vestigium

When does a quantum possibility become a fact?

vestigium — Latin for trace, record, footprint. All three are the same object here: the partial trace is the operation at the heart of nearly every script below; the record is what turns a superposition into an outcome; and the footprint left in the environment is why observers agree on what happened.

This is a laboratory for the measurement problem, built in small verified steps. Nothing in it is new physics — every result reproduces something already known, some of it for a century. That is the point: each experiment is checked against exact analytics or a real published measurement, so when the machinery is later pointed at an open question, the machinery itself is not in doubt. Two of our own bugs were caught by exactly these checks (both documented below).

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Foundations experiments

Each is a standalone script with its verification printed at the top of the run.

Experiment	What it shows	Verified against
weak_measurement.py	collapse as a gradual process under continuous monitoring	Born rule emerged: 30.6% of runs committed to the 30% branch (predicted 0.300 ± 0.024); conditional variance rides the exact Riccati curve to steady state 1/√(8k) within 0.2–1.0%
decoherence_frames.py	the which-path record accumulating collision by collision; quantum Darwinism; revival	V = cosᵏ(θ/2) to 2×10⁻¹⁶; V²+D² = 1 to 4×10⁻¹⁶; 4 of 12 environment qubits already hold 95% of the record; a recycled 2-qubit environment returns V to 1.0000 at collision 16 exactly as predicted
zeno.py	a watched quantum system freezes; telegraph dynamics at strong monitoring	survival matches [cos²(π/2N)]ᴺ to 0.0055 across N = 1…64 (Itano et al. 1990, trapped ions); flip rate fits k^−0.96 vs. the Zeno prediction k^−1
bohmian_fan.py	pilot-wave trajectories from the guidance equation (the Philippidis fan)	equivariance: 20,000 guided paths rebuild the Born fringes to 4.3% of peak with no Born rule imposed; 0 of 20,000 trajectories crossed the symmetry axis
csl_toy.py	objective collapse (CSL-type): superpositions die with size, no observer required	V(N) rides exp(−κ₀N²d²T); real-units panel reproduces the actual exclusion logic — Adler's rate puts the edge at ~10⁵ amu (right at Fein-class experiments), GRW's at ~10⁹ amu
teleport.py	entanglement + 2 classical bits moves an unknown state; neither ingredient works alone	fidelity 1.000000000000 over 2000 Haar-random states; with the bits withheld Bob's state is exactly I/2 (4×10⁻¹⁶) — no-signaling, constructively; entanglement-free ceiling 0.6706 vs. theory 2/3
wigner_friend.py	whether "a measurement happened" is relative to the observer	sealed lab: interference ⟨X_S X_F⟩ = 1 and reversal fidelity = 1, while the friend's own state is a definite I/2; once the record leaks both fall to 0 and ½. ⟨X_S X_F⟩ = cos(φ/2) to 2×10⁻¹⁶
bell_game.html	CHSH and GHZ as games you can lose	40,000 rounds: classical 74.56% against its 75% ceiling, quantum 85.30% vs. cos²22.5° = 85.36%; GHZ 100.00%, zero losses in 40,000 rounds where every classical plan caps at 75%

Hidden dimensions — the projections program

The idea "maybe fields are stacked in dimensions we don't see and we watch the shadow", made precise and run through three independent engines. Full write-up in PLAN_projections.md.

kk_projection.py	mass = motion in a hidden dimension (Kaluza–Klein)	rest-buzz frequencies 1.0022 / 2.0031 / 3.0027 against the exact tower 1 / 2 / 3; group velocities within 0.66% of Klein–Gordon
kk6_twisted_tower.py	two hidden loops with a twist — the axion as a measurable spectral splitting	blind protocol (formula scored only after measurement): all 10 winding sectors within 0.3%; the (1,1)/(1,−1) pair splits by 0.44867 vs. 0.44996 predicted, while (1,0)/(0,1) stay degenerate to 6.7×10⁻¹⁶
fractal_boundary.py	does a structured detector wall change where particles land?	yes for how many — periodic vs. Cantor masks at identical 29.6% coverage differ by ~67% in detection efficiency — but the fringes never move: the wall gates, it does not shift

The neural leg (can a network discover the hidden dimension from projections alone?) and the symbolic leg (is the Kaluza reduction a theorem?) live in the sister repos below. All three agreed.

Cross-validation probes

Independent numerics for the trivium cross-validation project — deliberately implemented without sharing code, so agreement means something.

• entropic_hinge.py + hinge_mp.py — the Longo relative-entropy identity underpinning the 2026 entropic-gravity result (Dorau & Much, PRL): relative entropy of a coherent excitation on a wedge = 2π × its boost energy. Verified to 0.02–0.21% on a harmonic chain at two lattice resolutions. Two findings worth more than the check: this computation is impossible in double precision (the modular weights live in e⁻¹⁰⁰-scale covariance tails — every float64 sweep carried 10–14% clip bands), and the Gaussian modular matrix has an operator-ordering trap that a thermal self-test passes silently — only a squeezed state distinguishes them. Both now permanent regression tests.

• entropic_time.py — does the "entropic time" of Barontini, PRR 2026 depend on which coarse-graining you choose? Five legitimate clocks from one exact two-mode Bose–Hubbard run. Same-family control agrees at |τ| = 0.984; the cross-family test disagrees at 0.181 inside the paper's own domain of validity, and coarsening the event set does not rescue it. But the regime scan is the real answer: agreement switches on near Λ ≈ 2–4. Reported as conditional support with a mapped boundary, not a refutation — real split-BEC junctions are interaction-dominated, so the construction is likely robust where it was run; the critique is the missing qualifier.

• log_coefficient_boundary.py — is the entanglement log coefficient non-universal permanently, or only in a regime? Prediction recorded before the run, then confirmed: exact free-fermion Ising chain gives a scaling collapse in ξ/L alone (matched ξ/L agrees to ≤0.058 across L = 64→512), converging on the universal c/6 to 0.6% at criticality, with universality switching on at ξ/L ≈ 2.5. The ordered branch is excluded on physics, not convenience — its ground state is exponentially degenerate, and the run self-flagged it (a ratio of 15.0 with the smallest mode energy at exactly 0.0).

• kappa_vs_mutual_info.py — if a quantity is regulator-contaminated in every regime, the move is not to hunt for a clean regime but to change channel. On one 2D lattice with four regulators sharing a continuum limit, the area-law coefficient κ spreads by 41.6% — and the same lattice refinement that drives the mutual information's spread from 2.18% down to 0.096% (as s^−2.26, converging) leaves κ's spread at 41.8% → 41.7%, unmoved. So κ's regulator dependence is a fixed property of the cut, while I(A:B)'s residual is a vanishing lattice artifact. Includes a two-probe numerical floor audit (1.25×10⁻⁶%, so the sub-percent residual is real, not noise) and one discarded leg left in the file — an IR-matching attempt built on an effective-mass estimator that is biased in 2D, which made the spread worse and was replaced.

The transferable lesson, now a standing entry in the family ledger: when probing whether a definition is robust, scan the physical regime — the interesting answer is usually a boundary, not a yes/no.

Interactive apps

Self-contained HTML, no build step, no server needed — open the file.

• double_slit_app.html — the full bench: coherence dial, which-path markers, the eraser, Born-sampled dots landing one at a time, live V / D / entanglement-entropy meters and duality curve, plus a two-photon delayed-choice mode (sort by the partner photon to pull fringes or anti-fringes out of flat noise).
• wave_double_slit.html — a live 2-D time-dependent Schrödinger solver: watch the packet spread, hit the absorbing wall, slip through the slits and build fringes.
• bell_game.html — design any classical strategy you like and watch it hit the 75% wall, then watch entanglement walk through it (85.4% for CHSH, a perfect 100% for GHZ).

Neural quantum states

sims/ — the machine-learning leg, kept separate on purpose.

• nqs_tfim.py — a neural network as a wavefunction (variational Monte Carlo) finds the transverse-field Ising ground state to ~0.4% of exact at criticality
• nqs_phase_transition.py — sweeping the field reproduces the quantum phase transition
• nqs_scaling.py — runs to N = 40 spins (Hilbert space ~1.1×10¹²), where exact diagonalization dies around N ≈ 20
• nqs_cnn.py — baking translation symmetry into the ansatz buys ~100× in accuracy. And a lesson: the plain ansatz got the energy right everywhere but the entanglement wrong in the ordered phase (it spontaneously broke the Z₂ symmetry) — entanglement is the stricter probe. Fixed in stage3_symmetric.py.

Running it

python3 -m venv .venv && source .venv/bin/activate
pip install numpy scipy matplotlib mpmath torch      # torch only for sims/
python qsim/weak_measurement.py

Each script prints its own verification and writes its figure beside itself. The high-precision leg (hinge_mp.py) needs mpmath and takes ~2 minutes.

What this is not

• Not new physics. Everything here reproduces known results. The value is a verified instrument and a legible account of why each result is what it is.
• Not a proof of anything speculative. The hidden-dimension work shows what the idea would explain (mass, charge) and what it would cost (unseen particle towers). There is no experimental evidence our universe is built that way, and the repo says so wherever it comes up.
• Honest about limits. Where a result rests on a convention, a lattice artifact, a finite-size effect, or an arbitrary tolerance, that is stated next to the number rather than in a footnote. Where a check was impossible at the precision first attempted, the failed attempt is left in the file.

Family

Four sibling projects, cross-validated against each other:

• ansatz-machine — propose → verify → evolve, hunting exact solutions of Einstein's field equations. Proved the Kaluza reduction used here, dilaton price tag and all.
• tabula-geometrica — can a neural network invent spacetime geometry from raw observation? It discovered mass as the hidden dimension's latent, and independently replicated this repo's Kaluza–Klein numbers.
• DeepStrain — deep-learning searches of real LIGO/Virgo data for black-hole signatures.
• trivium — the bridge: cross-validating the independent projects against one another, which is where several of the probes above came from.

License

MIT — see LICENSE.