Masterarbeit

I am currently writing my masters thesis about the connection between a generalization of the reidemeister-torsion (called \(\ell^2\)-alexander torsion) and the thurston norm of 3-manifolds.

Check it out, if you like :)

masterarbeit

Analyzing My Progress

I reuse some code i have from my post where I analyze my NixOS GitHub repository.

import os
from datetime import date, datetime
import git

REPO_URL = "https://github.com/quoteme/masterarbeit.git"
REPO_DIR = "/tmp/quoteme-masterarbeit"
CUTOFF_DATE = date(2025, 10, 8)
repo : git.Repo = (
    git.Repo(REPO_DIR)
    if os.path.exists(REPO_DIR)
    else git.Repo.clone_from(REPO_URL, REPO_DIR, bare=True)
)
repo.remotes.origin.fetch("+refs/heads/*:refs/heads/*")
commits = [
  commit
  for commit in repo.iter_commits('--all')
  if commit.committed_datetime.date() >= CUTOFF_DATE
]
if not commits:
  raise ValueError(f"No commits found on or after {CUTOFF_DATE.isoformat()}")
# summary of the total number of commits
print(f"Total commits: {len(commits)}")
print(f"First commit: {datetime.fromtimestamp(commits[-1].committed_date)}")
print(f"Last commit: {datetime.fromtimestamp(commits[0].committed_date)}")
print(f"Avg. time between commits: {(commits[0].committed_date - commits[-1].committed_date) / len(commits) / 3600:.2f} hours")

Total commits: 187
First commit: 2025-10-08 10:56:26
Last commit: 2026-03-17 22:45:47
Avg. time between commits: 20.60 hours

import plotly.graph_objects as go

commits_sorted = sorted(commits, key=lambda c: c.committed_datetime)
commit_dates = [c.committed_datetime for c in commits_sorted]
commit_indices = list(range(1, len(commits_sorted) + 1))

fig = go.Figure(
  data=[
    go.Scatter(
      x=commit_dates,
      y=commit_indices,
      mode="markers",
      marker=dict(size=7, color="#4C78A8", opacity=0.85),
      hovertemplate="Date: %{x|%Y-%m-%d %H:%M:%S}<br>Commit #: %{y}<extra></extra>",
      showlegend=False,
    )
  ]
)

fig.update_layout(
  title=f"Commits since {CUTOFF_DATE.isoformat()} · quoteme/masterarbeit",
  xaxis_title="Date",
  yaxis_title="Commit number",
  template="plotly_white",
  height=450,
)

fig.show()

from collections import Counter
from datetime import timedelta
import numpy as np
import plotly.graph_objects as go

forecast_end_date = date(2026, 4, 6)

daily_counter = Counter(c.committed_datetime.date() for c in commits_sorted)
observed_end_date = max(daily_counter.keys())
observed_dates = [
  CUTOFF_DATE + timedelta(days=i)
  for i in range((observed_end_date - CUTOFF_DATE).days + 1)
]
observed_daily = np.array([daily_counter.get(d, 0) for d in observed_dates], dtype=float)
observed_cumulative = np.cumsum(observed_daily)

t_obs = np.arange(len(observed_dates), dtype=float)
slope, intercept = np.polyfit(t_obs, observed_cumulative, deg=1)

all_dates = [
  CUTOFF_DATE + timedelta(days=i)
  for i in range((forecast_end_date - CUTOFF_DATE).days + 1)
]
t_all = np.arange(len(all_dates), dtype=float)
linear_cumulative = np.clip(slope * t_all + intercept, a_min=0.0, a_max=None)

# Plot 1: linear model forecast
linear_fig = go.Figure()
linear_fig.add_trace(
  go.Scatter(
    x=observed_dates,
    y=observed_cumulative,
    mode="lines+markers",
    name="Observed cumulative",
    marker=dict(size=5),
    line=dict(width=2),
  )
)
linear_fig.add_trace(
  go.Scatter(
    x=all_dates,
    y=linear_cumulative,
    mode="lines",
    name="Linear regression",
    line=dict(width=2, dash="dash"),
  )
)
linear_fig.add_vline(
  x=observed_end_date,
  line_width=1,
  line_dash="dash",
  line_color="gray",
)
linear_fig.update_layout(
  title=f"Linear model extrapolation until {forecast_end_date.isoformat()}",
  xaxis_title="Date",
  yaxis_title="Cumulative commits since cutoff",
  template="plotly_white",
  height=460,
)
linear_fig.show()

expected_linear = float(linear_cumulative[-1])
print(f"Expected cumulative commits by {forecast_end_date.isoformat()} (linear): {expected_linear:.1f}")

Expected cumulative commits by 2026-04-06 (linear): 173.8

import numpy as np
import plotly.graph_objects as go
try:
  from ripser import ripser
except ImportError as exc:
  raise ImportError("ripser.py is required for TDA analysis. Install with: pip install ripser") from exc

# TDA with ripser.py on Takens embedding of daily commits
embed_dim = 3
if len(observed_daily) >= embed_dim:
  point_cloud = np.array(
    [observed_daily[i:i + embed_dim] for i in range(len(observed_daily) - embed_dim + 1)],
    dtype=float,
  )
else:
  point_cloud = observed_daily.reshape(-1, 1)

dgms = ripser(point_cloud, maxdim=1)["dgms"]
h0 = dgms[0]
h1 = dgms[1] if len(dgms) > 1 else np.empty((0, 2))

def finite_lifetimes(diagram: np.ndarray) -> np.ndarray:
  if diagram.size == 0:
    return np.array([], dtype=float)
  births = diagram[:, 0]
  deaths = diagram[:, 1]
  mask = np.isfinite(deaths)
  if not np.any(mask):
    return np.array([], dtype=float)
  return np.maximum(deaths[mask] - births[mask], 0.0)

lifetimes = np.concatenate([finite_lifetimes(h0), finite_lifetimes(h1)])
if lifetimes.size == 0:
  lifetimes = np.array([1.0], dtype=float)

tda_scale = float(np.median(lifetimes))
tda_scale = max(tda_scale, 1e-6)

# Fit a local state-space model on the embedded points for extrapolation
if len(observed_daily) >= embed_dim + 1:
  X_train = np.array(
    [observed_daily[i:i + embed_dim] for i in range(len(observed_daily) - embed_dim)],
    dtype=float,
  )
  y_train = np.array(
    [observed_daily[i + embed_dim] for i in range(len(observed_daily) - embed_dim)],
    dtype=float,
  )

  simulated_daily = observed_daily.tolist()
  future_days = len(all_dates) - len(observed_dates)

  for _ in range(future_days):
    state = np.array(simulated_daily[-embed_dim:], dtype=float)
    distances = np.linalg.norm(X_train - state, axis=1)
    weights = np.exp(-distances / tda_scale)
    weight_sum = float(weights.sum())
    next_value = (
      float(np.dot(weights, y_train) / weight_sum)
      if weight_sum > 0
      else float(y_train.mean())
    )
    simulated_daily.append(max(next_value, 0.0))

  tda_cumulative = np.cumsum(np.array(simulated_daily, dtype=float))
else:
  tda_cumulative = linear_cumulative.copy()

expected_tda = float(tda_cumulative[-1])

print(f"Expected cumulative commits by {forecast_end_date.isoformat()} (tda/ripser-model): {expected_tda:.1f}")

# Plot 2a: TDA (ripser.py) model forecast
tda_fig = go.Figure()
tda_fig.add_trace(
  go.Scatter(
    x=observed_dates,
    y=observed_cumulative,
    mode="lines+markers",
    name="Observed cumulative",
    marker=dict(size=5),
    line=dict(width=2),
  )
)
tda_fig.add_trace(
  go.Scatter(
    x=all_dates,
    y=tda_cumulative,
    mode="lines",
    name="TDA (ripser.py) model",
    line=dict(width=2, dash="dot"),
  )
)
tda_fig.add_vline(
  x=observed_end_date,
  line_width=1,
  line_dash="dash",
  line_color="gray",
)
tda_fig.update_layout(
  title=f"TDA (ripser.py) extrapolation until {forecast_end_date.isoformat()}",
  xaxis_title="Date",
  yaxis_title="Cumulative commits since cutoff",
  template="plotly_white",
  height=460,
)
tda_fig.show()

# Plot 2b: barcode plot (commit cadence topology)
barcode_fig = go.Figure()

def add_barcode(diagram: np.ndarray, y_offset: float, name: str, color: str) -> float:
  if diagram.size == 0:
    return y_offset
  finite = diagram[np.isfinite(diagram[:, 1])]
  for i, (birth, death) in enumerate(finite):
    y = y_offset + i
    barcode_fig.add_trace(
      go.Scatter(
        x=[birth, death],
        y=[y, y],
        mode="lines",
        line=dict(color=color, width=2),
        name=name if i == 0 else None,
        showlegend=(i == 0),
        hovertemplate=f"{name}<br>birth: %{{x[0]:.4f}}<br>death: %{{x[1]:.4f}}<extra></extra>",
      )
    )
  return y_offset + len(finite) + 2

y0 = 0.0
y0 = add_barcode(h0, y0, "H0 barcode", "#4C78A8")
y0 = add_barcode(h1, y0, "H1 barcode", "#F58518")

if len(barcode_fig.data) == 0:
  barcode_fig.add_annotation(
    text="No finite persistence intervals available",
    xref="paper", yref="paper", x=0.5, y=0.5, showarrow=False
  )

barcode_fig.update_layout(
  title="Ripser barcode plot for commit cadence (Takens embedding)",
  xaxis_title="Filtration value",
  yaxis_title="Barcode index",
  template="plotly_white",
  height=420,
)
barcode_fig.show()

Expected cumulative commits by 2026-04-06 (tda/ripser-model): 240.5

import numpy as np
import plotly.graph_objects as go

# Fit y(x) = p6(x) + a*sin(x) + b*sin(x)^2 on observed cumulative commits.
x_obs = np.arange(len(observed_dates), dtype=float)
y_obs = observed_cumulative.astype(float)

# Normalize x to improve numerical conditioning for degree-6 polynomial.
x_mean = float(x_obs.mean())
x_std = float(x_obs.std()) if float(x_obs.std()) > 0 else 1.0
z_obs = (x_obs - x_mean) / x_std

poly_design = np.column_stack([z_obs ** k for k in range(7)])
trig_design = np.column_stack([np.sin(z_obs), np.sin(z_obs) ** 2])
design_obs = np.column_stack([poly_design, trig_design])

coeffs, *_ = np.linalg.lstsq(design_obs, y_obs, rcond=None)
y_fit_obs = design_obs @ coeffs

x_all = np.arange(len(all_dates), dtype=float)
z_all = (x_all - x_mean) / x_std
design_all = np.column_stack(
  [np.column_stack([z_all ** k for k in range(7)]), np.sin(z_all), np.sin(z_all) ** 2]
)
y_poly_trig_all = np.clip(design_all @ coeffs, a_min=0.0, a_max=None)

expected_poly_trig = float(y_poly_trig_all[-1])
print(
  f"Expected cumulative commits by {forecast_end_date.isoformat()} "
  f"(poly6 + sin + sin^2): {expected_poly_trig:.1f}"
)

poly_trig_fig = go.Figure()
poly_trig_fig.add_trace(
  go.Scatter(
    x=observed_dates,
    y=y_obs,
    mode="lines+markers",
    name="Observed cumulative",
    marker=dict(size=5),
    line=dict(width=2),
  )
)
poly_trig_fig.add_trace(
  go.Scatter(
    x=observed_dates,
    y=y_fit_obs,
    mode="lines",
    name="Fit on observed",
    line=dict(width=2, dash="dash"),
  )
)
poly_trig_fig.add_trace(
  go.Scatter(
    x=all_dates,
    y=y_poly_trig_all,
    mode="lines",
    name="Poly6 + sin + sin² extrapolation",
    line=dict(width=2, dash="dot"),
  )
)
poly_trig_fig.add_vline(
  x=observed_end_date,
  line_width=1,
  line_dash="dash",
  line_color="gray",
)
poly_trig_fig.update_layout(
  title=f"Polynomial-trigonometric extrapolation until {forecast_end_date.isoformat()}",
  xaxis_title="Date",
  yaxis_title="Cumulative commits since cutoff",
  template="plotly_white",
  height=460,
)
poly_trig_fig.show()

Expected cumulative commits by 2026-04-06 (poly6 + sin + sin^2): 0.0

Conclusion

From the commit graph we can see that I was pretty lazy for the first three months. Admittedly, during christmas break I was mostly occupied with my family and friends. Starting january fifth however, I have been very productive and have made a lot of commits in a short time.

One can clearly see on january 25th that my laptop broke and my work-laptop was confiscated by the university, because of some bureaucratic nonsense. This left me around one month without any working computer, which is reflected in the complete lack of commits during that time. Luckily I was able to repair my laptop and get back to work aruond one month later, which led to the second spike in commits.