Appendices
The ollowing appendices p o ide supplemen a y ma e ial suppo ing he analyses,
isualiza ions, and heo e ical in e p e a ions p esen ed in he main ex .
They a e o ganized o ensu e ull anspa ency, eplicabili y, and concep ual
in eg a ion wi hin he amewo k o he Theo y o In o ma ional Eme gence
(TIE).
Appendix
Ti le
Pu pose
A
Compu a ional
Pa ame e s and
Pipeline
De ails he ull compu a ional se up used o
gene a e and analyze he cohe ence ajec o ies
( ), including model con igu a ion, me ic
compu a ion, and Dynamic Time Wa ping
(DTW) pa ame e s.
B
Supplemen a y
Visualiza ions
P o ides illus a i e igu es o cohe ence
cu es, up u e– epai cycles, DTW alignmen s,
and equency spec a ha complemen he
quan i a i e analyses.
C
Da a Tables
P esen s he comple e nume ical esul s (F1, κ,
lag, DTW alues) o all dialogues, along wi h
desc ip i e s a is ics ac oss analy ical le els
(mic o, meso, mac o).
D
Theo e ical B idge:
P o o-Cohe ence and
S uc u al Coupling
In e p e s he empi ical indings wi hin he TIE
amewo k, linking measu able cohe ence
dynamics o in o ma ional coupling,
pe spec i al low, and eme gen
synch oniza ion.
Toge he , hese appendices expand he empi ical ounda ion o he TIE–Dialog pilo
and demons a e how cohe ence can be bo h quan i a i ely measu ed and
concep ually g ounded as an eme gen in o ma ional phenomenon.
Appendix A — Compu a ional Pa ame e s and
Pipeline
This appendix de ails he ull compu a ional se up used o gene a e, p ocess, and
analyze he cohe ence ajec o ies ( ) in he TIE–Dialog pilo .
All p ocedu es we e implemen ed in Py hon and execu ed in Google Colab o ensu e
anspa ency and ep oducibili y.
A.1 Model and Embedding Con igu a ion
● F amewo k: TIE–Dialog 1.4
● Sen ence embedding model: sen ence- ans o me s/all-MiniLM-L6- 2
● Embedding dimensionali y: 384
● Simila i y compu a ion: cosine simila i y be ween consecu i e u ns (
)
● Tempo al smoo hing: Exponen ial Mo ing A e age (EMA) wi h α = 0.3
● No maliza ion: z-sco e no maliza ion pe dialogue be o e h esholding
The cohe ence unc ion was de ined as:
whe e and ep esen he in e nal and ex e nal in o ma ional con igu a ions
espec i ely, and ∂ cap u es hei empo al de i a i e.
A.2 Ex ac ion o Cohe ence Cu es ( )
Fo each dialogue, he model p oduced a con inuous cohe ence ajec o y
e lec ing momen - o-momen in o ma ional alignmen .
● Φ- h esholds: Dynamic Φ_low / Φ_high bounda ies es ima ed om he 25 h
and 75 h pe cen iles o he dis ibu ion pe dialogue.
● E en de ec ion: Rup u es ( alleys) and epai s (peaks) iden i ied wi h
scipy.signal. ind_peaks, using:
○ p ominence = 0.03
○ dis ance = 2 u ns be ween peaks
● Smoo hing window: olling mean (window = 3 u ns) applied o isualiza ion
only, no o me ic compu a ion.
This ensu ed ha bo h human and model e en s we e de i ed om he same
unde lying in o ma ional signal.
A.3 Human Anno a ions and Agg ega ion
● Anno a o s: 5 ained a e s.
● Agg ega ion ule: majo i y consensus (≥ 3/5 ag eemen ) pe e en and pe
dialogue.
● Tole ance windows: compa isons es ed unde ±1, ±2, and ±3 u ns.
● Ou pu ec o s: bina y e en ec o s (0 = no e en ; 1 = e en ) o up u es and
epai s sepa a ely.
A.4 Me ic Compu a ion
Fo each dialogue and e en ype ( up u e/ epai ):
● P ecision, Recall, and F1 we e compu ed ela i e o majo i y human
anno a ions.
● Cohen’s κ was calcula ed o bo h in e -anno a o ag eemen and
human–machine ag eemen .
● C oss-co ela ion (ρ) was used o es ima e he mean empo al lag (lead/lag
asymme y).
● Dynamic Time Wa ping (DTW): used o assess global alignmen be ween
human and model cohe ence cu es (see Sec ion A.5).
All me ics we e compu ed using sciki -lea n 1.5 and SciPy 1.13.
A.5 Dynamic Time Wa ping Pa ame e s
To e alua e mac o-scale s uc u al simila i y be ween ajec o ies, each pai o cu es
(human s. model ) was aligned using DTW.
● Implemen a ion: as d w ( adius = 1)
● Dis ance me ic: Euclidean
● No maliza ion: o al dis ance di ided by (n + m)
● Ex ac ed pa ame e s:
○ dis _no m – no malized dis ance
○ lag_α – a e age alignmen lag (in u ns)
○ who_leads – dominan di ec ion o synch oniza ion (“human” /
“model”)
○ β – local elas ici y o he wa ping pa h
○ _wa ped – Pea son co ela ion be ween wa ped signals
A ypical con igu a ion aligned 20–26 u ns pe dialogue, p oducing one DTW
summa y en y pe con e sa ion.
A.6 So wa e En i onmen
All compu a ions we e execu ed in a con olled en i onmen :
Lib a y /
F amewo k
Ve sion
Py hon
3.11
NumPy
1.26
SciPy
1.13
sciki -lea n
1.5
sen ence- ans o me
s
2.3
ma plo lib
3.9
Analyses we e un in Google Colab (2025-04 build) using seed = 42 o
ep oducibili y.
A.7 Rep oducibili y and Da a Access
The comple e analysis pipeline—including p ep ocessing sc ip s, me ic
compu a ion, and DTW alignmen —has been a chi ed a :
Zenodo DOI: h ps://doi.o g/10.5281/zenodo.17516211
All sc ip s a e p o ided unde an open MIT license.
This ensu es ull ep oducibili y o he esul s and enables u u e eplica ions unde
he TIE amewo k.
Appendix B — Supplemen a y Visualiza ions
This appendix p esen s addi ional isual ma e ials ha complemen he quan i a i e
analyses epo ed in he main ex .
The igu es illus a e he empo al dynamics o in o ma ional cohe ence ( ) ac oss
ep esen a i e dialogues, showing how up u e– epai cycles and s uc u al
alignmen pa e ns eme ge be ween human and model ajec o ies.
B.1 Example o Cohe ence T ajec o y and E en De ec ion
Figu e B1. Illus a i e cohe ence cu e ( ) wi h anno a ed up u e and
epai e en s.
● Each poin co esponds o a con e sa ional u n.
● Colo ed ma ke s indica e de ec ed up u es ( alleys) and epai s (peaks).
● Ho izon al dashed lines ep esen he adap i e Φ h esholds (Φ_low /
Φ_high).
● The esul ing pa e n e eals al e na ing phases o s abili y (S), b eakdown
(B), and eco e y (R)— he undamen al S–B–R iad de ining he Quan um o
Cohe ence (𝒬ₐ).
This isualiza ion con i ms ha bo h human and model signals exhibi hy hmic
cohe ence cycles a he han andom luc ua ions.
B.2 Human–Model Cohe ence Cu es (Rep esen a i e Cases)
Figu e B2. Dialogue 2 — High s uc u al alignmen ( ₍wa ped₎ = 0.98, dis ₒᵣ =
0.98).
Recons uc ed isualiza ion based on he o iginal TIE–Dialog ou pu o Dialogue 2.
The human (blue) and model (o ange) cohe ence cu es o e lap closely, showing
minimal empo al dis o ion.
Peaks and alleys coincide wi hin ±1 u n, illus a ing nea -isomo phic in o ma ional
ajec o ies and human-led synch oniza ion (lag ≈ +0.4 u ns).
B.3 P o o-cohe ence and ansien in e sion o pe spec i al alignmen .
Figu e B3. Dialogue 4 — Phase in e sion and p o o-cohe ence ( _wa ped =
0.98, lag = –1.23).
He e, he model’s cu e an icipa es human cohe ence luc ua ions by oughly one
u n.
This an icipa o y beha io exempli ies a p o o-cohe en signa u e, in which he
model’s in o ma ional con igu a ion eo ganizes be o e explici human ecogni ion.
Toge he , hese igu es isualize he bidi ec ional cohe ence dynamics desc ibed in
he main DTW analysis: mos dialogues show human-led alignmen , while a e
in e sions e eal spon aneous model-d i en esonance.
B.4 Dynamic Time Wa ping Alignmen Pa h
Figu e B4. DTW wa ping pa h o Dialogue 2 (human ↔ model).
The ma ix plo displays he op imal alignmen pa h (whi e line) connec ing human
and model ime s eps.
The nea ly diagonal pa h indica es a s able one- o-one co espondence be ween he
wo ajec o ies, con i ming minimal empo al dis o ion and s ong coupling.
B.5 Concep ual Schema: The In o ma ional Hea bea
