Protocol v1 Application: Diocletian Baths / Santa Maria degli Angeli Interior
Important note:
Manual visual extraction from the provided image, not automated pixel-level geometry.
Working hypothesis:
This image should not behave like Brunelleschi’s church interior.
Brunelleschi produced:
Type III Classical Axis Attractor
entrance → nave → altar → dome/light
Diocletian / Santa Maria degli Angeli should produce:
Type IV Imperial Circulation-Field Attractor
floor field → people → lateral movement → gathering → altar/volume
1. Candidate Attractors
A1 = altar-axis
central view → altar
A2 = circular floor-field attractor
large compass-like marble floor circle in the foreground
A3 = lateral circulation attractor
left ↔ center ↔ right movement across the hall
A4 = imperial circulation-field attractor
floor circle → open hall → dispersed people → side zones → altar/volume
2. Pπ Measurement: Perspective / Place Coherence
Main architectural lines marked: 20
Included line groups:
side wall edges, column alignments, arch curves projected as directional structures, ceiling/vault boundaries, floor pattern axes, central altar approach, lateral floor geometry, side chapel/door alignments.
Supporting line counts:
A1 altar-axis:
13 / 20
Pπ(A1) = 0.650
A2 circular floor-field attractor:
12 / 20
Pπ(A2) = 0.600
A3 lateral circulation attractor:
11 / 20
Pπ(A3) = 0.550
A4 imperial circulation-field attractor:
16 / 20
Pπ(A4) = 0.800
Interpretation:
The altar-axis is clearly present, but the dominant place-field includes the floor geometry, side movement, human distribution, and hall volume. A4 receives the broadest architectural support.
3. Sφ Measurement: Golden-Spiral / Temporal-Form Coherence
Spiral rule:
r = r₀e^((ln φ / π)θ)
Protocol:
Anchor the spiral in the foreground circular pavement field, allow scale and rotation, and test whether the spiral path or tangent order passes through major spatial-temporal features.
Key features considered: 11
Feature groups:
foreground circular pavement, radial floor geometry, central open hall, scattered human positions, left circulation zone, right circulation zone, column/arch rhythm, side zones, altar zone, high light/vault zone, total volume of the hall.
Matched feature counts:
A1 altar-axis:
7 / 11
Sφ(A1) = 0.636
A2 circular floor-field attractor:
8 / 11
Sφ(A2) = 0.727
A3 lateral circulation attractor:
7 / 11
Sφ(A3) = 0.636
A4 imperial circulation-field attractor:
10 / 11
Sφ(A4) = 0.909
Interpretation:
The spiral does not simply reinforce a single altar line. It is strongest when read as expanding from the circular floor field through people, lateral paths, volume, and altar/light.
4. Tφ Measurement: Dominant Temporal-Flow Coherence
Important refinement:
For this monumental Roman/sacred space, Tφ should not mean domestic habitation.
Here Tφ means dominant temporal-flow field:
L = light/volume alignment
M = movement/circulation alignment
C = cultural/functional continuity alignment
A1 altar-axis:
L = 0.75
M = 0.60
C = 0.75
Tφ(A1) = 0.700
A2 circular floor-field attractor:
L = 0.70
M = 0.80
C = 0.75
Tφ(A2) = 0.750
A3 lateral circulation attractor:
L = 0.55
M = 0.90
C = 0.70
Tφ(A3) = 0.717
A4 imperial circulation-field attractor:
L = 0.80
M = 0.95
C = 0.90
Tφ(A4) = 0.883
Interpretation:
The highest temporal-flow coherence belongs to the field/circulation attractor. The space gathers bodies, distributes movement, and preserves Roman imperial volume beneath later sacred use.
5. Final Lock Scores
Lock(π, φ | A) = Pπ(A) × Sφ(A) × Tφ(A)
A1 altar-axis:
0.650 × 0.636 × 0.700 = 0.289
A2 circular floor-field attractor:
0.600 × 0.727 × 0.750 = 0.327
A3 lateral circulation attractor:
0.550 × 0.636 × 0.717 = 0.251
A4 imperial circulation-field attractor:
0.800 × 0.909 × 0.883 = 0.642
6. Result
A* = arg max_A Lock(π, φ | A)
A* = A4
A4 = imperial circulation-field attractor
Therefore:
⊗(π, φ) = A* = 1