{
  "schema_version": 1,
  "title": "Reproduction: Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling",
  "emoji": "🌐",
  "space_id": "snaykey/repro-spherical-watermarking",
  "paper": {
    "openreview_id": "SBfIuo2Ets"
  },
  "tags": [
    "icml2026-repro",
    "paper-SBfIuo2Ets"
  ],
  "updated_at": "2026-07-31T00:00:00Z",
  "root": {
    "slug": "index",
    "title": "Reproduction: Rotation-Invariant Spherical Watermarking via Third-Order SO(3) Representation Coupling",
    "file": "pages/index.md",
    "children": [
      {
        "slug": "executive-summary",
        "title": "Executive summary",
        "file": "pages/executive-summary/page.md",
        "children": []
      },
      {
        "slug": "claim-1-triad-bispectrum-construction",
        "title": "The method (TRIAD) constructs a third-order spherical bispectrum by coupling three irreducible SO(3) representations via tensor products and projecting onto the trivial representation using Clebsch-Gordan coefficients, yielding a rotation-invariant scalar that preserves phase information (Section 3).",
        "file": "pages/claim-1-triad-bispectrum-construction/page.md",
        "children": []
      },
      {
        "slug": "claim-2-thm41-so3-invariance",
        "title": "Theorem 4.1 proves the third-order bispectrum invariant is strictly invariant under arbitrary SO(3) rotations, with perturbations to higher-order harmonic coefficients producing detectable changes in the invariant (Theorem 4.1).",
        "file": "pages/claim-2-thm41-so3-invariance/page.md",
        "children": []
      },
      {
        "slug": "claim-3-embedding-degrees-6-8-14",
        "title": "Watermarks are embedded into spherical harmonic coefficients at degrees 6, 8, and 14 via SO(3)-equivariant operations to avoid perceptible artifacts in low-frequency (coarse) content (Section 3).",
        "file": "pages/claim-3-embedding-degrees-6-8-14/page.md",
        "children": []
      },
      {
        "slug": "claim-4-rotation-bitaccuracy-vs-baselines",
        "title": "Under arbitrary 3D rotations, TRIAD maintains near-100% bit accuracy while baseline watermarking methods (with or without rotation augmentation) collapse in performance (Section 5).",
        "file": "pages/claim-4-rotation-bitaccuracy-vs-baselines/page.md",
        "children": []
      },
      {
        "slug": "claim-5-fidelity-psnr-ssim",
        "title": "Watermarked panoramic images retain high visual fidelity, with PSNR of 39.22 dB and SSIM of 0.9946 (Section 5).",
        "file": "pages/claim-5-fidelity-psnr-ssim/page.md",
        "children": []
      },
      {
        "slug": "claim-6-distortion-robustness-capacity",
        "title": "TRIAD also achieves 100% bit accuracy under JPEG compression, Gaussian blur, Gaussian noise, and resizing, though embedding capacity is constrained to roughly 32-64 bits because harmonics above degree 16 are vulnerable to lossy compression and aliasing (Section 5).",
        "file": "pages/claim-6-distortion-robustness-capacity/page.md",
        "children": []
      },
      {
        "slug": "conclusion",
        "title": "Conclusion",
        "file": "pages/conclusion/page.md",
        "children": []
      }
    ]
  }
}