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Open problem

FPRD-C03

Joint guard–disorder law at the critical frontier

Exact statement

Determine whether the forced continuation admits an all-length joint estimate for rw≤R,δw≤B−Drw, r_w\le R,\qquad \delta_w\le B-Dr_w, strong enough to improve the leading candidate exponent, or instead construct an exact accepted-trace counterfamily showing that actual forced-suffix disorder can preserve exponential mass.

StatusOpen; marginal routes are closed and no exponent improvement is claimed
External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The exact seam and recovery calculus survives, but the remaining asymptotic question is a correlation problem. Guard capacity and fixed-weight word supply cannot be treated as independent marginals.

Definitions

  • rwr_w is the full guard residue, δw\delta_w is the deficit from maximal fixed-weight completion, and B−DrwB-Dr_w is the remaining recovery allowance.
  • A useful result must concern the actual forced suffix or an equivalent joint statistic.

Hypotheses and scope

  • Critical contracting layers of the accelerated Collatz calibration.
  • Exact guards, fixed remaining weight, and the least admissible cylinder representative are retained.

Proof or evidence

No proof is asserted. The source guide derives the marginal no-gain and forced-family obstructions, then states two honest alternatives: prove sufficient joint loss or construct an exact counterfamily for actual forced-suffix disorder.

Surviving frontier and exact alternatives →

Verification notes

The source claim ledger, latest brief, supplement, failure ledger, archived verifier, and current repository were compared. They agree that this is the restart gate and not a theorem. No later repository or Library artifact was found that closes it.

Limitations

  • The current best recorded candidate bound remains exponential.
  • A fixed factor over logarithmic blocks would not by itself improve the leading exponent unless the loss scales strongly enough.
  • No Collatz, Terras, or paradoxical-finiteness conclusion is claimed.

Open work

Analyze the actual uniquely forced suffix, not another marginal capacity envelope or a larger finite enumeration.

Notes

Marginal guard counts, unconditional disorder thresholds, universal one-step contraction, and capacity-only logarithmic-block contraction are insufficient routes. The open problem concerns the correlation generated by the actual forced suffix, not independent marginals. A fixed factor per logarithmic block would not by itself improve the leading exponent; the target needs polynomial loss per logarithmic block or fixed-factor loss on constant-size blocks. No Collatz or finiteness conclusion is currently claimed.