Prediction Timing — A Priori vs Post-Diction

The first question any honest reader should ask of a zero-parameter theory with 67 numerical agreements is: are these predictions a priori, or are they post-dictions of already-known data dressed up as derivations? This page answers that question directly, while separating internal program status from formal verification and external acceptance.

Precision-tier taxonomy (Tier A / B / C)

Timing is not the only axis along which the 67 predictions sort. Each also carries a cascade precision tier in the Calibration Cascade that states the best precision its calibration route can reach in principle:

• Tier A (~0.025 ppm) — mass-ratio route. Predictions that are dimensionless ratios (leptons, hadron mass ratios, Koide-style relations) where SI-calibration error cancels exactly. Testable today at PDG/CODATA precision — no future experiment required.
• Tier B (~3 ppm) — closing-identity route. SI-anchored observables routed through the G–α closing identity (V.T20). Testable at ~ppm precision; most need specific future experiments (PSI muonic-atom campaigns ~2030, PDG-grade electroweak updates).
• Tier C (~0.8%) — fine-structure leading-order route. Leading-order α-derived or structural/binary predictions (proton stability, no SUSY, r = ι_τ⁴). Testable only by the specific named experiments (CMB-S4 2028–2035, Hyper-K, JUNO/DUNE, LEGEND/nEXO).

The key timing consequence: Tier A predictions are already testable at the framework’s full claimed precision, and many are the retro-consistency post-dictions in Category A below. Tier B and Tier C predictions depend on specific future experiments on explicit timelines (see Category C).

The structural claim vs the historical claim

Two distinct readings of “a priori” operate in physics:

1. Structural a priori — a prediction is structurally a priori if it is forced by the framework’s kernel without any free parameter tuned to the target observation. In this reading, the Numerical Prediction Catalogue records are a priori in claim shape: they flow algebraically from the single constant ι_τ = 2/(π+e), which is itself structurally fixed by the seven kernel axioms (see Is ι_τ forced or fitted?), not chosen to match any experiment.

2. Historical a priori — a prediction is historically a priori if it was published before the experimental value was known. In this reading, the prediction records fall into three genuinely different categories depending on whether the target measurement pre-existed the derivation or post-dates it.

The first reading is what the framework claims. The second reading is the honest journalistic fact and deserves its own accounting. This page provides that accounting.

Three categories

Category A — Pre-existing measured constants (structural a priori, historical post-diction)

These are predictions for quantities that were experimentally known before the τ-framework was developed. The τ-value is computed algebraically from ι_τ; the experimental value comes from decades of independent measurement. The agreement is non-trivial because ι_τ itself is not fitted — it is fixed by kernel structure — but the timing is post-diction-shaped: we knew what to match before we derived the derivation.

Representative examples (status confirmed internally addressed at published precision; cascade tier in brackets):

• Electron mass — τ derives m_e to 0.025 ppm agreement with the 2014 CODATA value. [Tier A — mass-ratio route]
• Fine-structure constant — τ derives α^-1 via the sector-coupling hierarchy, matching at precision tier 10-1000 ppm. [Tier C — leading-order α route]
• Koide relation — τ derives Q = 2/3 at −9 ppm agreement with the charged-lepton mass ratio. [Tier A — mass-ratio route]
• Weak mixing angle sin²θ_W — τ derives to −0.65 ppm. [Tier B — closing-identity route]
• Higgs self-coupling — τ derives to +8.0 ppm. [Tier B — closing-identity route]

Approximately 50 predictions fall into Category A. They are the framework’s retro-consistency surface: every well-known constant the framework should reproduce to publish credibly. Their explanatory weight rests on the fact that ι_τ is structurally fixed by seven axioms whose justification has nothing to do with these target values. Category A is heavy in Tier A mass-ratio entries, which means most of Category A can be re-checked today against PDG/CODATA without waiting on any new measurement.

Category B — Tension accounts (a priori commitment to a specific side of an open discrepancy)

These are predictions for quantities where competing experimental values exist and the framework commits to a specific τ-derived value that lies cleanly on one side of the current tension. The framework was published before the tension had a settled internal account; the forward commitment is real.

Representative examples (cascade tier in brackets):

• Hubble constant h — τ derives h = 2/3 + ι_τ²/17 = 0.6735 at −120 ppm from late-universe SH0ES/JWST, at +ppm-scale tension with early-universe CMB-derived values. The framework commits to the early-universe-consistent reading via orbit-depth-dependent readout. [Tier B — closing-identity route]
• W boson mass — τ derives a value that addresses the CDF II anomaly; future ATLAS/CMS confirmation is a forward test. [Tier B — closing-identity route]
• Muon g−2 — τ derives within the sector-coupled framework; the public account depends on hadronic vacuum polarization calculation evolution. [Tier B — closing-identity route]
• S₈ tension — τ places S₈ at a specific value internally addressed within the same orbit-depth framework as h. [Tier B — closing-identity route]

Approximately 10 predictions fall into Category B. These are genuinely forward-committed on live empirical questions and mostly sit at Tier B — ppm-precision achievable once the relevant experiment publishes its next-generation result.

Category C — Genuine forward predictions (decisive future tests)

These are predictions for quantities that have not yet been measured at the precision required to confirm or falsify. The framework commits to specific values; future experiments on named timelines are the tests.

Representative examples (cascade tier in brackets):

• CMB-S4 tensor-to-scalar ratio — τ predicts r = ι_τ⁴ ≈ 0.0136, falsifiable at 14σ by CMB-S4 (expected 2028–2035). This is the sharpest single falsification test of the framework’s cosmology. [Tier C — leading-order route; experiment-gated]
• Neutrinoless double-beta decay (0νββ) — τ predicts Majorana neutrinos with 0νββ at a specific half-life derived from the normal-ordering mass spectrum and C-sector zero holonomy (IV.T146). Falsifiable by confirmed non-detection at or beyond the predicted sensitivity, or by detection at a half-life inconsistent with the τ-derived value at ≥5σ. [Tier C — binary; LEGEND/nEXO/CUPID gated]
• Neutrino mass sum — τ predicts Σm_ν = 0.089 eV with normal ordering. Testable by KATRIN (near-term) and cosmological surveys (DESI, Euclid). [Tier B/C — DESI/Euclid gated]
• Proton stability — τ predicts τ_p = ∞ exactly. Any confirmed proton decay refutes the framework. [Tier C — binary; Hyper-K gated]
• No magnetic monopoles — τ predicts monopoles are structurally forbidden. Any confirmed detection refutes the framework. [Tier C — binary]
• No supersymmetry — τ predicts no superpartners at any scale. Continued LHC null results confirm; any confirmed sparticle detection refutes. [Tier C — binary]

Approximately 7 predictions are genuine Category-C forward tests. These are the ones that most directly settle the framework’s fate. The 30 predictions in the Falsification Pack (N1–N30) are Category-C or Category-B in this taxonomy. Category C is experiment-gated: unlike Tier A mass-ratio entries, these cannot be tested today — they wait on CMB-S4 (2028–2035), PSI muonic-atom campaigns (~2030), LEGEND/nEXO/CUPID (2030s), JUNO/DUNE/Hyper-K (late 2020s onward).

Summary table

Cascade tiers are defined in the Calibration Cascade: Tier A ≈ 0.025 ppm mass-ratio route, Tier B ≈ 3 ppm closing-identity route, Tier C ≈ 0.8% fine-structure leading-order or binary-structural route.

The sharpest test: CMB-S4

The single most load-bearing forward test is the CMB-S4 measurement of the tensor-to-scalar ratio r. The τ-prediction is:

r = ι_τ⁴ = (2/(π+e))⁴ ≈ 0.01363

CMB-S4 sensitivity targets r at σ(r) ≈ 0.001 over the 2028–2035 observing window. If the measured value is inconsistent with 0.01363 at ≥5σ, the τ-framework’s cosmological sector fails its principal empirical test. If the measured value is consistent, the framework clears the single sharpest discriminant that orthodox physics and τ both stake a specific prediction on.

This is the test the framework voluntarily lives or dies by.

What this ledger does NOT claim

• It does not claim per-prediction pre-registration. The prediction catalogue does not have verified out-of-sample measurement dates preceding the framework’s first-edition publication. The structural a priori claim rests on ι_τ being kernel-fixed, not on having archived predictions dated before experiments ran.
• It does not claim equal weight across categories. A Category-A agreement is evidence that ι_τ captures the relevant scale but is not a prediction in the philosopher-of-science forward-looking sense. A Category-C agreement is.
• It does not claim the categorization is exhaustive or uncontested. A phenomenologist might recategorize specific predictions; the numbers (~50/~10/~7) are structural estimates at precision-tier granularity.

What would change this ledger

Two developments would sharpen the historical-a-priori column:

1. Third-party pre-registration of the Category-C forward predictions with a public time-stamped repository (OSF, arXiv). The framework has not done this yet; it is on the engagement-lane backlog.
2. Per-prediction publication-date metadata in the prediction-catalogue data schema. Currently _data/predictions/predictions.json has no publication_date field per entry; adding it with first-edition → second-edition provenance is the minimal data uplift.

Until those land, this ledger is the honest framework-level statement.

Cross-links

• Predictions Browse — the full 67-prediction catalogue with filters
• Falsification Pack — 30 sharpest predictions against named experiments on explicit timelines
• Calibration Cascade — source, unit-context, and dependency overlay
• Numerical Prediction Supplement (PDF, 1.11 MB, 209 pp) — long-form derivation artifact
• Red-team FAQ — common skeptical questions answered honestly
• Release Manifest — pinned release state and build verification