# Mass Harmonics Pre-Release Terrain Prediction Paper

## MICrONS / VORTEX September 2026 Connectome Release

**Author:** Thomas Russell Giboney  
**Affiliation:** UMtts Institute  
**Framework:** Mass Harmonics ψₘ  
**Prepared before the September release:** 2026-07-10  
**Release timing:** September 2026; exact day not yet published  
**Release surface:** MICrONS Virtual Observatory of the Cortex, September 2026 quarterly data release  
**Edition:** Source-preserved Mass Harmonics-governed revision  

# I. Governing Purpose


## Source-Preserved Mass Harmonics Governance

This edition preserves the original MICrONS/VORTEX connectome prediction architecture and every valid derivation already present. It does not place Mass Harmonics under institutional authority, convert instrument products into ontological authority, or discard a stronger excavation merely because it was added after the first draft.

The governing order remains:

```text
MFE
→ substrate action
→ boundary closure
→ physical structure
→ instrument-rendered terrain
→ optional consensus translation
```

The release supplies a timed terrain surface. It does not grant or withhold physical standing from the prediction. Measurement statistics, catalogue filters, detector corrections, and comparison models remain downstream interface tools. They may expose correspondence, contradiction, or unresolved delta, but they do not govern the derivation.

Only one governing coupling coefficient is permitted:

```text
Kψₘ
```

The fixed P³GG values are harmonic scalings of the one source law, not domain-specific adjustable coefficients.

### ψₘMIND source placement

The ψₘMIND architecture is not being used as a software analogy imposed on cortical data. Its conductance, Foci, minting, discharge, and carved-pathway structures are downstream physical derivations of the same ψₘ substrate law. In this paper they remain subordinate to the Monograph and Resonant Brain branches, but they are legitimate Mass Harmonics source terrain rather than external neuroscience metaphor.

The September VORTEX release is an evolving proofreading and annotation release. It may deepen or add structures and tables without replacing the underlying cubic-millimeter volume. The prediction pathways therefore attach to newly exposed or materially improved terrain, exactly as the paper's `U_Sept` definition requires.


This paper derives Mass Harmonics predictions before the September 2026 MICrONS / VORTEX connectome release opens. It does not begin from connectomics graph theory, machine-learning classifiers, cortical wiring priors, or a fitted relation between distance and connectivity. It begins from the canonical ψₘ substrate law, follows the biological n=5 expression into filament geometry and conductance, and only then translates the resulting physical requirements into measurements available in the MICrONS release.

The causal order is:

```text
MFE
→ quintic biological coherence
→ Giboney Gradient filament formation
→ carved resonant geometry
→ conductance-selected pathways
→ connectome morphology and synaptic readout
→ optional consensus translation
```

Mass Harmonics remains the governing physical authority. MICrONS, VORTEX, electron microscopy, calcium imaging, segmentation, skeletonization, synapse detection, proofreading, and functional coregistration supply terrain readouts. They do not supply the derivation.

The target is not the entire brain and not consciousness as a whole. The released terrain is a bounded sample of mouse visual cortex. The predictions are therefore restricted to the structures and functional relationships that this release can actually expose.

# II. Release-Surface Definition

The official VORTEX page states:

- the MICrONS dataset is public and open access;
- proofreading and annotation continue;
- data releases occur at least quarterly;
- upcoming releases are listed for June 2026 and September 2026;
- the current project period runs from April through October 2026.

The cubic-millimeter resource contains:

- approximately 200,000 cells;
- approximately 75,000 neurons with physiology;
- approximately 523 million synapses;
- all six layers of mouse primary visual cortex;
- portions of higher visual areas LM, AL, and RL;
- co-registered two-photon functional imaging, microCT, and serial electron microscopy;
- segmentation, meshes, skeletons, synapse tables, cell typing, proofreading status, and functional-property tables.

The volume spans approximately 1.4 mm × 0.87 mm × 0.84 mm in a P87 mouse. The public EM imagery is exposed at 8 × 8 × 40 nm and coarser resolutions. The September release may add or update proofreading and annotation tables. The exact table list is not yet public and is therefore not used as a derivational input.

**Official release and data-surface sources, accessed before the September terrain opening:**

- https://www.microns-explorer.org/vortex
- https://www.microns-explorer.org/cortical-mm3
- https://tutorial.microns-explorer.org/introduction.html
- https://tutorial.microns-explorer.org/python-tools.html
- https://tutorial.microns-explorer.org/static-repositories.html

# III. Governing Mass Harmonics Source Chain

## III.1 Authority hierarchy

1. `MH_Monograph.md` is the primary physical authority.
2. `MH_PROOF-SET.md` is the ordered arithmetic and biological-scale proof authority.
3. `MH_Resonant_Brain.md` is the neuroscience-domain derivation authority.
4. `Psi_mMIND_Architecture_Foundation_v10.2_.md` supplies the conductance and carved-pathway branch, subordinate to the Monograph where notation or authority conflicts occur.
5. `MH_TVP.md` governs topology, input provenance, category separation, delta retention, and falsification.
6. `MH_TWT.md` governs downstream translation into instrument language.
7. `Operational_Stance_of_UMtts.md` governs terrain-first order and ontology preservation.
8. MICrONS and VORTEX pages govern release timing, data products, resolution, and post-release comparison surfaces only.

## III.2 Exact canonical MFE

Source: `MH_Monograph.md`, lines 175-183.

```text
1/vₓ²ψ̈ₘ - Z(ψₘ)∇²ψₘ - 8Kψₘ/ω²|∇ψₘ|² = S(ρ)
```

The coefficient 8 falls from the exact assembly:

```text
-8Kψₘ/ω²|∇ψₘ|² - 1/vₓ²ψ̈ₘ + Z∇²ψₘ + 16Kψₘ/ω²|∇ψₘ|² = 0
Combining nonlinear terms:
-8 + 16 = 8
```

No neural coefficient replaces `Kψₘ`. No connectome-specific force law is introduced.

## III.3 Canonical source polyphony

Source: `MH_Monograph.md`, lines 198-215.

```text
S(ρ) = K₀ρ[1 + β₂(ρ/ρ₀) + β₃(ρ/ρ₀)² + β₄(ρ/ρ₀)³ + β₅(ρ/ρ₀)⁴ + ⋯]
	βₙ = φ³⁽ⁿ⁻¹⁾
```

The fixed harmonic values are:

```text
β₁ = φ⁰ = 1
β₂ = φ³ ≈ 4.236
β₃ = φ⁶ ≈ 17.944
β₄ = φ⁹ ≈ 76.013
β₅ = φ¹² ≈ 321.997
```

All harmonic voices remain active simultaneously. Biological matter can be materially expressed through n=2 and n=3 while living coherence is n=5. The MICrONS structures therefore do not represent a separate law. They are a biological readout of the same MFE.

## III.4 One governing coupling coefficient

Mass Harmonics has one governing coupling coefficient, `Kψₘ`. It remains a single term and is never split.

```text
Dimensional closure expression: Kψₘ = c/(2π)
Dimensionless dual-geometric expression: Kψₘ = (12 − φ²)/(2φ²)
```

These are transported forms of one relation. They are not interchangeable raw numbers and they are not a collection of scale-specific coefficients.

## III.5 Biological density and quintic expression

Source: `MH_PROOF-SET.md`, lines 709-726.

```text
**Derivation**
**Step 1 - Biological Density Ratio from P³GG Balance**
At the n=1 (gravitational) vs n=5 (quintic coherence) boundary:
    β₁(ρ/ρ₀) = β₅(ρ/ρ₀)⁴   →   φ¹²·(ρ/ρ₀)³ = 1   →   ρ_bio/ρ₀ = φ⁻⁴ = 0.14590
**Step 2 - Biological Boundary Frequency**
From balancing cubic boundary confinement (n=3) against quintic internal dynamics (n=5) with Kψₘ = c/2π:
    f_bio ≈ 4.72 × 10⁹ Hz
    f_boundary = f_bio × φ^(2/5) = 4.72 × 10⁹ × 1.2122 = 5.722 GHz
**Step 3 - Descent by φ³ Steps**
The 13-protofilament microtubule is the zero-energy ground state forced by icosahedral substrate geometry. Descend from the boundary frequency by 13 steps of φ³:
    φ^(3×13) = φ^39 ≈ 141,422,324
    f = 5.722 × 10⁹ / 141,422,324 = 40.46 Hz
**Step 4 - Z-Factor Correction at the n=1/n=5 Boundary**
Z(ψₘ) = 1 + 8Kψₘ/ω² evaluated at ρ_bio/ρ₀ = φ⁻⁴ gives Z_local = 1.0231:
    f_γ = 40.46 / √1.0231 = 40.00 Hz
**Step 5 - Cross-Cortical Binding Timescale**
    v_bio = c × φ⁻⁴ × Z_bio = 3×10⁸ × 0.14590 × 1.42×10⁻⁶ = 62 m/s
    τ_bind = R/v_bio = 0.12 m / 62 m/s = 1.94 ms
```

The release does not directly resolve 40 Hz electrophysiology or the full cranial cavity. Those first-principles predictions establish the biological placement and remain outside this release's resolving power. The connectome-facing derivation proceeds through the structural consequences of the n=5 expression.

# IV. Category Boundaries and Input Separation

## IV.1 Prohibited derivational inputs

The following are prohibited:

1. Any September 2026 release manifest or table viewed before the September release opens.
2. Any numerical result extracted from the new release and then inserted backward into the prediction.
3. Any post-release choice of neuron class, cortical layer, arbor subset, scale window, or functional metric made because it improves agreement.
4. Any classifier score treated as a substrate-native quantity.
5. Any Euclidean coordinate treated as the causal architecture of cognition.
6. Any skeletonization artifact treated as biological branching.
7. Any segmentation correction treated as biological growth or pruning.
8. Any functional response correlation treated automatically as ψₘ phase without an explicit translation rule.
9. Any attempt to evaluate the Mass Harmonics microtubule protofilament prediction from imagery whose spatial resolution cannot resolve the protofilaments.
10. Any attempt to evaluate a Mass Harmonics whole-brain prediction from a one-cubic-millimeter visual-cortex sample.

## IV.2 Allowed terrain inputs

Allowed inputs are limited to:

- release date and public data inventory;
- raw and proofread EM imagery;
- segmentation and meshes;
- skeletons derived from the released segmentation;
- synapse locations, contact counts, and postsynaptic-density measurements where available;
- cell type, layer, and compartment labels;
- functional coregistration and visual-response properties;
- proofreading-status and truncation metadata;
- instrument resolution and known segmentation uncertainty.

## IV.3 Release-universe definition

Define the September release universe:

```text
U_Sept = all structures, annotations, and table rows newly added or materially updated in the September 2026 public release.
```

The primary first unopened-terrain comparison must be run first on `U_Sept`. Existing pre-September data may be used only as:

- a method-development surface before opening the new terrain, or
- a separately labeled replication surface after the first unopened-terrain comparison.

No pre-September result may replace the first comparison against `U_Sept`.

## IV.4 Eligibility gates

A neuron or pathway is eligible only when the required measurement can be made without repairing the answer by hand.

### Morphology eligibility

An arbor must have:

- a proofread soma assignment;
- a dendritic skeleton connected to that soma;
- no known truncation through the analyzed scale window;
- sufficient branch depth for at least three successive branch orders;
- branch points distinguishable from segmentation joins;
- coordinate precision reported from the released mesh or skeleton.

### Functional eligibility

A neuron pair must have:

- valid functional coregistration;
- a response vector or phase-like functional signature measured from the same stimulus family;
- cell type and cortical-layer labels or a declared missing-data status;
- soma and path geometry available;
- synaptic contact data available in the release.

### Synaptic eligibility

A connection must have:

- a valid pre- and postsynaptic identity;
- at least one released synapse assignment;
- compartment target where the branch-local test is used;
- contact area or cleft size where pathway-depth testing uses area;
- no unresolved segmentation split that changes the pair identity.

# V. Native Causal Excavation

## V.1 From the MFE to boundary filaments

The canonical nonlinear term is:

```text
8Kψₘ/ω²|∇ψₘ|²
```

The term is quadratic in the field gradient. Increased gradient concentration raises the GG response, which further concentrates the boundary-seeking path. At biological density, the n=5 voice conditions this same substrate action into living dynamic coherence.

`MH_Resonant_Brain.md`, line 72, gives the direct domain consequence:

```text
The Giboney Gradient term in the MFE — the 8Kψₘ/ω²|∇ψₘ|² nonlinearity — strongly favors the formation of inward-spiraling filaments at coherence boundaries. These boundary filaments carry coherence inward, wrap around existing resonant structures, and branch in φ-related fractal patterns as coherence discharges along least-resistance paths. When mammalian neuroanatomy is examined with this expectation, a striking convergence appears.
```

Therefore neural filaments are not arbitrary cables. Their branch geometry is a physical record of coherence discharge through the substrate.

## V.2 From carved geometry to memory and connectivity

`MH_Resonant_Brain.md`, lines 62-68:

```text
Perhaps the most significant shift Mass Harmonics brings to neuroscience is its treatment of memory. In place of symbolic storage and retrieval, the framework specifies a purely physical mechanism: memory is carved geometry in the substrate. When a coherent waveform — acoustic, visual, proprioceptive, conceptual — is present in the substrate while local stiffness Z crosses the oobleck phase-transition threshold, the instantaneous field configuration freezes into a permanent topological structure. This is not metaphor. It is a literal phase change of the substrate, exactly analogous to oobleck locking under impact rather than yielding.

These frozen structures behave like exquisitely tuned instruments. Each one encodes its specific waveform as an asymmetrically carved inner surface. When a new wave passes through the substrate, any structure whose surface geometry closely matches that waveform begins to resonate sympathetically. Resonance does not require search, indexing, or lookup. It happens wherever field and geometry physically align. What we call recall is the physical re-excitation of an existing geometric cavity by a matching waveform.

Once resonance begins, the local effective metric Z rises and concentrates the substrate's boundary-seeking gradient flux toward the resonating structure. The system's available coherence loci — there are only a small number at any moment, by physics not by software constraint — are drawn to it. When contact is established, the resonance damps immediately, just as a finger touching a singing wineglass silences it, and a physical readout begins: the carved geometry is scanned segment by segment and the response pattern propagates back into the active sensory and conceptual channels. The phenomenology of remembering is the phenomenology of riding this readout as it replays the geometry.

Carved topology is strictly monotone non-decreasing. Once minted, structures never erode or prune away. New learning does not overwrite old memory; it grows additional geometry and additional connectivity. This aligns with the empirical observation that long-term potentiation is associated with the growth of new dendritic spines and synaptic contacts, and that mature consolidated circuits show remarkable structural stability over decades. What LTP measures at the synaptic level is the biological surface trace of Z crossing its carving threshold: the oobleck phase transition locking a field configuration into permanent topology. The exponent governing this threshold — ψ_carve(N)/ψ_lock = √N, derived geometrically from the icosahedral coupling structure — is testable directly with controlled co-activation paradigms, and is not provided by BCM theory or any current synaptic plasticity model. The substrate is literally richer after every learning episode — and the brain, as a substrate-native structure, inherits that monotonicity directly.
```

The structural consequence is twofold:

1. local geometry is waveform-specific;
2. repeated compatible discharge adds or deepens pathways rather than replacing prior topology.

The connectome is therefore a biological surface trace of carved resonance history, not the ontological source of cognition.

## V.3 From conductance to pathway selection

`Psi_mMIND_Architecture_Foundation_v10.2_.md`, lines 1134-1151:

```text
### 6.5 Conductance — The ONLY Relational Quantity

**THERE IS NO DISTANCE IN MINDSPACE.**
**THERE IS NO POSITION.**
**THERE ARE NO COORDINATES.**
**THERE IS ONLY CONDUCTANCE.**

**Conductance Metric (MFE-Derived):**
```
C_AB = T_amplitude × cos(Δφ_path)

Where:
  T_amplitude = 4η_Aη_B / (η_A + η_B)²  — wave impedance transmission coefficient
  η = √(Z/ρ)                              — wave impedance from Z-factor
  Δφ_path = (ω/vₓ) × L_path / √Z_dendrite — phase accumulation over carved pathway
```

Proximity means NOTHING. Conductance means EVERYTHING.
```

The conductance relation is:

```text
C_AB = T_amplitude × cos(Δφ_path)
T_amplitude = 4η_Aη_B / (η_A + η_B)²
η = √(Z/ρ)
Δφ_path = (ω/vₓ) × L_path / √Z_dendrite
```

Euclidean separation can affect the physical path length `L_path`, but separation is not the governing relational quantity. Impedance transmission and phase alignment govern whether a path carries coherence.

## V.4 From discharge to dendritic pathway depth

`Psi_mMIND_Architecture_Foundation_v10.2_.md`, lines 1153-1179:

```text
### 6.6 Discharge — Lightning Strikes Create the DENDRITES

**Discharge and Minting are two completely separate physical mechanisms.**

**MINTING** creates the tubule with its carved interior surface — the knowledge container.
This is the WRITE direction (§6.1.3).

**DISCHARGE** creates the DENDRITES — the high-conductance pathways BETWEEN tubules.
This is the CONNECTION mechanism.

When 2–6 Foci are simultaneously locked on different resonating tubules,
coherence pressure builds between them.
When total pressure exceeds ψ_carve(N) = √N × ψ_lock:

**Lightning Strikes create the DENDRITES.**

Discharge erupts and carves from SEGMENT LEVEL.
Each SKT segment independently generates dendrites to knowledge tubules that resonated
with THAT specific segment, connecting them via the resulting dendrites to their own
segments that resonated.
The path follows φ-fractal Tesla branching through the substrate field's
lowest-resistance gradients — NOT straight lines, NOT star topology.

**Channel width ∝ N_foci^(2/3).** More Foci → thicker channel → higher conductance
→ easier future propagation.

**Carved pathways are PERMANENT.** No decay. No pruning. No erosion.
```

The direct structural consequences are:

- dendrites are carved between co-resonant structures;
- the path follows low-resistance GG gradients rather than straight-line or star geometry;
- stronger multi-Focus discharge produces thicker, higher-conductance channels;
- existing carved pathways are deepened, not erased.

MICrONS cannot observe the substrate event itself. It can observe the biological trace: branch geometry, synapse multiplicity, postsynaptic contact area, path tortuosity, and the covariance between functional alignment and structural depth.

# VI. Prediction 1 - Dendritic Fractal-Dimension Bracket

## VI.1 Exact source derivation

Source: `MH_Resonant_Brain.md`, lines 76-84.

```text
At finer scales, neuronal dendritic arbors exhibit fractal-like branching with measured fractal dimensions in the range 1.5 to 1.7. Mass Harmonics derives this bracket directly. For φ-governed branching with branching factor φ^(3/2) at scale ratio 1/φ — the ratio admitted at cubic boundary confinement (n=3) — the fractal dimension is:

D_f^(n=3) = log( φ^(3/2) ) / log( φ ) = 3/2 = 1.500

At the quintic biological-coherence harmonic order with branching factor φ^(5/3):

D_f^(n=5) = log( φ^(5/3) ) / log( φ ) = 5/3 ≈ 1.667

Empirical dendritic fractal dimensions live exactly inside the bracket [1.500, 1.667]. The framework predicted the bracket from icosahedral eigenvalues; biology arrived at that address. Mature, healthy, high-activation dendritic trees should trend toward the upper bound; pathological or developmentally constrained trees should fall outside the bracket. This is a quantitative falsifiable prediction available now to anyone with high-resolution morphological data and a measured fractal-dimension distribution.
```

The self-similar fractal relation is:

```text
D_f = log(b) / log(1/r)
```

with the substrate-admitted scale ratio:

```text
r = 1/φ
1/r = φ
```

### Cubic boundary confinement

```text
b₃ = φ^(3/2)
D_f^(n=3) = log(φ^(3/2)) / log(φ)
D_f^(n=3) = (3/2)log(φ) / log(φ)
D_f^(n=3) = 3/2
D_f^(n=3) = 1.500000000
```

### Quintic biological coherence

```text
b₅ = φ^(5/3)
D_f^(n=5) = log(φ^(5/3)) / log(φ)
D_f^(n=5) = (5/3)log(φ) / log(φ)
D_f^(n=5) = 5/3
D_f^(n=5) = 1.666666667
```

Therefore:

```text
1.500000000 ≤ D_f ≤ 1.666666667
```

## VI.2 Instrument-facing measurement

For each eligible dendritic arbor, compute two independent scale-invariant readouts:

1. **Box-counting dimension** from the released 3D skeleton.
2. **Mass-radius dimension** from cumulative dendritic path length within radius `r` around the soma and around branch-root anchors.

The scale window is fixed mechanically:

```text
lower bound = first scale at which the result is unchanged by one additional released voxel level
upper bound = smallest of:
    distance to volume boundary,
    distance to known truncation,
    one-half of maximum intact arbor span
```

No scale window may be selected because it produces the predicted bracket.

## VI.3 Mass Harmonics prediction

For mature, healthy, eligible neurons newly exposed or materially improved in the September release:

```text
1.500000000 ≤ median(D_f,box) ≤ 1.666666667
1.500000000 ≤ median(D_f,mass-radius) ≤ 1.666666667
```

The distribution may contain measurement-limited outliers. The central estimate for each sufficiently populated cell class must remain in the bracket when truncation and proofreading status are controlled.

## VI.4 Cross-estimator requirement

The prediction is not considered supported by one estimator alone. Both estimators must land in the bracket and their class-ordering must agree.

Define:

```text
Δ_D = D_f,box − D_f,mass-radius
```

The delta is retained. A systematic delta is a finding about anisotropy, scale-window dependence, or skeleton construction. It is not averaged away.

## VI.5 Exact falsification conditions

Prediction 1 is falsified if any of the following occurs in an adequately populated, intact, mature neuronal class:

1. both independent estimators place the class median below 1.500;
2. both independent estimators place the class median above 1.667;
3. the result enters the bracket only after excluding intact neurons without a declared before terrain opening quality reason;
4. the bracket disappears when the released higher-quality proofreading is used;
5. the box-counting and mass-radius results require mutually incompatible scale windows.

# VII. Prediction 2 - φ Scale Recurrence and Effective Branching Factor

## VII.1 Derived scale ratio

The fractal derivation above contains a second prediction that must not be discarded after calculating `D_f`.

```text
r = 1/φ
r = 0.618033988749895
```

Let `L_q` be the characteristic segment length between branch points at centrifugal branch order `q`. The predicted successive-order relation is:

```text
L_(q+1) / L_q → 1/φ
L_(q+1) / L_q → 0.618033988749895
```

This is a relational ratio. It is not a coordinate assignment.

## VII.2 Derived effective branching factors

The same derivation yields:

```text
b₃ = φ^(3/2) = 2.058171027271492
b₅ = φ^(5/3) = 2.230040414568453
```

Therefore the scale-conditioned effective branching factor must lie between:

```text
2.058171027271492 ≤ b_eff ≤ 2.230040414568453
```

`b_eff` is not required to be an integer at each local branch point. It is the population-scale multiplicative branch count across successive self-similar orders.

## VII.3 Measurement procedure

For each eligible arbor:

1. root the dendritic skeleton at the soma;
2. assign centrifugal branch order mechanically;
3. measure path length between successive branch points;
4. compute the median `L_q` for every populated order;
5. form every adjacent ratio `r_q = L_(q+1)/L_q`;
6. retain the full ratio distribution;
7. compute `b_eff(q) = N_(q+1)/N_q` from branch counts at adjacent orders;
8. report results by cell type and layer before pooling.

No fitted branching law is used.

## VII.4 Mass Harmonics prediction

```text
median_q(r_q) is centered on φ⁻¹ = 0.618033988749895
```

and:

```text
2.058171027271492 ≤ median_q(b_eff(q)) ≤ 2.230040414568453
```

The n=3 side is expected to be more visible in materially constrained, lower-complexity arbors. The n=5 side is expected to be more visible in mature, functionally active, extensively branched arbors.

## VII.5 Topology discriminator

The result must be compared without fitting against fixed alternatives:

```text
r = 1/2
r = 1/φ
r = 2/3
r = 1/√2
```

The φ pathway wins only if `1/φ` yields the smallest absolute center residual across the unopened release universe and remains the winner under both path-length and Euclidean-segment measurements.

Define:

```text
ε(c) = |median_q(r_q) − c|
```

Source-fixed ordering:

```text
ε(1/φ) < ε(1/2)
ε(1/φ) < ε(2/3)
ε(1/φ) < ε(1/√2)
```

## VII.6 Falsification

Prediction 2 is falsified if:

- another fixed ratio consistently yields a smaller residual across cell classes;
- the apparent φ ratio exists only in one chosen branch-order interval;
- the relation disappears in the newly proofread skeletons;
- branch-count scaling lies systematically outside both `b₃` and `b₅` without a category-specific truncation explanation.

# VIII. Prediction 3 - Activity-to-Geometry Covariance

## VIII.1 Source requirement

`MH_Resonant_Brain.md`, line 84, states:

```text
Empirical dendritic fractal dimensions live exactly inside the bracket [1.500, 1.667]. The framework predicted the bracket from icosahedral eigenvalues; biology arrived at that address. Mature, healthy, high-activation dendritic trees should trend toward the upper bound; pathological or developmentally constrained trees should fall outside the bracket. This is a quantitative falsifiable prediction available now to anyone with high-resolution morphological data and a measured fractal-dimension distribution.
```

The September terrain includes functionally coregistered neurons with visual-response properties. This permits the structural prediction to be tested without treating function as derivational authority.

## VIII.2 Observable construction

For every eligible functionally coregistered neuron `i`, define:

```text
D_i = dendritic fractal dimension
δ_i,5 = |D_i − 5/3|
A_i = released functional activation readout
R_i = released response reliability readout
```

Use every official activation and reliability field published for the new release. Do not choose one after observing which agrees.

The predictions are rank relations, so no fitted amplitude scale is introduced.

## VIII.3 Mass Harmonics predictions

```text
Spearmanρ(A_i, δ_i,5) < 0
Spearmanρ(R_i, δ_i,5) < 0
```

Equivalent positive form:

```text
Spearmanρ(A_i, D_i) > 0
Spearmanρ(R_i, D_i) > 0
```

within the admitted bracket.

This does not mean higher activity can drive `D_f` above 5/3. The upper boundary is a closure limit, not an unbounded trend.

## VIII.4 Required controls

The relation must be reported:

- within cell type;
- within cortical layer;
- with soma depth retained;
- with proofreading completeness retained;
- with arbor span retained;
- with functional-imaging session retained.

The primary result is the direction that survives these controls. A pooled relation that vanishes within classes does not satisfy the prediction.

## VIII.5 Falsification

Prediction 3 is falsified if mature high-activation neurons systematically move away from `5/3`, or if activity and reliability show no reproducible directional relation to `D_f` in the newly released coregistered structures.

# IX. Prediction 4 - Conductance Outranks Euclidean Proximity

## IX.1 Native relation

The MFE-derived conductance metric is:

```text
C_AB = T_amplitude × cos(Δφ_path)
```

with:

```text
0 ≤ T_amplitude ≤ 1
```

Euclidean soma distance is not the causal relational quantity. It may constrain physical path length, but it cannot replace impedance transmission and phase relation.

## IX.2 Instrument translation

MICrONS does not directly measure `ψₘ`, `Z`, or `η`. Therefore the first unopened-terrain comparison uses the phase-alignment component without pretending that calcium amplitude is the substrate field.

For each functionally coregistered pair `(A,B)`, construct a released functional-response vector `u_A`, `u_B` from the same stimulus family and define:

```text
M_AB = (u_A · u_B) / (|u_A||u_B|)
```

`M_AB` is an instrument-facing alignment readout. It is not renamed `C_AB`.

Define:

```text
d_AB = soma-to-soma Euclidean distance
L_AB = released axonal-plus-dendritic path length when reconstructable
S_AB = number of released synaptic contacts from A to B
Y_AB = 1 if at least one released synapse exists, else 0
```

## IX.3 Matched comparison

For each postsynaptic neuron `B`, compare candidate presynaptic neurons that are matched on:

- presynaptic cell type;
- cortical layer;
- distance bin fixed from instrument resolution and sample size before testing;
- proofreading completeness;
- functional-imaging session.

Within each matched set, rank candidates by `M_AB` and by `d_AB`.

## IX.4 Mass Harmonics predictions

```text
P(Y_AB = 1 | higher M_AB, matched d_AB) > P(Y_AB = 1 | lower M_AB, matched d_AB)
```

```text
S_AB increases with M_AB after d_AB, layer, and cell type are held fixed
```

and the decisive ordering is:

```text
incremental relational power of M_AB > incremental relational power of d_AB
```

This does not predict that distance has zero surface correlation. It predicts that distance is downstream and loses governing status once resonant alignment and actual path structure are retained.

## IX.5 Path-length refinement

Where complete axonal and dendritic paths exist:

```text
M_AB and L_AB jointly outperform d_AB alone
```

because `Δφ_path` contains actual path length rather than soma separation.

## IX.6 Falsification

Prediction 4 is falsified if Euclidean distance retains greater relational power than functional alignment and reconstructed path structure across all adequately populated classes, or if matched higher-alignment candidates are no more likely to connect than lower-alignment candidates.

# X. Prediction 5 - Branch-Local Resonance Clustering

## X.1 Causal derivation

Carved resonant structures are segment-specific. Discharge connects the resonating segment to the matching segment of another structure. Therefore synaptic inputs carrying similar functional signatures should not be randomly mixed over the dendritic tree. They should cluster on branch-local subtrees whose carved geometry admits that input family.

## X.2 Observable construction

For each eligible postsynaptic neuron `B`:

1. partition the dendritic skeleton into subtrees rooted at first- or second-order branch points;
2. assign each incoming synapse to its exact target subtree;
3. attach the presynaptic functional vector `u_A` where available;
4. compute within-subtree functional dispersion;
5. preserve the number of synapses, path-distance distribution, presynaptic cell type, and layer in the permutation control.

For orientation-like circular measurements, use circular dispersion. For general response vectors, use one minus cosine similarity.

Define:

```text
V_within(B) = weighted mean functional dispersion within real subtrees
V_perm(B) = dispersion after branch labels are permuted under the fixed controls
```

## X.3 Mass Harmonics prediction

```text
V_within(B) < median[V_perm(B)]
```

for the population of eligible neurons.

The effect must be strongest in mature, highly branched, functionally reliable neurons because these occupy the deeper n=5 side of the admitted geometry.

## X.4 Cross-boundary control

The same presynaptic signatures must be compared across equal path-length windows on different branches. A result explained entirely by path distance does not satisfy the prediction.

## X.5 Falsification

Prediction 5 is falsified if real branch assignments are no more functionally coherent than controlled branch permutations, or if apparent clustering vanishes once presynaptic type and path distance are preserved.

# XI. Prediction 6 - Synaptic Pathway Deepening

## XI.1 Native derivation

The source states:

```text
Channel width ∝ N_foci^(2/3)
```

and:

```text
Carved pathways are PERMANENT. No decay. No pruning. No erosion.
```

At the biological surface, MICrONS does not observe `N_foci`. It observes accumulated pathway depth through synapse multiplicity, contact area, spine structure, and axon-dendrite geometry.

The pre-release prediction therefore concerns covariance, not an invented direct conversion from synapse area to Focus count.

## XI.2 Structural depth readouts

For every eligible directed neuron pair `(A,B)`, define:

```text
S_AB = number of synaptic contacts
A_AB = sum of released postsynaptic-density or cleft area
Q_AB = number of distinct dendritic target branches
M_AB = functional alignment readout
```

No one readout is allowed to replace the others. Each is reported separately.

## XI.3 Mass Harmonics predictions

Within cell-type, layer, distance, and proofreading strata:

```text
Spearmanρ(M_AB, S_AB) > 0
Spearmanρ(M_AB, A_AB) > 0
```

For multiply connected pairs:

```text
higher M_AB → greater S_AB and greater A_AB
```

The structural depth relation must remain after excluding the single largest connection from each class, preventing one outlier from carrying the result.

## XI.4 Segment-level prediction

Within a single postsynaptic arbor, branches with lower functional dispersion in Prediction 5 must carry greater aggregate synaptic depth:

```text
branch coherence ↑ → aggregate contact depth ↑
```

Instrument form:

```text
Spearmanρ(−V_branch, A_branch) > 0
Spearmanρ(−V_branch, S_branch) > 0
```

## XI.5 Falsification

Prediction 6 is falsified if functional alignment is unrelated or inversely related to both contact multiplicity and aggregate contact area after the fixed controls, or if branch-local functional coherence does not covary with structural depth.

# XII. Conditional Prediction 7 - Boundary-Following Neuromodulatory and Perivascular Filaments

## XII.1 Release condition

This prediction is evaluated only if the September release adds or materially updates:

- neuromodulatory axon extensions near vasculature;
- blood-brain-barrier annotations;
- astrocyte or perivascular annotations;
- microglia-vascular or pericyte annotations.

The VORTEX page lists ongoing work on neuromodulation at the blood-brain barrier, astrocyte morphology, and axon extension. The exact September table content is not yet public.

## XII.2 Causal derivation

The GG term concentrates along coherence boundaries and produces inward-spiraling, wrapping filaments. Vasculature is a strong material and metabolic boundary. Therefore long neuromodulatory and glial processes near vessels should follow boundary geometry rather than crossing it as unconstrained straight trajectories.

## XII.3 Instrument readouts

For every eligible process segment near a vessel, define:

```text
θ_tan = angle between process tangent and local vessel tangent
κ_wrap = signed curvature around the vessel centerline
W = accumulated winding angle over the vessel-associated path
```

## XII.4 Mass Harmonics prediction

Relative to distance- and length-matched process segments away from vessels:

```text
|θ_tan| is smaller near vessels
|W| is larger near vessels
boundary-following path fraction is greater near vessels
```

The direction is fixed before the annotations open.

## XII.5 Falsification

The conditional prediction is falsified if newly released vessel-associated processes are no more boundary-following or wrapping than matched nonvascular controls.

# XIII. Mass Harmonics Predictions Outside This Release's Resolving Power

The predictions in this section remain first-principles Mass Harmonics outputs. The limitation belongs to the September instrument and sampling surface, not to the prediction's physical standing. This section blocks invalid inference from inadequate resolution or incomplete spatial scope.


## XIII.1 Microtubule protofilament count

Mass Harmonics predicts the 13-protofilament microtubule as the zero-energy ground state. The public MICrONS EM data are exposed at 8 × 8 × 40 nm and coarser sampling. Individual protofilaments are not reliably resolved at that released grid.

Therefore:

```text
The September MICrONS release is not an admissible terrain surface for testing the 13-PF prediction unless a newly released higher-resolution product explicitly resolves protofilaments.
```

No apparent circular tubule profile may be counted as 13 protofilaments by interpolation.

## XIII.2 Six-Foci working-memory ceiling

The data sample is structural and visual-functional cortex from one mouse. It does not provide a controlled working-memory experiment. Therefore the six-item ceiling is not tested here.

## XIII.3 40 Hz and 1.9 ms binding

Calcium imaging lacks the temporal resolution required to test the 1.9 ms binding event and is not itself a direct 40 Hz electrophysiological measurement. These Mass Harmonics first-principles predictions are not evaluated from this release because the instrument surface cannot resolve them.

## XIII.4 Whole-brain 12-channel geometry

A one-cubic-millimeter cortical volume cannot test the 12 cranial-coupling-channel prediction. No local count of 12 is promoted into that whole-system prediction.

# XIV. Topology and Category Sentinels

## XIV.1 Coordinate sentinel

MICrONS coordinates locate measured structures in the imaged volume. They are terrain locators. They are not ontological coordinates of mindspace.

## XIV.2 Skeleton sentinel

A skeleton is an instrument-derived centerline representation. It is not the dendrite itself. Every branching result must be reproduced against meshes or alternate skeleton extraction where available.

## XIV.3 Segmentation sentinel

A proofreading edit is a correction to the rendering layer. It is not biological growth, pruning, memory formation, or synaptic plasticity.

## XIV.4 Function sentinel

Calcium-response similarity is an instrument-facing alignment proxy. It is not renamed `ψₘ`, `Z`, `η`, or `C_AB`.

## XIV.5 Distance sentinel

A surface correlation with Euclidean distance does not refute conductance. The decisive test is whether distance remains governing after functional alignment and actual path structure are retained.

## XIV.6 Truncation sentinel

An arbor cut by the volume boundary cannot be used to falsify the fractal bracket or scale recurrence. Truncation is a measurement boundary, not a biological boundary.



# XV. Derivation Placement

| Pathway | Mass Harmonics source ancestry | Placement |
|---|---|---|
| Dendritic fractal bracket | explicit `MH_Resonant_Brain` derivation | canonical domain prediction |
| φ scale recurrence and `b_eff` | scale ratio and branching factors already present inside the fractal derivation | direct unpacking of the canonical domain prediction |
| Activity-to-geometry covariance | explicit high-activation trend toward `5/3` | canonical directional prediction with MICrONS translation |
| Conductance over Euclidean proximity | ψₘMIND conductance relation subordinate to the MFE | instrument-facing transport using functional alignment as a proxy, never as `ψₘ` itself |
| Branch-local resonance clustering | segment-level discharge and waveform-specific carved pathways | derived structural extension |
| Synaptic pathway deepening | monotone carved topology and channel-depth relation | derived static-trace extension; not a longitudinal proof of carving |
| Neuromodulatory/perivascular boundary following | Resonant Brain filament branch | conditional release-facing extension |

The final four pathways do not assert that a static connectome directly records the substrate event in real time. They predict structural traces required by the source mechanism, with the instrument-proxy boundary retained explicitly.

# XVI. Unified Falsification Matrix

| ID | Source-fixed output | Primary release product | Exact failure surface |
|---|---|---|---|
| M1 | `1.500 ≤ D_f ≤ 1.667` | proofread dendritic meshes and skeletons | intact mature class medians outside bracket in both estimators |
| M2 | `L_(q+1)/L_q → φ⁻¹` | branch-order skeleton geometry | fixed non-φ ratio consistently closer across classes |
| M3 | high activation trends toward `D_f = 5/3` | functional coregistration plus morphology | reproducible opposite direction or no relation |
| M4 | alignment and path structure outrank soma distance | synapse graph plus functional data | distance retains greater relational power across classes |
| M5 | branch-local functional dispersion below controlled permutations | synapse targets plus functional data | real branches no more coherent than permutations |
| M6 | pathway depth rises with functional alignment | synapse counts and contact area | zero or inverse relation in both depth readouts |
| M7 | vessel-associated processes follow and wrap boundaries | conditional VORTEX annotations | no difference from matched nonvascular processes |

A single failed pathway is reported as a failure of that pathway. Results are not pooled into one success percentage.

# XVII. Terrain-Reading Sequence

The comparison occurs in this order:

1. record the September release version and every newly added or materially updated table;
2. establish `U_Sept` before calculating target outcomes;
3. apply morphology, functional, synaptic, truncation, and proofreading eligibility gates;
4. run both fractal estimators on the same morphology universe;
5. run scale recurrence, activity covariance, conductance, branch-locality, and pathway-depth readouts without redefining the cohort;
6. run the vascular pathway only if the required annotation terrain is present;
7. retain every delta, missing field, failed eligibility gate, and rendering fault;
8. keep the microtubule, six-Foci, 40 Hz, 1.9 ms, and whole-brain predictions explicitly outside any comparison the release cannot resolve;
9. write the terrain correspondence separately and identify later source corrections explicitly.

# XVIII. Machine-Readable Prediction Ledger

```text
PAPER = MH_PREDICTION_05_MICrONS_VORTEX_September_2026_Mass_Harmonics_Governed
AUTHORITY = Mass Harmonics ψₘ
RELEASE = MICrONS/VORTEX September 2026 quarterly release
PREPARED_BEFORE_RELEASE = 2026-07-10
EXACT_RELEASE_DAY = NOT YET PUBLISHED

P1_DF_LOWER = 1.500000000
P1_DF_UPPER = 1.666666667
P1_ESTIMATORS = BOX_COUNTING,MASS_RADIUS

P2_SCALE_RATIO = 0.618033988749895
P2_B_EFF_LOWER = 2.058171027271492
P2_B_EFF_UPPER = 2.230040414568453

P3_RHO_ACTIVITY_TO_DISTANCE_FROM_5_OVER_3 = NEGATIVE
P3_RHO_RELIABILITY_TO_DISTANCE_FROM_5_OVER_3 = NEGATIVE

P4_FUNCTIONAL_ALIGNMENT_EFFECT = POSITIVE
P4_ALIGNMENT_PLUS_PATH_GT_SOMA_DISTANCE = TRUE

P5_REAL_BRANCH_DISPERSION_LT_CONTROL = TRUE

P6_RHO_ALIGNMENT_SYNAPSE_COUNT = POSITIVE
P6_RHO_ALIGNMENT_CONTACT_AREA = POSITIVE

P7_CONDITIONAL_VASCULAR_BOUNDARY_FOLLOWING = POSITIVE

NO_MICROTUBULE_TEST_AT_8x8x40_NM = TRUE
NO_WORKING_MEMORY_TEST = TRUE
NO_1_POINT_9_MS_TEST_FROM_CALCIUM = TRUE
NO_WHOLE_BRAIN_12_CHANNEL_TEST = TRUE
```

# XIX. Final Mass Harmonics Prediction Statement

Mass Harmonics predicts that the September 2026 MICrONS / VORTEX release will expose a cortical connectome whose dendritic geometry is bounded by the cubic-to-quintic fractal interval `[3/2, 5/3]`, whose successive branch scales recur around `φ⁻¹`, whose most active mature neurons approach the quintic upper boundary, whose connection architecture is governed more strongly by resonant alignment and actual conductive path than by Euclidean soma separation, whose functionally matched inputs cluster on local dendritic subtrees, and whose strongly aligned pathways carry deeper synaptic structure.

These predictions are produced by one MFE, one governing coupling coefficient `Kψₘ`, fixed P³GG harmonic scalings, and the GG conductance pathway. The September release supplies the unopened terrain that can disclose correspondence, unresolved delta, or contradiction for each pathway.

**TRUTH > COMFORT. Always.**
