The ledger
Every ledger row an entry cites, printed once in full from geometric-observation's claims ledger, with the entries it bears on.
OT-7 [demonstrated]
The damage form, trace pairing, rank, and loading covariance are GL(d)-invariant under `P' = A⁻ᵀPA⁻¹`, while spectrum, effective rank, principal angles, and water-filling are O(d)-only — consumer-weighted damage is a geometric scalar, and P3's cliff cannot be bought down by reparameterization. LEDGER.md:30
Entries: commit hash; concentrated; covariance matrix; distortion; effective rank; eigenvalue, eigenvector; hash; Jacobian; kernel; observer; orthogonal; outer product; positive semidefinite; preregistration; rank; read operator; sealed; spectrum; trace; variance.
OT-3 [demonstrated]
Under subspace-confined second-order transcripts, fewer than d directions cannot identify a hidden leading eigenspace (theorem, adaptive to d−2 / oblivious to d−1); a known k₀-dim exclusion moves the cliff to exactly d−k₀ and never softens it. LEDGER.md:31
Entries: blind probe; budget; budget cliff; operating point; read subspace.
OT-2 [predicted]
Loading is a covariance, not a distance: reading error under a change of measure is priced by ε·‖E[h·A]‖ — predicted from the base measure alone — and a full-magnitude shift orthogonal to the operator's variation does nothing. LEDGER.md:33
Entries: covariance matrix; trace.
OT-6 [predicted]
The laws transfer outside compression with zero modification: blind-recovered P_C of a ranking consumer over embeddings; equal-Euclidean-energy perturbations; the trace picks the ranking-destroyer. LEDGER.md:35
Entries: blind probe.
OT-4 [refuted]
Operator drift predicts a real long-generation degradation and a derived refresh intervention moves it. LEDGER.md:36
Entries: block error rate; coherence time; deployment mismatch; drift; floor, ceiling; freshness; null model; refresh floor; refresh interval; teacher forcing.
OT-10 []
The noisy cliff: noise floors accuracy at a derived level; the cliff's location never moves. LEDGER.md:45
Entries: budget cliff.
OT-11 [void]
Feedback-free staleness: streaming-retrieval damage tracks measured drift; derived-cadence re-allocation removes it. LEDGER.md:48
Entries: bar; block error rate; cache; cold, warm; declaration; drift; footprint; freshness; harness; lag; ledger class; licensed, not licensed; posited versus measured; refresh floor; replica; retrieval-augmented pipeline; sealed.
GO-1 [predicted]
The consumer's invariant/nuisance split is identifiable ex ante from the consumer functional. LEDGER.md:62
Entries: attribution; classifier; consumer; decision boundary; decision tree; explained variance; finite difference; linear classifier; logistic regression; nuisance; observer; planted; principal component analysis; projection; quotient; rank; read direction; read operator; registered.
GO-2 (neg. half: not reconstruction) [demonstrated]
At matched bits, downstream preservation is not controlled by reconstruction error. LEDGER.md:63
Entries: anisotropic; anti arm; distortion; the flip; identity reader; isotropic; ledger class; licensed, not licensed; matched bits; output metric; preregistration; quantization; reconstruction error; whitening.
GO-2 (pos. half: consumer-projected covariance *controls*) [replicated]
Downstream preservation is controlled by the error covariance projected on the consumer's read subspace, tr(P_C·Σ_δ). LEDGER.md:64
Entries: the flip; matched bits; output metric; read direction; read distortion.
GO-3 [demonstrated]
The certificate's vacuity threshold predicts where single-stage retrieval dies. LEDGER.md:65
Entries: certificate; Gaussian; geodesic distance; graph; intrinsic dimension; inverted file; k-means; manifold; margin; rank certificate; recognizer; refusal; registered; Spearman correlation; spectral clustering; spectrum; sum of squared errors; sweep; template match; vacuity threshold; validity index; verdict; Weyl's law.
GO-4 [replicated]
Fixed-budget verdicts invert under budget-matched observation, per the wavelength mechanism. LEDGER.md:66
Entries: alignment; allocation; bit; budget; capacity; coupling null; the flip; operating point; sweep; truncation.
GO-5 [refuted]
An α=1 density/hubness quotient restores invariant fidelity in ≥1 non-spectral domain. LEDGER.md:67
GO-6 [demonstrated]
At matched rate, output coding ≤ surrogate ≤ reconstruction on the consumer metric; the output–reconstruction gap is governed by the $\ker P_C$ entropy share, and the surrogate–output gap vanishes as rate grows. LEDGER.md:68
Entries: allocation; control; distortion; kernel; principal component analysis; reconstruction error; surrogate.
GO-7 [replicated]
A stored description's description rate and its conditional Landauer reset content are operationally separate resources: the same finite-$n$ code index needing $\hat R\approx0.67$ bits/symbol to describe is fully recoverable from retained side information at bin rate $0.26=0.39\hat R$, fails increasingly below its conditional content, and fails absolutely (err 1.00 at every bin rate) without $S$. LEDGER.md:69
Entries: bit; codebook; Landauer's principle; nat.
GO-8 [replicated]
On two independent source families (binary Markov; Gaussian AR(1)), a fixed stored record's operational reset threshold rises with the age of the retained side information exactly as the staleness–work complement prices it: same record, same bins, same decoder — the decodable bin rate climbs $0.10\to0.55$ bits/symbol across ages 0–64 of a $p=0.05$ Markov chain, tracking $R_c-1+h_2(\hat d \ast q_t)$ within one grid step at every age, and a fixed bin rate flips from 1% error (age 0) to 100% (age 32). LEDGER.md:71
Entries: Gaussian; Landauer's principle.
GO-9 [replicated]
Coordinated reset is operationally cheaper than independent reset by the records' shared-structure information: with two consumer records sharing a component, recovering either record's bin residual with the *other record intact* lowers the decodable threshold by $\mathrm{gap}_{TC}=1-h_2(\hat d \ast \hat d)$ (measured 0.60 and 0.45 vs 0.476 predicted) — including on the record whose own reset side information is useless; mismatched pairing saves nothing. Held on two independent source families (binary; Gaussian). LEDGER.md:73
Entries: Landauer's principle.
GO-12 [predicted]
The dynamic region's opening control — staleness is access width, not delay: with full context-path access, pure-delay aging is information-free (the recoding identity $(Y,V,S^{(\Delta)})\overset d=(Y,V,P^\Delta S^{(0)})$ makes every $\sigma(S)$-measurable conditional functional exactly $\Delta$-invariant; circulant-exact, $O(1/n)$ edge leakage on finite windows); with time-local slice access the tax is GO-11's static quadratic with the substitution set by the \emph{encoder's} access — single-letter $(Y_t,V_t)$ records at $(\rho,\ s/a^{2\Delta})$, context-epoch-latent records at the strictly smaller $(\rho a^\Delta,\ \tau^2)$ (gap up to $0.053$ bits) — both strictly increasing in $\Delta$ with common limit $\tfrac12\log_2(1/D)$. GO-8's age-dependence is the slice regime's operational face. Theorem 1 (the conditional-variance reduction) settles the causal-prefix eraser in the single-record setting: every observation-subset $\sigma$-algebra enters through $q_{\mathcal G}=\mathrm{Var}(V_t\mid\mathcal G)$ alone; slice/prefix/path = single-sample/Kalman-fixed-lag/noncausal-Wiener variances; strict interpolation at every finite lag with exact gap $C^{2\Delta}(P_f-q_{\mathrm{path}})$; $W(\Delta)=kT\ln2\cdot L_{\mathrm{prefix}}$ is the dynamic conditional-Landauer curve. Theorem 2-spectral (070): the spectral conditional RDF — at the work endpoint, $L(D)$ is the equal-slope allocation of per-frequency static quadratics over the circulant spectrum, with classical reverse water-filling ($\tau^2\to\infty$) and the static theorem (flat spectrum) exact; per-mode convexity proven; the third promotion of the water level completed for the single-consumer face; Toeplitz transfer scoped imported-with-lemmas, $O(1/n)$ numerics. The weighted spectral theorem (071) closes Conjecture 1 at circulant scope: $J_w$ decomposes per-frequency at every $w$, each mode carrying Theorem 3's two-water-level system $(\gamma_0(\omega),\gamma_1(\omega))$ under ONE common distortion price (the conjectured ``pair of prices'' refuted-as-phrased, rescoped to $(w,\mu)$); convexity via the full-region moment argument + perturbation. The third promotion is complete on BOTH faces. LEDGER.md:78
Entries: budget; cache; cold, warm; eviction; footprint; shard.
GO-2/GO-12/GO-13 operational (KV serving, 077) [demonstrated]
Consumer-relative access width measured on a production serving stack (Qwen2.5-7B KV-cache eviction, matched budget): task quality tracks measured predictive uncertainty u about the consumer's future reads, not nominal scorer width — the 32-query snapshot beats the 1024-query scorer +0.4375±0.070 at 5% keep (bar 0.30) and survives 97% eviction with zero drop, while wide-window scoring is statistically indistinguishable from random eviction at extreme budgets; the recency-hoarding starvation signature replicated across three disjoint prompt sets (oracle-miss gap 0.370 vs bar 0.25). The novel equal-uncertainty analytic-equality control (degradation-titrated, constructible by design) REFUTED its own equality prediction on the pre-registered branch: with calibration health 4×–130× inside gates, equal scalar u did NOT give equal quality (V4 +0.078 vs 0.0625 tolerance; the pre-registered ρ=0.03 contrast firmed to +0.359±0.068, 5.3 SE) — equal scalar uncertainty is insufficient, error structure matters, consistent with GO-13 Theorem 1's own r≥2 scoping of equal-q universality (a scalar-context privilege). Successor arc: 056 honest miss → 075 ID burned on a disclosed design failure → 077 sealed and split-verdict. LEDGER.md:81
Entries: attention; deployment mismatch; eviction; head; KV cache.
NEG-16 (KV serving, end-task) [refuted]
*At matched bits and matched reconstruction error, steering KV quantization error into the attention read subspace degrades LongBench task score by the registered floors on a deployed-class model.* Refuted at its registered effect sizes on this model and task. LEDGER.md:92
Entries: anti arm; the flip; language model.
NEG-15 (Bell boundary) [demonstrated]
*Query-conditioned hubness supplies a mechanism for Bell-inequality violation without action at a distance.* Refuted as a mechanism; the settings-as-queries reframing survives only as vocabulary. LEDGER.md:93
Entries: audit; challenge set; hubness; ledger class; null model; posited versus measured; query set.
NEG-1 [refuted]
Fixed-scale, uniform-in-m bi-Lipschitz for the commute filter. LEDGER.md:94
Entries: bi-Lipschitz; commute time; degree; density; geodesic distance; graph; Laplacian; neighbourhood graph; rank-faithful; spectral clustering; spectral embedding.
NEG-2 [refuted]
Reconstruction cosine as a proxy for key quality. LEDGER.md:95
Entries: attention; contrastive objective; control; cosine; direction-only quantizer; dot product; embedding; Euclidean distance; harness; head; KL divergence; KV cache; language model; leakage; per-channel quantizer; perplexity; quantization; query, key, value; rotary position embedding.
NEG-4 [refuted]
Lightweight online (Lloyd) key calibration beats the calibration-free default on softmax-KL. LEDGER.md:97
Entries: baseline; calibration; codebook; confound; control; early stopping; expected calibration error; harness; matched bits; perplexity; reconstruction error; ROUGE; split.
NEG-5 [refuted]
GO-P-2026-001 as registered: on KV keys, invariant-preserving (asym-NF4) beats reconstruction-optimal (per-block Lloyd) at matched bits, and tangential distortion dominates reconstruction in predicting softmax-KL. LEDGER.md:98
Entries: confound.
NEG-6 [refuted]
Relative per-channel-demeaned error norm is the quotient-tangential quantity that controls softmax-KL. LEDGER.md:99
Entries: confound; nuisance; quotient.
NEG-7 [refuted]
Per-channel quantization is universally the invariant-preserving arm for softmax-key attention (a compressor property). LEDGER.md:100
Entries: nuisance.
NEG-8 [refuted]
The Var-ratio tang_qproj is a ≥0.9-Spearman rank proxy for softmax-KL under every consumer. LEDGER.md:101
Entries: softmax; Spearman correlation.
NEG-9 [refuted]
The projected-variance trace tr(P_C·Σ_δ) is a complete rank statistic for softmax-KL across all arms. LEDGER.md:102
Entries: correction; correlation; softmax; surrogate.
NEG-11 [refuted]
(GO-5, prospective ×4) The α=1 density/hubness quotient decisively and density-specifically restores invariant fidelity in a non-spectral domain. LEDGER.md:104
Entries: anti-hub; balanced accuracy; DBSCAN; density; distance concentration; hub; hubness; nearest neighbour; Poisson ceiling; query set; registered.
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. LEDGER.md:105
Entries: blind probe; planted; read subspace.
NEG-13 → resolved [missed]
(GO-P-2026-026, prospective, real LLM) Appendix-E's omission floor is a rate-irreducible downstream wall on trained Llama read operators. LEDGER.md:106
Entries: correction; floor, ceiling; nat.
NEG-14 [refuted]
(GO-P-2026-037, prospective) `a2_probe.median_unit_displacement` is a single-statistic predictor of the flip regime (unit_disp ≷ 1.0 ⇒ generic-polar-flip vs needs-blind-probe). LEDGER.md:108
Entries: abstention; aggregation; anti-hub; anti-hub recall; bar; detector; gate; hub; inverted file; min-over-strata; outlier; paired; percentile; product quantization; recall at k; refusal; rerank; Robin Hood index; sampling; seed; sensitivity; skewness; stratification; verdict.
GO-B-Llama [predicted]
Trained frontier LLM (Llama-3.2-3B), softmax-attention consumer — blind probe on real post-RoPE keys LEDGER.md:115
Entries: aggregation; blind probe; fine-tuning; Kendall correlation; paired; read subspace; recall at k; rerank; stratification.
GO-B-LOCATA [predicted]
Real microphone-array recordings (LOCATA), DOA consumer — held-out confirmation with the PolarQuant compressor LEDGER.md:117
Entries: direction-only quantizer.
GO-B-Llama-rematch [predicted]
Trained frontier LLM (Llama-3.2-3B), softmax-attention consumer — recon-matched dissociation on real post-RoPE keys LEDGER.md:118
Entries: aggregation; blind probe; fine-tuning; Kendall correlation; paired; read subspace; recall at k; rerank; stratification.
GO-B-legal (035→036) [predicted]
Legal-citation retrieval (CourtListener), cosine-ranking consumer, LaBSE embeddings — real large corpus, non-physical consumer LEDGER.md:119
Entries: anisotropic; audit; AUROC; baseline; blind probe; chunk; contrastive objective; cosine; embedding; encoder; fine-tuning; gate; latent semantic analysis; residualization; retrieval-augmented pipeline; split; TF-IDF.
GO-B-whale (038) [predicted]
Sperm-whale coda dialect (DSWP/Sharma 2024), Clan classifier — cetacean communication; promotes the exploratory (A2) verdict to a sealed flip LEDGER.md:120
Entries: anti arm; AUROC; classifier.
GO-B-blind (041) [predicted]
Blind, NON-ORACLE prospective flip on a fresh untouched domain (20 Newsgroups sci.space vs rec.autos), logistic classifier — the reviewer's decisive test: recover P_C non-oracle and commit the winning code + sign + magnitude *before* opening the test split LEDGER.md:121
Entries: anti arm.
GO-B-optim-D4 (034 · D4) [predicted]
Optimization — gradient compression, curvature (Hessian) read operator, on a REAL model (logistic regression); optional stretch LEDGER.md:122
Entries: boosting; coupling null; curvature; Hessian; logistic regression.
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 cost charged — capturing 94.6% of the known analytic optimum's gain on the positive-control arm (gate ≥ 75%) and improving 16.3% over the best consumer-agnostic policy on non-analytic consumers (gate ≥ 8%), with trace-matched ordering carried by the composition at 86.9% over 61 pairs (gate ≥ 65%). LEDGER.md:162
Entries: attribution; blind probe; consumer; contraction; importance; metric; read operator; sensitivity.