# Candidate receiver, growth, projection and image study

These modules are isolated prototypes. They import only this experiment's field
operator. None publishes production contracts, transports light, models living
matter or establishes a physical interpretation of the field.

## Observer-centered 4π receiver

`receiverSamples(experiment, {count=256, observer=[0,0,0], radius=2, time})`
returns an exact partition of the direction sphere plus one endpoint field sample
per cell. The sphere belongs to the observer: `position = observer + radius *
direction`. Moving the observer preserves the cells' address identities and
directions while moving their world endpoints and changing their evaluated fields.

Coordinates are `u = azimuth/(2π)` and `v = (1-cos(theta))/2`. The area element is
exactly `dOmega = 4π du dv`. Azimuth divides each band equally. A band's height is
its cell count divided by the total requested count, so all cells have exactly
`4π/count` solid angle, including when the count is prime. Cells cover the entire
sphere, with no planar camera field-of-view clipping. Floating-point summation of
the weights is checked against `4π`.

These are exact cell areas, **not exact quadrature of an arbitrary field**. Each
cell uses its midpoint. Polar cells can be elongated; area equality is not a claim
of uniform angular diameter or optimal direction placement. The method evaluates
the endpoint field and does not perform ray tracing, line integration, occlusion,
optical transport or visibility.

The result includes `samples`, `observer`, `radius`, `configurationId`,
`solidAngleTotal`, and the coordinate scheme. Each sample has `id`, `direction`,
`position`, `vector`, `uv`, `cell` bounds and `dOmega`. The cell ID contains scheme,
resolution, band and azimuth index; it does not include observer position. A
separate 32-bit configuration fingerprint distinguishes field and observation
state for diagnostics. It is not a cryptographic identifier or a substitute for
the stored full configuration.

## Field-to-projection candidate

`projectionSamples(experiment, options)` extends receiver samples with:

- `receiverId`, `fieldSampleId`, and the configuration fingerprint;
- `intensity = 1-exp(-|F|)` in `[0,1]`;
- a bounded synthetic `rgb` encoding the signed ray-aligned fraction of `F`;
- `polarity`, `phase`, `coherence`, and `sourceIds`.

Source IDs name precisely those active anchors returning a nonzero contribution
at the endpoint. Phase/coherence are an amplitude-weighted phasor diagnostic of
those contributors; cancellation can make the net vector zero without removing
contributor lineage. Computing that lineage requires another per-anchor pass.
No sources gives intensity zero, an empty source list and diagnostic phase zero.

The RGB values are dimensionless authored colors. They are not watts, radiance,
photons, spectra, sensor response or a validated addressed optical contract. This
tests whether stable addresses, observation state and source lineage can travel
with a bounded field-derived value.

`compareProjectionSampling(experiment, {count=256, heldoutCount=1024, observer,
radius=2, time})` compares two piecewise-constant reconstructions of that **same
intensity function**:

1. Uniform cells, retaining exactly `count` endpoint samples.
2. A deterministic adaptive rectangular partition, also retaining exactly `count`
   samples. It starts with up to 16 full-sphere cells, evaluates five local pilot
   positions per cell, and bisects the cell with greatest area-weighted variation.
   Both children are rescored; ties preserve deterministic array order.

Every adaptive cell retains exact `4π*(u1-u0)*(v1-v0)` weight. The partition covers
the sphere; overlapping boundaries have zero area. The policies reconstruct at a
fixed independent Fibonacci validation sequence that planning never reads. Its
equal-weight RMSE, MAE and maximum error are finite estimates, not mathematical
error bounds. The returned adaptive cells make sampling locations and weights
reviewable.

`stats` reports uniform field calls, adaptive pilot calls, adaptive retained field
calls, validation calls, and priority-selection comparisons. **Equal retained
sample count does not mean equal computation.** Each field call additionally
visits the experiment's anchors. The adaptive selection loop is quadratic in the
retained sample count; it is a transparent prototype rather than an optimized
priority queue.

For the initial default single anchor with 128 retained samples, this prototype
measured intensity RMSE about `0.0181` for uniform cells and `0.00351` for adaptive
cells. However, adaptive used `1,200` pilot evaluations plus `128` retained
evaluations, versus `128` for uniform; both used the same `512` validation
evaluations. The ordinary vortex also improved (`0.0105` to `0.00141`). This is
evidence that additional adaptive sampling can help an authored scalar signal,
not that the toroidal/FCC construction has a unique reusable advantage. Regenerate
the experiment reports for current results; these values document the initial
candidate check only.

## Field-to-form candidate

`growthSurface(experiment, {count=400, time=1, fieldTime=time, strength=0.3, radius=1.7*scale,
center=firstAnchor.center})` starts from a sphere. At each undeformed base sample,
with outward unit direction `n`, it computes:

```text
F       = evaluateField(experiment, basePosition, fieldTime)
normal  = dot(F,n)
tangent = |F - normal*n|
delta   = radius * strength * tanh(time * (normal + 0.18*tangent))
position = center + (radius + delta)*n
```

Strength is restricted to `[0,0.9]`; radius is positive. Thus radial displacement
is bounded by `radius*strength` and radius remains positive. A zero field gives
zero displacement. The tangential gain `0.18` is an explicit authored choice that
lets circulation affect the shape. It is not a discovered growth law. Samples
retain their `basePosition`, `position`, signed `displacement`, input `vector`,
direction, stable ID, response components and source lineage.

`time` is a bounded exposure-age parameter in `[0,100]` that scales the response;
`fieldTime` selects the sampled field phase independently. It defaults to `time`,
preserving the original coupled-time behavior. The laboratory can hold exposure
age at 2 while animating field phase time from 0. Both values are returned and
bound into the configuration fingerprint. Field vectors and source phase lineage
use `fieldTime`; stable surface sample addresses do not depend on either value.
These snapshots are
**not time integration** of surface motion and do not establish organism formation
or temporal stability. `measureCandidateQuality` reports displacement RMS/max,
the analytic displacement bound, finite/bounded checks, nearest-direction radial
slope RMS as a roughness estimate, and RMS change between fixed snapshots. The
slope divides neighboring displacement differences by base-sphere arc distance;
it is not a surface curvature estimator. Smoothness or boundedness is not an
automatic preference for toroidal flow: radial flow can produce a smoother sphere,
and boundedness follows directly from `tanh` for every control.

## Explicit planar FCC [111] circle construction

`grantCandidate({rings=2, radius=1, phase=0})` includes a separately defined planar
circle construction. Let integer axial coordinates be `(a,b)` and set

```text
q = (a+b, -a, -b)
max(|a|,|b|,|a+b|) <= rings
worldPosition = q * radius/sqrt(2)
uAxis = (1,-1,0)/sqrt(2)
vAxis = (1,1,-2)/sqrt(6)
(u,v) = (radius*(a+b/2), radius*sqrt(3)*b/2)
```

All q have coordinate sum zero, so they lie in the central FCC [111] slice and
have valid even parity. Nearest-center distance equals `radius`. Drawing an
equal-radius circle at each center gives the explicit triangular/hexagonal
circle-center organization. One ring has 7 centers; two rings have 19. The test
compares every two-ring center to the core's independently constructed FCC slice
coordinates and checks nearest-center spacing. `phase` rotates the displayed
plane; the unrotated FCC source coordinates remain in `fccPosition`.

This makes the familiar 19-circle Flower-of-Life-style construction reproducible
under a stated radius and lattice rule. It does not equate arbitrary circle
packings with that design and does not establish that a 3D torus, a Vector
Equilibrium, or the toroidal field is Flower of Life. The circles do not arise by
silently projecting a torus at every FCC center.

## Robert Edward Grant image candidate and missing source

**The requested source raster was not attached to this experiment.** The laboratory
therefore provides a clearly labeled, unvalidated geometric candidate composition:
the explicit 19-circle plane plus optional torus latitude curves in orthographic
projection. The latter has major radius `1.55*radius`, minor radius `0.62*radius`,
tilt `π/3`, 18 latitudes and 96 segments per curve. These are authored here,
recorded in returned metadata, and not attributed to Grant. No pixel comparison,
similarity score, feature extraction or provenance inference has been performed.

**A raster does not reveal the exact authored generator.** Even an exact pixel
match cannot uniquely recover a hidden construction: distinct geometry, masking,
rendering and compositing pipelines can lead to the same image. Providing the
missing raster would permit a reference-driven *candidate* reconstruction and
comparison, but would not make exact generator recovery identifiable by itself.

The minimum source material for exact, verifiable recovery is:

1. The actual uncropped original reference at its original resolution, with known
   orientation, dimensions and color profile.
2. One authoritative generator representation: editable vector/CAD/3D construction
   with its dependencies, or original generator code and exact version, plus all
   numeric parameters and any random seeds.
3. The construction sequence/constraints, coordinate system, layers, masks and
   compositing rules needed to interpret that representation.
4. Projection/camera, crop, line widths, colors, rendering settings and any fonts or
   external assets needed to reproduce the output.
5. A known reference output or author confirmation against which to verify it.

An author-provided sufficient generator and render manifest can package several
of these together. Until that source exists, the result remains a candidate.

## Reproduction and scope

Run `node --test tests/candidates.test.mjs` from this experiment's directory.
Tests verify 4π coverage, arbitrary-count equal weights, stable replay and
addresses, moved-observer endpoints, exact source attribution, dormant and bounded
growth, adaptive coverage and accounted pilot work, and the independent 19-circle
FCC construction. No test treats a visual resemblance or built-in bound as proof
of reusable field behavior.

The prototypes do not claim complete electromagnetism, cosmological proof,
consciousness physics, physical zero-point extraction, or recovery of Grant's
exact construction.