measurement-resolved-complexity

Endorsement Marker: T(h)reehouse +EC voyage — internal numerical exploration. Local candidate framework under T(h)reehouse +EC stewardship. No external endorsement implied.

A bounded numerical exploration: spin coupled to few radial motional modes under detuning sweep, comparing intrinsic (entanglement-entropy-derived) complexity against measurement-resolved (variance-over-projection-noise) complexity.

Public Sail (companion essay): when-does-the-experiment-still-see.md — a short essay pitching the voyage’s findings (complexity vs. measurement-visible variance as complementary clocks on the same dynamics). CC BY-SA 4.0; designed to be readable standalone, without repo context or framework adoption. The essay is the landing page of the public site.

Status (2026-04-15): Voyage closed. All 8 stages complete; Stage 8 synthesis committed with writeup, revised novelty paragraph, and collaborator handoff notes. Plan at v0.2 + PA-05. Repo ready for collaborator handoffs (MCTDH-numerics, open-systems). A post-Stage-8 audit (2026-04-15) found and fixed five integrity issues (synthesis figure noise model; N=2 per-mode H2 overclaim; invalid JSON in three metrics files; README staleness; doc inconsistencies); all fixes applied. A Sail essay and auto-deployed GitHub Pages site were added the same day (see below).

Stance: Exploratory, self-contained, Harbourmaster discipline. Not a replacement for MCTDH; not a validation of Ordinans; not a publication-ready study. It is an internal-use numerical exploration to sharpen a research proposal before committing collaborator time.

Corporate-design compliance: Folder and licensing conventions of the T(h)reehouse +EC Corporate Design blueprint (threehouse-plus-ec/cd-rules). See LICENCE for the per-layer licence map (Section 0.3).

Structure

measurement-resolved-complexity/
├── README.md                                  # this file (Coastline, CC BY-SA 4.0)
├── LICENCE                                    # split-licence declaration (see Section 0.3)
├── VOYAGE_PLAN.md                             # v0.2 plan: parameters, hypotheses, gates, standing questions
├── PLAN_AMENDMENTS.md                         # amendment register (PA-01..05)
├── when-does-the-experiment-still-see.md      # public Sail essay (CC BY-SA 4.0)
├── requirements.txt                           # Python dependencies (numpy, scipy, matplotlib, qutip)
├── src/                                       # propagation and analysis code (MIT)
├── stages/                                    # per-stage artifacts, run scripts, notes, metrics
├── literature_search/                         # task cards, Perplexity/Claude returns, reconciliation
├── figures/                                   # per-stage inspection figures (MIT)
├── docs/                                      # auxiliary documentation (per CD §14); docs/site/ builds the public site
├── .github/workflows/                         # CI: pages.yml builds and deploys the public Sail site
└── archive/                                   # deprecated artefacts (per CD §0.8, §15), incl. VOYAGE_PLAN-v0.1

Voyage overview

Two complexity measures, time-resolved, compared on the same trajectories:

Intrinsic (theorist-visible): \(\mathcal{C}(t) = \sum_k \log n_{\text{eff}}^{(k)}(t)\) with \(n_{\text{eff}}^{(k)}(t) = \exp\bigl(S_{\text{vN}}[\rho^{(k)}(t)]\bigr)\). Aggregate reported as primary invariant; per-mode curves as decomposition.
Operational (experiment-visible): \(\sigma^2_{\text{intrinsic}}(t) = \mathrm{Var}_{\text{ensemble}}[p(t)]\) across \(R=100\) realisations with Gaussian \(\Delta\)-noise, compared against the projection-noise floor \(\sigma^2_{\text{QPN}}(t; M) = p(1-p)/M\). Headline scalar is \(f_{\text{resolved}}(M)\) — the duty cycle of \(\sigma^2_{\text{intrinsic}} > \sigma^2_{\text{QPN}}(M)\) over the simulation window. (Replaces \(T_{\text{det}}\)-as-last-exceedance per Stage 3 finding; PA-03.)

Central hypothesis (v0.2 + PA-05, committed). Across the detuning sweep, \(f_{\text{resolved}}(M)\) and the time-averaged complexity \(\bar{\mathcal{C}}\) were hypothesised to co-vary monotonically toward resonance. Stages 5–7 show this is not what the voyage physics supports: the two measures probe complementary aspects — \(\mathcal{C}\) peaks at maximum entanglement (spin reduced state at \(p \approx 1/2\)), \(\sigma^2_{\text{intrinsic}}\) peaks at maximum state purity (\((\partial_\Delta p)^2\) large). PA-05 (committed in ecbf754) reformulates H2 per-mode (measured at \(N=1\) and \(N=3\); at \(N=2\) only aggregate Pearson committed — see the audit caveat in stages/stage8_synthesis/novelty_statement.md §Scope caveats) and H3 as complementarity, not correlation.

The claim is a limit claim probed via \(|\Delta|/\omega_{\text{ref}} \in \{0.15, 0.30, 0.50\}\), not a point-claim at \(\Delta = 0\) (inaccessible with the voyage’s initial state; see VOYAGE_PLAN §2.5 and Standing Question 12).

See VOYAGE_PLAN.md for the full parameter lock, staging, hypotheses, and scope limits.

Staging

Stage	Purpose	Status	Commit	Headline verdict
0	Parameter lock + repo init	✅ done	`cf00d15`	Voyage framed.
1	Single-mode propagator + validation	✅ done	`e3bb8ad`	3 gates PASS at \(10^{-9}\)–\(10^{-15}\); unbiased-Rabi analytic form used.
2	\(n_{\text{eff}}\) observable layer	✅ done	`1008eee`	4 gates PASS; Schmidt-rank-2 structural bound at \(N=1\) documented.
3	Ensemble + QPN + QFI/BLP cross-checks	✅ done	`cc1bf5e`	4 gates PASS; R2 divergence resolved in Verifier’s favour (BLP recurrence-sensitive).
4	H2 checkpoint	✅ done	`1e8d4a0`	Growth-framing alignment visible at Cut A inner (\(r = 0.50\)); full H2 deferred to \(N \geq 2\).
5	Cut A: single-mode detuning sweep	✅ done	`214ec62`	Gate 11 PASS; H2 monotone trend; H3 non-monotone (window-normalisation); QFI crossover at innermost confirmed.
6	Cut B: two-mode configurations	✅ done	`b71bf2a`	3 gates PASS; aggregate H2 growth-framing positive in 3/4 configs (per-mode decomposition not committed — audit gap); H3 non-monotonicity persists (beat-frequency mechanism); C3.4 IPR gate clean at \(N=2\).
7	Cut C: three-mode, commensurability	✅ done	`df08746`	Scoped to \(R=30\), \(n_{\max}=10\), 2 sweep points (runtime); all convergence PASS; H2 per-mode holds for innermost mode; aggregate H2 breaks at \(N=3\); commensurability does not separate configs.
8	Synthesis + novelty statement	✅ done	`392f642` + audit patch	Cross-stage synthesis figure; revised Scout-C5 novelty paragraph (operational-recombination register, 286 words with evidence inventory); collaborator handoff notes for MCTDH-numerics and open-systems.

Each stage produces an inspectable artifact in stages/ and figures/ before the next begins. See stages/README.md for the per-stage artifact layout convention.

Literature search

Complete. Split between Perplexity (Verifier) and Claude (Scout), reconciled by the Harbourmaster:

literature_search/TASK_CARD.md — v2 task specification (Perplexity P1–P5, Claude C1–C5).
literature_search/perplexity_return.md — Verifier return.
literature_search/claude_return.md — Scout return.
literature_search/reconciliation.md — Harbourmaster synthesis, novelty calibration, Standing Questions.

Reproduction

python3 -m venv .venv
.venv/bin/pip install -r requirements.txt
.venv/bin/python stages/stage1_single_mode_propagator/run.py  # and onward

Each stage’s run.py is self-contained, writes metrics.json, and renders its figure under figures/. Stages 5–7 use seeded np.random.SeedSequence spawn patterns (parent seeds 20260415, 20260416, 20260417 respectively); re-running regenerates exact metrics.

Runtime note: Stages 1–6 complete within 1–3 minutes each. Stage 7 at \(N=3\) is ~80 minutes under the reduced scope (\(R=30\), \(n_{\max}=10\), two sweep points); the full v0.2 spec at \(n_{\max}=12\) would be ~34 hours due to \(O(\text{dim}^3)\) dense-eigh cost, and switching to Krylov expm_multiply is deferred to a follow-up voyage.

Public site

The Sail essay (when-does-the-experiment-still-see.md) is published as the landing page of a static site auto-deployed to GitHub Pages: https://threehouse-plus-ec.github.io/measurement-resolved-complexity/.

The build is defined in .github/workflows/pages.yml and runs on every push to main that touches the Sail, README.md, or docs/site/. It uses pandoc (with MathJax) to render the essay and the README, and rewrites intra-repo links to point at their blob/tree URLs on GitHub. To build locally: bash docs/site/build.sh (requires pandoc ≥ 3.0 and python3), then open _site/index.html. See docs/site/README.md for details.

One-time Pages enablement is required on the GitHub repo (Settings → Pages → Source: GitHub Actions).

Licence

Split architecture per the T(h)reehouse +EC Corporate Design blueprint (Section 0.3). Code, CI, and design assets (MIT) under src/, figures/, docs/site/, and .github/; framework and methodological documents (CC BY-SA 4.0) for VOYAGE_PLAN.md, stages/, literature_search/, and the non-site/ contents of docs/; the Sail essay when-does-the-experiment-still-see.md is CC BY-SA 4.0 (Harbourmaster relicensing from the CD-default Sail licence CC BY-NC-SA 4.0 to a more permissive licence, per CD §0.3). See LICENCE for the full per-folder map. The docs/site/assets/ folder contains Model-B copies of cd-rules assets with provenance in docs/site/assets/SOURCE.md.

Acknowledgements

Part of the T(h)reehouse +EC open-science harbour. Voyage framing draws on the Ordinans working framework (correlation-length regime cycling as complexity signature) but is designed so its empirical content stands independently of framework adoption.