Study 19 — Retrospective Composition Discrimination and Measured-Input Dossier, Part 1

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_STUDY19_PAPER.md  ·  SHA-256 5abed8022c98a153a1e38a930e6786b663a27239dcec28bffa9b74e25d6a5bd9  ·  rendered as-is (GitHub-style ```math fences converted to display math).

Date: 2026-09-01
Release status: Study 19; no version-label change
Exact classification: RETROSPECTIVE NON-FITTED BRANCH DISCRIMINATION
Scientific grade change: none

Abstract

The uploaded Pierre Auger public-data files reproduce 498 rows after the declared cuts, corresponding to 494 unique event identifiers after four duplicate rows are removed by a fixed file-priority rule. No spectrum reconstruction is used. The 494-event energy distribution maps the frozen local branch to predominantly very heavy charge windows and the remote branch to intermediate/heavy windows.

Published Auger composition information does not provide a tabulated continuous charge likelihood in the required bins. This study therefore reports both the literal four-template likelihood and a bounded elemental-group construction. With an explicit log-uniform interpolation inside the four published elemental groups, the population-mean overlap is 0.0971–0.2389% local and 12.543–16.449% remote for the two published hadronic-model solutions at the nominal energy scale. Including model choice and the ±14% common energy scale gives central envelopes of 0.0142–0.7059% local and 8.6676–22.9800% remote. Adding conservative feasible envelopes from the digitized marginal fraction error bars gives approximately 0–3.6476% local and 1.5420–32.1325% remote; these intervals overlap. The verdict is therefore:

REMOTE FAVORED, WITH NO BRANCH EXCLUSION.

This conclusion is conditional on the declared within-group interpolation. The literal H/He/N/Fe representative-template calculation instead gives small overlap for both branches and nominally larger local overlap. That contradiction is a genuine granularity effect and is retained. A seven-event hybrid-Xmax cross-check is model-dependent and non-discriminating.

The remote-input dossier finds no literature-supported joint prior for \((f_\Omega,\beta_w,\epsilon_c,\eta_{\rm acc},\zeta_{\rm acc})\). In particular, the frozen reference values \(\beta_w=0.3,\eta_{\rm acc}=1,\zeta_{\rm acc}=1\) are not all the values suggested by the closest simulations: the relevant large-angle outflow is typically simulated at \(0.1\text{--}0.2c\), while the static-box calibrations conditionally map to \(\eta_{\rm acc}=1.6\) and \(\zeta_{\rm acc}=0.65\). The expanding-flow values and the STF geometry factor remain free. No amendment is made.

1. Scope, inheritance, and integrity tripwire

The Study 18 baseline archive has SHA-256 e322752ddbbbe3d206bf11595be12f67c7695e6617bf1d89eea6d8209899e263. Every entry in its internal SHA256SUMS.txt verifies. Its embedded v9.6 archive has SHA-256 c301a8013409eab230f69330af7309df7d20564f3d4520454f0b95bc40731545, exactly as required. The baseline numbers and the work order agree; the tripwire found no discrepancy.

The inherited state is

\[ \tau_{\rm src}=C\mathcal R^{-8/5},\qquad \Delta_{\rm mag}=A\mathcal R^{-2},\qquad Y=CX-A, \]

with \(X=\mathcal R^{2/5}\), \(Y=\mathcal R^2L\), and

The 1,212 d number is used only to identify the already frozen retrospective branch windows. It is not fitted. The 71 d, approximately 54 yr, and 360/730/1466 \(R_S\) records are not used in any coefficient or model selection.

2. Uploaded Auger population

2.1 Provenance and hashes

The uploader stated the provenance as: Pierre Auger Observatory public dataset behind the “Test Authority” population, V1.5; public data 2004–2018; cut \(E>20\) EeV and zenith \(<80^\circ\); \(N=494\). The supplied archive is summary (5).zip, SHA-256 0499fb34d4d2bd968b1704ebc4cccace361b4841482994d2b4701816de18d8bd. The official release is the Pierre Auger Open Data 2021 release, DOI 10.5281/zenodo.4487612.

The cut yields 498 file rows. Fixed priority Inclined → SD1500 → SD750 and opaque event-ID deduplication remove four rows: one repeated SD1500 record (81847956000) and three SD750 records already in SD1500 (141362166000, 151290615700, 180195053200). This gives 494 unique events without moving a threshold. Event IDs are administrative keys only and never enter a physics array.

The release period is accepted from release provenance. No timestamp is read to rederive it. The Task A checker indexes no header containing time or gps; its asserted timing-column-read counter is zero.

2.2 Actual energy distribution

The unique population has energy quantiles (minimum, 5%, 25%, 50%, 75%, 95%, maximum)

\[ (20.022,20.3753,22.672,26.8385,34.5550,56.78645,144.115)\ {\rm EeV}. \]

For each event, the branch charge interval is

\[ Z_i\in[E_i/\mathcal R_{\rm high},\,E_i/\mathcal R_{\rm low}]. \]

Across all 494 events, the 0/25/50/75/100% quantiles of the lower and upper charge-window edges are:

At central energies, an exact Fe template falls inside 309 local windows and 80 remote windows; exact H, He, and N templates fall inside none. This already shows why a four-point charge representation is too coarse for the remote window, which typically begins just above nitrogen and extends through intermediate charges.

3. Published composition likelihood

3.1 Primary Auger inputs

The principal mass-fraction input is O. Tkachenko for the Pierre Auger Collaboration, PoS(ICRC2023)438, Figure 1. It is a PRELIMINARY four-element-group MCMC fit to Auger FD \(X_{\max}\) distributions using EPOS-LHC and Sibyll 2.3d. QGSJetII-04 was omitted by Auger because it does not describe the distributions well. Values below are vector-digitized marker centers; brackets are the union of the plotted thick/thin marginal error-bar extents. Fractions are correlated, so the brackets must not be read as an independent simultaneous box.

An independent moment audit uses A. Abdul Halim et al. (Pierre Auger Collaboration), Phys. Rev. D 111, 022003 (2025), Table IV. In the same three bins, the published DNN moments are respectively \(\langle X_{\max}\rangle=774.7,775.3,778.6\) g cm\(^{-2}\) and \(\sigma(X_{\max})=30.7,27.3,26.3\) g cm\(^{-2}\), with the statistical and systematic errors retained in that table. These moments corroborate an intermediate and narrowing composition but do not alone determine a charge likelihood.

Of the uploaded events, 408 lie in 19.3–19.6, with bin counts 203, 132, 73. The remaining 86 are retained in the 494-event kinematic summary but excluded from the likelihood average because this work order selected the 19.3–19.6 composition band. No high-energy fraction is extrapolated.

3.2 Consistency measure and uncertainty propagation

For branch \(b\), the literal-template overlap is

\[ O_b={1\over N}\sum_i\sum_g f_{g,k(i)} P\!\left(\mathcal R_{b,\min}\le {E_i\over Z_g} \le\mathcal R_{b,\max}\right). \]

Per-event reported energy errors are integrated with 80-point Gauss–Hermite quadrature. The Auger common energy-scale systematic is evaluated at −14%, nominal, and +14%; the 14% source is the Pierre Auger Collaboration, Phys. Rev. D 102, 062005 (2020). Hadronic-model spread is EPOS-LHC versus Sibyll 2.3d.

Because Figure 1 calls H, He, N, and Fe “elemental groups,” a bounded charge mapping is also constructed. Boundaries are geometric midpoints in charge: \([1,\sqrt2]\), \([\sqrt2,\sqrt{14}]\), \([\sqrt{14},\sqrt{182}]\), and \([\sqrt{182},26]\). The strict lower bound counts a group only if its entire interval is within the event window; the upper bound counts any intersection. Neither is a measured internal group shape. The reported central interpolation assumes uniform density in \(\ln Z\) within each group and is explicitly labeled an interpolation.

For the marginal-fraction envelope, a linear program imposes the digitized marginal bounds and \(\sum_g f_g=1\), but ignores unknown posterior correlations. This is intentionally conservative.

3.3 Results

All values are population-mean overlap fractions for the 408 constrained events.

The strict whole-group lower construction is effectively zero for both branches because neither event-dependent window encloses one of the deliberately broad group cells in full. The any-intersection upper construction is correspondingly broad; with independent marginal error bars relaxed it can approach unity for remote and is not a probability estimate.

The exact-template calculation is an adversarial cross-check: it nominally prefers local, because the discrete \(Z=7\) N marker sits just outside most remote windows while the tiny Fe component can enter local. The continuous group interpolation reverses the result, yielding remote/local overlap ratios 52.5 (EPOS) and 169.4 (Sibyll). The reversal demonstrates that the result is limited by published charge granularity, not statistical precision.

Verdict: remote favored under the declared group interpolation. The conservative envelopes overlap, so neither branch is excluded and this study does not claim a Bayes factor, p-value, or new grade.

4. Uploaded hybrid-Xmax cross-check

Seven unique cut-passing records carry FD \(X_{\max}\). They are evaluated with the generalized-Gumbel calibration of L. Arbeletche and V. de Souza, Astropart. Phys. 116 (2020) 102389, Eq. (2), Eqs. (7)–(8), and updated Table VI. Five equal-prior templates (p, He, C, Si, Fe) are convolved with each event’s reported \(X_{\max}\) uncertainty. This is a likelihood evaluation, not a fitted population model.

The model spreads are 10.246–18.373% local and 13.439–17.030% remote. The ordering changes with model, and Auger itself omits QGSJetII-04 from its four-fraction fit. Seven hybrid events are also a strongly selected subset. The cross-check is therefore non-discriminating and does not override the population result.

5. The 71-day neutral-messenger structure

The 71-day structure is a GRB association. It has no charged-particle magnetic delay and receives no detected-particle charge assignment. The inherited remote range 8.660254615109844–15.009716216977287 EV is only a source-tier accelerator inference. It does not enter the composition likelihood.

6. Measured-input dossier, part 1

The dossier was assembled before any timing residual was viewed. The starting source is G. R. Farrar, arXiv:2506.22625v2 (2025), accepted by ApJ Letters.

6.1 Remote-source parameters

Primary sources are L. Comisso, G. R. Farrar, and M. S. Muzio, ApJL 977 L18 (2024); K. Kiuchi et al., Nature Astronomy 8, 298 (2024); H. Hamidani, K. Kiuchi, and K. Ioka, MNRAS 491, 3192 (2020); and M. Pais et al., ApJ 976, 35 (2024).

There is no defensible joint range because \(f_\Omega\), the expanding-flow \(\eta_{\rm acc}\), and the expanding-flow \(\zeta_{\rm acc}\) remain free, and the inputs are correlated. Consequently Study 19 does not evaluate a new \(F\), does not replace the frozen reference tuple, and does not amend \(C_{\rm rem}\).

6.2 Population-level transport inputs

Sources: M. S. Pshirkov et al., Phys. Rev. Lett. 116, 191302 (2016); Planck Collaboration, A&A 594, A19 (2016); MAGIC Collaboration, A&A 670, A145 (2023); R. Jansson and G. R. Farrar, ApJ 761, L11 (2012); M. Unger and G. R. Farrar, ApJ 970, 95 (2024); M. Haverkorn et al., ApJ 680, 362 (2008); and G. R. Farrar and M. S. Sutherland, arXiv:1711.02730.

Thus \(A_{\rm EG}\) and \(A_G\) remain coefficient formulas, not measured numbers. At the Study 19 rigidities, 0.66–2.55 EV, published GMF propagation calculations also show common large deflections, multiple images, and strong direction/coherence dependence below 10 EV. The charged small-angle \(\mathcal R^{-2}\) transport branch is not established population-wide.

7. Firewall, classification, and limits

The checker asserts all of the following counters are zero: new fits to observation; timing values used to solve coefficients; timing values used to select model elements; Task A timing-column value reads; grade upgrades; new gravity gates; new source geometries; frozen-artifact edits.

The Study 19 verdict is retrospective and non-blind. It cannot upgrade a grade. The composition result is limited by (i) preliminary fraction plots rather than posterior tables, (ii) correlated error bars unavailable numerically, (iii) charge width inside each elemental group, (iv) hadronic-model dependence, (v) 86 population events above the requested composition band, and (vi) seven hybrid records only. No fabricated precision fills these gaps.

8. Conclusion

The actual Auger energy distribution and the published intermediate-mass trend make the remote branch more composition-compatible under the only declared continuous group interpolation. The central effect is large, but the published granularity is insufficient for exclusion. The literal four-template result pulls the other way and is kept as a warning against treating representative nuclei as complete charge groups.

The remote normalization remains empirically open. Existing simulations give useful one-parameter information but not the joint inputs required for a new \(F\), while population magnetic-field bounds do not yield a universal transport coefficient. The next defensible step is posterior-table acquisition for composition and a pre-timing, event-specific source/line-of-sight dossier.