{
  "schema_version": 1,
  "builder_plan": {
    "scenario": "Start with one repeated product task that has a measurable failure or cost.",
    "change": "Read the methods and identify one change you can isolate in that workflow.",
    "baseline": "Your current implementation on the same held-out tasks.",
    "steps": [
      "Locate the paper's implementation and check its license, model support, data needs, and hardware requirements. Stop here if you cannot obtain the required artifacts.",
      "Save a small set of representative product tasks and expected outcomes. Keep evaluation tasks out of any training or tuning, and choose quality and cost limits before running.",
      "Run the baseline and the proposed change on identical inputs. Keep other settings fixed and repeat paired runs to expose variation.",
      "Save per-task outputs, failures, timings, and all usage costs. Review regressions before expanding the test."
    ],
    "measure": "Successful outcomes, response time, human rework, and total cost per successful task.",
    "decision": "Keep the change only if it meets your preselected quality and latency limits and improves the metric you care about after setup and operating costs. Otherwise retain the baseline. This is an exploration plan, not a validated recommendation."
  },
  "builder_review": null,
  "arxiv_id": "2609.13500",
  "title": "One Spectrum, Two Resources: Data-Memory Scaling in Autoregressive Prediction",
  "summary": "The paper does not propose a deployable technique; it proves a minimax law linking dataset size and learned-state memory through a single predictive-energy spectrum, replacing heuristic capacity-data sizing rules with a theoretical curve. It costs nothing to adopt directly but offers no implementation, serving path, or quantified efficiency gain; the weight-only quantization section is an examination of existing pretrained models, not a new compression method. The law's assumptions (positive-entropy autoregressive retrieval source, optimal bit allocation, two-sided arithmetic bounds) may not hold for real pretraining workloads, so its exponents may not transfer to production model sizing decisions.",
  "rationale": "This is a theoretical scaling-law result without an actionable method, so it is relevant background for capacity planning but not something a constrained-infrastructure team can adopt or benchmark now.",
  "technique": "Data-memory scaling law for autoregressive prediction",
  "family": "outro",
  "recommendation": "observar",
  "published": "2026-09-11",
  "as_of": "2026-10-18",
  "editorial_status": "indexed",
  "source_url": "https://arxiv.org/abs/2609.13500",
  "independent_implementations": 0,
  "total_implementations": 0,
  "stars": 0,
  "citations": 0,
  "claims": [
    {
      "claim_id": "claim-01",
      "statement": "The paper does not propose a deployable technique; it proves a minimax law linking dataset size and learned-state memory through a single predictive-energy spectrum, replacing heuristic capacity-data sizing rules with a theoretical curve. It costs nothing to adopt directly but offers no implementation, serving path, or quantified efficiency gain; the weight-only quantization section is an examination of existing pretrained models, not a new compression method. The law's assumptions (positive-entropy autoregressive retrieval source, optimal bit allocation, two-sided arithmetic bounds) may not hold for real pretraining workloads, so its exponents may not transfer to production model sizing decisions.",
      "basis": "inferred",
      "result": "",
      "baseline": "",
      "conditions": "",
      "source_url": "https://arxiv.org/abs/2609.13500",
      "source_page": null,
      "source_excerpt": ""
    }
  ],
  "exposure_map": [
    {
      "dimension": "quality",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "compute",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "latency",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "operations",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "compatibility",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "security",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "data_and_training",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    },
    {
      "dimension": "reproducibility",
      "basis": "not_evaluated",
      "finding": "",
      "interpretation": "",
      "limitation": "",
      "next_check": "",
      "source_url": "",
      "source_page": null,
      "source_excerpt": ""
    }
  ],
  "risks": [],
  "minimum_test": [],
  "open_questions": [],
  "independent_tests": [],
  "lab_reproductions": [],
  "report_available": false,
  "validation_tier": "unknown",
  "evidence_tier": "unknown",
  "infrastructure_basis": "unknown",
  "equations": [
    {
      "anchor": "S3.E3",
      "label": "(3.3)",
      "section": "3 The Energy-per-Coordinate Spectrum: Minimax Risk and Identifiability",
      "role": "proposed_method",
      "latex": "\\boxed{\\mathfrak{R}^{*}_{\\rm value}(n,B)\\asymp_{R}\\Phi_{\\mu}(n^{-1})+\\Phi_{\\mu}(\\tau_{B}).}",
      "mathml": "<math display=\"block\"><mrow><mi>ℜ</mi><msup><mrow></mrow><mo>∗</mo></msup><msub><mrow></mrow><mi>value</mi></msub><mo stretchy=\"false\">(</mo><mi>n</mi><mo>,</mo><mi>B</mi><mo stretchy=\"false\">)</mo><mo>≍</mo><msub><mrow></mrow><mi>R</mi></msub><mi mathvariant=\"normal\">Φ</mi><msub><mrow></mrow><mi>μ</mi></msub><mo stretchy=\"false\">(</mo><mi>n</mi><msup><mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy=\"false\">)</mo><mo>+</mo><mi mathvariant=\"normal\">Φ</mi><msub><mrow></mrow><mi>μ</mi></msub><mo stretchy=\"false\">(</mo><mi>τ</mi><msub><mrow></mrow><mi>B</mi></msub><mo stretchy=\"false\">)</mo><mo lspace=\"0em\">.</mo></mrow></math>",
      "context": "For the bounded-logit value experiment,",
      "headline": "",
      "explanation": "",
      "objective": "",
      "symbols": {},
      "evidence": "",
      "evidence_url": "",
      "source_url": ""
    },
    {
      "anchor": "S3.EGx1",
      "label": "(3.1)",
      "section": "3 The Energy-per-Coordinate Spectrum: Minimax Risk and Identifiability",
      "role": "metric",
      "latex": "\\mathcal{S}_{q}(n) :=\\sum_{i}\\min\\{q_{i},n^{-1}\\}=\\Phi_{\\mu}(n^{-1}),",
      "mathml": "<math display=\"block\"><mrow><mrow><msub><mi>𝒮</mi><mi>q</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><mi>n</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mrow><mphantom></mphantom><mo lspace=\"0.278em\" rspace=\"0.278em\">:</mo><mrow><mphantom></mphantom><mo>=</mo><mrow><mstyle displaystyle=\"true\"><munder><mo movablelimits=\"false\">∑</mo><mi>i</mi></munder></mstyle><mrow><mi>min</mi><mo>⁡</mo><mrow><mo stretchy=\"false\">{</mo><msub><mi>q</mi><mi>i</mi></msub><mo>,</mo><msup><mi>n</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy=\"false\">}</mo></mrow></mrow></mrow><mo>=</mo><mrow><msub><mi mathvariant=\"normal\">Φ</mi><mi>μ</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><msup><mi>n</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo stretchy=\"false\">)</mo></mrow></mrow></mrow></mrow><mo>,</mo></mrow></mrow></math>",
      "context": "Let <math display=\"inline\"><mrow><msub><mi>q</mi><mi>i</mi></msub><mo>&gt;</mo><mn>0</mn></mrow></math>, <math display=\"inline\"><mrow><mrow><msub><mo>∑</mo><mi>i</mi></msub><msub><mi>q</mi><mi>i</mi></msub></mrow><mo>&lt;</mo><mi mathvariant=\"normal\">∞</mi></mrow></math>, and let <math display=\"inline\"><mi>μ</mi></math>, <math display=\"inline\"><msub><mi mathvariant=\"normal\">Φ</mi><mi>μ</mi></msub></math>, and <math display=\"inline\"><msub><mi>τ</mi><mi>B</mi></msub></math> be defined above. Then",
      "headline": "",
      "explanation": "",
      "objective": "",
      "symbols": {},
      "evidence": "",
      "evidence_url": "",
      "source_url": ""
    },
    {
      "anchor": "S3.EGx1-2",
      "label": "(3.2)",
      "section": "3 The Energy-per-Coordinate Spectrum: Minimax Risk and Identifiability",
      "role": "metric",
      "latex": "D_{q}(B) :=\\inf_{\\begin{subarray}{c}b_{i}\\geq 0\\\\\n\\sum_{i}b_{i}\\leq B\\end{subarray}}\\sum_{i}q_{i}2^{-2b_{i}}=\\Phi_{\\mu}(\\tau_{B}).",
      "mathml": "<math display=\"block\"><mrow><mrow><msub><mi>D</mi><mi>q</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><mi>B</mi><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mrow><mphantom></mphantom><mo lspace=\"0.278em\" rspace=\"0.278em\">:</mo><mrow><mphantom></mphantom><mo rspace=\"0.1389em\">=</mo><mrow><munder><mo lspace=\"0.1389em\" movablelimits=\"false\" rspace=\"0.167em\">inf</mo><mtable rowspacing=\"0pt\"><mtr><mtd><mrow><msub><mi>b</mi><mi>i</mi></msub><mo>≥</mo><mn>0</mn></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mstyle displaystyle=\"false\"><msub><mo maxsize=\"0.700em\" minsize=\"0.700em\" stretchy=\"true\">∑</mo><mi>i</mi></msub></mstyle><msub><mi>b</mi><mi>i</mi></msub></mrow><mo>≤</mo><mi>B</mi></mrow></mtd></mtr></mtable></munder><mrow><mstyle displaystyle=\"true\"><munder><mo movablelimits=\"false\">∑</mo><mi>i</mi></munder></mstyle><mrow><msub><mi>q</mi><mi>i</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><msup><mn>2</mn><mrow><mo>−</mo><mrow><mn>2</mn><mo lspace=\"0em\" rspace=\"0em\">​</mo><msub><mi>b</mi><mi>i</mi></msub></mrow></mrow></msup></mrow></mrow></mrow><mo>=</mo><mrow><msub><mi mathvariant=\"normal\">Φ</mi><mi>μ</mi></msub><mo lspace=\"0em\" rspace=\"0em\">​</mo><mrow><mo stretchy=\"false\">(</mo><msub><mi>τ</mi><mi>B</mi></msub><mo stretchy=\"false\">)</mo></mrow></mrow></mrow></mrow><mo lspace=\"0em\">.</mo></mrow></mrow></math>",
      "context": "Let <math display=\"inline\"><mrow><msub><mi>q</mi><mi>i</mi></msub><mo>&gt;</mo><mn>0</mn></mrow></math>, <math display=\"inline\"><mrow><mrow><msub><mo>∑</mo><mi>i</mi></msub><msub><mi>q</mi><mi>i</mi></msub></mrow><mo>&lt;</mo><mi mathvariant=\"normal\">∞</mi></mrow></math>, and let <math display=\"inline\"><mi>μ</mi></math>, <math display=\"inline\"><msub><mi mathvariant=\"normal\">Φ</mi><mi>μ</mi></msub></math>, and <math display=\"inline\"><msub><mi>τ</mi><mi>B</mi></msub></math> be defined above. Then",
      "headline": "",
      "explanation": "",
      "objective": "",
      "symbols": {},
      "evidence": "",
      "evidence_url": "",
      "source_url": ""
    }
  ],
  "equations_status": "selected",
  "core_kind": "formula",
  "equations_fetched_at": "2026-09-30",
  "equations_source_url": "",
  "equations_source_sha256": "",
  "exposures_reviewed_at": "",
  "exposures_source_sha256": ""
}