Standart Model Sabitleri İçin Nümerolojik Arama Kapsamlı Bir Şekilde Başarısız Oldu

Özet (abstract)

WHAT WAS ATTEMPTED, PLAINLY. A modified-inertia gravity framework fixes its acceleration scale to the cosmological constant, a0 = cH_Lambda/Z with Z = sqrt(32pi/3) = 5.78881, and in doing so supplies exactly two dimensionless germs: the generation count 3 and the kernel germ sqrt(8pi/3). The attempt was to find out whether those same two germs also generate any dimensionless constant of the Standard Model -- whether the coefficient that works for gravity extends to the mass and coupling sector. Expressions were built by constructive enumeration (a base leaf plus D-4 steps from a fixed 30-entry menu), value-identical expressions deduplicated at mpmath precision, and every distinct value confronted with 19 measured dimensionless SM targets spanning eleven orders of magnitude in relative precision, through three gates. THE ATTEMPT FAILED, EXHAUSTIVELY, AND THAT RESULT STANDS. 174,890,804 raw candidates; 42,534,139 distinct values (33,309,838 float64-distinguishable); 82,613 in-window hits; ZERO surviving the gate; ZERO re-labelings. Depths 3-9 were already exhaustive clean nulls, so the range 3-10 is PROVEN EMPTY rather than unexamined, and the depth sets are nested. This null is untouched by every correction below, because gate/fdr.py never uses the enumeration multiplicity at all: its look-elsewhere multiplier is n_targets_searched and its E_chance comes from a 25-germ mini-library. THE INFORMATIVE RESULT IS WHERE THE HITS LAND. Hit count tracks measurement-window width and nothing else. The six most precisely measured targets return EXACTLY ZERO hits across 42.5 million values; the loosely measured PMNS angles return 15,212 / 26,142 / 20,799. Re-measured off the committed arrays, hits/2w is flat at rho ~ 3e5 across five decades of window width over all 19 targets. THIS IS VERSION 2, AND IT CORRECTS FIVE LOAD-BEARING CLAIMS OF THE UNPUBLISHED v1 DRAFT, TWO OF WHICH WERE FALSE. (1) WITHDRAWN AS FALSE -- the search has NO VALID HELD-BACK VALIDATION SET. v1 claimed two targets were held back so a survivor would have to PREDICT them. Both are exact algebraic functions of targets the search IS allowed to fit: r_tau_mu = r_tau_e/r_mu_e exactly, and koide_Q_lep = (1+A+B)/(1+sqrtA+sqrtB)^2 with A=r_mu_e, B=r_tau_e. Measured: full-pool span residuals 1.686e-10 and 3.300e-10 (spanned), fitted exponents (-1.0000,+1.0000), transfer gain EXACTLY 1.000000 sigma per input sigma, conditional information 0.0000 bits; the repo's own score_holdout returns passes_2sigma=True from a pool prediction. This is ALGEBRAIC, so it survives a perfect name-based guard. Worse, the target v1 called the stronger test is unscoreable: r_tau_mu has ZERO retained records. General trap: any holdout reachable from the fitted pool by the search's own operations (MUL, DIV, SQRT are all in the menu) is free. (2) WITHDRAWN AS FALSE -- 'forced' is not enforced. On the enumerated path Gate B is a CONSTRUCTIVE TAUTOLOGY: the germ layer emits both forced germs plus exactly one free germ by construction, so no enumerated candidate can fail the germ-content test (the gate is correct against germ ABSENCE when probed directly, 9/9 unit probes, it simply never binds on-path). Separately, a germ whose net signed exponent is zero -- multiplied then divided, i.e. algebraically cancelled and NOT load-bearing -- still counts as present. The honest claim is weaker: the enumeration is RESTRICTED to a germ-decorated vocabulary by construction, which bounds the space and makes the null exhaustive, but does not certify that a survivor would have used the germs essentially. (3) THE DEPTH-CEILING FORMULA WAS WRONG IN BOTH PARAMETERS, though its qualitative claim survives. B = 30 is the literal step-MENU LENGTH -- the enumerator's work, not its yield: after the dimensionless/finite/positive filter the b_s=6 layer collapses from 8.019e9 sequences to 22,708 skeletons and the germ layer multiplies back only polynomially. The REALIZED per-depth factor is 4.41 on distinct values (3.82 on local density), i.e. 1.94-2.14 bits/depth, NOT log2(30)=4.91; 30^(D-4) over-counts by 17x at D10 and 7.9e7x at D18. D0 = 4 is unfoundable: budget_splits(4) is EMPTY, so N(4)=0 and depth 4 cannot be built (first non-empty depth is 5). The look-elsewhere count must be DISTINCT VALUES not raw candidates (value-identical expressions hit or miss together; verified by re-enumerating depth 6 with multiplicity: raw 236,624, distinct 107,719, hits 259 == the committed 259). And E = 1 is not an informativeness criterion but a 63% false-alarm rate; a family-wise 5% threshold over 19 targets x 8 depths gives E* = 3.3e-4. Corrected ceilings: 1/alpha D = 11.0 (published 10.4), m_p/m_e D = 10.3 on the window the code applies or 12.7 on the CODATA ratio (published 13.1). The published LEVEL survived only by cancellation of four errors; the SLOPE was wrong by 2.5x, so every slope-dependent claim is void, including 'each additional depth costs 4.9 bits'. Re-tested adversarially against the hypothesis that the conclusion reverses: it does NOT. Single-target matching still dies by ~D11-13 and depth 18 is still statistically empty (corrected chance counts at D18: 3.87 for 1/alpha, 10.6 for m_p/m_e, 3.02 for a_e), so our own depth-10-to-18 sampling campaign was empty BY CONSTRUCTION. (4) TWO WINDOW DATA ERRORS. GATE_POWER_ANALYSIS.py:41 writes 3.2e-11/1836.15 for m_p/m_e, dividing a relative uncertainty by the value a second time, where CODATA's ABSOLUTE uncertainty is 3.2e-8 -- the window was 1000x too tight, so v1's '44.7 bits for m_p/m_e' is really 30.1. m_mu/m_e carries a separate factor-10 error. Consequently v1's headline 'the two most precisely measured numbers in physics supply 76.3 bits' is really 61.7. Both are advertised-threshold errors only; the running gate reads windows from the dataset, so no committed verdict is affected. (5) THE MAIN METHODOLOGICAL CONTENT: OUR PROPOSED WAY PAST THE CEILING PRICED AN OBJECT THAT CANNOT EXIST. v1 recommended simultaneous multi-target matching with the threshold SUM_i log2(1/w_i) > log2(N(D)) + margin. That charges the look-elsewhere ONCE while crediting k targets' information, which describes ONE EXPRESSION MATCHING k CONSTANTS AT ONCE. An expression evaluates to a single number and distinct SM targets have disjoint windows, so that event has probability zero. The object the search actually retains is a SKELETON (a structural template) reaching k targets via k DIFFERENT GERM RECIPES -- verified on the committed records, never one value. So the cost is paid k times: cost(k,D) = log2(N_skel(D)) + k*log2(R_recipe(D)) against avail(k) = SUM over k INDEPENDENT targets of log2(1/2w_i). The k-linear term is what both prior readings omitted, and it is why the same data yielded k_min = 2 under one accounting and 3 under the other -- that disagreement is VOID. With the term restored k_min = 2 at depth 12, 3 at depth 15, 4 at depth 18. THE EMPIRICAL CALIBRATION IS HARSHER AND IT IS THE ONE THAT BINDS. A label-permutation null over the 78,170 assignable depth-10 records (2,651 skeletons), preserving both per-skeleton hit multiplicity and the lopsided per-target marginal, shows CHANCE ALONE puts a skeleton on 10 of 19 targets simultaneously. Real multiplicities sit BELOW the null at every k (z = -15.3 at k=2 through -0.1 at k=10); observed max k = 10 against chance max 11.0. No k up to 12 is rare enough to clear E*. So an apparent 11-target interlock in a search of this shape is NOISE, and any future interlock claim must be calibrated against this null rather than analytic bits. INTERLOCK BITS ALSO NEED AN INDEPENDENT TARGET SET. a_e and 1/alpha are effectively ONE observable -- the mass-independent QED series from alpha alone reproduces measured a_e to 2.4e-9 -- and they sit in DIFFERENT sector fields, so a sector count cannot catch it. Worked false positive: k=3 on {a_e, 1/alpha, m_p/m_e} advertises 93.8 bits, clears v1's depth-18 threshold of 78.7, and has true independent content 65.2, BELOW it. The registry holds 9 exactly-redundant pairs; within the fittable pool the worst correlation is rho(r_b_tau, r_t_b) = -0.974 through shared m_b, so the maximal independent set is 18/19. One distinction must not be blurred: for THEORY-linked pairs the look-elsewhere bits DO legitimately add, because the enumeration cannot build the QED series or RG running -- a_e/alpha is a k-COUNT error, not a bits-arithmetic error. Only ALGEBRAIC edges make a hit free. THE INTERLOCK SEARCH, RUN PROPERLY, IS ALSO A NULL -- AND THIS ONE IS VALIDATED. INTERLOCK_SEARCH.py implements the above over the 18-target independent set, calibrated by permutation null, and REFUSES to report a null until it passes controls: a planted skeleton reaching k=18 targets is recovered (p = 0.0000) and a planted skeleton at k=10, inside the chance band, is correctly NOT flagged (p = 0.815). Only then does it run. At depth 10 a claim would need k >= 13; the observed maximum is 10 against a chance maximum of 11.0, p = 1.0000. NOTHING SURVIVES. This ordering matters more than the result: v1 proposed the interlock remedy without ever demonstrating that a search built on it could recover a known interlock, and the analytic rule would have reported the k=11 coincidences already present in the data as an 85-bit discovery. WHY NOTHING WAS THERE -- FOUR STRUCTURAL OBSTRUCTIONS, each established separately and each standing without the search. (1) NUMBER FIELD: Z carries a transcendental sqrt(pi) while the flavour and coupling data are algebraic, so an exact identity requires the sqrt(pi) to cancel -- in which case the germ was not load-bearing. (2) PERIOD RING: half-integer versus integer weight with the weight-1 slot empty, the rings disjoint exactly where a bridge would live. (3) DICTIONARY/CATEGORY: u = a0/g is an acceleration RATIO while a renormalisation scale is an ENERGY; the only dimensional bridge, a0/2c with hbar and c, lands ~38 orders below the electron. (4) VARYING CONSTANTS, the one experimental closure: if any SM cons

Yazarların özeti; kaynağından alınmıştır. Open MIND, 2026 · DOI ↗