# 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](residual_frontier_exhaustion_boundary_v1.json)

**Verifier:** [residual boundary verifier](../../../verification/frontier-physics-targets/verify_residual_frontier_exhaustion_boundary.mjs)

## 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](corpus_completion_exit_criteria_v1.md). 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.