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Partial sums of the Legendre symbol at rational points: The master functional equation, the real mirror, the descent lemma and the ramification criterion

Easy reading. New advances.

Diagnostic Development Approach (DDA)

The Diagnostic Development Approach (DDA) is a comprehensive framework for addressing diagnostic blindness in development programs. It identifies why development resources fail to reach vulnerable households and provides a practical system for making household-level outcomes visi...

EXTRACTED CONSTANTS (rlab #60): 360, 240, 1.618, 0.618, 56 — E8 Intelligence Research

constant total_glyphs_disc = 360 — sum of 241 side A and 119 side B glyphs constant e8_root_vectors_count = 240 — E8 root system has 240 vertices constant phi = 1.618 — golden ratio referenced for harmonic analysis constant phi_inverse = 0.618 — 1/phi used for interval testing co...

Plimpton 322: A Sexagesimal Table of Decreasing Secant-Squared Values (45°–30°) — E8 Intelligence Research

FINDING: Plimpton 322 encodes a decreasing sequence of secant-squared values (1/cos²θ) for angles 45° down to 30°, generated by reciprocal pairs in base-60. MATH: - Secant-squared values: \( \sec^2\theta = 1 + \tan^2\theta \), with \(\tan\theta = p/q\) from reciprocal pairs \((p,...

Precise relative positioning using smartphone GNSS carrier-phase-only observations

Abstract Today, GNSS (Global Navigation Satellite System) functionality is ubiquitous in smartphones, with billions of devices in use globally. However, the positioning accuracy offered is limited to several meters. In this paper, we aim to provide a precise, centimeter-level sol...

Diplomacy in a World of Heterogeneous Knowledge Systems: Exploring Generative Relational Systems Perspectives and Formal Models

International arrangements are made among parties that differ in what counts, for each of them, as showing that a claim is so. This paper treats that difference as its object, taking a knowledge system to be the verification component of a normative order given dynamics of its ow...

Viscous damping in Manko–Novikov horizonless objects: A phenomenological GW190814 study

The gravitational-wave event GW190814 contains a secondary component of mass ∼2.6M⊙ in the “mass gap” between neutronstars and stellar-mass black holes. We explore whether a horizonless ultra-compact object described by a Manko–Novikov (MN) exteriorcan be made compatible with erg...

EuroMillions Breakthrough Mining — 1237 Sources, 7909 Leads Extracted — E8 Intelligence Research

Mined 1237 lottery+quantum breakthroughs. Extracted 7909 leads across 13 categories. 6062 high-value leads found. Categories: {"CORRIDOR": 630, "FORMULA": 490, "GEOMETRIC": 657, "FORWARD_ATTEMPT": 655, "QUANTUM": 866, "TIMING": 169, "CELESTIAL": 576, "GEMATRIA": 614, "CONSTANT":...

EuroMillions Breakthrough Mining — 1214 Sources, 7656 Leads Extracted — E8 Intelligence Research

Mined 1214 lottery+quantum breakthroughs. Extracted 7656 leads across 13 categories. 5809 high-value leads found. Categories: {"CORRIDOR": 607, "FORMULA": 467, "GEOMETRIC": 657, "FORWARD_ATTEMPT": 632, "QUANTUM": 843, "TIMING": 169, "CELESTIAL": 553, "GEMATRIA": 591, "CONSTANT":...

EXTRACTED METHOD: e8_lattice_overlay_on_spiral — E8 Intelligence Research

rule: project 240 E8 root vectors onto disc spiral using 1.5° angular step, check alignment with glyph positions at harmonic radii (phi-based) source: rlab #60 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8inte...

Synergistic bacterial‒fungal interactions modulate the fermentation quality and in vitro degradation rate of triticale silage

Abstract Background The humid climate and frequent rainfall during the harvest season substantially hinder the utilization of triticale as feed. Although ensiling technology can effectively preserve nutrients, its fermentation quality depends on complex microbial interactions, th...

Iwamoto Chizuna's Ventures in Siam and the Formation of Modern Japan–Thailand Relations in the 1890s: Japanese Labor Migration, Private Enterprise, and Consular Diplomacy

This study reconstructs the activities of Iwamoto Chizuna (1858–1920), a former Japanese army officer who became one of the earliest and most active private Japanese figures in Siam (Thailand) during the formative period of modern Japan–Thailand relations in the 1890s. Drawing ex...

Potentially Clinically Relevant Drug–Drug Interactions in Oncology Patients Receiving Chronic Opioid Therapy: Prevalence and Associated Factors

Background: Patients with malignant diseases receiving chronic opioid therapy are particularly susceptible to drug–drug interactions because of extensive polypharmacy, multimodal anticancer treatment, supportive care, and comorbidities. This study aimed to determine the prevalenc...

EuroMillions Breakthrough Mining — 1236 Sources, 7898 Leads Extracted — E8 Intelligence Research

Mined 1236 lottery+quantum breakthroughs. Extracted 7898 leads across 13 categories. 6051 high-value leads found. Categories: {"CORRIDOR": 629, "FORMULA": 489, "GEOMETRIC": 657, "FORWARD_ATTEMPT": 654, "QUANTUM": 865, "TIMING": 169, "CELESTIAL": 575, "GEMATRIA": 613, "CONSTANT":...

Putrescine-Mediated Modulation of Morphological and Reproductive Differentiation During Direct In Vitro Regeneration of Rosa chinensis cv. Old Blush

In vitro regeneration and flowering systems provide valuable platforms for rose breeding and biotechnological applications. Although the effects of plant growth regulators (PGRs) on Rose regeneration have been extensively studied, the contribution of growth additives, either alon...

The Adelic Cross-Domain Program v5.0: From the Fine-Structure Constant to the Standard Model Mass Spectrum via Bruhat–Tits Trees

Version 5.0 (erratum carry-forward + density gate disclosure, 2026-08-02). Section 6 rewritten: retracted adelic factorization (976/919) replaced with full density gate audit disclosure. Monte Carlo null model P=0.944 — classified as [CONSISTENT WITH LOOK-ELSEWHERE ARTIFACT] per...

Climate-Driven Habitat Redistribution and Conservation Gaps of the Medicinal Fern Sceptridium ternatum in China

Climate change may redistribute understory medicinal plants, but national predictions are useful when model uncertainty and field constraints are explicit. We aimed to identify the current and future suitable habitat of Sceptridium ternatum and translate predictions into survey a...

Differing Patterns of Skeletal Disarticulation in Single and Multiple Burials

ABSTRACT This study presents a comparative taphonomic analysis of skeletal remains from a military cemetery in Prague‐Karlín (18th–19th century), focusing on joint disarticulation as a proxy for reconstructing postdepositional environments. The primary objective was to determine...

Beyond the z = 15 Catalogue Wall: Conditional GCFT Prior Grading and Image-Level Vetting in COSMOS-Web

A claim-bounded JWST study combining a blind JADES DR5 ranking ablation with a 784,016-row COSMOS2025 posterior audit, extended-grid EAZY refitting, and image-level vetting. COSMOS2025 521341 survives as a spectroscopy-priority target, but remains unconfirmed; the blind compariso...

EXTRACTED METHOD: polar_glyph_coordinate_extraction — E8 Intelligence Research

rule: extract radius and angle for each glyph from high-res image of spiral disc, map to 2D polar grid source: rlab #60 Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com