{
  "abstract": "Reconstructing a damaged musical fragment is an inverse problem: the observed sequence contains partial information, while a raga encodes constraints limiting allowable completions. This paper formalizes a mathematical framework for this, proposing the Artificial Rosetta Stone (ARS). We separate three claims often conflated: a symbolic sequence can be reconstructed probabilistically; a sequence can be consistent with an explicit grammar; and a historical performance can be authenticated. We only support the first two. We model a raga via a finite alphabet and constraint system, using an order-k Markov model for melodic probabilities. A symmetric Dirichlet prior yields a tractable posterior. We pose missing-note reconstruction as a constrained MAP problem. For fixed-length sequences and finite-order constraints, optimization admits an exact dynamic-programming solution with worst-case time complexity $O(TN^{k+1})$. We derive the parameter count $N^k(N - 1)$, prove a concentration bound under explicit mixing assumptions, and analyze estimation error propagation. A reproducible synthetic experiment uses six raga-inspired alphabets, orders $k \\in \\{1, 2, 3\\}$, and masking rates up to 50%. This is a proof of concept, not historical reconstruction. A real-audio feasibility pilot evaluates 30 usable sequences from 42 Yaman clips via automated pitch extraction, segmentation, and quantization. Lacking documented provenance and relying on automated transcription, this is not expert-validated archival reconstruction. Claims are tied to stated conditions, not universal properties of Hindustani music. Code: https://github.com/mathacker23/ArtificialRosettaStone.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01064",
  "author_total": 2,
  "authors": [
    {
      "name": "Saanvi Raghavendran"
    },
    {
      "name": "Abhishek Bhattacharjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eps9180y5gg5d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01064",
  "fulltext_url": null,
  "id": "eps9180y5gg5d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01064",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "cs.SD"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1711|Music and Audio Processing"
    ]
  ],
  "openalex": "W7206150785",
  "pdf_url": "https://arxiv.org/pdf/2609.01064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eps9180y5gg5d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:10Z",
      "native_id": "2609.01064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Artificial Rosetta Stone: Constrained Maximum A Posteriori (MAP) Reconstruction of Symbolic Raga Sequences via Order-k Markov Models",
  "title_text": "Artificial Rosetta Stone: Constrained Maximum A Posteriori (MAP) Reconstruction of Symbolic Raga Sequences via Order-k Markov Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:10Z",
  "url": "https://research.draconitic.com/paper/eps9180y5gg5d",
  "venue": "arXiv",
  "versions": []
}