cosmic-ray-flux-spectrum

Orientation — UHECR flux/spectrum (Premise B, cosmic-ray pillar)

Slice: the independent empirical pillar behind “Nature has already run ~10^31 LHC-equivalent collisions” — the primary ultra-high-energy cosmic-ray (UHECR) flux/spectrum measurements themselves (not the compact-star survival argument, not the safety-report syntheses, not BH production/Hawking theory).

Sources by topic (best-first within each group)

Modern high-statistics spectrum (the numbers a flux-to-collisions calculation should actually use): S-75 - Pierre Auger Collaboration 2025- spectrum across declinations -90 to +44.8, S-73 - Auger-TA joint working group 2020- combined UHECR energy spectrum, S-67 - Aab et al. 2020 (PRL)- Auger spectral features above 2.5x10^18 eV, S-69 - Aab et al. 2020 (PRD)- Auger measurement of the cosmic-ray energy spectrum, S-71 - Abu-Zayyad et al. 2013- Telescope Array surface-detector spectrum

GZK-suppression controversy and its resolution (bears on how reliable the extreme-energy tail flux is): S-64 - Abraham et al. 2008- Pierre Auger observation of flux suppression above 4x10^19 eV, S-60 - Abbasi et al. 2008- HiRes first observation of the GZK suppression, S-63 - Abbasi et al. 2008-2009- HiRes full monocular UHECR flux (Astropart. Phys. 30), S-49 - Takeda et al. 1998- AGASA spectrum extends beyond the GZK cutoff (the no-cutoff outlier the others resolved), S-55 - Takeda et al. 2003- AGASA energy determination and spectrum, S-52 - Hayashida et al. 2000- updated AGASA event list above 4x10^19 eV

Historical anchors (earliest primary evidence of extreme energies, mid-range spectrum baseline): S-46 - Bird et al. 1995- the ‘Oh-My-God’ ~3x10^20 eV cosmic ray, S-43 - Bird et al. 1994- Fly’s Eye cosmic-ray energy spectrum above 10^17 eV, S-41 - Linsley 1963- first cosmic ray above 10^20 eV (Volcano Ranch)

Primary flux-to-collisions/safety computations distinct from LSAG/Giddings-Mangano (methodological ancestors, RHIC-era, own their own flux analysis rather than citing a safety report): S-76 - Jaffe, Busza, Sandweiss, Wilczek 2000- RHIC disaster-scenario review, S-77 - Dar, De Rujula, Heinz 1999- cosmic-ray bound on RHIC-collider safety

search_scope

Web search (no institutional Scholar/OpenAlex access in this run) for: Bird et al. 1995 ApJ 441 “Oh-My-God” event; Pierre Auger Observatory spectrum papers (2008 suppression, 2020 PRL/PRD, 2025 declination); HiRes monocular spectrum and GZK-suppression papers (Abbasi 2008 PRL, Astropart. Phys. 30); AGASA spectrum papers (Takeda 1998, 2003; Hayashida 2000 event list); Telescope Array surface-detector spectrum (Abu-Zayyad 2013); the Auger-TA joint spectrum working-group reconciliation (2020); Linsley 1963 first >10^20 eV detection; and, for the “natural experiment” computation itself, the RHIC-era safety papers (Jaffe/Busza/Sandweiss/Wilczek 2000, Dar/De Rujula/Heinz 1999) that predate and methodologically anchor the LHC-era LSAG/Giddings-Mangano reports (those reports are out of scope for this slice — mine via found_via in slices 1/3). Each search fed a small number of arXiv/DOI/ADS lookups to pin down exact venue, volume and arXiv id; citation counts were not independently verified against Semantic Scholar/INSPIRE in this pass (marked unknown except S-46, verified via a citation-aggregator hit).

exclusions

1. GZK-cutoff theory papers (Greisen 1966; Zatsepin & Kuzmin 1966) — dropped as out of scope: this slice is the empirical flux/spectrum measurements, not the theoretical prediction the measurements test.
2. LSAG report and Giddings & Mangano PRD 2008 (“Astrophysical implications of hypothetical stable TeV-scale black holes”) — explicitly assigned to slices 1/3 per brief; not minted here, only referenced as target found_via context for S-76/S-77.
3. AGASA/HiRes/Auger composition (mass-composition, Xmax) papers — dropped as out of scope: this slice is flux/spectrum (how many collisions), not primary-particle identity.
4. Pure reviews/compilations (e.g. “Cosmic Rays from the Knee to the Highest Energies,” “Ultrahigh Energy Cosmic Rays” reviews) — mined for citation leads only, per instructions no source node minted for a review.
5. AGASA detector-design/instrumentation papers (e.g. Chiba et al. NIM) — dropped, not a flux/spectrum measurement.

Slice shape and gaps

~16 primary sources covering three independent detection technologies (fluorescence: Fly’s Eye/HiRes; ground array: AGASA/Telescope Array/Auger’s surface detector; hybrid: Auger) across 1963-2025, plus two RHIC-era papers that pioneered the flux-to-safety-bound computation this slice ultimately feeds. Coverage is solid for the modern era (Auger/TA/joint spectrum) and the historical anchors (Linsley, Bird). Gap: I did not find a distinct modern (post-2010, LHC-era) primary paper that explicitly redoes the “integrate flux above 14 TeV c.m. over Earth’s/Sun’s lifetime to ~10^31 collisions” arithmetic outside the LSAG/Giddings-Mangano reports — the RHIC-era Jaffe et al./Dar et al. papers are the closest genuinely independent instances I could locate; it’s possible the LHC-era version of this specific calculation lives only inside the safety reports themselves (slices 1/3’s territory), in which case step 3 extraction should flag that the flux data (this slice) and the flux-to-collisions arithmetic (slices 1/3) are cleanly separable but the latter has no fully independent modern primary source. Also did not verify citation counts against a live database (Semantic Scholar/INSPIRE); all but S-46 marked unknown for step 2 to fill if load-bearing.