Exploration: Locality of Information and Resonant Propagation

Status: Exploration. Investigates the locality structure of information in the Planck substrate: what each Planck cell carries, how the global Hilbert space relates to local computation, how D's local action aggregates into resonant propagation at larger scales, and the structural parallel between physical information propagation and the methodology's probabilistic lattice navigation.

Builds on: analysis-planck-information-substrate.md (6 primitives, SSA topology), exploration-cellular-automata-and-the-substrate.md (CA picture), exploration-where-information-lives.md (information in the state), synthesis-planck-information-substrate-complete.md (triple fusion, self-referential grid)

1. The Question

The Planck information substrate analysis establishes: D is the update rule, |ψ⟩ is the configuration, space IS the entanglement pattern. But a structural question remains: what is the locality of the information that D needs to operate?

The global Hilbert space H is enormous (~10¹²² dimensions for the observable universe). It seems unreasonable that each Planck cell "carries" this vast configuration space. The universe must be a distributed information store — global information distributed across local carriers — with D operating on locally-available information. But where exactly are the boundaries? What does each cell carry? And what happens when we move from the pure-local (one Planck cell) to larger scales?

2. The Local Information Structure

2.1 What each Planck cell carries

The Hilbert space has a tensor product structure reflecting locality:

H = ⊗_x H_x

where H_x is the local Hilbert space at Planck-scale site x. Each H_x is FINITE-DIMENSIONAL — a small quantum system with a bounded number of states.

What a single cell carries:

• Its own quantum state |ψ_x⟩ ∈ H_x (a finite-dimensional quantum state — a few qubits worth)
• Its connection structure to neighbors (encoded in D's commutator support — which other sites it interacts with)
• That's it. Nothing else.

The cell does NOT carry:

• The global state |ψ⟩ (that's the collection of ALL cells' states plus all their correlations)
• The states of distant cells (those are inaccessible until they propagate through the network)
• The full configuration space (that's a mathematical description of all POSSIBLE states, not something any cell needs)

2.2 What D needs for one update

D is a first-order differential operator. "First-order" translates directly to locality: D needs only the state at a cell and the states at its immediate neighbors.

In CA language:

|ψ_x(t+1)⟩ = f(|ψ_x(t)⟩, {|ψ_y(t)⟩ : y ∈ neighbors(x)})

The information required for one update step at site x:

• The state of x itself: |ψ_x⟩
• The states of x's neighbors: {|ψ_y⟩} for y adjacent to x
• The rule D (universal, same everywhere — not "carried" per-cell but implicit in the dynamics)

The computational information footprint is exactly one neighborhood. For a Planck-scale graph with connectivity k (number of neighbors per cell), the update requires k+1 local Hilbert space states. If each H_x has dimension d, the information needed is (k+1) × log₂(d) qubits — a tiny, fixed amount regardless of the universe's total size.

2.3 The three nested locality boundaries

The gap between these boundaries is structurally significant:

• D operates at one Planck length (ultra-local)
• But entanglement extends across the boundary of a region (non-local correlations)
• And the total information in a region is bounded by the boundary area (holographic)

The computational boundary is INSIDE the entanglement boundary, which is INSIDE (or equal to) the information-theoretic boundary. Each boundary is a different structural constraint on how information organizes.

2.4 Why the global Hilbert space is not "carried" anywhere

The global Hilbert space H = ⊗_x H_x has dimension d^N where d = dim(H_x) and N ~ 10¹²² is the number of Planck cells. This is an incomprehensibly large space. But it is:

1. A mathematical description of all POSSIBLE configurations of all cells simultaneously. It exists as a description space, not as something any physical entity needs to store.

2. Factored by locality. The tensor product structure means the full state decomposes into local contributions PLUS correlations. A product state |ψ⟩ = ⊗_x |ψ_x⟩ needs only N × log₂(d) bits — each cell's state independently. The "extra" information beyond this is ENTANGLEMENT — correlations between cells that can't be reduced to individual cell states.

3. Bounded by the area law. The entanglement between a region and its complement scales with the BOUNDARY area, not the volume. This means the non-local information (the part that CAN'T be decomposed into local states) is concentrated at interfaces, not spread throughout volumes.

The universe doesn't carry H. Each cell carries H_x. The correlations between cells (entanglement) are a relational property — they "live" in the joint state of cell pairs, not at any single location. And the total correlation content is bounded by boundary areas, not volumes.

3. From Local to Global: Resonant Propagation

3.1 The local emanation picture

Each Planck cell continuously runs D against its local state and its neighbors' states. The output: an updated local state that reflects the cell's response to its immediate environment.

But this update PROPAGATES. Cell x updates based on its neighbors → cell x's new state affects ITS neighbors at the next time step → those neighbors' updates propagate further → and so on. One local update at x becomes a ripple through the network.

Each cell is continuously emanating its D-operator convergent state. The cell runs D, produces a determination (an updated state), and that determination immediately becomes input for all neighbor cells. The neighbors incorporate it, produce their own determinations, and emanate those in turn.

This is not metaphorical. In the QCA picture: at each Planck time step, every cell simultaneously evaluates D on its neighborhood and updates. The collective result is a wave of state-updates propagating through the entire lattice at the speed determined by D's spectral properties — which IS the speed of light.

3.2 Aggregation into resonant propagation waves

At the single-cell level: one cell updates, affecting neighbors.

At larger scales, something qualitatively different emerges: resonant propagation patterns — sustained, coherent structures in the update flow that persist across many cells and many time steps.

These are what we observe as particles, fields, and forces:

Each scale is the same process (D applied locally, propagating outward) but viewed at a different resolution. The propagation patterns at one scale become the "background" within which smaller-scale patterns propagate. This is exactly the renormalization group picture: physics at scale Λ is the effective theory that results from integrating out (averaging over) the dynamics at scales below Λ.

3.3 Information resonance exchange

When two coherent structures (two propagation patterns at comparable scales) overlap in the lattice, their D-operator updates INTERFERE. The interference can be:

• Constructive: The patterns reinforce each other's amplitudes → stronger combined pattern (attractive interaction, binding)
• Destructive: The patterns cancel each other's amplitudes → weakened or redirected patterns (repulsive interaction, scattering)
• Resonant: The patterns' interference produces a STABLE new pattern that persists → bound state, composite structure

Two "point" structures (localized propagation patterns) are continuously in information resonance exchange. Each emanates its D-operator convergent state outward. Where the emanations overlap, they interfere. The interference pattern feeds back into both structures' local updates. This continuous exchange IS what we call "interaction" in physics.

The key structural insight: this exchange is ALWAYS happening, at every scale, between every pair of structures whose emanation cones overlap. A hydrogen atom is two resonance patterns (proton + electron) continuously exchanging through their overlapping emanation fields. A galaxy is ~10⁶⁸ resonance patterns all exchanging simultaneously. The universe is ALL resonance patterns exchanging with all others within their causal cones.

3.4 Scale-dependent phenomena as interference at that scale

The user's insight is precise: depending on the scale you're interested in, you get phenomena related to propagation changes interfacing with each other.

At EVERY scale, the same structure: D operates locally → propagation patterns form → patterns interfere where they overlap → the interference produces the phenomena characteristic of that scale.

4. Convergence and the Unknown Beyond the Boundary

4.1 What "beyond the boundary" means locally

For a cell x at time t, the state of cells beyond its immediate neighborhood is UNKNOWN — not in an epistemic sense (we don't know it) but in a physical sense (the information hasn't arrived yet). The state at a cell y that is n steps away from x in the lattice can only influence x after n Planck time steps (the time for propagation through n cells at the speed of light).

The boundary of the known, from any cell's perspective, is the past light cone. Everything outside the light cone has not yet converged at this cell — its D-operator updates have not yet propagated here. From x's perspective, the state of y is literally undetermined until y's emanation reaches x.

This is not a limitation of observation — it's structural. D is local. Information propagates at c. What hasn't arrived hasn't arrived.

4.2 Convergence as propagation of the update rule

Convergence, in this picture, IS the propagation of D's update across space. When cell x's update propagates to cell y and cell y incorporates it, x's state has CONVERGED at y's location. Before propagation: y doesn't include x's contribution. After propagation: y's state reflects x's emanation.

The convergence domain primitives map directly:

The convergence domain, which was identified as an abstract pattern across quantum measurement, Bayesian inference, evolution, etc., HERE appears as the PHYSICAL process: D propagating across the lattice IS convergence dynamics. The universe IS a convergence process — the continuous narrowing of amplitudes into determinations at every point, at every moment.

4.3 Probability as the structure of the not-yet-converged

The user's insight: we see probabilities as inherent structure because the update rule's state outside our boundary is unknown until it has converged.

This directly connects QM's probabilistic character to the locality structure:

1. At any point x, the full quantum state |ψ⟩ includes contributions from cells whose emanations haven't yet reached x.
2. From x's local perspective, these distant cells' contributions are INDETERMINATE — not unknown-but-definite (classical uncertainty) but genuinely un-arrived (quantum indeterminacy).
3. The quantum state at x reflects what HAS converged here: the emanations from within x's past light cone. Everything else is represented as AMPLITUDE — potential contributions that haven't yet been determined locally.
4. When a new emanation arrives (propagation from a previously-beyond-boundary cell reaches x), the local state UPDATES — what was amplitude (potential) becomes determination (actual). This IS measurement/decoherence.

Probability in QM is not a statement about our ignorance. It's a statement about the LOCAL convergence state — what has and hasn't been determined at this location by the propagation of D across the lattice.

This resolves a tension in the analysis: the Ds3 (complex amplitude) character of QM seemed fundamental but also seemed to demand explanation. In the locality picture: Ds3 IS the structure of not-yet-locally-converged information. Complex amplitudes with phase represent contributions that can still interfere — emanations from different paths through the lattice that haven't yet been absorbed into a definite determination. When they DO converge (decoherence), the phase information is lost and the distribution becomes classical (Ds2: real probability). The Ds3→Ds2 transition IS convergence.

5. The Methodology Parallel

5.1 The structural isomorphism

The methodology's probabilistic lattice navigation (§2.5, session summary §2.6) IS the same structure as physical information propagation:

This is not an analogy. The methodology and the physical substrate share the convergence domain structure because BOTH are instances of convergence. The methodology IS a convergence process (the session summary proved this: Space = product lattice, Distribution = probability over positions, etc.). Physics IS a convergence process (D propagating across the lattice). They're both governed by the same abstract pattern — the convergence domain's 6 primitives.

5.2 Locality in the methodology

The analyst is always LOCAL within the lattice — at a specific position (current knowledge state), with direct access to adjacent positions (one structural reasoning step away), and with the rest of the lattice accessible only through chains of reasoning (propagation through the lattice).

When the analyst looks out from their current position:

• Nearby positions are CONSTRAINED (structural reasoning from the current position narrows them)
• Distant positions are UNCERTAIN (the analyst's knowledge hasn't propagated there yet)
• The distribution over positions is SHAPED by what has already been determined — like a light cone defining what has converged

The probability distribution IS the analyst's convergence state. Where the distribution is narrow: convergence has occurred (like a cell where many emanations have arrived). Where the distribution is wide: convergence hasn't reached yet (like a cell beyond the light cone).

5.3 The reverse walk as reverse propagation

In physics: a reverse walk starts from a known determination (e.g., the observable universe) and reconstructs what must have converged to produce it — tracing emanation paths backward.

In the methodology: a reverse walk starts from a known endpoint (e.g., the universal genetic code) and reconstructs the trajectory that produced it — tracing structural necessities backward.

Both are the same operation: given a converged state, infer the convergence process that produced it by propagating constraints backward through the lattice.

The forward/reverse walk intersection (§2.6 of the session summary) maps to the physical picture too:

P_actual(position at t) ∝ P_forward(t) × P_reverse(t)

In physics: the actual state at a spacetime point is constrained both by what CAN propagate forward from initial conditions AND by what MUST be true given the known future. Retrodiction (reverse propagation of constraints) is as valid as prediction (forward propagation). The actual trajectory is the intersection of both constraint sets.

5.4 The probability funnel as light cone structure

The session summary's probability funnel — wide at uncertain origins, narrowing through constraints, convergent at crystallization, widening at diversification — maps to the physical light cone structure:

The funnel IS the light cone, viewed probabilistically. The narrowing is the increasing overlap of constraint-propagation from different sources. The convergent point is where enough constraints have propagated to determine the state. The widening is the new emanation from the determined state.

6. Two-Point Resonance and Continuous Exchange

6.1 The two-point picture

Consider two coherent structures (localized propagation patterns) A and B separated by distance d in the lattice. Their interaction:

1. A continuously emanates its D-operator convergent state in all directions
2. B continuously emanates its D-operator convergent state in all directions
3. After propagation time d/c, A's emanation reaches B and B's reaches A
4. Each incorporates the other's emanation into its local state
5. This changes each structure's emanation, which then propagates back
6. The process is continuous: a perpetual information resonance exchange

Every pair of structures within causal contact is in continuous resonance exchange. The "force" between them is the effect of this exchange on their propagation patterns. Attractive: the exchange drives them toward each other (their combined pattern is lower-energy). Repulsive: the exchange drives them apart. Neutral: the exchange doesn't change their relative configuration.

6.2 What determines the exchange character

The character of the resonance exchange depends on:

• The structures' internal propagation patterns (what quantum numbers they carry — energy, charge, spin)
• The interference type at their overlap (constructive, destructive, resonant)
• The medium between them (what other propagation patterns exist in the intervening lattice)
• The distance (emanation amplitude falls off with distance — inversely, for massless fields; exponentially, for massive fields)

In QFT language: the exchange of virtual particles between two structures IS the resonance exchange of propagation patterns through the intervening lattice. The photon field IS the electromagnetic resonance channel. The graviton field (or its NCG equivalent) IS the geometric resonance channel. Each force IS a specific resonance mode of the lattice.

6.3 Convergence and reconvergence

The user's phrase "convergence and reconvergence" captures a key dynamic: two structures don't just converge once and stay static. They continuously reconverge as each incorporates the other's updated emanation.

Time 0:  A emanates → propagates → arrives at B
         B emanates → propagates → arrives at A
Time 1:  A (now incorporating B's emanation) emanates → ...
         B (now incorporating A's emanation) emanates → ...
Time 2:  A (now incorporating B's response to A) emanates → ...
         B (now incorporating A's response to B) emanates → ...
...

This is a feedback loop: A's output becomes B's input becomes A's input becomes B's output, ad infinitum. The loop either:

• Converges to a stable pattern (bound state — the two structures reach a resonance equilibrium)
• Diverges (scattering — the structures' interaction destabilizes and they fly apart)
• Oscillates (metastable — the structures cycle through resonance patterns, like Rabi oscillations in atomic physics)

Bound states ARE converged resonance exchange loops. An atom is a proton and electron whose resonance exchange has converged to a stable pattern (the electron's wavefunction is the converged emanation pattern from both structures interfering constructively at specific radii).

7. From Planck Cell to Observable Universe: The Scale Chain

7.1 How local aggregates to global

The transition from single-cell D-operator updates to the observable universe involves a hierarchy of aggregation:

Level 0: The cell. D applied to one cell + neighbors. Time: 1 Planck time. Space: 1 Planck length. Information: one local state update.

Level 1: Coherent excitation. Many cells oscillating in a correlated pattern — a wave packet. This IS a particle (a propagating mode of the lattice). The particle's properties (mass, charge, spin) are the resonance pattern's properties (frequency, coupling constants, angular momentum).

Level 2: Bound resonance. Multiple coherent excitations locked in stable resonance exchange — atoms, molecules. The binding IS the convergence of the inter-excitation resonance loop to a stable pattern.

Level 3: Aggregate matter. Many bound resonances in statistical equilibrium — macroscopic matter. The thermodynamic properties (temperature, pressure, phase) are the STATISTICAL properties of the aggregate resonance pattern.

Level 4: Gravitational structure. Aggregate matter's energy density curves the lattice connectivity — large-scale geometry responds to the distribution of resonance patterns. Gravitational structure IS the lattice's response to non-uniform energy distribution.

Level 5: Cosmological structure. The lattice's overall evolution — expansion, large-scale connectivity changes. Cosmology IS the global dynamics of the lattice as a whole.

At EACH level, the same fundamental process: D operates locally, emanation propagates, patterns interfere, stable resonances form, and the ensemble of resonances at one level becomes the "cells" of the next level up. The universe is a hierarchy of resonances built on resonances built on D.

7.2 What's available at each scale

The information accessible to a structure at scale s:

• Local (scale s): The structure's own resonance pattern and its immediate environment. Fully determined. This is the structure's "state."
• Near (scale s to ~10s): The resonance exchange partners within the structure's immediate emanation cone. Partially determined — the structure has been exchanging with these partners long enough for convergence.
• Far (scale >10s): Structures beyond the immediate exchange range. The state at these locations is PROBABILISTIC from the local perspective — emanation has arrived but is attenuated; the full convergence hasn't occurred.
• Beyond horizon: No information has arrived. Completely undetermined locally.

This is the locality structure at every scale, not just the Planck scale. An atom "knows" its immediate environment (its electron cloud, nearby atoms). It has partial information about more distant atoms (through electromagnetic resonance exchange). It has no information about the other side of the universe. The same structure repeats at the scale of organisms, planets, galaxies — always the same locality boundaries, just at different scales.

8. The Methodology's Lattice as a Physical Lattice

8.1 The deep parallel

The methodology treats its product lattice as a space of POSITIONS that a manifestation can occupy, with the analyst navigating through it by structural reasoning. The physical substrate IS a lattice of cells that structures navigate through by emanation propagation.

The parallel goes deeper than shared convergence domain structure:

8.2 Why the parallel holds

The parallel isn't coincidental. The methodology is ITSELF an information-processing system operating on a structured state space. Any such system exhibits convergence domain behavior. The physical substrate is also an information-processing system on a structured state space. Both are governed by:

1. Locality: The operator (D or structural reasoning) is local — acts on current position + neighbors
2. Propagation: Updates propagate through the lattice at a finite speed
3. Convergence: The distribution over positions narrows as constraints propagate
4. Crystallization: Some convergence events are irreversible (decoherence/code freezing/analytical determination)
5. Area bounds: The non-local information is bounded by the interface, not the volume

These are convergence domain invariants — structural features that appear in ANY system with the 6 convergence primitives.

8.3 What this means for the methodology's formal structure

The methodology's lattice is not JUST a qualitative map. It's a structure that satisfies the same axioms as the physical lattice:

• Computable: The product lattice is finite and enumerable (n ≤ 8 primitives, k ≤ 6 levels each)
• Probabilistic: Positions are occupied by distributions, not points
• Constrained: The coherent sub-lattice is a small fraction of the total (12-30%)
• Local: Analysis propagates one step at a time through the dependency structure
• Convergent: The distribution narrows as analysis proceeds

The formal parallel suggests that the same mathematical tools used for lattice QFT (lattice field theory — computing propagation on discrete lattices) might be applicable to the methodology's lattice. Not in the sense of importing physics — in the sense that the MATHEMATICAL STRUCTURE of propagation on constrained lattices is the same in both cases.

9. Open Questions and Research Directions

9.1 Quantifying the local information budget

Question: What is the precise dimension of H_x (the local Hilbert space at a Planck cell)?

The Bekenstein bound gives the total: ~10¹²² bits for the observable universe. If N ~ 10¹²² cells, the average local information is ~1 bit per cell (one qubit). But this average hides structure:

• Near a black hole horizon: maximum information density (1 bit per Planck cell)
• In empty space: much less (most cells in "vacuum" state)
• The vacuum ISN'T empty — it has vacuum fluctuations (non-zero amplitude for field excitations)

Research needed: What does the spectral triple framework say about dim(H_x)? The LQG program suggests H_x is spanned by the possible spin quantum numbers at a spin network node — a finite but non-trivial space. The QCA program suggests H_x is determined by the number of quantum fields (SM has ~100 degrees of freedom per point at the lattice scale). These give different answers.

9.2 The neighbor structure and its dynamics

Question: Is the neighbor structure (which cells are connected) static or dynamic?

In the spectral triple: D defines the neighbor structure. If D is fixed (same operator at all times), the neighbor structure is static — a fixed lattice. But:

• General relativity says geometry is DYNAMIC (spacetime curves in response to matter)
• In the spectral triple, the inner fluctuations of D change the geometry
• Does this mean the NEIGHBOR STRUCTURE changes? Or does D's inner fluctuation change the WEIGHTS of existing connections without changing which cells are connected?

Research needed: How do D's inner fluctuations translate to the CA picture? Do they change the graph topology (which cells are neighbors) or only the edge weights (how strongly neighbors couple)? Wolfram's dynamic hypergraph says: topology changes. Standard lattice QFT says: topology fixed, couplings vary. The spectral triple may distinguish between these — the commutator [D, a] defines adjacency, and inner fluctuations D → D + A (gauge field) modify the commutator.

9.3 The Ds2/Ds3 locality question

Question: Does the Ds2 vs Ds3 ground level affect the locality structure?

If Ds3 (QCA): each cell carries genuine quantum amplitude (complex, with phase). Entanglement between cells is REAL. The locality structure is: local cells carry quantum states, correlations between cells are non-local entanglement, the area law bounds the entanglement.

If Ds2 ('t Hooft): each cell carries a classical state (definite value from a finite set). Entanglement is APPARENT — arising from coarse-graining. The locality structure is SIMPLER: each cell carries a classical bit, correlations are classical, the quantum character emerges only at the coarse-grained level.

The locality story changes depending on which is true:

• Ds3: locality is limited by entanglement (real non-local correlations exist, bounded by area law)
• Ds2: locality is total at the ground level (all information is local; non-locality is an effective-theory artifact)

9.4 Resonance exchange and the propagator

Question: Is the resonance exchange picture formally equivalent to the QFT propagator?

The QFT propagator G(x,y) gives the amplitude for a disturbance at x to influence y. In the resonance exchange picture, this would be: the weight of x's emanation when it arrives at y after propagating through the lattice. If these are the same mathematical object, then the ENTIRE QFT scattering matrix (S-matrix) is a consequence of the resonance exchange structure.

Research needed: Does the spectral triple's heat kernel (which gives the propagator via analytic continuation) exactly reproduce the resonance exchange picture? The heat kernel K(x,y,t) = ⟨x|e^{-tD²}|y⟩ IS the propagation amplitude from x to y in "time" t. In the CA picture, this should correspond to the amplitude that x's update propagates to y after t Planck time steps. The connection is likely exact but needs verification.

9.5 The methodology as a Bayesian propagation network

Question: Can the methodology's lattice walk be formalized as a Bayesian network on the product lattice?

If each node in the product lattice is a random variable (the manifestation's partial level on that coordinate), and the edges are conditional dependencies (from the dependency structure), then the lattice IS a Bayesian network. Analysis = belief propagation. Forward walks = predictive inference. Reverse walks = diagnostic inference. The intersection = the posterior given all evidence.

Research needed: Formal comparison between the methodology's probabilistic lattice and standard Bayesian network/belief propagation frameworks. The constraint structure (coherent sub-lattice) acts as a prior. The physics layer (rates, costs) acts as a likelihood. The empirical evidence narrows the posterior. This is well-studied mathematics that could make the methodology quantitatively computable.

9.6 Does the area law have a methodology analog?

Question: In the methodology's lattice, does something analogous to the area law hold?

The physics area law says: entanglement between a region and its complement scales with boundary area, not volume. In the methodology: when you analyze a sub-lattice (a specific transition), the amount of cross-domain constraint (how much other domains constrain this transition) might scale with the NUMBER OF BRIDGE PRIMITIVES (the "boundary" between domains), not with the number of internal primitives (the "volume" of the domain).

If true, this would mean: the methodology's constraint propagation has the same scaling as physical information propagation. The bridge between domains IS the boundary between regions. The bridge primitive count IS the boundary area. And the constraint content flowing through the bridge is bounded by this count — the area law for structural analysis.

Preliminary evidence: Domain analyses show that cross-domain constraints flow through bridge primitives (the bridge IS the interface). The number of bridge primitives is always ~6 (the same as domain primitives — suggesting boundary/volume scaling ≈ 1, which matches the holographic observation that the information-bearing boundary has the same dimensionality as the effective bulk).

10. Summary

10.1 The locality structure, resolved

The Planck information substrate's locality is clear:

1. Each Planck cell carries a tiny local quantum state (a few qubits in H_x)
2. D needs only the cell and its neighbors to compute one update (first-order, one Planck length)
3. The global Hilbert space is the mathematical description of all possible collective states — no cell carries it; it's the aggregate of all local states plus their correlations
4. Entanglement (the non-local information) is bounded by boundary areas (area law) and concentrated at short range
5. The global state is the distributed information store — each cell contributes its local piece; the whole is the collection

10.2 The propagation structure

Each cell continuously emanates its D-operator convergent state. These emanations aggregate into resonant propagation waves at successively larger scales. The phenomena at any given scale are the interference patterns of resonances at that scale. Two coherent structures continuously exchange information through their overlapping emanation cones — convergence and reconvergence in perpetual feedback.

10.3 The methodology parallel

The methodology's probabilistic lattice navigation shares the convergence domain structure with physical information propagation: locality (one step at a time), propagation (constraints chain through the lattice), convergence (distributions narrow to determinations), area-law-like bounds (cross-domain constraint flows through bridges). The parallel is not analogy but shared structural pattern — both are instances of the convergence domain operating on structured state spaces.

10.4 What probability IS in this picture

Probability is the structure of the not-yet-converged. At any local position (physical cell or methodology position), the state beyond the propagation boundary is AMPLITUDE — potential contributions that haven't yet been locally determined. Convergence IS propagation arriving. Determination IS emanation absorbed. The Ds3→Ds2 transition (quantum → classical) IS the convergence of distant emanations into local determinations.