{
  "checked_on": "2026-10-11",
  "slide_id": "research-mixing-development",
  "paper": {
    "title": "Cosmological Collider Signals at Strong Mixing",
    "version": "2607.14891v2",
    "version_date": "2026-08-31",
    "url": "https://arxiv.org/html/2607.14891v2"
  },
  "sources": {
    "conversation": "resources/evidence/chat-research/strong-mixing.original.html",
    "early_notes": "/Users/wangyi/Dropbox/ai/strong-mixing/note/notes.tex",
    "correction_audit": "/Users/wangyi/Dropbox/ai/strong-mixing/note/corrections.md",
    "later_calculation_record": "/Users/wangyi/Dropbox/ai/strong-mixing/J-analytical/README.md",
    "later_manuscript": "/Users/wangyi/Dropbox/ai/strong-mixing/paper-new/paper.tex",
    "notes_input_request": "resources/evidence/strong-mixing-case/notes-input-request.json"
  },
  "evidence_limits": [
    "The preserved conversation contains 16 captured messages; missing turns and linked generated PDF/ZIP files were not recovered.",
    "Corrections audit the supplied human note/notes.tex, as identified by the user and the preserved our notes input request. This is distinct from the original GPT-Pro outputs; the correction list does not attribute those note errors to GPT.",
    "The published v2 is authoritative for the final result and equation numbering. Local correction-audit disposition notes contain older status statements and are not treated as the published result.",
    "A request in chat is distinguished from a calculation shown in the captured response. In particular, requesting phase and mass-limit calculations does not establish their completion.",
    "The comparison establishes subsequent mathematical work, not who performed each individual step. The paper abstract records GPT-assisted calculation and author checks."
  ],
  "rows": [
    {
      "topic": "Check human calculation notes",
      "earlier": "GPT supplies propagators and soft coefficients. The supplied human notes contain normalization, external-leg, sign and prefactor errors audited in corrections.md.",
      "earlier_evidence": [
        "Captured assistant message 10: explicit soft Gamma coefficients and fits",
        "corrections.md items 1, 2, 4, 8 and 12; their notes.tex anchors"
      ],
      "paper": "Canonical normalization and Wightman external legs are defined correctly. The soft coefficient uses -1/lambda; the hard-branch subtraction has the corrected sign.",
      "paper_locations": [
        "Section 2.2, equation (20)",
        "Section 2.3, equations (21)-(25)",
        "Section 3, equation (37)",
        "Section 4.1, equation (50)"
      ]
    },
    {
      "topic": "Complete the hard integral analytically",
      "earlier": "The chat reports exact nonoscillatory two-dimensional hypergeometric integrals and a Mellin-Barnes representation, explicitly leaving the generic final summation open.",
      "earlier_evidence": [
        "Captured assistant message 10: generic MB contour summation not completed"
      ],
      "paper": "Both continuous integrations are evaluated into an absolutely convergent single sum of beta and 3F2(1) factors. The endpoint tail and cancellation-aware branch combination make evaluation more effective.",
      "paper_locations": [
        "Section 4.2, equations (54)-(56)",
        "Appendix D.1-D.3"
      ],
      "precision": "This is a convergent special-function series, not a finite Gamma-only closed form. Tail acceleration is an asymptotic improvement, not a rigorous global error certificate."
    },
    {
      "topic": "Redo the large-mass expansion",
      "earlier": "The user requests amplitude, phase, Boltzmann suppression and polynomial mass powers in captured message 11. The captured response only links downloadable outputs. A separate early notes saddle attempt is audited as invalid.",
      "earlier_evidence": [
        "Captured user message 11 and assistant message 12",
        "corrections.md items 14-15",
        "J-analytical/README.md: endpoint/WKB correction record"
      ],
      "paper": "The leading physical hard contribution is an endpoint layer, not the early finite-saddle estimate. The paper obtains fixed-mixing JWKB results for C, J and CJ, including relative 1/rho corrections and the signal phase.",
      "paper_locations": [
        "Section 5, equations (57)-(60)",
        "Appendix E"
      ],
      "precision": "The expansion holds at fixed lambda as rho becomes large; its practical regime is lambda^2/rho much smaller than one. Removing Boltzmann suppression outside that regime remains a future question."
    },
    {
      "topic": "Independent numerical checks",
      "earlier": "Numerical figures and plotting code already exist in chat. The plotting reply describes coupled-mode ODE evaluation, not direct symbolic hypergeometric evaluation; the later reply also describes soft-coefficient Frobenius fits.",
      "earlier_evidence": [
        "Captured assistant messages 6 and 8",
        "Captured assistant message 10"
      ],
      "paper": "Figures 1-4 compare the analytic series, independent finite-cutoff double integration and JWKB on the same parameter grid, showing the amplitudes and phases of J and CJ.",
      "paper_locations": [
        "Section 5 and Figures 1-4"
      ],
      "precision": "This validates the displayed squeezed hard coefficients and signal factors; it is not a claim that every momentum shape and parameter regime has been numerically checked."
    }
  ],
  "scope": "The published calculation focuses on the squeezed bispectrum from the cubic entropy self-interaction. Trispectra, chemical potentials and mass-distribution extensions discussed in chat are not claimed as completed paper results.",
  "reproduction": "Read the preserved HTML messages and compare the cited equations in the pinned arXiv v2. No new physics calculation was run for this slide.",
  "note_authorship": "Human-authored calculation notes, per user clarification on 2026-10-11. Input and audit records confirm these are supplied notes rather than an audit of the initial GPT chat."
}