Falsification Pack (N1–N30)

The 30-prediction Falsification Pack identifies the sharpest points where Category τ makes specific, testable claims that named experiments can verify or refute. Each prediction carries an ID (N1–N30), a domain, a named experiment, a timeline, and a current program-side tracking status. The full card grid, filterable by domain and status, sits below.

Three falsification tiers

The Numerical Prediction Supplement (209 pp) tier-tags every N-test by the sharpness of the discriminant it offers. The public site now exposes those dependencies through the Calibration Cascade and the Numerical Prediction Catalogue. The three tiers are not categories of importance — every N-test is on the critical path — they are categories of how decisively a measurement settles the question. Different tiers demand different experimental postures and different loss conditions for the framework.

• Tier A — calibration-class precision (13 entries). N9, N10, N13, N15, N16, N17, N18, N24, N25, N26, N28, N29, N30. These predictions carry τ-derived values at approximately 0.025 ppm precision (closing identity at the calibration cascade L0 → L4 level). A single measurement falling outside the predicted window falsifies the claim at many-σ separation. N9 (r = ι_τ⁴) is the flagship: CMB-S4’s σ(r) ≈ 0.001 makes N9 decisive at roughly 14σ on the 2028–2032 window. Tier A is where τ stakes its sharpest numerical bets.
• Tier B — closing-identity precision (7 entries). N6, N11, N12, N14, N20, N21, N22. These carry τ-derived values at approximately 3 ppm precision, one rung softer than Tier A because the derivation chains through a closing identity rather than a direct L0 kernel exit. The discriminant is still a number, not a yes/no — but the decisive σ-margin is narrower and the experiment must match systematic control to the stated tolerance.
• Binary — yes/no structural falsifiers (10 entries). N1, N2, N3, N4, N5, N7, N8, N19, N23, N27. These are not precision tests but structural predictions: a single positive detection — of a fourth-generation fermion, a supersymmetric partner, a dark-matter particle, a proton decay event, an inverted neutrino hierarchy, a non-zero neutron EDM, a phantom-crossing dark-energy equation of state, a w ≠ 2 magnetic winding number, etc. — falsifies the Sector Exhaustion Theorem or the corresponding bridge axiom. Binary falsifiers cannot be partially confirmed; they either stand unbroken through the 2025–2035 window or the framework revises.

Why the tier matters for reading the pack. Tier A predictions are the ones journalists and funding panels should watch: they settle quickly once the relevant campaign publishes. Tier B predictions are where the framework carries the most model-risk from its own calibration assumptions — a Tier B failure is informative about the closing identity itself, not just the sector. Binary predictions are the slowest-moving but most lethal discriminants: one confirmed SUSY partner or one confirmed dark-matter interaction refutes the bridge axiom regardless of how many Tier A tests pass.

What the pack rests on — the experimental programs

Every N-test names real hardware on a public timeline. The falsification pack is not hypothetical: it rides on the same observational and laboratory programs that the mainstream communities are running anyway. The main campaigns the pack depends on are:

• CMB and inflation — BICEP Array, CMB-S4, LiteBIRD, Planck legacy reanalyses (N9–N12, N14–N16, N19)
• Large-scale structure and dark-sector cosmology — DESI, Euclid, Vera C. Rubin Observatory/LSST (N6, N13, N17, N23, N25)
• Direct dark-matter detection — LZ, XLZD, PandaX, XENONnT, DARWIN, ADMX (N3)
• Neutrino physics — JUNO, DUNE, Hyper-Kamiokande, KATRIN, Project 8, nEXO, LEGEND, CUPID, KamLAND-Zen (N5–N8)
• Collider and precision particle physics — LHC Run 3+, FCC, CEPC, muon g−2 at Fermilab, nEDM and n2EDM at PSI (N1, N2, N4)
• Gravitational-wave astronomy — LIGO/Virgo/KAGRA, LISA, Einstein Telescope (N20, N24, N26)
• Black-hole imaging and timing — Event Horizon Telescope and next-generation ngEHT, pulsar timing arrays (N18, N22)

If any one of these programs returns a result incompatible with τ’s derived number at ≥5σ, the corresponding prediction is falsified. See the card grid below for the full mapping of each N-test to its responsible experiment, timeline, and current observational status.

The sharpest seam — N9 at CMB-S4

The flagship discriminant is N9: τ predicts a tensor-to-scalar ratio r = ι_τ⁴ ≈ 0.01363, where ι_τ = 2/(π+e) is the master constant. CMB-S4’s design sensitivity σ(r) ≈ 0.001 implies that, if the measured value is inconsistent with 0.01363, the discrepancy will register at roughly 14σ. This figure is τ’s internal projection (scope: τ-effective) from the published experiment-design target — not an experimental consensus figure, and not a claim CMB-S4 has made on τ’s behalf. It is the statistical headroom the framework is voluntarily staking itself on.

A companion seam is N10 (spectral index n_s = 1 − 2/57), which CMB-S4 and LiteBIRD jointly constrain on the same 2028–2032 observing window.

What happens if one falsifies

The pack is designed so that individual failures are sector-specific, not framework-terminal. A single falsified prediction impairs the τ-derivation for that specific sector and forces revision of the sector’s bridge claim — the scope-label for that prediction would move from τ-effective to contradicted, and the connected field briefing (e.g., Particle Physics or Cosmology) would carry the updated verdict.

The framework-terminal scenarios are two:

1. Cascade failure — three or more independent falsifications across different domains would falsify the master constant ι_τ itself, because the 67 zero-parameter agreements in the Numerical Prediction Catalogue descend algebraically from the same kernel. A broad cluster of failures cannot be localized to a single sector.
2. Structural impossibility — a confirmed detection of proton decay (N8), supersymmetric partners (N2), a magnetic monopole, a fourth-generation fermion (N1), or a dark-matter particle (N3) falsifies the Sector Exhaustion Theorem on which the τ ontology closes. Any one of these is sufficient to refute the bridge axiom.

This posture is deliberate. The framework publishes 30 named tests and voluntarily accepts that the cumulative structure is more fragile than any of its individual pieces. For the honest a-priori vs post-diction accounting of how these tests sit against the wider 67-prediction ledger — and for the taxonomy of retro-consistency, tension-account, and forward-test categories — see the Prediction Timing Ledger.

How to read a falsification card

Each card below carries:

• N-ID (N1–N30) and domain tag (particle physics, CMB/inflation, dark sector, collective dynamics, BBN, black holes)
• Tier — A (calibration-class, ~0.025 ppm), B (closing-identity, ~3 ppm), or binary (yes/no structural falsifier); see the three-tier explanation above for what each tier commits the framework to
• Named experiment(s) responsible for the test, with a 2025–2035 timeline (plus or minus — some extend through 2040+)
• Current status — internally matched to current public data (program-side match to an existing public measurement), consistent with current public data (present data does not break the τ-derived value; decisive test awaits the named experiment), or committed test path (published commitment, not yet live). These are program tracking labels, not external acceptance labels.
• Scope label — pack entries are τ-effective unless the card states otherwise (quantitative τ-derivation with a measurable discriminant); a small number carry conjectural flags where the derivation requires an axiom still in compute-then-axiomatize status (see Scope Labels)

The complete typeset document (209 pp) with full derivations, tables, experimental timelines, and falsification logic per test is available as a free download: Numerical Prediction Supplement (PDF, 1.11 MB).