Residual frontier exhaustion boundary
Date: 26 October 2026
Status: current-input corpus-ready finite work exhausted; dated saturation is governed separately by the release certificate
Machine authority: residual frontier boundary
Verifier: residual boundary verifier
The honest result
The corpus has reached a current-input computational exhaustion boundary, not the end of the science. The maintained register contains 55 topics: nine are closed and 46 are not. The full-corpus census assigns every explicit gate-bearing source to an owner, and the residual register assigns every nonclosed topic to one of five reasons it cannot be closed by another self-contained repository calculation. No topic is left in an unnamed “perhaps more algebra” bucket.
The controlling endpoint is the corpus completion exit contract. It additionally requires systematic physics–mathematics adjacency generation, terminal-neighbourhood sweeps, experiment-grade three-layer go/no-go programmes, theory and literature audits, implication propagation, narrative and retrieval closure, and an adversarial reproducible release. This document proves one milestone under that contract; it is not itself a completion certificate and must be regenerated whenever the topic universe changes.
The admission rule is deliberately strict. A corpus-ready finite task must already have a named carrier, all required source inputs, a bounded computation or proof, an independent verifier and a stopping rule. None of the 46 nonclosed topics currently satisfies all five without making a new physical or mathematical choice, acquiring an external record, or executing a declared public-data analysis. That does not mean no further thinking is possible. It means more calculation would cease to be evidence unless the missing choice were declared and sourced first.
The shape of what remains
| Boundary | Topics | What reopens it |
|---|---|---|
| Physical experiment, public-data analysis or calibrated hardware | 20 | a fabricated carrier or released dataset, independently calibrated controls, measured records and covariance |
| Compute scale or unreleased source | 3 | provisioned many-body compute or the named public source artifacts |
| Model, action or cross-grade construction | 18 | a sourced carrier/action/process/map that removes the present freedom before calculation |
| Blocked open problem | 2 | a genuine theorem or ultraviolet control, not a larger finite scan |
| Continuing governance | 3 | new corpus material requiring recensus, disorder audit or complexity accounting |
This decomposition is the practical shape of the admissibility zone. The filled region contains exact identities, finite verified models, no-go results, detector designs and several bench-ready protocols. Its edge is not one smooth curve. It is a set of differently typed boundaries: some are waiting for an instrument, some for compute, some for a physical action, and some for mathematics not presently known.
Where to look now
The nearest engineering arms are already concrete: the four-resonator quotient-scar bench; the projector-return and selector platforms; the scheduler-qualified seven/eight-qubit OPH record-law emulator; and the same-film causal tensor programme that must precede a no-refit Casimir prediction. The public-data arms now include AZ-143's thorium-229 release audit and shared-parent factorization and AZ-144's GW250114 Kerr posterior-predictive test. The microscopic capture lane is also sharply placed: AZ-122 shows that a normalized SSH packet plus coherent acoustic modes gives a stable sub-percent capture benchmark, but a material prediction begins only after bond derivatives, masses and springs are measured or independently calculated.
The nearest theory arms are equally specific. The hydrodynamic lane needs a nonlinear dynamical-KMS source theory rather than another positive matrix. The screened-energy lane needs an explicit polarizable carrier whose elimination reproduces the audited kernel. The ALP lane needs one gauge-complete physical helicity likelihood rather than more coordinate counting. The lattice/Moonshine lane needs a cross-grade operator or genus-two twined sewing, and the exceptional lane needs an action and stable vacuum before its dimension matches can become physics.
Implication
The hopeful statement is now operational: look here, with this missing thing. A successful result may yield a better engineered selector, detector, capture channel, transport definition or no-refit force prediction. A failed result is also useful because each branch has a kill test and a typed fallback. New physics is not promised by the map. It becomes plausible only where a conventional, fully sourced model fails after the named detector and nuisance controls have closed.
The stopping rule is therefore part of the result. Until a reopening datum arrives, autonomous elaboration should not promote these branches. It should maintain provenance, improve access and prepare the exact experiment or calculation that the datum will make admissible.