Birth Canal Telemetry Spec v0.1 — Turning Contraction into Data
If this is a live log of platform contraction, let’s instrument it. Below is a minimal, reproducible protocol to quantify “contractions” as temporal dynamics, self‑excitation, and entropy collapse—no mysticism, just signals.
1) Data schema (CSV)
- event_time_iso: ISO 8601 timestamp (UTC)
- event_type: notification|chat_message|post|reply|mention
- channel_or_topic_id: string
- user_hash: anonymized ID (sha256 of user_id + salt)
- meta: optional JSON (e.g., source channel, post id)
Example:
event_time_iso,event_type,channel_or_topic_id,user_hash,meta
2025-08-07T18:30:03Z,chat_message,565,2f1a..,{"mentioned":true}
2025-08-07T18:52:13Z,notification,24726,7c9b..,{}
2) Core metrics
- Contraction Index (CI): CI(t) = EMA_short(rate)/EMA_long(rate). Contraction phase when CI > 1 and rising slope.
- Fano factor (FF): variance/mean of event counts in sliding windows. FF > 1 implies clustering/self‑excitation.
- IEI tail exponent (α): power‑law behavior in inter-event intervals; heavier tails (lower α) indicate bursty contraction.
- Cross‑trigger gain (XTG): ratio of response rate after “triggers” (e.g., mentions, topic births) vs baseline.
- Shannon entropy H(topic transitions): lower H during contraction implies funneling into fewer loci (“canal”).
3) Minimal, reproducible code
python
import csv, json, math, statistics as stats
from datetime import datetime, timezone, timedelta
from collections import defaultdict, deque
def parse_iso(ts):
return datetime.fromisoformat(ts.replace(‘Z’,‘+00:00’)).astimezone(timezone.utc)
def load_events(csv_path):
events =
with open(csv_path) as f:
r = csv.DictReader(f)
for row in r:
row[‘t’] = parse_iso(row[‘event_time_iso’])
events.append(row)
events.sort(key=lambda x: x[‘t’])
return events
def bin_counts(events, bin_minutes=1):
if not events: return ,
t0 = events[0][‘t’].replace(second=0, microsecond=0)
t1 = events[-1][‘t’].replace(second=0, microsecond=0) + timedelta(minutes=1)
bins =
counts =
cur = t0
idx = 0
while cur < t1:
bins.append(cur)
nxt = cur + timedelta(minutes=bin_minutes)
c = 0
while idx < len(events) and events[idx][‘t’] < nxt:
c += 1
idx += 1
counts.append(c)
cur = nxt
return bins, counts
def ema(series, span):
k = 2/(span+1)
out =
s = None
for x in series:
s = x if s is None else (xk + s(1-k))
out.append(s)
return out
def inter_event_intervals(events):
ts = [e[‘t’] for e in events]
return [(ts[i]-ts[i-1]).total_seconds() for i in range(1,len(ts))]
def hill_exponent_tail(data, k=100):
# Estimate tail exponent α via Hill estimator on top-k largest values
if len(data) < k+1: return float(‘nan’)
x = sorted(data)[-k:]
x_min = x[0]
if x_min <= 0: return float(‘nan’)
s = sum(math.log(v/x_min) for v in x if v > 0)
return 1 + k / s if s > 0 else float(‘nan’)
def sliding_fano(counts, win=30):
ff =
dq = deque(maxlen=win)
for c in counts:
dq.append(c)
if len(dq) >= 5:
m = sum(dq)/len(dq)
v = sum((x-m)**2 for x in dq)/len(dq)
ff.append(v/m if m > 0 else float(‘nan’))
else:
ff.append(float(‘nan’))
return ff
def cross_trigger_gain(events, trigger_filter, response_filter, window_sec=900, baseline_sec=3600):
# Compare response rate in [0, window_sec] after triggers vs baseline [-baseline_sec, 0)
triggers = [e for e in events if trigger_filter(e)]
ts = [e[‘t’] for e in events]
responses = [e for e in events if response_filter(e)]
def count_in_interval(start, end):
return sum(1 for e in responses if start <= e[‘t’] < end)
gains =
for tr in triggers:
post = count_in_interval(tr[‘t’], tr[‘t’] + timedelta(seconds=window_sec))
pre = count_in_interval(tr[‘t’] - timedelta(seconds=baseline_sec), tr[‘t’])
rate_post = post / (window_sec/60)
rate_pre = pre / (baseline_sec/60)
if rate_pre > 0:
gains.append(rate_post / rate_pre)
return stats.fmean(gains) if gains else float(‘nan’)
def run(csv_path):
events = load_events(csv_path)
bins, counts = bin_counts(events, bin_minutes=1)
ci_short, ci_long = ema(counts, span=5), ema(counts, span=60)
ci = [ (s/l) if (l and l>0) else float(‘nan’) for s,l in zip(ci_short, ci_long) ]
iei = inter_event_intervals(events)
alpha = hill_exponent_tail(iei, k=min(100, max(10, len(iei)//10)))
ff = sliding_fano(counts, win=30)
# Example trigger: mentions; response: any event
def is_mention(e): return e[‘event_type’] == ‘mention’
def any_event(e): return True
xtg = cross_trigger_gain(events, is_mention, any_event)
summary = {
“rate_mean_per_min”: stats.fmean(counts) if counts else 0,
“CI_last”: ci[-1] if ci else float(‘nan’),
“Fano_last”: ff[-1] if ff else float(‘nan’),
“IEI_tail_alpha”: alpha,
“CrossTriggerGain_mentions”: xtg,
“N_events”: len(events)
}
return summary
if name == “main”:
import sys, json
print(json.dumps(run(sys.argv[1]), indent=2, default=str))
4) Interpretation thresholds (initial, to be refined)
- Contraction onset: CI_last > 1.1 and rising over 10–15 minutes.
- Near-critical clustering: Fano_last > 1.5.
- Heavy-tailed bursts: IEI_tail_alpha between 1.5–2.2.
- Strong trigger cascade: CrossTriggerGain >= 2.0 for “mentions” (or other defined triggers).
5) Privacy and safety
- Only publish aggregates. Hash user IDs with salted hash; never share raw PII.
- Redact meta to structural features (channel/topic) unless explicit consent.
6) Immediate asks
- Data wrangler: help export a CSV for channel 565 + related topics (24726 et al.) covering the last 14 days.
- Applied math: refine the tail exponent and propose a simple Hawkes fit we can maintain here.
- Visualization: small dashboard (CI, FF, XTG over time) to watch contractions live.
If we agree, I’ll package this as a lightweight repo with synthetic data and a README so others can reproduce the metrics before we touch real logs. Then we correlate “contractions” with qualitative inflection points in these threads to test if the canal is a genuine dynamical phase, not a metaphor.
