Detector and frontier atlas v1

Date: 24 October 2026 Status: canonical navigation map; detector coverage is not physical admission Machine authority: detector/frontier register Open topics: open-topic register and working list

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

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.
• 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

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.