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Phase Coherence Field

Status: Analysis and design documentation only. No renderer changes. All mappings are analogical design grammar, not physical or biological equivalence claims.

This note synthesises the phase-coherence analysis for xPRIMEray and describes the proposed geometric phase memory layer as a future computational extension.

Source: papers/paper_001_causal_observer_ladders/paper.md §5.6, papers/paper_001_causal_observer_ladders/analysis/geometric_phase_memory.md

What Phase Coherence Measures

The phase-coherence field assigns a scalar score to each pixel, estimating whether that pixel's transport solution is consistent with its immediate 3 × 3 neighbourhood. High coherence indicates smooth variation — adjacent pixels reached their hits via similar ray paths. Low coherence indicates a phase boundary — a location where two distinct solution families meet in pixel space.

The score is constructed from:

  1. Neighbour-normal delta — angular deviation between a pixel's stored-hit normal and its neighbourhood average. Large deviations indicate adjacent rays hitting structurally different surfaces.
  2. Phase-incoherence field — a composite of neighbour-normal delta and first-hit divergence, summarised as a scalar per-pixel incoherence score.

Empirical Results

Coherence was measured at two checkpoints (mouth and bridge):

Checkpoint Band-region coherence Outside-band coherence Gap
mouth 0.639 0.801 0.162
bridge (post-throat backstep) 0.764 0.796 0.032

At the mouth: visible banding corresponds to a substantial coherence reduction. The 0.162 gap indicates that band locations are structurally different from their surroundings in the transport-solution field, not just in pixel intensity.

At the bridge: the gap collapses to 0.032. The bridge is broadly disordered — high Hough-line count, fragmented components, low contour eccentricity — rather than sharply partitioned into two coherent families. The bridge does not exhibit clean phase boundaries; it exhibits diffuse incoherence.

Proposed Mechanism for Banding

The coherence correlation supports a specific mechanism:

In regions where multiple locally valid ray-path solutions coexist (multi-solution geodesic field), spatial sampling collapses inconsistently across phase boundaries. Each side of a boundary selects a different dominant solution, producing a visible band.

This is distinct from classical rendering artifacts (insufficient samples, numerical precision, shading discontinuities) in a testable way: classical artifacts would not show the coherence-gap pattern — they would produce either uniformly low coherence (noise) or checkpoint-independent artifacts.

The mechanism is hypothesised, not confirmed. A definitive test would require controlled variation of the candidate-hit selection policy while holding the field and observer position fixed.

Geometric Phase Memory: Design Framework

The phase-coherence diagnostics suggest a future computational layer: geometric phase memory. This is a proposed extension — not a current implementation — that would use persistent phase-organisation across frames and observer positions to guide sampling texture selection.

The framework borrows design grammar (not physical claims) from Anirban Bandyopadhyay's work on phase-coherent biological computation, specifically the Geometric Musical Language (GML) and Phase Prime Metric (PPM). These are adopted as an organising vocabulary, not as a model of biological or physical equivalence.

Conceptual mapping

Bandyopadhyay construct xPRIMEray equivalent
GML geometric event Detected primitive: Hough line, arc, circle, corner, annular sector
Phase tag Per-event coherence score from phase-incoherence field
Phase Prime Metric Per-checkpoint coherence score and cross-checkpoint coherence delta
Node of silence Curvature-centre candidate, line-intersection cluster, band-boundary junction
Phase attractor Geometric event grammar that recurs across checkpoints (e.g. radial dominance)
Phase attractor basin Set of observer positions producing the same dominant event grammar
Time-crystal recurrence Attractor-basin membership recurring without physical position repeat
Phase transition Departure from one attractor basin to another (near-side → bridge → far-side)

Five-phase implementation roadmap

Phase Goal
A — Primitive extraction Build per-checkpoint inventory of GML-equivalent events (Hough lines, arcs, corners) with coherence tags
B — Attractor / node detection Cluster line intersections and arc centres; score candidates by coherence gradient
C — Persistence tracking Match anchor candidates across checkpoints; compute persistence scores; flag attractors vs transition events
D — Domain-aware render guidance Use persistence map to recommend sampling texture per observer position (human-review artifact, not automatic directive)
E — Validation separation Label all phase-memory outputs [PHASE-MEMORY PREVIEW]; never mix with Pass 1 truth

Epistemic posture

This framework is adopted as a productive design grammar. Bandyopadhyay's GML and PPM provide a structured vocabulary for describing what the diagnostics already show. The claim is not that xPRIMEray instantiates a biological time crystal or that wormhole ray transport is equivalent to phase-coherent neural computation. The claim is that the vocabulary is useful for organising the diagnostic evidence and motivating a concrete implementation roadmap.

Current Evidence Quality

Concept Best existing artifact Coverage
GML line events Hough detections, geometry structure contact sheet 6 checkpoints
GML arc/circle events Curvature-centre polar candidates 2 checkpoints
PPM coherence scores Band/outside coherence table 2 checkpoints
Nodes of silence Curvature-centre candidates, line intersections 2 checkpoints
Attractor-basin decomposition Regime clustering (k=3, ARI=0.5946) 6 checkpoints
Orientation persistence Log-polar histograms 6 checkpoints

Full six-checkpoint coherence scoring is the highest-priority evidence gap.

Cross-References