge uniqueness up to a constant, and local EL/log‑axis stationarity.
When many recognitions are averaged into smooth fields, the way ledger “content” bends under shape changes looks exactly like spacetime curvature. The curvature term is the ledger’s second‑derivative response.
Recognition Physics is the framework of reality itself—built from acts of distinction where systems register differences. Every act carries unavoidable cost; that cost gives time its arrow and enforces two‑sided balance (every push has a pull, every mark a counter‑mark). Apply this rule universally and the familiar world doesn't just appear—it becomes inevitable: the speed of light, the minimal tick of time, three spatial dimensions, and stable patterns we call particles and fields. Quantum rules are the statistics of overlapping recognition paths. Gravity is the geometry induced when large collections of distinctions shape the stage they traverse. The fundamental constants aren't assumed—they're derived.
This framework proves why the universe must have these exact numbers, this speed limit, these dimensions. It treats recognition—not human minds, but the bare capacity to draw distinctions—as fundamental. Matter is what stable recognitions look like from the outside; experience is what some recognitions are like from the inside. Reality is a self‑running computation whose atoms are acts of noticing. See the logical foundations and operating formulas.
Physics becomes a calculus of balanced change rather than a catalog of particles. Constants become theorems. Measurement is primitive—not an add‑on—because observation is the basic move. The same balancing rules build electrons and experiences, unifying mind and matter as one grammar spoken in two dialects. Explore the encyclopedia for deeper dives.
Absolute nothing cannot even assert "I am nothing" without ceasing to be nothing. Reality therefore contains process—differences that make a difference: the tiniest noticings.
A lone unbalanced mark would explode the ledger with unpayable debt. Every change comes with a counter‑change; every move can, in principle, be undone. Conservation laws and path‑economy follow. Time's arrow is net cost grinding forward.
Nontrivial knots in the weave of noticings require three spatial directions; fewer cannot support them and more make untangling too easy. Walking the smallest 3‑D voxel visits its eight corners in an eight‑beat cycle—the universe's minimal heartbeat. One tick is the minimum time to hand a difference from place to place, so a maximum speed is inevitable.
A photon is a pure relay of difference—change that always pays its cost forward. Massive particles are loops that keep part of the cost on hold, yielding inertia. Quantum probabilities arise by summing alternative recognition paths; the squared‑amplitude rule is the unique consistent map from overlapping stories to chances.
Where recognitions cluster densely, routing differences becomes expensive and the background rules deform. Space bends not because matter sits on space but because traffic reshapes the network. Gravity is the geometry of the universe's bookkeeping for change.
Numbers decide. This framework derives specific dimensionless quantities (the fine‑structure constant), proves why exactly three large spatial dimensions appear, predicts cosmological fractions, and resolves several tensions—without adjustable knobs. Procedures are published; results check against independent data. The manuscripts detail derivations of constants, particle masses, and large‑scale structure, together with concrete tests for current and near‑future experiments. Our latest work shows how galaxy rotation curves emerge from information bandwidth limits—no dark matter needed.
Matter reduces to the most stable patterns within the balancing game. The rock is real because its pattern of distinctions is robust against being nudged.
There is no outside server. The computation is what reality is, not what it runs on.
Recognition is the minimal capacity to register a difference, not a claim that atoms have opinions. Complex minds are large, richly recursive recognizers built from the same rules.
Prove constants from necessity; if a number cannot be deduced, it is not fundamental.
Measurement is the first move—drawing a boundary, paying the cost.
Every other framework in physics starts with assumptions—then fits parameters to match observation. Recognition Physics starts with tautology—what must be true—then derives what we observe. This is the difference between modeling reality and measuring it.
When you derive the fine-structure constant from pure logic, you're not fitting—you're reading reality's source code. When particle masses emerge from the golden ratio, you're not discovering a pattern—you're seeing the only way stable forms can exist. When three spatial dimensions prove necessary for non-trivial knots, you're not explaining a choice—you're proving an inevitability.
This framework doesn't compete with quantum mechanics or general relativity—it derives them. They are what the balancing rules look like at different scales. The speed of light, Planck's constant, the gravitational constant—these aren't inputs, they're outputs. Consequences of the only way a self-consistent reality can operate.
This changes what physics is. From cataloging phenomena to proving necessities. From "how" to "why it must be." From parameters to principles. See our 43 verified predictions and mathematical proofs.
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