Study 20 — High-Energy Composition Completion and F-Constraint Specification

VERIFICATION RECORD — audit companion to The Selective Transient Field from First Principles (Backbone Edition V9.6.1). This section publishes the programme's technical record as it exists: the machine-verified release stack and the post-freeze calculation records, rendered from the frozen source files without editorial rewriting. It is written for auditors, not readers; the reader-facing statement of the theory is the Backbone Edition. Every document below is hash-pinned; the packages that carry the checkers and data are listed on the record landing page.

Source file STF_STUDY20_PAPER.md  ·  SHA-256 3b5213ff37cd0061ccb5043d0d57dccea4d02b5b6eee6ea0496b68fe6fa55726  ·  rendered as-is (GitHub-style ```math fences converted to display math).

Date: 2026-09-01
Authority: focused follow-up to Study 19
Scientific grade change: none
Task A classification: RETROSPECTIVE NON-FITTED BRANCH DISCRIMINATION — COVERAGE COMPLETION
Task B surface classification: POSTERIOR_CONSISTENCY_SURFACE — retrospective, not frozen, not a measurement, and not usable for parameter selection

Executive result

The Study 19 package is reproduced at SHA-256 243fc7c8c67fdc5bb5ed187a3f72ab6de62f850bae022b89f7321c5a4f2dbfbe. Its internal checksum set, embedded v9.6.1 baseline (e322752ddbbbe3d206bf11595be12f67c7695e6617bf1d89eea6d8209899e263), Auger archive, and Auger member hashes all pass. No frozen record was edited.

The unchanged Auger cut again gives 494 unique events. Above (10^{19.6}) eV there are 86: 49, 20, 10, and 7 in the bins 19.6–19.7, 19.7–19.8, 19.8–19.9, and (geq19.9), respectively. Five have (E>100) EeV.

The final published four-group fraction point in Auger PoS(ICRC2023)438 Figure 1 covers 19.6–19.8 and constrains 69 events. Its central fractions are:

PRD 111, 022003 (2025), Table IV gives (X_{}) moments above 19.8, and the companion PRL 134, 021001 (2025) extends those moments to a stated 100 EeV. Neither paper publishes an H/He/N/Fe likelihood or fraction table. Therefore 12 events from 19.8 to 100 EeV are moments-only and five above 100 EeV are outside the stated range. Assigning either set fitted fractions would violate the zero-fit rail. The unchanged overlap calculation consequently treats these 17 events as the honest probability bound ([0,1]).

For the newly fraction-constrained 69 events, the nominal log-uniform-(Z) overlaps are essentially zero for local and 0.0268 (EPOS-LHC) or 0.0623 (Sibyll2.3d) for remote. Including model and the common (pm14%) energy-scale envelope gives:

Thus the measured-fraction completion strengthens the central remote preference. The fully conservative marginal envelopes overlap, so Study 19’s recorded verdict is unchanged: remote favored; no branch exclusion. This is a completion, not a re-litigation and not a grade upgrade.

1. Frozen state and firewall

Study 19 controls (p=8/5), (q=2), the local and remote rigidity bands, reference (F=), every grade, and every counter. The checker imports these values from the byte-pinned Study 19 package. Event arrival-time and timestamp values are structurally inaccessible: any request for a header containing time or gps increments a failure counter and raises. The event ID is used only as an opaque duplicate key. All hard-rail counters are asserted zero.

2. Task A method

The population is rebuilt from the embedded Auger archive with (E>20) EeV and zenith (<80^), retaining the Study 19 source-file priority and four duplicate removals. Energy and its reported uncertainty are propagated event by event with the same 80-node Gauss-Hermite calculation. The charge supports remain the Study 19 Voronoi cells in (Z), with uniform density in (Z) explicitly declared as interpolation rather than measurement.

The Figure 1 point was recovered from native PDF vector coordinates, not raster estimation. Central marker values are normalized to sum to unity. The union of thick and thin error-bar extents supplies marginal feasible intervals; their correlation is not invented. Linear programming gives the minimum and maximum overlap subject to those intervals and unit total fraction.

Table IV values were transcribed exactly for the four high bins. They are used to document the observed heavier/purer trend and the publication’s coverage, but not converted into new elemental fractions. The companion PRL PDF is embedded and hash-pinned (ab670584fcdfd098e7207f7ee8f492b2f2752cb56e21c652596d8db416e69e81). Its abstract, Figure 2, and discussion report first and second moments, not a four-group fit. This absence is the reason for the bounded result.

3. Task B part 2 — executable F measurement

The factor is

\[ F=\frac{\zeta_{\rm acc}\min(\beta_w/\eta_{\rm acc},\epsilon_c)}{\sqrt{2f_\Omega\beta_w}}, \qquad C\propto F^{8/5}. \]

The executable target adopted here is a one-sigma multiplicative uncertainty of 10% on (C). This requires

\[ \sigma_{\ln F}\leq \frac{\ln(1.10)}{8/5}=0.05957. \]

For four independent active terms contributing equal log variance, each derivative-weighted contribution must be at most 0.02978. That translates to about 2.98% for unit-log-derivative parameters (({}) and ({}), or (_c)) and 5.96% for half-log-derivative parameters ((w) and (f)). These allocations are planning targets only; the simulator must publish the full covariance matrix. It must also publish the joint posterior of (w/{}) and (_c) with less than 5% probability of choosing the wrong side of the min branch.

A result pins (F) only if all five STF-defined quantities are posterior samples from a common physical ensemble, the active min branch is identified, the covariance-propagated target is met, and no STF timing residual is used.

Nearest primary work: L. Comisso, G. R. Farrar, and M. S. Muzio, ApJL 977, L18 (2024), DOI 10.3847/2041-8213/ad955f; K. Kiuchi et al., Nature Astronomy 8, 298–307 (2024), DOI 10.1038/s41550-024-02194-y; K. Hayashi et al., PRL 134, 211407 (2025), DOI 10.1103/PhysRevLett.134.211407; E. M. Gutiérrez et al., arXiv:2506.18995v2 (2025); F. Bacchini et al., arXiv:2602.15939v1 (2026); and G. R. Farrar, arXiv:2506.22625v2 (2025).

4. POSTERIOR_CONSISTENCY_SURFACE

This surface imports the retrospective 1,212-day association only to scale the remote rigidity band as (R(F)=F R_{}). It is not frozen, measured, or usable to select (F). The input is the same Study 19 408-event composition likelihood. The Auger-favored groups are He and N, whose combined Study 19 support is (Z); the operational score remains the unchanged full composition-weighted (Z) overlap, avoiding a new fitted threshold.

The frozen local comparator is (F=1), whose central model+scale overlap envelope is ([0.0001424,0.0070595]). On a declared (F=0.25)–100 grid with step 0.05:

• nominal consistency (both nominal hadronic models exceed their own (F=1) score): (F=1.05)–40.35;
• robust consistency (the minimum model+scale score exceeds the maximum (F=1) score): (F=1.55)–28.70;
• robust falsification within the audited grid (the maximum score is below the minimum (F=1) score): (F=0.25)–0.70 or (F=67.15)–100;
• intermediate regions are indeterminate under the declared model/scale envelope.

The exact frozen reference (F=) lies inside the robust-consistency band. Grid endpoints are resolved to 0.05 and are not fitted. Values outside 0.25–100 are not classified by this surface. The numerical grid is retained in F_CONSISTENCY_SURFACE.csv.

5. Limitations and non-results

No source-published four-group likelihood was found above (10^{19.8}) eV in the controlling Auger papers. The 17-event gap is bounded, not filled. No joint literature prior for the five (F) parameters is created. No (F) measurement is claimed. No event timing column is read. No coefficient is solved from a timing value. No grade, gate, source geometry, frozen branch, or version label is changed.

All quantitative results are regenerated by study20_checks.py; clean_room_verify.py verifies the package hashes and byte-compares regenerated RESULTS.json and the surface CSV.