# Detector and frontier atlas v1

**Date:** 24 October 2026  
**Status:** canonical navigation map; detector coverage is not physical admission  
**Machine authority:** [detector/frontier register](detector_frontier_register_v1.json)  
**Open topics:** [open-topic register](open_topics_register_v1.json) and [working list](open_topics_v1.md)

## Result

The corpus currently resolves twenty distinct frontier regions with thirty-nine detector bundles. The machine register, rather than this prose count, is authoritative for status totals as bundles are added or reclassified.

The word **detector** is used operationally:

> a detector is a declared map from latent alternatives to records, together with the controls and nuisance model needed to interpret those records.

It may be a laboratory instrument, a computational observable, a mathematical certificate or—in the deepest unresolved cases—the missing action and observable dictionary itself.

## 1. The twenty frontier regions

| ID | Frontier region | Geometric shape | Present edge |
|---|---|---|---|
| FA-01 | Structural reachability | finite image in a formal carrier | well-typed environment image unknown |
| FA-02 | Representation stability | quotient fibres over presentations | global normalization theorem absent |
| FA-03 | Detector resolution | vertical refinement tower | global injectivity absent |
| FA-04 | Positivity and rank | stratified cones | physical form selection open |
| FA-05 | Orientation and phase | branched double cover | calibrated pseudoscalar channel open |
| FA-06 | Projector holonomy | loops with lifted frame transport | joint device measurement open |
| FA-07 | Dynamical selection | basins and neutral manifolds | independent physical selector open |
| FA-08 | Measurement conditioning | trajectory fibres over an ensemble map | full instrument experiment open |
| FA-09 | Thermodynamic cost | precision-speed-dissipation region | matched resource ledger open |
| FA-10 | Metastability | rate functions and escape paths | platform trajectory census open |
| FA-11 | Spectral boundaries | poles, cuts, bands and thresholds | one-carrier closure open |
| FA-12 | Material and Casimir response | causal tensor response surface | no-refit same-film closure open |
| FA-13 | Transport rank | positive matrix spectral cone | low-frequency thermodynamic rank open |
| FA-14 | Defects and topology | discrete index sectors with fibres | transported data beyond index open |
| FA-15 | Disorder, causality and scale | robustness tubes | joint scaling and stable invariants open |
| FA-16 | Arithmetic and codes | discrete islands and cliffs | new source-derived form/functor open |
| FA-17 | Operator translation | broken arrows between charts | physical intertwiner absent |
| FA-18 | Consistency and continuum | allowed regions and uniform limits | new bound or uniform theorem absent |
| FA-19 | Flavour, gravity and cosmology | joined likelihood manifolds | common action and scale map absent |
| FA-20 | Exceptional unification | candidate global assembly | complete physical theory absent |

These regions are not mutually exclusive. A single experiment can cross several boundaries—for example, projector tomography can probe positivity, orientation, holonomy and selection—but it must report which coordinate each record actually measures.

## 2. Actual detector stack

### Computational structure detectors

- **DET-001 — kernel elaboration and canonicalization:** records elaboration, type, normalized expression and presentation mobility.
- **DET-002 — Monster constructor-shape address:** records capped constructor counts, prime address and overflow scars.
- **DET-003 — adaptive syntax-scar ladder:** adds labels, local roles, rooted depth and corpus-relative separation depth.

These detectors map FA-01 through FA-03. They are exact within the pinned computational policy and have no direct claim to physical observability.

### Geometry, holonomy and selection detectors

- **DET-004 — projector and mode tomography:** reconstructs (P), (Y) and (operatorname{Tr}(PY)).
- **DET-005 — coherent transfer and holonomy interferometry:** reconstructs complex transfer, loop-order commutator, forward/reverse lifted phase and the coherently referenced endpoint-frame matrix. A central sign uses one-loop/two-loop parity because it is reversal-even.
- **DET-006 — complex spectral and biorthogonal tomography:** records complex eigenvalues, left/right modes and singular values.
- **DET-007 — three-record selector bundle:** records even response, odd response and branch populations on the same runs; phase-referenced four-setting tomography reconstructs the Gram-disk coordinate and separates centre, nearest-origin and boundary selected points. Wave 7.59 adds a hard limit: two-column channel volume and nearest-origin entropy can select the same point, so their principles require an additional path, intervention or cost record.
- **DET-008 — return-map identification:** estimates fixed points, basins and tangent spectral radius.
- **DET-009 — instrument and trajectory tomography:** separates conditioned trajectories from the unconditional channel.
- **DET-010 — thermodynamic resource ledger:** records heat, work, entropy production, activity, mixing time and reset cost.
- **DET-011 — rare-event recorder:** records dwell times, first passage, switching paths and full hysteretic distributions.
- **DET-039 — record-law channel and local-closure tomography:** reconstructs complete positive record instruments, their Choi blocks, fixed states and observables, peripheral/contractive spectra, information-loss kernels and schedule-dependent overlap closures. Its phase-referenced `g` and `k` probes separate laws that share every classical current record; a generic positive principal minor is retained as a false `H_2(R)` bridge control. The computational baseline is now exact: disjoint seams commute, adjacent seams retain order, and a full fixed `M_56(C)` block contains continuously many complex two-level corners but no source-canonical real Jordan slice. Hardware execution remains open.

Together these span FA-04 through FA-10. No single headline signal—endpoint return, phase, contraction or hysteresis—closes the bundle.

### Material, spectral and force detectors

- **DET-012 — full thermoelectric/Hall tensor:** jointly measures electrical, thermopower, thermoelectric, thermal and magnetic channels.
- **DET-013 — frequency, phase and lag spectroscopy:** measures complex response, poles, linewidths and relaxation. Wave 7.65 adds the minimal small-index AM/FM record: a calibrated carrier and both coherent sidebands. Power-only, one-sideband, sideband-excluding bandwidth and ringdown-only ablations are certified insufficient in that model. Wave 7.70 adds an addressed-perturbation control: a genuine pre-fold D4 star moves from two accessible modes to four when its three outer channels are unequally detuned.
- **DET-014 — hybrid avoided-crossing spectroscopy:** resolves modes, splittings, lifetimes and hybridization.
- **DET-037 — transition-operator lifetime and polarization ledger:** joins prepared initial/final sectors, the addressed tensor or multipole component, time-domain survival, partial branching, frequency-domain line shape, polarization/angular dependence, environmental reopening channels and detector acceptance. It prevents a possible destination, an allowed representation coupling, a nonzero amplitude and a measured rate from being treated as one fact. The full ledger is [AZ-127](../admissibility/admissibility_127_transition_operators_selection_rules_and_lifetime_frontier.md).
- **DET-015 — adversarial thermal-Hall bundle:** joins thermal Hall with spectra, disorder, angle and nonlinear response.
- **DET-016 — broadband optical tensor:** supplies causal diagonal/off-diagonal response and imaginary-frequency continuation.
- **DET-017 — Casimir force/torque metrology:** records force, torque, distance law, angular equilibria and switching.
- **DET-018 — surface/geometry nuisance metrology:** records Kelvin potential, roughness, domains, drift and ordinary magnetic backgrounds.

These span FA-05 and FA-11–FA-12. Their nearest complete target is a same-film causal tensor that predicts a differential Casimir observable without refitting.

### Transport and boundary detectors

- **DET-019 — particle-energy spectral block:** measures (C_{NN},C_{NE},C_{EE}), determinant and eigen-directions.
- **DET-020 — finite-(q) continuity/gauge audit:** derives currents from continuity and collides energy-density conventions.
- **DET-021 — low-frequency KPM/typicality window:** resolves where integrated rank lives in frequency.
- **DET-022 — scattering phase and Wigner–Smith delay:** measures phase, proper delays and threshold scaling.
- **DET-023 — pole, residue and localization atlas:** now executes bound/continued-sheet pole tracking, localization and a radiative toy ledger; the corrected finite-band Levinson identity remains open.
- **DET-024 — defect index and embedding response:** holds topology fixed while testing phase and response fibres.
- **DET-025 — causal spread and scrambling probes:** compares fronts, OTOCs and mixing with calibrated speed bounds.
- **DET-026 — three-scale coarse-graining audit:** measures semigroup residual and invariant survival.

These cover FA-11 and FA-13–FA-15. The immediate computational edge is the low-frequency two-current rank; the immediate model edge is the three-sector spectral-boundary Hamiltonian.

### Formal, arithmetic and statistical detectors

- **DET-027 — relation-emulator schedule:** nine path, fourteen triangle and one direct `QR-003` channel, plus the typed-path admission/rejection receipt and an opaque-signature wrapper negative control. Wave 7.72 shows why this formal detector must retain endpoint typing and ALE provenance: graph paths alone admit zero source-native scientific transformations.
- **DET-028 — arithmetic lattice and code invariants:** exact Gram, discriminant, norm, weight, distance and radical data. Wave 7.71 adds restricted logical-group order, Pauli-orbit size, forbidden-transition and leakage records, with generator removal, a universal-compiler positive control and held-out gate words. These records verify the declared finite alphabet without paying for unrestricted logical tomography.
- **DET-029 — efficient information:** nuisance-projected Fisher/Schur separation and information per calibrated cost. Wave 7.65 adds held-out modulation classification and latent-depth error, with exact power-only equivalence as a mandatory null control. Wave 7.70 requires model-containment testing before classification: the normalized G2 transfer lies exactly inside the generic two-mode family, so only the pre-fold rank jump remains discriminating.
- **DET-030 — complexity card:** preparation, sampling, detection, verification and error scaling.
- **DET-038 — three-resonator loop-parity determinant:** independently calibrates three coupling magnitudes on an open chain, closes the loop in both parity sectors and tests the exact cubic pole-product shift with a shared complex-response fit. A two-edge node-gauge flip and an open-chain run are mandatory null controls.
- **DET-036 — flavor-changing meson ALP likelihood:** binned visible and missing-energy \(B\to K^{(*)}a\) records, decay-length acceptance and a profiled \(\widetilde c_{WW}\)/current/gluon/UV-flavor information block. AZ-079 isolates a direct \(c_{WW}\) matching term, but AZ-081 shows that the published MFV source-complete kernel recombines it into \(\widetilde c_{WW}\), so this detector does not supply an independent \((A_2,c_{WW})\) row in that scope. Mass sidebands, charged/neutral and \(K/K^*\) splits, form-factor covariance and a one-coupling comparator make it a constraint and cross-scale validation arm.

These span FA-03 and FA-16–FA-18. DET-038 is the physical calibration precursor; DET-027 is sufficient for the declared emulator, not yet for a physical relation carrier.

### Missing translation-level detectors

- **DET-031 — flavour/neutrino joined likelihood.**
- **DET-032 — torsion/spin-force comparison bundle.**
- **DET-033 — cosmological joined likelihood.**
- **DET-034 — uniform continuum/mass-gap certificate.**
- **DET-035 — typed action and observable dictionary:** field content, action, representation map, anomaly ledger, scale matching, endpoint signatures, irreversible losses and a held-out prediction, checked against generic graph programmability.

These are called missing detectors because no corpus-specific model presently maps the proposed latent structure into their ordinary observables. They occupy FA-17–FA-20 and are the fundamental firewall.

## 3. Detector bundles by question

| Question | Minimum bundle |
|---|---|
| Did a projector return? | DET-004 |
| Did its coherent frame rotate? | DET-004 + DET-005 |
| Was apparent rotation differential loss? | DET-005 + DET-006 |
| Was one state dynamically selected? | DET-007 + DET-008 |
| Was selection only postselection? | DET-008 + DET-009 |
| Do identical classical histories conceal different record laws? | DET-009 + DET-039, with coherent `g`/`k` references and every outcome retained |
| Does a local fixed object glue globally? | DET-026 + DET-039, with seam-order, scheduler and overlap controls |
| What did selection cost? | DET-009 + DET-010 |
| Was persistence equilibrium or kinetic? | DET-007 + DET-011 |
| Is a long lifetime caused by a weak/closed operator channel? | DET-013 + DET-014 + DET-037 |
| Does a linewidth equal a population lifetime? | DET-013 + DET-037, with pure dephasing and detector response separated |
| Was a transverse material signal intrinsic? | DET-012–DET-015 + DET-029 |
| Did one material tensor predict Casimir? | DET-012 + DET-016–DET-018 |
| Is transport genuinely rank two? | DET-019–DET-021 |
| Is a state bound, resonant or interfacial? | DET-022 + DET-023 |
| Does a defect carry more than its index? | DET-023 + DET-024 |
| Is an invariant stable across scale/disorder? | DET-025 + DET-026 + DET-030 |
| Does the formal relation carrier reconstruct? | DET-027 + withheld channels |
| Is an exceptional arithmetic identification possible? | DET-028 plus a missing DET-035 |
| Can inherited anomaly response be separated from a direct weak operator? | W-associated kernel + DET-029 + DET-036 |
| Is new physics distinguishable? | relevant physical bundle + DET-029 + DET-035 |

## 4. Admission rule

A detector result advances a frontier only if:

1. the latent alternatives are named;
2. the forward detector map is frozen;
3. nuisance directions and control parity are declared;
4. at least one positive and one negative control are retained;
5. the detector bundle separates the leading conventional alternative;
6. the result survives held-out settings;
7. complexity and backaction are reported;
8. a residual equivalence class is retained when separation fails.

More repetitions of a detector that maps two mechanisms to the same record do not move the frontier.

## 5. Current exhaustion boundary

The inventory is exhausted at the level of detector *types* represented in the current corpus: structural, geometric, dynamical, channel/instrument, thermodynamic, material, spectral, topological, arithmetic, statistical and fundamental-translation detectors are all present. Exhaustion of the science has not been reached. The open work is to instantiate, join, calibrate and adversarially test these bundles on shared carriers. DET-039 makes the channel layer explicit: a state-space symmetry, an unread channel, a committed instrument and an accepted public record are not interchangeable. The remaining work is tracked in the open-topic register rather than inferred from this taxonomy.