Passive transport measurement protocol

Scope: a supporting measurement/error contract for two declared pure-EPI transport models. Physical admission is not_admitted; an admitted physical prediction has not been tested. The execution plan owns P1-P5 and any reopening. No data search, acquisition or refit is active.

The mathematical candidates below remain useful with their own hypotheses. Their observation maps are proposed realizations, not identification of primitive EPI with every sensor reading or proof of material emergence. The user has a computer and no laboratory apparatus; apparatus descriptions are requirements for a matching public terrestrial source, not purchase tasks.

The archived source reviews and Volts experiment preserve inspected-source metadata, rejected routes, source hashes and the unfavorable affine-control comparison. The separate TCLab record retains its own model and evaluated data. These observations cannot become unseen again.

Historical source and experiment routes

These earlier anchors refer to the archived review and experiment, not additional current tasks.

Derived fixed-reference candidate

On the same fixed symmetric positive P2 support, select pure EPI pressure and capacities (nu,0), with nu>0. All other pressure channels are inactive; otherwise the capacity difference itself could contribute another channel. The canonical nodal equation gives

p = (r-x, x-r),           x' = nu*(r-x),           r' = 0
d = x-r,                 d' = -nu*d
x(t) = exp(-nu*t)*x(0) + (1-exp(-nu*t))*r.

This follows from the nodal law without importing the circuit or cooling equation. The arithmetic mean is NOT conserved; the reference r is. An inactive node may retain nonzero pressure: stationarity is not structural equilibrium. The existing diffusion energy owner accepts degenerate mobility; positive-capacity certificates using d_i/nu_i do not cover this boundary.

Physical use requires an independently specified constant reference and support, adequate state observation and bounded external loading. Flat bath measurements do not prove that a bath is a zero-capacity TNFR node; an active controller may instead be an external input. A varying reference requires a distinct driven model and its complete input history, not a fitted final asymptote. No held-out value may estimate r or the clock conversion.

For this candidate, existing log/exp enclosures can be reused with contrast x-r and decay factor exp(-nu*t). The capacity ratio divides by elapsed time, not twice elapsed time. There is no constant-mean rejection rule. Do not fabricate a second observed channel or reuse the equal-capacity adapter unchanged. The mathematical implementation now lives in p2_transport_reference.py: bound_fixed_reference_capacity and bound_fixed_reference_transport reuse the same contrast/log, decay/exp and convex interval kernels as the equal- capacity model. The reference may be a declared interval and the initial contrast may have either strict sign. The returned outer intervals do not prove one common latent fit. These functions do not mutate a live graph or admit empirical observations. Physical admission still requires the source contract; this remains one candidate within P2.3, not another queue.

Reference apparatus and canonical equal-capacity prediction

The reference design uses two nominally equivalent capacitive elements, observed simultaneously, prepared separately and then interconnected through one fixed passive link. Charging sources are disconnected before the declared observation interval. Record wiring, switch timing, sensor input loading, component characterization and ambient conditions. Equivalence and negligible external forcing over the finite interval require measured bounds; component labels alone do not establish them. The initial experiment changes only the prepared contrast, keeping the link and apparatus fixed.

The hardware is a candidate realization, not an imported circuit law. The proposed TNFR model is the isolated EPI channel on fixed P2 support, with one common positive capacity and no active phase or capacity-feedback channel. Each physical voltage is mapped to a signed EPI coordinate x_i by a fixed sensor scale and offset. Both channels must share the same structural unit after independently calibrated sensor correction. Define structural time by t = b * (tau - tau_0), where tau is the independently checked acquisition clock and b > 0 is fixed before capacity estimation. A declared unit convention for b is permitted if labeled as a convention; it is not evidence of a universal physical-to-structural conversion.

The canonical diffusion owner then gives, without using a circuit governing law as an axiom,

p_1 = x_2 - x_1,                 p_2 = x_1 - x_2
dx_1/dt = nu * p_1,              dx_2/dt = nu * p_2,       nu > 0
m = (x_1 + x_2)/2,               d = x_1 - x_2
dm/dt = 0,                      dd/dt = -2 * nu * d
d(t) = d(0) * exp(-2 * nu * t)
x_1(t) = m(0) + d(t)/2,          x_2(t) = m(0) - d(t)/2

These are predictions of the stated nodal model. Pressure is calculated from the two observed coordinates, never defined as a measured derivative divided by fitted capacity. Only the product nu * b is identifiable from a physical-time contrast trace if both are unknown. Fixing the clock bridge is therefore an admission condition, not a second fit parameter. Estimate one positive nu from calibration runs alone and freeze its uncertainty set. Nonpositive or unidentifiable capacity blocks this positive-capacity model; it is not clipped into its domain.

For P2, uniformly scaling the single positive edge weight leaves L_rw unchanged. Changing a resistor or link strength cannot be represented merely by rescaling that edge at fixed capacity. This first protocol consequently does not sweep link strength or infer a universal relation between capacity and hardware component values. An intervention is a recorded preparation, not automatically a canonical glyph or a U3 certificate.

State, clock and measurement admission

Item	Required frozen specification	Current missing evidence
State map	Two sensor identities; common EPI unit; fixed offsets/scales; range and linearity bounds	Apparatus and sensor calibration absent
Time	Raw timestamps, synchronization/skew bounds, finite positive bridge, origin rule and gap policy	Physical clock, sampling period and uncertainty absent
Support and input	Known P2 wiring, fixed link, source disconnection, observation interval and loading/leakage bounds	Wiring and external-input characterization absent
Capacity	Calibration-only common positive rate and identified uncertainty; no outcome-dependent choice	No calibration runs
Phase	Unavailable as an oscillatory observable; phase channel explicitly inactive in the selected model	Physical adequacy of that restriction untested
State sufficiency	Actual generator and observation map; distinguish unknown source terms from measurement noise	Model-specific apparatus check pending
Reserved observations	Disjoint preparation/run IDs, hashes, initial-sample allowance and fixed forecast horizon	No acquired runs or reserved data
Decision	Predeclared joint finite-trajectory acceptance tube, rejection and abstention rules	Instrument, calibration and numerical error budgets unset

With both EPI coordinates measured, the selected two-state model has observation matrix C = I. Its algebraic state observability is immediate; this does not prove that the apparatus has only those two relevant states. With contrast alone, the mean is hidden but the contrast equation closes under the common-capacity hypotheses. Do not promote that to a full-state claim. Reuse observability on the actual generator and observation map, and the hidden-source distinction in derived EPI memory if a reduction is proposed. An algebraic rank result supplies neither noise conditioning nor an instrument error bound. A material unmodeled leakage/loading contribution requires a revised admitted model, not a retrospectively invented pressure.

Calibration, forecast and finite decision

Use separate whole preparations for calibration and evaluation. Calibration may estimate only the declared common capacity after sensor and clock mapping are fixed. Freeze the fit rule, accepted domain, parameter interval, data identities and code revision. No graph, normalization, filter, channel, capacity, tolerance or horizon is selected using a reserved outcome.

The evaluation initialization allowance is the first synchronized sensor pair, with its uncertainty, at a predeclared forecast origin after the switching interval. Choose this origin from the hardware timing/calibration rule, not from the later relaxation trace. Forecast all subsequent requested timestamps before reading their values. No full-record centering, Hilbert transform, interpolation across unexplained gaps or future-aware smoothing is needed for this prediction.

Primary observation: the held-out contrast trajectory under the frozen capacity and clock bridge. The constant-mean prediction is a separately reported check of the same admitted model, not an ignored nuisance when it fails. Construct a simultaneous finite-trajectory tube from the declared initial-state, sensor, time, capacity and numerical uncertainty. A collection of pointwise confidence intervals is not automatically such a tube. If the uncertainty cannot be bounded at the declared scope, report inconclusive. Exceeding the frozen acceptance rule rejects this mapping on these runs; agreement supports only its declared finite domain. Report every reserved run, including failures, missing samples and exclusions with reasons.

Implemented continuous-time uncertainty boundary

The numerical part of admission now has an executable owner: p2_transport_reference.py, with measurement/run integration in validation/p2_transport.py. It uses the existing rational logarithm and negative-exponential enclosures; it introduces no pressure term, circuit governing law or new nodal solver. All uncertainty bounds below are supplied hypotheses. Their instrumental justification is still missing and remains a physical admission gate.

Continuous capacity, distinct from the Euler control

The earlier P1 finite-increment fit remains an engineering control. Even for an ideal noiseless P2 trajectory sampled at a common structural step h, its fitted coefficient is

nu_Euler = (1 - exp(-2*nu*h)) / (2*h) < nu,     nu>0, h>0.

It cannot be silently relabeled as the continuous physical rate. Irregular pooled increments do not in general have this single-step conversion. The new calibration uses each declared run's fixed first and last samples; interior samples are not fitted, and endpoint consistency does not validate the whole calibration trajectory. Durations and endpoint selection must not be changed after opening reserved outcomes.

After fixed sensor conversion, suppose the initial and final contrast have one resolved common sign. Reverse both signs if negative, giving positive intervals D0=[a,b] and D1=[c,d]. For elapsed structural time T=[sL,sU], sL>0, require resolved decay d/a<1. Then

r = D1 / D0 is enclosed by [c/b, d/a] = [rL,rU]
nu is enclosed by [-log(rU)/(2*sU), -log(rL)/(2*sL)].

Rational log bounds round the interval outward. Initial/final mean intervals must overlap. Each run must resolve nonzero contrast and positive decay; incompatible, sign-ambiguous or unidentifiable inputs raise explicit errors. Intersect all run capacity enclosures. A nonempty intersection is a necessary outer consistency condition, not proof of one joint latent fit. Finally round the capacity bounds outward to binary64 rational endpoints to limit arithmetic growth; a lost positive lower bound or infinite upper bound blocks this path. This computational enclosure is separate from measurement uncertainty.

Reserved joint outer tube

P2MeasurementBounds freezes two offsets/scales, total EPI-coordinate errors, timestamp error and a positive structural-time bridge interval. Coordinate errors include uncertainty in the sensor conversion itself. A bound eps_t on each timestamp gives elapsed-time error 2*eps_t; time zero is the same initial event, so its duration interval is exactly zero. Unresolved positive durations are rejected. The declared sensor/clock bounds must hold jointly throughout the full finite experiment; no confidence level is inferred. Both channels in each pair must represent the same latent observation time. Acquisition skew needs synchronization evidence or an independently derived coordinate-error allowance for time alignment. Timestamp error alone cannot align asynchronous channels or justify their constant-mean test.

For capacity in [nuL,nuU] and elapsed time in [tL,tU], the decay lies in [exp(-2*nuU*tU), exp(-2*nuL*tL)], evaluated with rational enclosures. Coordinates use the positive semigroup directly:

x1(t) = ((1+e)*x1(0) + (1-e)*x2(0))/2
x2(t) = ((1-e)*x1(0) + (1+e)*x2(0))/2,   e=exp(-2*nu*t).

Monotonicity in the initial coordinates and corner extrema in e give sound boxes while preserving the mean/contrast dependency. The mean and contrast are also retained as separate observable tests. The shared exponent cap is 4096 and the reference accepts at most 10,000 samples; these are computation guards, not physical constants. Rational output endpoints must not be converted to ordinary floats and called certified bounds.

calibrate_p2_transport checks the known undirected two-node positive edge; forecast_p2_transport consumes only frozen calibration, reserved identities, initial measurements and timestamps. The latter must be a predeclared schedule or clock metadata available without inspecting future response values. write_p2_transport_forecast saves exact rational endpoints as hexadecimal numerator/denominator strings; retain its content hash before opening outcomes. score_p2_transport reuses the whole-acquisition separation and requires that issued hash, matching units/times and unchanged initialization.

Disjoint coordinate, mean or contrast boxes give incompatible_with_declared_bounds. If every outer box overlaps, the result is only not_falsified_by_enclosures: different boxes may admit different latent parameters. That is neither a joint-feasibility proof nor statistical acceptance. The physical status remains not_admitted_by_this_score in both cases. Excessive tube width requires a preregistered resolution/power decision; it cannot become positive evidence just because all observations overlap.

Independent analytic/Decimal fixtures and wrong-mean, wrong-identity and changed-forecast controls exercise this boundary. These are software/model tests, not measured data. Existing manifest/sidecar owners can bind the saved bytes without acquiring a second evidence ledger. P1's Euler tests and their historical checkpoint remain unchanged.

Proposed pilot resources, not instrument tolerances

The following are provisional engineering caps for admission planning. They do not authorize acquisition with unresolved physical tolerances and are not TNFR constants or a statistical power calculation. Under the computer-only constraint these apparatus/preparation rows are requirements a matching public archive would need to document, not tasks for the user to build or acquire equipment.

Resource	Proposed cap and stop rule
Apparatus	One P2 setup, two synchronized observation channels, one unchanged link
Preparations	Two calibration runs at one nonzero prepared contrast; two held-out contrast conditions with three independent preparations each: eight total
Record size	At most 10,000 paired samples per run and 100 MiB for the complete raw/calibration/prediction bundle
Acquisition duration	At most 30 minutes per run; choose a shorter fixed horizon only from apparatus/calibration evidence before held-out acquisition
Data search/download	This metadata review is complete. Before any later signal download, pin exact files and compressed/expanded bounds; proposed pilot caps 100 MiB compressed and 250 MiB expanded
Computation	One frozen calibration specification and one prediction per reserved preparation; no automatic refitting or larger campaign after rejection/inconclusiveness

Sampling interval, voltage/temperature limits, switch settling allowance, clock accuracy, sensor skew, error bars and acceptance thresholds remain unset. They must be supplied by the selected instrument and calibration, not by these sample/storage budgets. If an adequate record cannot fit the caps, revise and version the protocol before observing reserved outcomes.

Evidence bundle and current exit gate

Reuse CoreExperimentManifest and EvidenceSidecar. Retain this annex, exact raw/calibration/evaluation file identities, source revision, raw timestamps/masks, immutable fit, forecasts and complete result ledger in one accessible bundle. validate_metadata() checks declarations only; validate_for_admission(root_dir=...) additionally checks real file bytes. Neither establishes physical adequacy, temporal commitment or scientific truth. Preserve an independently auditable pre-evaluation forecast record; a later digest alone cannot prove when a prediction was issued.

Declare the five measurement-provenance questions explicitly: future samples, outcome-derived wiring, fitting on evaluation data, evaluation labels and post-selection. An affirmative answer can describe exploratory evidence but cannot silently become prospective validation. Numerical certificate tolerance is separate from the instrument/statistical budget.

P2 remains not_admitted until one accessible public-data choice resolves the missing table, freezes all tolerances and resources, and passes the state/clock/identifiability gate. Volts remains a historical exploratory record of the earlier fixed-reference model/map pair, not an evaluation of the revised generative candidate and not reserved data for a later redesign. The execution plan owns when this parked branch resumes; another fit to this same curve cannot supply missing apparatus evidence or independent preparations. No apparatus purchase/acquisition is requested. No admitted physical prediction has yet been tested.