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Research Papers

Series: xPRIMEray Wormhole Invariant Trilogy  ·  Status: Draft (pre-submission)  ·  DOI: pending

This directory holds the xPRIMEray paper family: structured research notes positioned as arXiv-facing manuscripts. Each paper defines, validates, or extends a geometric invariant governing wormhole rendering correctness.

Paper Series

Paper 000 — Series Overview

Unified Summary of the Wormhole Invariant Trilogy

Concise series overview framing the three invariant papers as one coherent rendering-correctness program. Establishes shared terminology, notation conventions, and the relationship between the positive invariant (proto-caustic annulus), the negative invariant (low-value sector budget), and their coupled phase-space stability region.

Paper 001 — Positive Invariant

Proto-Caustic Invariant in Geometry-Aware Wormhole Transport

Defines the destination-side annulus as the primary positive geometric invariant. Demonstrates that wormhole transport correctness can be validated by checking whether destination-side ray intersections form a stable annular structure, independent of scene parameters. Establishes the hermetic throat fixture as the ground-truth harness for this invariant.

Supplement: Paper 001a — Artifact Atlas for Causal Observer Ladders

Artifact companion for the causal observer ladder workflow. Collects generated ladder figures, clustering plots, anomaly summaries, periodicity figures, and morphology references in one paper-side location, together with a minimal LaTeX shell for citation and reuse.

Paper 002 — Negative Invariant

Low-Value Sector Budget as a Negative Invariant in Geometry-Aware Wormhole Transport

Defines the low-value outer-ring query-share budget as the complementary negative invariant. Shows that an excessive fraction of rays landing in geometrically unproductive sectors is a reliable indicator of transport misconfiguration, providing a budget-based rejection criterion dual to the annular contract of Paper 001.

Paper 003 — Coupled Phase Space

Coupled Invariants and Stability Phase Space in Geometry-Aware Wormhole Transport

Studies the positive and negative invariants jointly and identifies a bounded stable operating region. Maps the under-constrained, stable, and rejected zones of the two-invariant phase space. Provides a parameter-space stability diagram (Figure E) usable as a diagnostic tool during scene authoring.

Paper 004 — Hermetic Throat Validation

Hermetic Throat Validation in Geometry-Aware Wormhole Transport

Formalizes the hermetic throat fixture as a deterministic validation harness. Proves that the fixture provides ground-truth coverage of both invariants from Papers 001 and 002, and establishes observer-ladder protocols for Penrose causal consistency checking. Includes LaTeX source for journal submission.

→ LaTeX source

Shared Resources

Conventions

  • Each paper directory contains paper.md (working manuscript) and optional main.tex for journal submission.
  • Figure references point to deterministic harness artifacts under Docs/wormhole_test/figures/.
  • Maintain the metadata header block at the top of each paper.md.
  • Preserve the common section structure unless there is a strong paper-specific reason to diverge.
  • Treat this family as arXiv-facing research-note scaffolding, not marketing copy.
  • BibTeX citation templates are in Shared Related Work.

Figure Quartet Reference

Each harness run produces five canonical figures:

ID File Description
A figure_A_main_render.png Raw render output — no overlays
B figure_B_composed_overlay.png Render + research diagnostic overlay
C figure_C_ring_density.png Portal-sector ray density map
D figure_D_metrics_table.png Invariant values + performance summary
E figure_E_phase_space.png Coupled invariant phase-space plot

Figures are stored in Docs/wormhole_test/figures/.