Table 2 Operational map from axioms to...

Table 2

Operational map from axioms to observables in socio-technical interaction. Shaded rows indicate theorems demonstrating pathological rather than normative interaction patterns (π_ij = relational state; λ = leakage; Θ = timing norms; ε = symmetry/complementarity threshold; H̄ = mean entropy

Item	Construct (level)	Candidate measures (DV)	Experimental manipulation (IV)	Predicted observable effect	Notes / analysis
A1: Unavoidability	Belief update (information)	Confidence ratings on key propositions (pre/post); Bayesian surprise; proposition addition/removal above threshold θ; response-time change	Presence/absence of observable behavior (incl. silence); visibility/noise; co-presence vs. no-observation	Observable B_i(t) produces measurable change in Bel_j(t+1): confidence shifts \|Δc\| > ε, or new propositions entering above θ; larger effects under clearer observation	Pre-post paired t-tests on confidence scores; Bayesian surprise metrics; mixed-effects models with subject random intercepts
A2: Meta-inevitability	Relational content R(M)	Stance coding (dominance/affiliation); rights–duties attributions; perceived intent	Hold C(M) constant; vary relational cues (politeness, address terms, prosody)	Non-zero R(M) ratings even with “neutral” content; stronger effects with richer cues	Inter-rater reliability; ordinal models
A3: Multi-code realizability	Code/medium and variance	Posterior interpretive entropy; between-rater variance; misinterpretation rate	Same C(M), encode: digital vs. analog-rich vs. mixed	Lower H̄ for mixed/analog-rich vs. digital encodings, conditional on channel/leakage (see A10)	Information-theoretic comparisons of H/ℎ across conditions; standard homogeneity tests (e.g. Levene, 1960; Brown and Forsythe, 1974) if using parametric models on per-subject entropy scores
A4: Subjective punctuation	Segmentation p_i and attribution	Episode boundary placement; “who started/escalated” judgments	Ambiguous onset/offset; timeline reconstruction prompts	Divergent p_i ⇒ reciprocal blame without changing C(M)	Cross-tab of attributions; κ for boundary agreement
A5: Relational patterning	Dyadic state π_ij(t)	Continuous dominance/affiliation ratings; turn-share; interruption rate	Repeated meta-signals (leveling vs. dominance); feedback constraints	Thresholding: \|π_ij\| crosses ε → stable symmetry (≤ε) or complementarity (>ε)
A6: Turn-taking and timing	Floor rights / norms Θ	Latency, overlap, floor acquisition rate; perceived dominance	Enforce short vs. long latencies; allow/forbid overlap	Short latencies ↑ dominance attribution; miscoordination ↑ R(M) variance	Mixed-effects; latency as predictor of dominance
A7: Repairability	Error handling	Repair initiation/resolution rates; uncertainty reduction	Vary repair cost (time/penalty); block vs. invite repair	Higher cost ↓ repair → ↑ misattribution and escalation	Mediation: repair → uncertainty ↓ → blame ↓
A8: Common ground	Grounding / presupposition	Grounding moves; acceptance vs. challenge rates	Introduce novel terms with/without grounding	Missing grounding ↑ failure-to-uptake despite clear code	Logistic models for uptake
A9: Relevance/ Cooperation	Contribution design	Relevance ratings; perceived engagement/dominance	Insert off-goal, over-informative, or under-informative turns	Irrelevance shifts (R(M))): disengagement or dominance, context-dependent	Interaction terms: task goal × relevance
A10: Public vs private channels	Signaling vs. state; leakage (λ)	Prosodic/physio proxies; micro-expressions; perceived sincerity	Induce strategic encoding; vary leakage via channel constraints	Moderate (λ) ↓ interpretive entropy; very low/high (λ) ↑ uncertainty	Quadratic (inverted-U) fits for λ
T1: Communicativity of silence	Silence as B_i(t)	Belief Δ; inferred intent after silence	Respond vs. remain silent following prompt	Silence produces systematic Bel_j update	Compare to baseline noise; equivalence tests
T2: Punctuation asymmetry ⇒ blame	Divergent p_i	Mutual blame index; escalation ratings	Provide same stream, manipulate cut-points via instructions	Reciprocal blame emerges from punctuation differences alone	Preregistered contrast of blame symmetry
T3: Meta-signals stabilize patterns	π dynamics	Convergence to symmetric/complementary regime	Repeated dominance vs. leveling meta-signals	Trajectories converge to \|π_ij\| ≤ ε (symmetric) or > ε (complementary)
T4: Early-anchor vulnerability	Anchoring × timing	Persistence of initial misinterpretation	Early misleading anchor; restrict correction windows (latency)	Anchors resist later corrections when outside (Θ)	Interaction: timing × correction; partial η²
T5: Credibility via code choice	Code × leakage	Entropy/order of certainty about R(M)	Cross code conditions, vary λ	Across code conditions, compare group-mean posterior interpretive entropy H̄; expect lower H̄ for mixed/analog-rich encodings at moderate leakage, with higher uncertainty at very low or very high leakage (inverted-U in λ). This “minimum” is a descriptive characterization of uncertainty under the model, not a normative optimization target; lower entropy need not imply better relational outcomes	Comparative entropy ordering across conditions; avoid optimization language. Fit monotone segments by code and a quadratic (or GAM) curve for λ to test an inverted-U
T6: Symmetrical escalation	Punctuation divergence × reactivity	Escalation trajectory; mutual blame indices; behavioral intensity (volume, interruptions)	Manipulate p_i vs p_j alignment; vary repair availability; measure reactivity (α parameter)	Divergent p_i, p_j + no repair → increasing intensity; aligned p_i, p_j OR repair access → de-escalation	Time-series models; breakpoint analysis; mediation analysis (repair → intensity ↓) \|
T7: Meta-communication paradox	Meta-communicative dominance × relational threshold	π_ij trajectory; dominance attribution ratings; behavioral vs verbal symmetry signals	Manipulate: confederate makes 0, 1, or 3 explicit symmetry statements (“I value equality”) while holding behavioral turn-taking constant; measure near threshold (ε ± 0.1)	Explicit symmetry assertions increase \|π_ij\| (Δπ > 0.2); monotonic increase with statement count; behavioral demonstration (no verbal framing) decreases π_ij toward 0; third-party coders rate verbal claims as “trying to control definition” more than behavioral symmetry	Inverted-U or monotonic fits; third-party coding for “trying to control definition”; dissociation between verbal claims and behavioral effects; confederate paradigm

Item	Construct (level)	Candidate measures (DV)	Experimental manipulation (IV)	Predicted observable effect	Notes / analysis
A1: Unavoidability	Belief update (information)	Confidence ratings on key propositions (pre/post); Bayesian surprise; proposition addition/removal above threshold θ; response-time change	Presence/absence of observable behavior (incl. silence); visibility/noise; co-presence vs. no-observation	Observable B_i(t) produces measurable change in Bel_j(t+1): confidence shifts \|Δc\| > ε, or new propositions entering above θ; larger effects under clearer observation	Pre-post paired t-tests on confidence scores; Bayesian surprise metrics; mixed-effects models with subject random intercepts
A2: Meta-inevitability	Relational content R(M)	Stance coding (dominance/affiliation); rights–duties attributions; perceived intent	Hold C(M) constant; vary relational cues (politeness, address terms, prosody)	Non-zero R(M) ratings even with “neutral” content; stronger effects with richer cues	Inter-rater reliability; ordinal models
A3: Multi-code realizability	Code/medium and variance	Posterior interpretive entropy; between-rater variance; misinterpretation rate	Same C(M), encode: digital vs. analog-rich vs. mixed	Lower H̄ for mixed/analog-rich vs. digital encodings, conditional on channel/leakage (see A10)	Information-theoretic comparisons of H/ℎ across conditions; standard homogeneity tests (e.g. Levene, 1960; Brown and Forsythe, 1974) if using parametric models on per-subject entropy scores
A4: Subjective punctuation	Segmentation p_i and attribution	Episode boundary placement; “who started/escalated” judgments	Ambiguous onset/offset; timeline reconstruction prompts	Divergent p_i ⇒ reciprocal blame without changing C(M)	Cross-tab of attributions; κ for boundary agreement
A5: Relational patterning	Dyadic state π_ij(t)	Continuous dominance/affiliation ratings; turn-share; interruption rate	Repeated meta-signals (leveling vs. dominance); feedback constraints	Thresholding: \|π_ij\| crosses ε → stable symmetry (≤ε) or complementarity (>ε)
A6: Turn-taking and timing	Floor rights / norms Θ	Latency, overlap, floor acquisition rate; perceived dominance	Enforce short vs. long latencies; allow/forbid overlap	Short latencies ↑ dominance attribution; miscoordination ↑ R(M) variance	Mixed-effects; latency as predictor of dominance
A7: Repairability	Error handling	Repair initiation/resolution rates; uncertainty reduction	Vary repair cost (time/penalty); block vs. invite repair	Higher cost ↓ repair → ↑ misattribution and escalation	Mediation: repair → uncertainty ↓ → blame ↓
A8: Common ground	Grounding / presupposition	Grounding moves; acceptance vs. challenge rates	Introduce novel terms with/without grounding	Missing grounding ↑ failure-to-uptake despite clear code	Logistic models for uptake
A9: Relevance/ Cooperation	Contribution design	Relevance ratings; perceived engagement/dominance	Insert off-goal, over-informative, or under-informative turns	Irrelevance shifts (R(M))): disengagement or dominance, context-dependent	Interaction terms: task goal × relevance
A10: Public vs private channels	Signaling vs. state; leakage (λ)	Prosodic/physio proxies; micro-expressions; perceived sincerity	Induce strategic encoding; vary leakage via channel constraints	Moderate (λ) ↓ interpretive entropy; very low/high (λ) ↑ uncertainty	Quadratic (inverted-U) fits for λ
T1: Communicativity of silence	Silence as B_i(t)	Belief Δ; inferred intent after silence	Respond vs. remain silent following prompt	Silence produces systematic Bel_j update	Compare to baseline noise; equivalence tests
T2: Punctuation asymmetry ⇒ blame	Divergent p_i	Mutual blame index; escalation ratings	Provide same stream, manipulate cut-points via instructions	Reciprocal blame emerges from punctuation differences alone	Preregistered contrast of blame symmetry
T3: Meta-signals stabilize patterns	π dynamics	Convergence to symmetric/complementary regime	Repeated dominance vs. leveling meta-signals	Trajectories converge to \|π_ij\| ≤ ε (symmetric) or > ε (complementary)
T4: Early-anchor vulnerability	Anchoring × timing	Persistence of initial misinterpretation	Early misleading anchor; restrict correction windows (latency)	Anchors resist later corrections when outside (Θ)	Interaction: timing × correction; partial η²
T5: Credibility via code choice	Code × leakage	Entropy/order of certainty about R(M)	Cross code conditions, vary λ	Across code conditions, compare group-mean posterior interpretive entropy H̄; expect lower H̄ for mixed/analog-rich encodings at moderate leakage, with higher uncertainty at very low or very high leakage (inverted-U in λ). This “minimum” is a descriptive characterization of uncertainty under the model, not a normative optimization target; lower entropy need not imply better relational outcomes	Comparative entropy ordering across conditions; avoid optimization language. Fit monotone segments by code and a quadratic (or GAM) curve for λ to test an inverted-U
T6: Symmetrical escalation	Punctuation divergence × reactivity	Escalation trajectory; mutual blame indices; behavioral intensity (volume, interruptions)	Manipulate p_i vs p_j alignment; vary repair availability; measure reactivity (α parameter)	Divergent p_i, p_j + no repair → increasing intensity; aligned p_i, p_j OR repair access → de-escalation	Time-series models; breakpoint analysis; mediation analysis (repair → intensity ↓) \|
T7: Meta-communication paradox	Meta-communicative dominance × relational threshold	π_ij trajectory; dominance attribution ratings; behavioral vs verbal symmetry signals	Manipulate: confederate makes 0, 1, or 3 explicit symmetry statements (“I value equality”) while holding behavioral turn-taking constant; measure near threshold (ε ± 0.1)	Explicit symmetry assertions increase \|π_ij\| (Δπ > 0.2); monotonic increase with statement count; behavioral demonstration (no verbal framing) decreases π_ij toward 0; third-party coders rate verbal claims as “trying to control definition” more than behavioral symmetry	Inverted-U or monotonic fits; third-party coding for “trying to control definition”; dissociation between verbal claims and behavioral effects; confederate paradigm

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