[infra] Revise README narrative

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

Author: JonathanMace

README.md

@@ -1,34 +1,34 @@
 # Browntone
 
-There is a persistent piece of acoustic folklore — sometimes called the *brown note* — which holds that a sufficiently powerful infrasonic tone can induce involuntary loss of bowel control. The idea surfaces reliably in urban legend compilations, military apocrypha, and at least one memorable episode of *South Park* (Parker and Stone, "The Brown Noise," S3E17, 1999). It has never been demonstrated experimentally. Nobody, to our knowledge, has previously bothered to work out *why* it does not work.
+The *brown note* is one of the more durable pieces of acoustic folklore: an infrasonic tone supposedly capable of inducing involuntary loss of bowel control. The story turns up in urban legends, military apocrypha, and popular culture, including *South Park* (“World Wide Recorder Concert”, also known as “The Brown Noise”, S3E17, 2000). It has never been demonstrated experimentally.
 
-This repository contains the analytical framework, code, and manuscript drafts for a research programme that began by taking the question seriously and ended up somewhere rather more interesting.
+We took the claim seriously enough to ask the more interesting question. If the abdomen really does possess a low-frequency resonance, can airborne sound excite it strongly enough to matter? This repository contains the analytical framework, code, and manuscript drafts for the research programme that grew from that problem: first a debunking, then a broader theory of resonance, geometry, and inverse identifiability in fluid-filled soft shells.
 
 ## The Question
 
-The human abdomen does possess a real flexural resonance near 4 Hz — firmly in the infrasonic range. Whole-body vibration at these frequencies is known to produce gastrointestinal discomfort; military and occupational health literatures have documented this for decades. The brown note conjecture simply asks: can *airborne* sound at the same frequency exploit the same resonance?
+The human abdomen does possess a genuine flexural resonance near 4 Hz, well inside the infrasonic range. Whole-body vibration in this band has long been associated with gastrointestinal discomfort. The folklore question is therefore not absurd in outline; it is simply wrong in mechanism. Can *airborne* sound exploit the same mode?
 
-The answer, it turns out, is no, and the reason is instructive. At the n = 2 flexural mode, the acoustic wavelength exceeds the body by two orders of magnitude (ka ≈ 0.01), the air–tissue impedance mismatch is enormous, and the incident pressure field barely couples to the mode shape at all. Mechanical excitation through the body wall suffers none of these penalties. The coupling asymmetry exceeds 10⁴. The resonance is genuine; the airborne path to it is negligible.
+Paper 1 shows that it cannot. At the canonical *n* = 2 flexural mode, the acoustic wavelength is vastly larger than the body (*ka* ≈ 0.011), the air–tissue impedance mismatch is severe, and the modal coupling is correspondingly feeble. Mechanical excitation through the seat, floor, or body wall is orders of magnitude more effective. The resonance is real; the loudspeaker pathway to it is negligible.
 
 That much is [Paper 1](papers/paper1-brown-note/).
 
 ## Where It Leads
 
-A model that can explain why something *doesn't* happen is only modestly interesting. What made the project worth continuing was the realisation that the same oblate-spheroidal shell framework — built to model the abdomen — raises a question that is considerably harder than the one we started with.
+What began as a debunking exercise quickly became a more general inverse-problem question: when a resonance spectrum moves, when does it actually identify the parameter that moved? The same oblate-spheroidal shell framework that answers the folklore question also exposes that harder problem.
 
-People tap watermelons in the supermarket and listen for a deep thump. This is real folk acoustics, practised worldwide, and it works about as well as you would expect an untrained ear and an uncontrolled impact to work. [Paper 7](papers/paper7-watermelon/) formalises the practice: a fluid-filled spheroidal shell model maps tap-tone frequency to effective rind stiffness. The forward model is straightforward. The inverse question — *can you actually recover the stiffness from the spectrum?* — is not, and its answer depends on the geometry in a way that is not obvious.
+That is where [Paper 7](papers/paper7-watermelon/) enters. People tap watermelons and listen for a deep thump; the practice is old, widespread, and only intermittently reliable. Paper 7 turns that bit of market folklore into a clean modelling problem: a fluid-filled spheroidal shell whose tap-tone frequency tracks effective rind stiffness. The forward model is useful. The inverse question — can stiffness be recovered from the spectrum, rather than merely correlated with it? — is the real prize.
 
-That question is the subject of [Papers 8–10](papers/paper8-kac/). When does a resonance spectrum identify the parameters that produced it? When does it fail? The answer, briefly: an equivalent-sphere model can predict frequencies to within 10% and yet be catastrophically ill-conditioned for parameter recovery. Oblate asphericity is precisely what restores identifiability — and prolate asphericity does not. The mechanism is geometry-selective, and the gap between the two cases spans ten orders of magnitude in conditioning.
+[Papers 8–10](papers/paper8-kac/) take up that question directly. They show that an equivalent-sphere reduction can reproduce the lowest flexural frequencies to within about 10% and still be a poor inverse model. Oblate geometry restores the missing information; prolate geometry does not do so in the same way; and the exact sphere is a singular point of the inverse problem. The forward problem and the inverse problem are not the same problem, however similar their spectra may look.
 
 ### [Paper 10](papers/paper10-capstone/) — the capstone
 
-Paper 10, targeting *Proceedings of the Royal Society A*, consolidates the formal results: a rank-collapse theorem for the spherical case, a lifting proposition for the oblate case, near-spherical asymptotics via Kato perturbation theory, and a forward-vs-inverse adequacy result showing that predictive accuracy does not imply invertibility. It includes a sensitivity study across stiffness, aspect ratio, mode count, and basis size, demonstrating that the identifiability lifting is robust rather than parameter-specific. The discussion argues that the same forward ≠ inverse gap arises wherever resonance data are used for parameter recovery — in structural health monitoring, elastography, geophysics, and agricultural acoustics alike.
+Paper 10 gives the programme its theoretical centre of gravity. Targeting *Proceedings of the Royal Society A*, it makes the central point explicit: a forward model may be accurate enough for prediction and still be unusable for parameter recovery. The paper consolidates the rank-collapse result for the spherical reduction, the oblate lifting result, the corrected near-spherical asymptotics from Kato perturbation theory, and the formal separation between forward adequacy and inverse adequacy. It also shows that the lifting survives parameter sweeps and measured-mode variations rather than depending on one convenient canonical point. The broader claim is sober but important: whenever resonance data are used to infer hidden parameters, geometry decides which inferences are defensible.
 
 **Latest draft:** [papers/paper10-capstone/drafts/draft_2026-04-04_1712.pdf](papers/paper10-capstone/drafts/draft_2026-04-04_1712.pdf)
 
-## The Supporting Cast
+## Supporting Papers
 
-Papers 2–6 explore the same shell framework across complementary organs and forcing conditions. They are supporting analyses rather than standalone contributions, but each tests a distinct aspect of the model.
+Papers 2–6 stress-test the same shell framework across neighbouring organs and forcing pathways. They are not side quests; each isolates a mechanism that matters somewhere in the programme.
 
 | Paper | What it examines |
 |-------|-----------------|
@@ -38,11 +38,11 @@ Papers 2–6 explore the same shell framework across complementary organs and fo
 | [P5](papers/paper5-borborygmi/) | Borborygmi — constrained-bubble acoustics reproduce clinical gut-sound frequencies |
 | [P6](papers/paper6-sub-bass/) | Sub-bass coupling — at concert levels, the floor matters more than the air |
 
-[Paper 8](papers/paper8-kac/) and [Paper 9](papers/paper9-lifting-theorem/) develop the identifiability theory that Paper 10 consolidates: rank deficiency of equivalent-radius models, the oblate lifting mechanism, and the oblate–prolate asymmetry.
+[Paper 8](papers/paper8-kac/) and [Paper 9](papers/paper9-lifting-theorem/) supply the theory that Paper 10 consolidates: rank deficiency in equivalent-radius models, identifiability lifting in oblate shells, and the oblate–prolate asymmetry.
 
 ## Scope and Limitations
 
-This is an analytical programme. All results derive from shell-theoretic models; an experimental phantom-validation protocol has been designed but not yet executed (see [docs/](docs/)). Paper 7 recovers rind stiffness, not eating ripeness — the link to consumer-relevant quality requires cultivar-specific calibration not yet performed. Papers 1–9 are submission-ready drafts; Paper 10 is under final review.
+This is an analytical programme. The results come from shell-theoretic models, not from completed benchtop validation, although an experimental phantom protocol has been designed (see [docs/](docs/)). Paper 7 recovers rind stiffness, not eating quality; that consumer-facing step still requires cultivar-specific calibration. Papers 1–9 are submission-ready drafts. Paper 10 is the capstone currently under final review.
 
 ## Getting Started
 
@@ -51,18 +51,7 @@ pip install -e .[dev]
 python -m pytest tests/ -v          # 487 regression tests
 ```
 
-```python
-from src.analytical.natural_frequency_v2 import AbdominalModelV2, flexural_mode_frequencies_v2
-from src.analytical.energy_budget import self_consistent_displacement
-
-model = AbdominalModelV2(
-    E=0.1e6, a=0.18, c=0.12, h=0.01, nu=0.45,
-    rho_wall=1100, rho_fluid=1020, K_fluid=2.2e9,
-    P_iap=1000, loss_tangent=0.25,
-)
-freqs = flexural_mode_frequencies_v2(model, n_max=5)
-disp = self_consistent_displacement(model, mode_n=2, spl_db=120)
-```
+If you want the scientific story, start with the papers. If you want the working implementation behind them, start with `src/analytical/natural_frequency_v2.py` for the canonical abdominal model, `src/analytical/energy_budget.py` for the airborne-coupling analysis, and `src/analytical/kac_identifiability.py` for the inverse-problem machinery.
 
 ## Citation
 
@@ -96,4 +85,3 @@ This work was produced with AI assistance; see [docs/ai-assisted-research.md](do
 ## Licence
 
 [MIT](LICENSE)
-