APPENDIX - Fringe Spacing Geometry Module¶

Purpose: Convert the “interferometry grid / invisible tripod” idea into a quantitative, falsifiable geometry claim. This appendix is not a claim that any specific emitter existed; it is a specification of what the model would have to match if an interference geometry is asserted.

Outputs: (1) fringe spacing as a function of crossing angle and wavelength, (2) reverse-calculated frequency bands for candidate feature scales, (3) explicit assumptions and falsifiers, (4) a minimal correlation test protocol.

Status / routing: This appendix already carries two conditional geometry constraints: band placement from the ENE / East-Northeast ↔ Erin-sector crossing angle and fringe orientation from the ENE↔Erin-sector bisector. The companion spatial-analysis bundle is the active validation lane for the stronger map-level claim: whether a computed fringe/node map fits independent boundary features better than chance. Failure of that locked correlation program would reject the strongest quantitative fringe-map version, not reset the broader dossier or all geometry burdens to zero.

0. Definitions¶

• Crossing angle (\(\theta\)): the angle between the two incoming wave vectors at the target region (equivalently, the angle between the two source bearings as seen from the target, under a plane-wave approximation).
• ENE directional proxy: a bookkeeping label for the east-northeast arrival sector at the WTC used by the reconstruction’s geometry (bearing ~79.3° from true north). It is not a site attribution.
• Erin-sector proxy: a bookkeeping label for the southeast arrival sector associated with Hurricane Erin’s carried role in the reconstruction’s geometry (bearing ~149.7° from true north), treated as an external input with bounded uncertainty.
• Wavelength (\(\lambda\)): the carrier wavelength of the two coherent fields.
• Fringe spacing (\(d\)): spacing between adjacent maxima (or minima) in the interference pattern in the plane normal to the bisector direction.

1. Fringe spacing for two coherent plane waves¶

For two equal-frequency plane waves with crossing angle \(\theta\), the interference fringe spacing is:

Equivalently:

Implication: once \(\theta\) is fixed, the geometry fixes the ratio \(d/\lambda\).

2. Example ratio for the ENE↔Erin-sector crossing angle (~70.4°, from geodetic bearings)¶

If \(\theta \approx 70.4^\circ\), then:

So, under this assumption:

Important: The crossing angle \(\theta \approx 70.4°\) is derived from geodetic bearings (ENE proxy at 79.3° and Erin-sector proxy at 149.7° from the WTC; difference = 70.4°). The ENE proxy bearing is fixed. The 149.7° Erin bearing is carried here as a proxy anchor for the Erin-sector arrival direction — reproducible from an Erin-sector proxy point (e.g., ~35°N, 70°W) and to be explicitly source-indexed in the dossier audit trail rather than treated as a tuned value. The model may use an effective scattering centroid with offset Δθ; Δθ is uncertainty to propagate, not tune (see sensitivity analysis in Section 4.1).

3. Reverse calculation: “What frequency gives a fringe spacing comparable to feature scale \(d\)?”¶

Given an observed feature scale \(d_{feature}\) and a chosen \(\theta\), solve for:

Convert to frequency using a phase velocity \(v_{ph}\) (do not silently assume \(c\) if your propagation model implies otherwise):

3.1 First-order table (\(\theta=70.4^\circ\) from ENE↔Erin-sector bearings; \(v_{ph}=c\) as free-space assumption)¶

With \(d \approx 0.866\,\lambda \Rightarrow \lambda \approx d/0.866\):

“Fringes” across a 100 m scale	Implied fringe spacing \(d\)	Implied \(\lambda\)	\(f\) (if \(v_{ph}=c\))
0.5 fringe	200 m	231 m	1.30 MHz
1 fringe	100 m	115 m	2.60 MHz
1.5 fringes	67 m	77 m	3.90 MHz
2 fringes	50 m	58 m	5.20 MHz
3 fringes	33 m	38 m	7.81 MHz

Caution: This table is not proof of an emitter band. It is a geometry-to-band mapping conditional on (i) two-source coherent interference, (ii) a valid \(\theta\), and (iii) a defensible mapping from “feature boundary scale” to fringe spacing.

3.2 Candidate “multi-feature” frequencies (reverse-calculated, conditional on geometry)¶

If one treats certain feature scales as candidate “boundary spacings” (e.g., ~100 m knife-edge boundary scale, ~63 m tower face width, ~25 m WTC 6 principal sub-aperture / WTC 3 bisection features), then the reverse-calculation produces the following frequencies:

Frequency (if \(v_{ph}=c\))	Fringe spacing \(d\)	Candidate feature scale
2.6 MHz	100 m	WTC 4 boundary-scale spacing (1 fringe across 100 m)
4.1 MHz	63.5 m	Tower face width (~63 m)
5.2 MHz	50 m	“2 fringe” boundary-scale spacing across 100 m
10.0 MHz	26 m	WTC 6 principal dark-core / sub-aperture lateral scale and WTC 3 bisection-scale features (~25-26 m)

Interpretive guardrail: “Feature scale match” is not evidence by itself. It becomes meaningful only if a computed node/fringe map at those frequencies correlates with multiple independent boundary features under the dedicated correlation audit.

4. Sensitivity and evaluation workflow¶

Because \(d/\lambda = 1/(2\sin(\theta/2))\), changes in \(\theta\) shift the inferred \(\lambda\) and therefore the inferred \(f\).

Workflow note: angle-sensitivity sweeps and full reporting of derived-band variation are routed to the companion spatial-analysis bundle built on top of this geometry module.

4.1 Computed sensitivity: ±5° in \(\theta\) (65°–75°)¶

Using \(v_{ph} = c\) and the four candidate feature scales from Section 3.2:

Feature scale	\(\theta=65°\)	\(\theta=68°\)	\(\theta=70.4°\) (central)	\(\theta=72°\)	\(\theta=75°\)	Spread
WTC 4 boundary (~100 m)	2.79 MHz	2.68 MHz	2.60 MHz	2.55 MHz	2.46 MHz	±6.3%
Tower face width (~63 m)	4.43 MHz	4.26 MHz	4.13 MHz	4.05 MHz	3.91 MHz	±6.3%
2-fringe / WTC 6 sub-aperture scale 2× (~50 m)	5.58 MHz	5.36 MHz	5.20 MHz	5.10 MHz	4.93 MHz	±6.3%
WTC 6 principal sub-aperture / WTC 3 strip (~26 m)	10.74 MHz	10.32 MHz	10.01 MHz	9.82 MHz	9.48 MHz	±6.3%

Key observations:

1. Low sensitivity: ±5° in \(\theta\) shifts all implied frequencies by only ±6.3%. The multi-feature alignment is not a fine-tuned result — it survives substantial angle uncertainty.
2. Referenced HF-class overlap check: At the angle extremes, the 100 m feature drops just below 2.8 MHz (at \(\theta=75°\): 2.46 MHz) and the ~26 m feature scale just grazes above 10 MHz (at \(\theta=65°\): 10.74 MHz). The middle two features (63 m and 50 m) remain solidly in-band regardless of angle choice.
3. Implication for the dossier: the geometry is not a knife-edge construction. Locked sweep outputs and derived-band handling are routed to the companion spatial-analysis bundle built on this geometry module.

5. Assumptions (must be stated)¶

This module requires explicit assumptions, but they do not all govern the same claim level.

• Baseline geometry-bookkeeping layer: bearings, crossing angle, bisector orientation, and reverse-calculated band placement under stated propagation assumptions.
• Stronger quantitative fringe-map layer: coherence, two-source dominance, valid local crossing-angle mapping, and a threshold model under which damage boundaries can plausibly track fringe intensity.

If the stronger layer fails, the strongest quantitative fringe-map explanation fails even if weaker band-placement or orientation constraints remain as conditional geometry observations.

1. Coherence: the two sources are sufficiently phase-stable over the relevant time window to produce a persistent interference structure.
2. Two-source dominance: other paths/sources do not wash out the pattern or dominate coupling.
3. Propagation model: the mapping from source vectors to a local crossing angle at ground/structure scale is valid (waveguide / refraction / multipath must be bounded).
4. Coupling threshold model: “damage boundaries” correspond to crossing a coupling threshold that can plausibly track a fringe intensity gradient.

6. Falsification protocol (minimal)¶

1. Lock inputs: specify source coordinates/timing and compute \(\theta\) from the stated geometry.
2. Pick a band: select candidate frequencies from the reverse-calculation and carry them into the evaluation workflow.
3. Compute a map: generate a fringe/node intensity map across the WTC complex (with stated approximations).
4. Define “match”: pre-register what constitutes a match (e.g., boundary alignment within X meters across Y independent features).
5. Fail fast: if the predicted map does not correlate with the damage boundary features beyond chance, the strongest quantitative “interference geometry explains boundary placement” claim is rejected. The weaker band-placement and orientation constraints are then left to stand or fall on their own terms rather than being treated as automatically erased.

7. Where this is referenced¶

• White Paper: prediction-facing summary and test protocol (to avoid burying falsifiability in appendices).
• Bridge Mechanism Physics Appendix, Section J: listed as a bounded engineering-requirements + test-plan module.
• Companion spatial-analysis bundle: active execution environment for the locked correlation audit and stronger null testing program referenced here.

8. Notes on band statements (avoid overclaim)¶

The reverse-calculated frequency range (2.6–10 MHz) overlaps with a known 2.8–10 MHz high-power HF operating class (see also Bridge Appendix, Section I for facility-scale parameters). That overlap is a geometric placement result, not a standalone proof:

• The geometry module can at most constrain "if interference geometry explains boundary placement, then candidate \(f\) lives near 2.6–10 MHz under stated propagation assumptions and crossing angle."
• Whether any real-world HF facility (HAARP or otherwise) can supply the required power-at-target, coherence, and collateral containment is a separate link-budget and feasibility question handled elsewhere (see Bridge Appendix, Section J).

8.1 Interpretive note: the band-placement finding¶

The finding¶

The ENE↔Erin-sector crossing angle (\(\theta \approx 70.4°\)) places the four reverse-calculated feature frequencies at 2.6–10 MHz — overlapping a known high-power HF operating class (2.8–10 MHz) very closely:

Frequency	Fringe spacing \(d\)	Feature matched
~2.6 MHz	~100 m	WTC 4 damage boundary scale (knife-edge at ~⅔ of building length)
~4.1 MHz	~63 m	Tower face width (63 m square cross-section)
~5.2 MHz	~50 m	WTC 4 boundary at 2-fringe spacing; WTC 6 principal sub-aperture scale at 2×
~10 MHz	~26 m	WTC 6 principal dark-core / sub-aperture lateral scale (~25-30 m); WTC 3 bisection strip width (~25 m)

The feature scales span a 3.85× bandwidth ratio (100 m / 26 m). The referenced HF operating class spans a 3.57× ratio (10 MHz / 2.8 MHz). These match to within 8% — close enough that the feature cluster overlaps that HF class with only slight overflow at both edges (2.60 MHz just below 2.8; 10.01 MHz just at 10.0).

How the crossing angle controls band placement¶

The fringe equation (\(f = c / 2d\sin(\theta/2)\)) means the crossing angle acts as a tuning knob — it slides the entire feature cluster up or down the frequency axis without changing its bandwidth:

Crossing angle \(\theta\)	\(f\)(100 m)	\(f\)(26 m)	Cluster lands at
40°	4.38 MHz	16.85 MHz	above the referenced HF class
70.4° (ENE↔Erin-sector)	2.60 MHz	10.01 MHz	overlaps the referenced HF class
120°	1.73 MHz	6.66 MHz	below the referenced HF class

The ENE↔Erin-sector angle places the cluster in a close-fit position, with nearly symmetric overflow around the referenced HF class.

Methodological precision: what the null does and does not test¶

The fringe equation has an important property: for any two feature scales \(d_1\) and \(d_2\), their frequency ratio is \(f_1/f_2 = d_2/d_1\), which is independent of \(\theta\). This means:

• What this appendix does not carry as evidence by itself: any crossing angle preserves the same inter-feature frequency ratios, so the mere existence of a four-scale cluster is not the carried claim. Random-angle screening is used as a methodological guardrail for exactly that reason: it prevents the scale cluster alone from doing argumentative work it cannot carry.
• What this appendix does carry as the non-trivial geometry claim: where on the frequency axis the cluster lands, whether the ENE↔Erin-sector angle places it in the referenced HF class, whether the independent bisector/orientation relation is simultaneously satisfied, and whether a pre-registered fringe/node map fits observed boundaries better than chance.

The null question (stated precisely)¶

The proper null question is: "Given the observed building dimensions in the WTC complex, how likely is it that their max/min scale ratio (\(\approx 3.85\times\)) approximates the bandwidth ratio of a referenced HF operational class (\(\approx 3.57\times\)) to within 8%?" This depends on the distribution of building dimensions and the number of candidate transmitter windows in the RF spectrum. That probability is routed to the companion spatial-analysis bundle rather than left implicit.

Bottom line¶

The non-trivial question is not whether the feature scales cluster at all. It is whether the carried ENE↔Erin geometry jointly closes band placement, the independent bisector/orientation relation, and the pre-registered spatial-correlation test. The companion spatial-analysis bundle is the validation lane for that stronger map-level claim: if a computed fringe/node intensity map at these frequencies does not correlate with observed damage boundaries better than chance, the strongest quantitative interference-geometry explanation of boundary placement is rejected. The weaker band-placement and orientation constraints would then remain to be interpreted on their own terms.

8.2 Fringe orientation finding (zero free parameters)¶

The finding¶

The fringe node lines run parallel to the bisector of the two source bearings — at 114.5° from true north (roughly ESE–WNW). The WTC complex was rotated approximately 29° east of true north, so the buildings' "east-west" faces run at 119° from north.

The offset is 4.5°.

This means fringe node lines are nearly parallel to the buildings' E-W faces. Damage boundaries within individual buildings would appear as strips or divisions running roughly E-W — dividing buildings into north and south portions. This matches the FEMA 403 observations:

• WTC 4: knife-edge boundary dividing the south wing (destroyed) from the north wing (intact) — consistent with a node line running parallel to the E-W building axis.
• WTC 3 (Marriott): bisection strip running roughly along the E-W building axis — consistent with a node line passing through the building in the same direction.
• WTC 6: scalloped vertical void / aperture complex — no preferred orientation at the feature-scale level (consistent with any fringe direction).

What this depends on¶

This test has zero fitted parameters. It depends only on:

1. ENE proxy bearing from WTC: 79.3° (geodetically determined)
2. Erin bearing from WTC: 149.7° (Erin-sector proxy bearing used by the reconstruction; treated as an external input with bounded uncertainty, not optimized)
3. WTC complex rotation: ~29° from true north (from site plans / NIST NCSTAR 1)

It does not depend on: phase offset (φ₀), exact building coordinates, frequency choice, or any fitting or optimization.

Geometric alignment note¶

If the bisector bearing were uniformly random, the probability of aligning within 4.5° of either building face direction (two chances, separated by 90°) is:

This is a compact way to express how tightly the bisector tracks the dominant building-face axis. It should be read as a local alignment statistic, not as the final orientation significance claim after broader comparison accounting. Formal significance handling for the orientation result is being handled in the companion spatial-analysis bundle; this geometry module states the orientation quantity to be scored.

Sensitivity to Erin's position¶

The orientation match holds to within 10° for Erin bearings from ~140° to ~160° (a ±10° range). This ±10° sweep corresponds to effective centroid uncertainty (storm center vs. aloft scattering centroid): the physically relevant source direction may be offset by Δθ from the storm's geometric center, and the sweep bounds that uncertainty rather than post-hoc tuning. The match is not fine-tuned to Erin's exact position. However, the tightest observed match (4.5°) occurs near the proxy bearing of 149.7°.

Why this is a second independent constraint¶

The band-placement finding (§8.1) depends on the crossing angle (Erin bearing − ENE proxy bearing = 70.4°). The orientation finding depends on the bisector angle ((Erin bearing + ENE proxy bearing) / 2 = 114.5°). These are algebraically independent: the crossing angle constrains the difference of the two bearings, while the bisector constrains their sum. Both matching simultaneously is more restrictive than either alone.

8.3 Null model & multiple comparisons¶

The orientation finding (§8.2) and band-placement finding (§8.1) define the null framework for the companion spatial-analysis bundle. This section states that framework directly.

8.3.1 Orientation finding null model¶

Evaluation baseline: The bisector direction of two source bearings is evaluated against the architectural axes of the WTC complex.

Null distribution: If the bisector bearing \(\beta\) is uniformly distributed on \([0°, 360°)\), the probability of \(\beta\) falling within \(\pm\delta\) of either building face direction (two orthogonal axes separated by 90°, giving two independent chances) is:

For \(\delta = 4.5°\): \(P = 4 \times 4.5° / 360° = 0.050\) (5.0%).

What the tolerance \(\delta\) means: The 4.5° value is the observed offset between the bisector (114.5°) and the nearest building face axis (119°). That observed offset is the orientation-match quantity to be scored.

Evaluation handling: The orientation test is treated as a single bisector-versus-building-face comparison. Source-pair handling, feature-set handling, and any broader multiple-comparison accounting are to be reported with the locked bundle outputs.

8.3.2 Band-placement null model¶

The band-placement finding (§8.1) has a more subtle null structure. The proper null question (stated in §8.1) is:

"Given the observed building dimensions in the WTC complex, how likely is it that their max/min scale ratio (\(\approx 3.85\times\)) approximates the bandwidth ratio of a referenced HF operational class (\(\approx 3.57\times\)) to within 8%?"

This requires specifying:

1. Feature-scale distribution: What is the distribution of "interesting feature scales" in a typical large building complex? If all urban complexes naturally produce feature clusters with ~3–4× bandwidth ratios, the coincidence with the referenced HF class is less surprising.
2. Transmitter-class distribution: How many specific real-world transmitter classes exist with defined operational windows in the 1–30 MHz range? Each is an independent "target" that increases the look-elsewhere probability.
3. Tolerance definition: The 8% match tolerance should be treated as the observed discrepancy, not a chosen threshold.

Bundle routing: This quantification is routed to the companion spatial-analysis bundle. Here, the band-placement finding is carried as a geometric placement result under active locked evaluation.

8.3.3 Joint significance¶

If both findings are treated as independent to first order (one depends on the crossing angle and the other on the bisector), the joint p-value for both matching simultaneously is:

The algebraic independence of the two tests (one constrains the sum of bearings, the other constrains the difference) means the two findings impose genuinely independent constraints on the source geometry. The companion spatial-analysis bundle is the execution environment for the locked evaluation built on those constraints.

8.4 Geometry drift → phase drift (sensitivity derivation)¶

The reconstruction requires Erin's position to remain stable enough that the fringe pattern stays registered on the WTC buildings. This section derives the sensitivity of fringe registration to Erin's effective scattering centroid position.

8.4.1 Setup¶

The fringe spacing at the target is \(d = \lambda / (2\sin(\theta/2))\), where \(\theta\) is the crossing angle between the two arrival directions. A fringe maximum (or minimum) is a surface of constant path-length difference \(\Delta L = n\lambda\) between the two sources. A shift in the fringe pattern by fraction \(\alpha\) of one period requires a path-length change:

At \(\theta = 70.4°\) and \(d = 26\) m (\(f \approx 10\) MHz):

At \(d = 100\) m (\(f \approx 2.6\) MHz):

8.4.2 Translating to Erin displacement¶

If Erin's effective scattering centroid shifts by \(\delta r\) in an arbitrary direction, the path-length change at WTC depends on the geometry of the ENE↔Erin-sector↔WTC triangle. For small displacements:

where \(\phi_E\) and \(\phi_B\) are the angles between the displacement direction and the Erin→WTC and ENE→Erin directions respectively. In the worst case (displacement along the fringe-variation axis), \(|\cos\phi_E - \cos\phi_B| \sim 1\), giving:

Frequency	\(\lambda\)	Half-fringe shift requires Erin displacement of
2.6 MHz	115 m	~58 m
5.2 MHz	58 m	~29 m
10 MHz	30 m	~15 m

8.4.3 Interpretation¶

• At the highest-frequency sensitivity case carried here (10 MHz), a ~15 m shift in Erin's effective scattering centroid shifts fringes by half a period. This is the stringent edge of the envelope, not the universal closure condition. It is comparable to (or tighter than) typical uncertainty in publicly reported storm-center positions, though the "effective scattering centroid" is a different quantity that depends on the ionospheric conductivity distribution rather than the storm center itself.
• At 2.6 MHz, the tolerance relaxes to ~58 m — still tight but more forgiving.
• During the event window (~102 minutes), Erin moved ~16 km (at ~6 mph). If the effective scattering centroid tracks the storm center, this represents many fringe periods of drift at 10 MHz but fewer at 2.6 MHz.

8.4.4 What this implies¶

The sensitivity analysis creates a clear geometry burden: the highest-frequency fringes (10 MHz, \(d = 26\) m) require positional stability tighter than is currently demonstrated over 102 minutes, while the lowest-frequency fringes (2.6 MHz, \(d = 100\) m) are more robust. The reconstruction therefore has to show one or more of the following:

1. The effective fringe pattern is dominated by lower frequencies where positional tolerance is more forgiving.
2. The "effective scattering centroid" is NOT the storm center but rather a feature of the ionospheric conductivity structure (e.g., the centroid of the FAC-enhanced region) that is more stable than the storm's surface position.
3. Higher-frequency features require tighter geometry lock than lower-frequency features, which is why Phase I preconditioning (Erin stalling) is carried as a reconstruction prerequisite.

8.4.5 Geometry closure burdens¶

These are geometry-closure burdens on the reconstruction, not repairs to Model A.

• Measurement refinement still needed: the relationship between Erin's surface position and its "effective scattering centroid" for ionospheric re-radiation. This is a critical geometry burden.
• Geometry closure test: compare the rate at which the fringe pattern drifts as Erin moves to the rate at which the coupling mechanism can produce irreversible damage. If damage accumulates faster than fringes drift, a slowly drifting pattern could still produce sharp boundaries via time-integrated exposure.
• Measurement refinement still needed: phase velocity \(v_{ph}\) uncertainty affects fringe spacing and therefore drift tolerance; if \(v_{ph} < c\) (waveguide propagation), fringes are tighter and tolerances are stricter.

8.5 Locked Correlation Protocol¶

The minimal falsification protocol (§6) specifies five steps. This section states the specific definitions to be used in the companion spatial-analysis bundle referenced by the reconstruction document.

8.5.1 Match metric¶

The spatial correlation test compares a predicted fringe intensity map to observed damage boundary data. The match metric is:

Distance-to-boundary residual: For each observed damage boundary feature (e.g., WTC 4 knife-edge, WTC 3 bisection strip edge), compute the perpendicular distance from the feature to the nearest predicted fringe node line. The residual for feature \(i\) is:

The aggregate match metric is:

where \(N\) is the number of independent features. Lower \(R\) = better match.

8.5.2 Pre-registered feature set¶

The following features are defined as the independent test targets, each contributing one residual:

Feature	Observable	Source
WTC 4 knife-edge	North-south boundary location (east-west position along building)	FEMA 403, Figure 5-16
WTC 3 bisection strip	Center-line of destruction strip (north-south position along building)	FEMA 403, Chapter 7
WTC 6 void / aperture-complex locus	Approximate locus of the WTC 6 principal dark-core / sub-aperture feature within the larger scalloped void / aperture complex	FEMA 403, Figure 5-19
WTC 5 partial collapse boundary	Edge of collapse region on southern face	FEMA 403, Chapter 6

Exclusions: WTC 1 and WTC 2 are excluded because they are the primary targets (total destruction) and cannot provide boundary-contrast information. Structures beyond the WTC complex boundary are excluded because the fringe model predictions become less constrained at distance.

8.5.3 Evaluation criterion¶

The test statistic is \(R\), where lower values indicate a better geometric match. The null hypothesis is:

The null distribution for \(R\) is generated by:
1. Computing \(R\) for 10,000 random fringe maps (uniform random phase offset \(\phi_0 \in [0, 2\pi)\) and uniform random frequency within the 2.6–10 MHz band).
2. Computing the percentile of \(R_{\text{observed}}\) in the null distribution.

The companion spatial-analysis bundle is the execution environment for this criterion and should report the locked evaluation outputs for it, including \(R_{\text{observed}}\), the null distribution, and the resulting percentile or p-value.

8.5.4 Fail-fast criterion¶

If, during the analysis, any of the following conditions are met, the test is stopped and the strongest quantitative interference-geometry explanation is rejected:

1. No feature within \(2d\) of any node line: If any of the 4 pre-registered features is more than \(2d\) from the nearest predicted node line (where \(d\) is the fringe spacing at the tested frequency), the prediction has failed for that frequency.
2. Orientation mismatch exceeds 20°: If the predicted fringe orientation deviates from the observed damage boundary orientation by more than 20° for any feature with a clear directional signature, the tested fringe-map configuration is rejected.
3. Best frequency requires \(v_{ph} < 0.5c\) or \(v_{ph} > 1.5c\): If phase-velocity tuning beyond this range is needed to fit the data, the propagation assumptions are implausible.

8.5.5 Interpretation routing¶

Interpretation follows the locked evaluation outputs from the companion spatial-analysis bundle. This geometry module defines the inputs, derived bands, and scoring protocol that bundle is required to execute.

• If the locked correlation program succeeds: the strongest quantitative fringe-map version is materially strengthened.
• If the locked correlation program fails: the strongest quantitative fringe-map version is rejected, while weaker band-placement and orientation constraints remain to be assessed on their own terms rather than being treated as automatic zero.

9. How this connects to the feasibility choke points¶

This module most directly constrains:

• Emitter spec (geometry-constrained): candidate frequency bands (conditional on geometry + propagation assumptions).
• Control/coherence: if boundaries are sharp, coherence/stability requirements must be consistent with propagation variability.
• Collateral containment: a computed node map must explain why adjacent structures sit in “safe zones” (anti-nodes) rather than being indiscriminately exposed.

By design, this module does not settle facility identity, bridge physics, or every implementation-level validation lane. It is the dossier's clearest falsifiable geometry program, not a standalone replacement for the rest of the reconstruction.