N22 · > ★★ **House correction — PI ruling R144 (S356), landed in the note S357.** **Row 22b is no longer typed an

★★ House correction — PI ruling R144 (S356), landed in the note S357. Row 22b is no longer typed an EDGE TARGET. The Scorecard now types it a Δm² RATIO PREDICTION, asserting m₁ = 0: m₁ drops out of the ratio, so R₂² = 0.029180 is a direct, JUNO-decidable statement of Δm²₂₁/Δm²₃ₗ. Against the comparators built from the printed rows it stands at −1.44σ (JUNO, 59.1 d) and +2.67σ (NuFIT 6.1) — the two disagree in sign and both are named — and the 1σ band of the ratio holds 10 members of the declared M1 monomial menu, density 186 per unit relative width. At JUNO design reach a −2.8% miss becomes −7.73σ, so the row is a falsifier and is printed as one. m₁ = 0 is an ASSERTION of this framework, not a derivation, and d(ν) = 2 remains selected, not derived (H202). JUNO's design-reach projection is a declared external input: verify before relying on it. Every figure in this box is read from Kernels/current/s1184_sibling_density_and_juno_calendar_results.json, none typed by hand.

>

What that means for the text below, and why it is still here. Everything under this box is the note as the drafting lane wrote it and the house verified it at R77, when row 22b was an edge target — including its title, its two "EDGE TARGET, not a hit" sentences, the Scorecard cell quoted verbatim in the code block, and N22_calc.py with its stdout, which echo that same cell and print status = EDGE TARGET, not a hit. None of it is rolled. It is the record of what was said then and of what was supplied to the lane, kept under H239 exactly as R77 kept the lane's own "not s1162" label. Read the typing from this box and from the Scorecard row; the sentences below are superseded on that one point and correct on every other.

>

Found because the R144 landing was checked per-file, passed, and then failed a corpus-wide check: the Scorecard row said PREDICTION while this note, one click away, still said EDGE TARGET (queue row S356.33). Nothing in the house measured whether a Scorecard row and its own note agree; scripts/scorecard_row_note_agreement_S357.py now does.

(title as written at R77; row 22b's typing is superseded — see the R144 box above)

Row 22 is a RECORDED NEGATIVE and row 22b an EDGE TARGET, not a hit. ★ SUPERSEDED on row 22b by PI ruling R144 — it is now a Δm² ratio prediction asserting m₁ = 0. The sentence is kept as written (H239); read the typing from the box above.

Row

House correction — R77 (S327h). Row 22: +820% → +821% (0.276393 / 0.030016, rounded once; the factor 9.21 is unchanged; still the RECORDED NEGATIVE). Row 22b (R77-c): the house re-ran s1162 (Kernels/current/s1162_vus_closed_form_r2_asymmetric_audit.py) twice on 2026-09-11. Both runs are byte-identical to its filed output, with z = 1.436 / 1.789. Its lines 70–73 compute the floor error by the same first-order propagation this note uses (Δm²₂₁ at its lower error, Δm²₃ₗ at its upper error). The −1.44 / −1.79 below are therefore s1162's certified distances, reproduced by the house. The drafting lane did not have s1162, and its script's label "not s1162" is kept verbatim as written. The suite calls this "exact asymmetric errors", but the method is first-order propagation, not a profile likelihood; that wording is queued for Rev32.12 (= Rev33.0, R156). Row 22b is still an EDGE TARGET, not a hit. ★ That sentence was true at R77 and is SUPERSEDED by R144 (see the box at the head of this note); R77's words are kept verbatim, H239. The cell quoted below, and the cell the script echoes, are the text as it was supplied to the drafting lane (the Scorecard through S327g). Scorecard and Registrar are unchanged in every other respect; the sealed papers keep the earlier figure until Rev32.12 (= Rev33.0, R156).

row 22

Δm² 21 /Δm² 3l φ⁻¹/√5 theory 0.27639 experiment 0.03002 (7.537e−5 / 2.511e−3, NuFIT 6.1) deviation +820% Refuted falsified 9.21× — this is the d = 1 reading; see 22b

row 22b

m ν2 /m ν3 = R 2 (d = 2 rung) 1/(φ⁴−1); R 2 ² vs Δm² 21 /Δm² 3l theory 0.02918 experiment 0.03002 (NuFIT 6.1); m 1 =0 NO floor √ratio = 0.17325 vs R 2 = 0.17082 deviation −2.8% · d = −1.44 / −1.79 (below floor) Structural (ladder tier) EDGE TARGET, not a hit — R 2 lies below the m 1 =0 floor and equality is impossible for any m 1 ≥ 0 — i.e. a 1.4–1.8σ tension with the m 1 =0 normal-ordering floor, printed as a tension (Rev32.5); stands only with normal ordering and m 1 ≲ 1 meV; d(ν)=2 is selected, not derived (Paper 5, Rev32.2)

Row 22 is a RECORDED NEGATIVE and row 22b an EDGE TARGET, not a hit. ★ SUPERSEDED on row 22b by R144 — see the box at the head of this note. The supplied excerpts report the asymmetric-distance certificate but do not include its kernel. The optional marginal-error arithmetic below is expressly not that certificate.

Theory value

row 22

The rejected literal reading gives

Its measured-ratio comparator is 0.03002 at the displayed precision.

row 22b

The selected ladder rung is

The physical boundary comparison instead uses R_2 against the normal-ordering floor \sqrt{\Delta m_{21}^2/\Delta m_{3\ell}^2}; these two comparison coordinates must not be mixed.

Derivation chain

row 22

1. Identify the literal Jordan-adjoint mass reading as the rejected interpretation, rather than a statement about the retained mixing carrier. The supplied record names the interpretation and its failure. (Paper 5, section 2, Literal mass reading and ratio mismatch, PDF p.80).
2. Evaluate the formula quoted in the Scorecard and the supplied measured splitting ratio; the excerpt prints their mismatch and factor. The equation antecedent is not present in the shipped LaTeX window. (p5_neutrino_cp_violation.tex:110-116).
3. NOT IN SUITE — a successful physical mass attachment for this literal reading. The source explicitly retains it as the falsified row, not a repairable hit within the note. (p5_neutrino_cp_violation.tex:125-126).

row 22b

1. Use the stated resolvent family and the selected neutrino rung; the source calls the assignment selected, not derived. (p2_mass_hierarchy_resolvent_quintics.tex:83-97; p5_neutrino_cp_violation.tex:116-126).
2. Square the rung for the splitting-ratio display, but compare the unsquared rung to the stated zero-lightest-mass floor. The source says equality is impossible at the central splittings for nonnegative lightest mass. (p5_neutrino_cp_violation.tex:118-124).
3. NOT IN SUITE — in the supplied material, the executable asymmetric-distance kernel or its full joint-error prescription. Its reported certificate is not reproduced merely by matching its rounded output. (p5_neutrino_cp_violation.tex:115-124). House note (R77-c): the kernel is s1162, in the release machinery. The house re-ran it and it reproduces; see the house correction under ## Row.

Registrar sync

row 22

LIB2-134 — Carries the literal mass interpretation, the failed splitting-ratio test and the mixing-carrier boundary.

Comparator LIB2-204 / SL-01 — value 7.537e-5 (+0.094e-5/−0.100e-5) eV^2 · scheme with/without SK · edition 2026 (A1546 lined).

Comparator LIB2-205 / SL-02 — value 2.511e-3 (+0.021e-3/−0.020e-3) eV^2 · scheme with SK-ATM · edition 2026 (A1546 lined).

row 22b

LIB2-140 — Carries the selected rung, below-floor boundary and explicit non-hit status.

Comparator LIB2-204 / SL-01 — value 7.537e-5 (+0.094e-5/−0.100e-5) eV^2 · scheme with/without SK · edition 2026 (A1546 lined).

Comparator LIB2-205 / SL-02 — value 2.511e-3 (+0.021e-3/−0.020e-3) eV^2 · scheme with SK-ATM · edition 2026 (A1546 lined).

Comparator LIB2-206 / SL-03 — value 2.521e-3 (+0.026e-3/−0.018e-3) eV^2 · scheme without SK-ATM · edition 2026 (A1546 lined).

LIB2-142 concerns a separate boundary mass summary, not selection of the rung. The supplied cosmological limits are not inputs to these ratios.

Calculation

Run python3 N22_calc.py. The complete self-contained script is below. All source cells are echoed unchanged. Computed displays use decimal half-up rounding; intermediate formula values are not display-rounded. A naive asymmetric distance uses the error toward the theory unless an explicit exception or alternate audit is printed.

#!/usr/bin/env python3
"""N22 — arithmetic from D1287 supplied sources.
No network, external packages, fitting operations or shared runtime files.
Printed source cells and unrounded arithmetic are distinct outputs.
"""

import math
from decimal import Decimal, ROUND_HALF_UP, getcontext
from fractions import Fraction

getcontext().prec = 40
PHI = (1.0 + math.sqrt(5.0)) / 2.0


def shown(value, places=9, signed=False):
    """Decimal half-up display; never use display-rounded inputs implicitly."""
    value = Decimal(str(value))
    rounded = value.quantize(Decimal(1).scaleb(-places), rounding=ROUND_HALF_UP)
    return format(rounded, ("+" if signed else "") + "." + str(places) + "f")


def compare(label, theory, reference, lower=None, upper=None):
    """Naive central-value arithmetic, not a likelihood or theory-error model.

    The asymmetric denominator points from the comparator toward the theory:
    lower error below the central value; upper error above it. Any different
    printed convention is audited separately, rather than silently substituted.
    """
    theory, reference = Decimal(str(theory)), Decimal(str(reference))
    if reference == 0:
        raise ValueError("A relative deviation needs a nonzero reference.")
    offset = theory - reference
    percent = 100 * offset / reference
    print(label + ".theory = " + shown(theory))
    print(label + ".reference = " + shown(reference))
    print(label + ".signed_percent = " + shown(percent, signed=True)
          + "%; rounded = " + shown(percent, 2, True) + "%")
    if lower is None or upper is None:
        print(label + ".d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)")
        return
    side = "lower" if offset < 0 else "upper"
    uncertainty = Decimal(str(lower if offset < 0 else upper))
    if uncertainty <= 0:
        raise ValueError("The selected comparator uncertainty must be positive.")
    distance = offset / uncertainty
    print(label + ".uncertainty_used = " + str(uncertainty) + " (" + side + ")")
    print(label + ".d = " + shown(distance, signed=True)
          + "; rounded = " + shown(distance, 2, True))

def main():
    print('=== row 22 ===')
    print('Scorecard (verbatim): Δm² 21 /Δm² 3l φ⁻¹/√5 theory 0.27639 experiment 0.03002 (7.537e−5 / 2.511e−3, NuFIT 6.1) deviation +820% Refuted falsified 9.21× — this is the d = 1 reading; see 22b')
    value = PHI**(-1)/math.sqrt(5.0)
    solar, atmospheric = 7.537e-5, 2.511e-3
    ratio = solar/atmospheric
    print("solar_splitting_eV2 = " + str(solar))
    print("atmospheric_splitting_with_SK_eV2 = " + str(atmospheric))
    print("theory_at_cell_precision = " + shown(value,5))
    print("splitting_ratio = " + shown(ratio,12))
    print("comparator_at_cell_precision = " + shown(ratio,5))
    compare("literal_full_formula", value, ratio)
    compare("printed_cells", "0.27639", "0.03002")
    print("full_ratio_factor = " + shown(value/ratio,9)
          + "; rounded = " + shown(value/ratio,2))
    print("deviation_at_cell_precision = " + shown(100*(value-ratio)/ratio,0,True)+"%")
    print("d_policy = unavailable: no ratio-level uncertainty or joint likelihood supplied")
    print("status = RECORDED NEGATIVE; d=1 is a rung label, not a statistical distance")
    print()
    print('=== row 22b ===')
    print('Scorecard (verbatim): m ν2 /m ν3 = R 2 (d = 2 rung) 1/(φ⁴−1); R 2 ² vs Δm² 21 /Δm² 3l theory 0.02918 experiment 0.03002 (NuFIT 6.1); m 1 =0 NO floor √ratio = 0.17325 vs R 2 = 0.17082 deviation −2.8% · d = −1.44 / −1.79 (below floor) Structural (ladder tier) EDGE TARGET, not a hit — R 2 lies below the m 1 =0 floor and equality is impossible for any m 1 ≥ 0 — i.e. a 1.4–1.8σ tension with the m 1 =0 normal-ordering floor, printed as a tension (Rev32.5); stands only with normal ordering and m 1 ≲ 1 meV; d(ν)=2 is selected, not derived (Paper 5, Rev32.2)')
    rung = 1.0/(PHI**4-1.0)
    solar, u_solar_lower = 7.537e-5, 0.100e-5
    print("selected_rung = " + shown(rung,12))
    print("rung_at_display_precision = " + shown(rung,5))
    print("squared_rung_at_cell_precision = " + shown(rung*rung,5))
    print("solar_splitting_eV2 = " + str(solar))
    print("naive_floor_audit_assumption = independent marginal errors; first-order propagation")
    print("assumption_provenance = NOT IN SUITE; arithmetic diagnostic only, not s1162")
    for name, atmospheric, u_atm_upper in (
            ("without_SK",2.521e-3,0.026e-3),
            ("with_SK",2.511e-3,0.021e-3)):
        ratio = solar/atmospheric
        floor = math.sqrt(ratio)
        sigma = floor/2.0*math.hypot(u_solar_lower/solar,u_atm_upper/atmospheric)
        naive_d = (rung-floor)/sigma
        print(name+".atmospheric_splitting_eV2 = "+str(atmospheric))
        print(name+".solar_lower_error_eV2 = "+str(u_solar_lower))
        print(name+".atmospheric_upper_error_eV2 = "+str(u_atm_upper))
        print(name+".ratio = "+shown(ratio,12))
        print(name+".floor = "+shown(floor,12))
        print(name+".floor_at_display_precision = "+shown(floor,5))
        print(name+".naive_floor_sigma = "+shown(sigma,12))
        print(name+".naive_floor_d = "+shown(naive_d,9,True)
              +"; rounded = "+shown(naive_d,2,True))
        print(name+".squared_rung_signed_percent = "
              +shown(100*(rung*rung-ratio)/ratio,9,True)+"%"
              +"; rounded_1dp = "+shown(100*(rung*rung-ratio)/ratio,1,True)+"%")
        assert rung < floor
    print("printed_squared_cells_percent = "
          +shown(100*(Decimal('0.02918')-Decimal('0.03002'))/Decimal('0.03002'),9,True)+"%")
    print("source_floor_distances = -1.44 / -1.79 (without / with SK); reported s1162")
    print("source_conditions = normal ordering; lightest mass approximately at most 1 meV")
    print("status = EDGE TARGET, not a hit; rung assignment selected, not derived")
    print()


if __name__ == "__main__":
    main()

row 22

Actual stdout for this entry; the text blocks in entry order concatenate to N22_stdout.txt.

=== row 22 ===
Scorecard (verbatim): Δm² 21 /Δm² 3l φ⁻¹/√5 theory 0.27639 experiment 0.03002 (7.537e−5 / 2.511e−3, NuFIT 6.1) deviation +820% Refuted falsified 9.21× — this is the d = 1 reading; see 22b
solar_splitting_eV2 = 7.537e-05
atmospheric_splitting_with_SK_eV2 = 0.002511
theory_at_cell_precision = 0.27639
splitting_ratio = 0.030015929908
comparator_at_cell_precision = 0.03002
literal_full_formula.theory = 0.276393202
literal_full_formula.reference = 0.030015930
literal_full_formula.signed_percent = +820.821720645%; rounded = +820.82%
literal_full_formula.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
printed_cells.theory = 0.276390000
printed_cells.reference = 0.030020000
printed_cells.signed_percent = +820.686209194%; rounded = +820.69%
printed_cells.d = NOT AVAILABLE (no uncertainty supplied for this comparison variable)
full_ratio_factor = 9.208217206; rounded = 9.21
deviation_at_cell_precision = +821%
d_policy = unavailable: no ratio-level uncertainty or joint likelihood supplied
status = RECORDED NEGATIVE; d=1 is a rung label, not a statistical distance

row 22b

Actual stdout for this entry; the text blocks in entry order concatenate to N22_stdout.txt.

=== row 22b ===
Scorecard (verbatim): m ν2 /m ν3 = R 2 (d = 2 rung) 1/(φ⁴−1); R 2 ² vs Δm² 21 /Δm² 3l theory 0.02918 experiment 0.03002 (NuFIT 6.1); m 1 =0 NO floor √ratio = 0.17325 vs R 2 = 0.17082 deviation −2.8% · d = −1.44 / −1.79 (below floor) Structural (ladder tier) EDGE TARGET, not a hit — R 2 lies below the m 1 =0 floor and equality is impossible for any m 1 ≥ 0 — i.e. a 1.4–1.8σ tension with the m 1 =0 normal-ordering floor, printed as a tension (Rev32.5); stands only with normal ordering and m 1 ≲ 1 meV; d(ν)=2 is selected, not derived (Paper 5, Rev32.2)
selected_rung = 0.170820393250
rung_at_display_precision = 0.17082
squared_rung_at_cell_precision = 0.02918
solar_splitting_eV2 = 7.537e-05
naive_floor_audit_assumption = independent marginal errors; first-order propagation
assumption_provenance = NOT IN SUITE; arithmetic diagnostic only, not s1162
without_SK.atmospheric_splitting_eV2 = 0.002521
without_SK.solar_lower_error_eV2 = 1e-06
without_SK.atmospheric_upper_error_eV2 = 2.6e-05
without_SK.ratio = 0.029896866323
without_SK.floor = 0.172907103159
without_SK.floor_at_display_precision = 0.17291
without_SK.naive_floor_sigma = 0.001452836829
without_SK.naive_floor_d = -1.436300256; rounded = -1.44
without_SK.squared_rung_signed_percent = -2.399112887%; rounded_1dp = -2.4%
with_SK.atmospheric_splitting_eV2 = 0.002511
with_SK.solar_lower_error_eV2 = 1e-06
with_SK.atmospheric_upper_error_eV2 = 2.1e-05
with_SK.ratio = 0.030015929908
with_SK.floor = 0.173251060338
with_SK.floor_at_display_precision = 0.17325
with_SK.naive_floor_sigma = 0.001358612416
with_SK.naive_floor_d = -1.789080579; rounded = -1.79
with_SK.squared_rung_signed_percent = -2.786264363%; rounded_1dp = -2.8%
printed_squared_cells_percent = -2.798134577%
source_floor_distances = -1.44 / -1.79 (without / with SK); reported s1162
source_conditions = normal ordering; lightest mass approximately at most 1 meV
status = EDGE TARGET, not a hit; rung assignment selected, not derived

Comparison

row 22

Theory 0.27639, comparator 0.03002, dimensionless, from NuFIT 6.1 NO with SK: the supplied solar and atmospheric splittings are in eV² (LIB2-204 / SL-01; LIB2-205 / SL-02). Signed deviation rounds to +821% at unit-percent precision; the printed +820% is coarser. The factor rounds to 9.21. No ratio-level uncertainty is supplied, so no statistical d is assigned.

row 22b

Use LIB2-204 / SL-01 with LIB2-206 / SL-03 without SK, or LIB2-205 / SL-02 with SK, NuFIT 6.1 NO. The with-SK squared-rung deviation rounds to −2.8%. The source reports −1.44 / −1.79 below-floor distances and retains its stated floor tension. A separately labelled independence-based marginal diagnostic matches those rounded distances, but neither establishes the source’s exact-asymmetric protocol nor a profile likelihood.

Tier and what this does not show

Literal tiers: Refuted for row 22; Structural (ladder tier) for 22b. The former is the recorded failed reading. The latter consumes a selected rung, normal ordering and the printed lightest-mass restriction; it is not a physical mass-ratio equality, a derived ordering or a new absolute mass scale.

Sources

LIB2-134; LIB2-140; LIB2-204; LIB2-205; LIB2-206; SL-01; SL-02; SL-03; Paper 5, section 2, Literal mass reading and ratio mismatch, PDF p.80; p2_mass_hierarchy_resolvent_quintics.tex:83-97; p5_neutrino_cp_violation.tex:110-126; s1104; s1162.