blind probe instrument

Equation

Book equation 0.8.

\[g_j\;\approx\;\frac{C(x+h\,e_j)-C(x-h\,e_j)}{2h},\qquad j=1,\dots,d.\]

Conditions

• The probe recovers the read operator at one operating point from calls to the consumer alone, two calls per input dimension for a central difference.
• Its budget law is a theorem for subspace-confined designs at an operating point, which is what its per-point estimators are, and does not cover allocations of calls across many operating points.
• The probe refuses when samples do not exceed the dimension and warns below a stated margin, since the identifiability miss of chapter 2 came from reading it past that point.

Conditions are curated in entries.toml rather than read from a record.

Ledger

• measures. GO-B-Llama [predicted]. Trained frontier LLM (Llama-3.2-3B), softmax-attention consumer — blind probe on real post-RoPE keys geometric-observation/claims/LEDGER.md:115.
• measures. GO-EC-3 [predicted]. A read operator recovered from a black-box consumer by query-only finite-difference probing, composed with the Kalman covariance as tr(P̂_C Σ), prospectively selects sensors that improve the held-out consumer at matched budgets with probe … geometric-observation/claims/LEDGER.md:162.
• refutes or corrects. NEG-12 [refuted]. (Gate B, prospective, real LLM) On a trained frontier attention layer the blind probe recovers the read operator above the sealed bar and projection beats reconstruction. geometric-observation/claims/LEDGER.md:105.

First stated

readscope, the blind probe as a specified instrument, PyPI readscope, readscope/PRINCIPLES.md and readscope/SPEC.md, and Volume 14 chapter 10.

Measurements

none

Failures and corrections

• NEG-12, [refuted]. (Gate B, prospective, real LLM) On a trained frontier attention layer the blind probe recovers the read operator above the sealed bar and projection beats reconstruction. geometric-observation/claims/LEDGER.md:105.
• readscope/README.md:102-116 at 856e678. What none of this changes: the budget law, in its proven scope. The cliff at k = d is a property of consumer calls, not FLOPs — a faster backend buys speed, never admission. The theorem behind it (PRINCIPLES.md, P3; OT-3) covers subspace-confined directional designs at an operating point, which is what this probe’s per-point estimators are; it does not cover every allocation of calls across many operating points, and the sketch expectation (1+1/k)·S + tr(S)/k·I shares S’s eigenspaces at every k — so whether many cheap points can average their way back to the population operator was a sample-complexity question, not a proven impossibility — and C-15 has now measured it: at equal total consumer calls, sub-dimensional budgets do not catch up, at any graded rank, within 8× the full-dimension spend (SPEC.md, C-15). The cliff is a property of total calls in the measured range; only the far asymptotic regime remains open.

Invariance envelope

none declared

Machine checked

lean/DataMiningAsObservation/ProbeCliff.lean, theorems centralDiff_affine, centralDiff_basis, exists_blind_direction, indistinguishable, budget_cliff, at observation-data-mining f3914f0; what the check covers is stated in the book’s appendix C.

Used in

Data Mining as Observation primer L, chapters 0, 1, 2, 4, 6, 7, 11, 12, 14.

Related

read operator; budget cliff; read distortion; the flip.

See also

Book equations stated beside the entry’s terms, not defining it: 0.9, 11.4.

Ledger rows that cite the entry’s records without naming it: OT-3, OT-6, GO-B-Llama-rematch, GO-B-Llama-rematch, GO-B-legal (035→036).

Sources-table rows that share a record with the entry without naming it: chapter 2 section 2.3, chapter 2 section 2.4, chapter 2 section 2.6, chapter 3 section 3.4, chapter 4 section 4.2, chapter 6 section 6.1, chapter 8 section 8.3, chapter 8 section 8.4, chapter 11 section 11.7, chapter 11 section 11.9.

Status

Generated 2026-09-10 by encyclopedia/generate.py; book at observation-data-mining f3914f0; the commit of every record is listed in the encyclopedia’s provenance.