{
  "abstract": "Many inference problems are constrained from two sides: forward information and a second constraint on outcomes. Dual Boundary Condition Inference (DBCI) multiplies them and renormalises. The rule is not new: it is the product-of-experts form and the unit-exponent member of the logarithmic-pooling family. The paper contributes a classification and reducibility characterisation. The algebra does not fix the exponent at which the inputs combine: given the statistic log p_fwd + log p_bwd, which already builds in the product form, maximum entropy supplies the family (p_fwd p_bwd)^lambda and selects no member. If the inputs are read as two equally weighted opinions, three requirements select lambda = 1/2: unanimity preservation, consistency under a common Bayesian update, and minimal symmetric Kullback-Leibler divergence. If they are read as separately applied factors, two requirements select lambda = 1: a neutral second input must leave the first unchanged, and an update to one input must pass through unchanged. For a rank-one intermediate projective measurement, the Aharonov-Bergmann-Lebowitz (ABL) rule realises this form with no extra parameter. Every positive exponent orders outcomes identically, so the choice is invisible to picking the likeliest outcome, but not to scoring a class by total mass. Under the relevant identifications, the same product form gives Bayes' rule, while a final effect proportional to the identity returns the ordinary forward Born probabilities. The second result is a Two-Boundary Reducibility Criterion: DBCI factors through the forward boundary exactly when the effective backward boundary, up to positive rescaling, does. So a fixed prior or model-fixed structural constraint adds no distinctions between cases sharing the same forward boundary, though it may encode substantial information and still materially affect the result.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27120",
  "author_total": 2,
  "authors": [
    {
      "name": "Luis Razo"
    },
    {
      "name": "Eliahu Cohen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbp3wxsjgmrb2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27120",
  "fulltext_url": null,
  "id": "dbp3wxsjgmrb2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27120",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1702|Bayesian Modeling and Causal Inference"
    ]
  ],
  "openalex": "W7214146773",
  "pdf_url": "https://arxiv.org/pdf/2609.27120",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbp3wxsjgmrb2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2609.27120",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27120"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Dual Boundary Condition Inference: A Two-Boundary Product Rule and Its Implications",
  "title_text": "Dual Boundary Condition Inference: A Two-Boundary Product Rule and Its Implications",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:06Z",
  "url": "https://research.draconitic.com/paper/dbp3wxsjgmrb2",
  "venue": "arXiv",
  "versions": []
}