Reference for UI implementors: how to score dialectical entities, what "good" and "bad" look like, and how to lay out the molecular visualization.
The thesis defines the polarity axis. It IS the reference point.
| Metric | Value | Notes |
|---|---|---|
| HS | Always 1.0 | Tautological — T defines its own apex |
No quality metrics — a thesis is the starting axiom.
The antithesis opposes the thesis. Its quality determines polarity strength.
| Metric | Range | What it measures |
|---|---|---|
| HS | 0.0–1.0 | How well A captures the antithesis apex concept |
| Mode | 0.0–1.0 | Type of opposition (privation → negation) |
| Arousal | 0.1–0.9 | Tension visibility/intensity |
HS Scale:
| Range | Quality |
|---|---|
| 0.9–1.0 | Perfect antithesis — exemplary |
| 0.7–0.9 | Strong — captures most of the apex |
| 0.5–0.7 | Moderate — some aspects, acceptable |
| 0.3–0.5 | Weak — still valid, poor quality |
| 0.1–0.3 | Very weak — barely an antithesis |
| 0.0–0.1 | Invalid — wrong category entirely |
Mode Scale (opposition mechanism):
| Value | Type | Description |
|---|---|---|
| 1.0 | Negation | Direct, active opposition |
| 0.9 | Inversion | Reversal of T's meaning |
| 0.8 | Devaluation | Diminishing T's worth |
| 0.7 | Hollowing | Emptying T of substance |
| 0.6 | Corruption | Degrading/perverting T |
| 0.5 | Distortion | Twisting T's form |
| 0.4 | Skew | Imbalancing T |
| 0.3 | Blocking | Obstructing T |
| 0.2 | Suppression | Holding T down |
| 0.1 | Distancing | Drifting from T |
| 0.0 | Privation | Complete absence of T |
Arousal Scale (tension activation):
| Value | Label | Description |
|---|---|---|
| 0.9 | Active | Fully manifest, immediate |
| 0.8 | Intense | Very active, urgent |
| 0.7 | High | Strong, clearly visible |
| 0.6 | Elevated | Becoming prominent |
| 0.5 | Moderate | Balanced, present tension |
| 0.4 | Mild | Noticeable but subdued |
| 0.3 | Low | Background tension |
| 0.2 | Latent | Barely perceptible |
| 0.1 | Dormant | Completely invisible |
The polarity is a container. Its quality is determined by the antithesis:
| Indicator | Source | Good | Bad |
|---|---|---|---|
| Tightness of opposition | HS_A | High (0.7+) | Low (<0.5) |
| Directness | Mode | Context-dependent | Context-dependent |
| Aliveness | Arousal | Context-dependent | Context-dependent |
Mode and Arousal are characterization, not quality — a "dormant" polarity isn't necessarily bad, it's just latent.
Each aspect has three complementarity scores plus HS:
| Metric | Range | What it measures |
|---|---|---|
| HS | 0.0–1.0 | Similarity to taxonomy apex for that position |
| K_T | 0.0–1.0 | How well the aspect complements the thesis |
| K_A | 0.0–1.0 | How well the aspect complements the antithesis |
| Ks | 0.0–1.0 | Combined: (K_T + K_A) / 2 — complementarity toward synthesis |
Ks interpretation:
- 0.0 = Actively undermines the system
- 0.5 = Neutral
- 1.0 = Strongly enhances the whole
Expected pattern for a balanced tetrad:
| Position | K_T | K_A | Ks | Pattern |
|---|---|---|---|---|
| T+ | High | Low-ish | Mid-high | Favors T but complements A somewhat |
| A+ | Low-ish | High | Mid-high | Favors A but complements T somewhat |
| T- | Low | Mid | Low | Undermines T, doesn't help A |
| A- | Mid | Low | Low | Undermines A, doesn't help T |
(A theory heuristic sometimes cited is K_T + K_A ≈ 1.0 per aspect in ideal systems, but nothing in code computes or enforces this — K_T and K_A are scored independently.)
Computed from the four aspects' Ks values:
| Metric | Formula | Range | Good | Bad |
|---|---|---|---|---|
| diff_t | Ks(T+) − Ks(T−) | −1 to 1 | ≥ 0.1 | < 0.1 |
| diff_a | Ks(A+) − Ks(A−) | −1 to 1 | ≥ 0.1 | < 0.1 |
| area (= theory's SP, Synthesis Potential) | diff_t + diff_a | −2 to 2 (well-formed tetrads ~0 to 2) | ≥ 0.7 | < 0.3 |
| area_normalized | area / 2 | −1 to 1 (well-formed tetrads ~0 to 1) | ~0.5 | ~0.15 |
| rectangularity | [Ks(T+)−Ks(A+)]² + [Ks(T−)−Ks(A−)]² | 0+ | < 0.01 | > 0.09 |
Empirical inequalities (pass/fail):
diff_t ≥ 0.1ANDdiff_a ≥ 0.1|diff_t − diff_a| ≤ 0.15Ks(T+) > 0.4ANDKs(A+) > 0.4Ks(T−) < 0.6ANDKs(A−) < 0.6
Structural validity checks (pass/fail):
| Check | Threshold | What it tests |
|---|---|---|
| Conceptual Coherence (CC) | both control scores ≥ 0.7 | "T+ without A+ yields T−" and "A+ without T+ yields A−" |
| Diagonal Contradiction | both ≥ 0.7 | T+ vs A− and A+ vs T− are genuine contradictions |
CC stores the average of the two control scores as its value, but the pass/fail
criterion is that each score clears 0.7 (ConceptualCoherenceEstimation.is_coherent)
— 0.5 + 0.9 does not pass. Diagonal Contradiction is not part of the standard
PerspectiveValidation run; it is an extra LLM call that only fires on user-edited
tetrads (edit_perspective). Generated tetrads are never gated on it.
Quality tiers (suggested UI grouping — not a built-in framework ranking; see note below):
| Tier | Criteria |
|---|---|
| Invalid | Fails CC (Diagonal Contradiction, too, but only on user-edited tetrads) |
| Bad | Fails any empirical inequality |
| Good | Passes all checks |
| Best | Passes all + highest area_normalized + lowest rectangularity |
Ranking, in practice: these tiers and an area_normalized ordering are guidance for
a UI — the framework does not implement them. The only ranking in code is
AnalysisPipeline._rank_polarities, which orders polarities by their antithesis
heuristic_similarity against a soft HS_THRESHOLD = 0.7 (if nothing clears it, the top
few are expanded anyway). If a UI wants to order valid tetrads, area_normalized (0–1,
higher = better) gated by the validity checks is a reasonable choice, with rectangularity
as a tiebreaker.
area_normalizedis a comparative hint, not an absolute grade. The~0.5/~0.15figures above are rough visual anchors for ordering tetrads against each other, not pass/fail cutoffs. The theory (SP / Synthesis Potential) defines no universal cutoff — seedocs/theory/scoring.md. Do not treat a singlearea_normalizedvalue as "good" or "bad" in isolation.
| Metric | Range | What it measures |
|---|---|---|
| Insight | 0.0–1.0 | Depth of understanding in the transition |
| Proactiveness | 0.0–1.0 | How actionable/practical the transition is |
| Feasibility | 0.0–1.0 | Practical achievability |
| HS | 0.0–1.0 | Similarity of Ac+/Re+ to their derived apex |
Insight scale (Y-axis — depth of transformation):
| Value | Level | Character |
|---|---|---|
| 1.0 | Transcendence | Paradigm shift |
| 0.9 | Redirection | Fundamental change |
| 0.8 | Inversion | Flipping perspective |
| 0.7 | Anticipation | Acting ahead |
| 0.6 | Leverage | Using leverage points |
| 0.5 | Composition | Combining elements |
| 0.4 | Reformulation | Restructuring approach |
| 0.3 | Variation | Deliberate small changes |
| 0.2 | Tuning | Fine-tuning |
| 0.1 | Procedure | Following protocol |
| 0.0 | Reflex | Automatic response |
Proactiveness scale (X-axis — action vs reflection):
| Value | Level | Zone |
|---|---|---|
| 0.0 | Observation | Re (reflection) |
| 0.1 | Detection | Re |
| 0.2 | Interpretation | Re (apex zone) |
| 0.3 | Framing | Re |
| 0.4 | Evaluation | Midpoint |
| 0.5 | Coordination | Ac (action) |
| 0.6 | Intervention | Ac (apex zone) |
| 0.7 | Implementation | Ac |
| 0.8 | Configuration | Ac |
| 0.9 | Governance | Ac |
| 1.0 | Stewardship | Ac |
Feasibility scale:
| Range | Meaning |
|---|---|
| 0.9–1.0 | Highly achievable |
| 0.7–0.8 | Moderately feasible |
| 0.5–0.6 | Challenging but achievable |
| 0.3–0.4 | Extremely difficult |
| 0.0–0.2 | Practically impossible |
| Metric | Range | What it measures |
|---|---|---|
| Causality Probability | 0.0–1.0 | Plausibility of this causal ordering vs alternatives |
The value stored on a Cycle or Wheel is the raw LLM plausibility score (0.0–1.0), not
a normalized one. Normalization to a layer-relative share (siblings sum to 1.0) is applied
only to Wheel Transitions (nth-root decomposed) and is otherwise computed on the fly
for display (raw P vs normalized %). A UI reading the estimation directly off a
Cycle/Wheel gets the raw score.
The perspective is displayed as a molecule with T and A as the nucleus and aspects as bonded satellites.
No formal X-axis. This is a spatial/relational layout, not a chart. Only vertical position (Ks) is a true metric axis.
| Element | Position/Distance | Encoded metric |
|---|---|---|
| T ↔ A distance | 1 − HS_A |
Polarity quality (tight = good) |
| Aspect vertical position | Ks value | Complementarity toward synthesis |
| Aspect bond length to parent | 1 − K_parent |
Affinity to parent concept |
| Trapezoid shape | Connect T+→A+→A−→T− | Area + rectangularity visible |
"K_parent" means:
- For T+ and T−: bond length =
1 − K_T - For A+ and A−: bond length =
1 − K_A
Ks
↑
│
T+ ○━━━━━━━━○ A+ ← Both high Ks (~0.6–0.7)
╲ ╱ ← Short bonds (high K)
T●━━━●A ← Close together (HS_A = 0.85)
╱ ╲ ← Short bonds
T- ○━━━━━━━━○ A- ← Both low Ks (~0.2–0.3)
│
└──────
✓ Compact nucleus (high HS_A → strong opposition)
✓ Tall vertical gap (high area → clear differentiation)
✓ Flat top/bottom edges (low rectangularity → balanced)
✓ Short bonds (high K → tight complementarity)
✓ Symmetric left/right
Ks
↑
│
T+ ○ ← High Ks (0.7)
╲
╲ (long bond)
T● ●A ← Far apart (HS_A = 0.4)
╱ ╲
○ A+ ╲ ← Mid Ks (0.45)
╲
T- ○ ○ A- ← A- very low (0.15)
│
└──────
✗ Sprawling nucleus (low HS_A → weak opposition)
✗ Tilted shape (high rectangularity → imbalanced sides)
✗ Long bonds (low K → aspects loosely related)
✗ Small vertical gap on one side (low area)
✗ Asymmetric — T-side taller than A-side
Ks
↑
│
T+ ○━━━━━━○ A+ ← Mid Ks (~0.50, 0.55)
╲ ╱
T●━●A ← Moderate closeness (HS_A = 0.7)
╱ ╲
T- ○━━━━━━○ A- ← Mid Ks (~0.35, 0.40)
│
└──────
~ Decent nucleus (acceptable HS_A)
~ Small vertical gap (low area = 0.30 → weak differentiation)
~ Shape is rectangular but flat (aspects mushed together)
~ Bonds mid-length
| Visual property | Metric | Good | Bad |
|---|---|---|---|
| T-A closeness | HS_A | Close (< 0.3 gap) | Far (> 0.5 gap) |
| Vertical gap (+ row vs − row) | area | Tall (> 0.7) | Squished (< 0.3) |
| Top/bottom edge horizontality | rectangularity | Flat (< 0.01) | Tilted (> 0.09) |
| Bond lengths to parent | K_T / K_A | Short (K > 0.6) | Long (K < 0.3) |
| Overall compactness | Combined | Dense molecule | Straggling/diffuse |
| Property | Encoding suggestion |
|---|---|
| Mode | Color/icon on T-A bond (e.g., negation=red, privation=grey) |
| Arousal | Bond thickness or pulse animation |
| HS of aspects | Node size or opacity |
| CC validity | Green/red border on the tetrad quadrilateral |
| Diagonal contradiction | Diagonal dashed lines with check/cross |
The paper (Generative Rules for Dialectical Synthesis) establishes:
-
The tetrad forms a trapezoid when plotted with Ks on the vertical axis and T-side / A-side on the horizontal.
-
In practice, no tetrad is a perfect rectangle. The goal is a trapezoid approaching rectangular shape with maximum surface area.
-
Balanced tetrads (A and D in Fig. 4) produce near-rectangular trapezoids where like-signed components occupy comparable Ks levels.
-
Distorted tetrads produce skewed, twisted, or compressed trapezoids — the shape visually communicates what's wrong:
- Compressed = low area, aspects not well-differentiated
- Tilted = high rectangularity, one side overdeveloped
- Narrow = low HS_A, weak polarity foundation
-
Selection criterion: "the best one typically shows trapezoid that is most similar to rectangular with the largest surface area" (paper, p. 10).
| Entity | Primary quality metric | Threshold | Secondary |
|---|---|---|---|
| Thesis | — | — | Defines the axis |
| Antithesis | HS_A | > 0.7 good, > 0.1 valid | Mode, Arousal |
| Aspect | Ks | T+/A+ > 0.4, T−/A− < 0.6 | HS, K_T, K_A |
| Perspective | area_normalized | ~0.5 excellent, ~0.35 good | rectangularity, CC, diagonals |
| Transition | Feasibility | > 0.7 feasible | Insight, Proactiveness, HS |
| Cycle/Wheel | Causality Probability | Raw on the node; layer-relative % (sum = 1.0) computed for display |
— |