TFPT scientific source excerpt
Original repository path: experiments/theory-contracts/historical-dynamics-source-recovery-20261103/HISTORICAL-COUPLING-IDENTITY.txt
Original file SHA-256: df78e3ab6d78c6b05b4be603cbe12bf898320e0563ebab8fb5ae7bc87c7aa77e
Inclusive original lines: 1-67
Line numbers below refer to the original source.
This bounded excerpt is source evidence; it is not a new proof/checker run.
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000001 | HIST20261103K. Actual historical gravitational/electromagnetic coupling identity.
000002 | Anonymized source-specific check, not a new comparison model.
000003 | 
000004 | 1. RECOVERED ORIGINAL STATEMENT
000005 | V25-C is the original project note with raw SHA256
000006 | f2c6b3404557b0da83d6ebeae5e159ac64c6f704e96c4e98a6885298718be7d8.
000007 | Its first part calls the following two polynomials the same equation
000008 | under a change of units, explicitly suggesting alpha <-> (2*pi)*k:
000009 |  I_k(k,L)=k^3-2*c3^2*k^2-8*b1*c3^6*L,
000010 |  I_alpha(alpha,L)=alpha^3-2*c3^3*alpha^2-8*b1*c3^6*L.
000011 | Here c3=1/(8*pi), b1=41/10 and the SAME L=log(1/phi0)>0 are retained.
000012 | Its later appended explanation instead calls them different channels
000013 | of the same underlying action. These are distinct claims. Their common
000014 | origin cannot be established by treating the first rescaling claim as
000015 | an already proved physical dictionary.
000016 | 
000017 | 2. SMALLEST DECISIVE IDENTITY TEST
000018 | Allow every real nonzero constant scale s and an overall nonzero
000019 | polynomial multiplier A, more freedom than the stated s=2*pi.
000020 | To express an actual change of variable at the same fixed nonzero L,
000021 | one needs the polynomial identity
000022 |  I_alpha(s*k,L)=A*I_k(k,L).
000023 | Its difference is exactly
000024 |  (s^3-A)*k^3+(2*A*c3^2-2*c3^3*s^2)*k^2
000025 |                   +8*b1*c3^6*L*(A-1).
000026 | The nonzero constant term in k forces A=1.
000027 | The cubic coefficient then forces s=1 over the reals.
000028 | The quadratic coefficient then forces c3=1, contrary to c3=1/(8*pi).
000029 | Thus NO real nonzero constant rescaling gives this claimed identity.
000030 | This also excludes the inverse interpretation of the stated arrow.
000031 | At L=0 the constant-term argument changes; that is not the specified
000032 | phi0 in (0,1) source. Rescaling L or b1 would change the given invariant
000033 | dictionary and requires its own actual source map.
000034 | 
000035 | 3. WHAT A GENUINELY SHARED ROOT WOULD REQUIRE
000036 | Subtracting the two actual equations gives the necessary condition
000037 |  k^3-2*c3^2*k^2=alpha^3-2*c3^3*alpha^2.
000038 | This is a nonlinear relation of two different dimensionless couplings,
000039 | not the claimed units conversion. It can relate particular roots,
000040 | but it does not transport a full action, its field variations, measure,
000041 | state, physical clock or mixed response functions.
000042 | 
000043 | For orientation only, the printed k=0.00847665 gives
000044 |  2*pi*k=0.0532603627341,
000045 | whereas the familiar alpha reference is approximately 0.00729735.
000046 | The two L values inferred from those supplied reference numbers are
000047 | approximately 2.93182489 and 2.93425670, respectively. These rounded
000048 | inputs are not a new precision exclusion or a prediction. In particular
000049 | the inserted scale mu in k=mu*kappa_phys is not derived by this check.
000050 | The exact polynomial coefficient contradiction above is the verdict.
000051 | 
000052 | 4. CONSEQUENCE FOR THE REQUESTED COMMON FUNDAMENTAL SOURCE
000053 | The historical claim that the two written cubics are automatically the
000054 | same law by changing units is excluded in its precise stated scope.
000055 | The appended claim of two sectors of one action still needs that actual
000056 | action and all of its variations, rather than this false rescaling.
000057 | No replacement joint potential or fitted relation has been selected.
000058 | Two stationarity equations or matching numbers alone do not establish
000059 | the primitive S_adm, its state/time map or H_tr,pos and physical spectrum.
000060 | 
000061 | This does not reopen or invalidate later TFPT alpha root, compiler,
000062 | E8, flavor, seam, clock or whole-source results in their actual scopes.
000063 | It corrects one recovered historical identification at the point where
000064 | it was used to argue for a single fundamental action. Preserve the
000065 | normalization-invariant matter result and nonlinear field map already
000066 | derived from the supplied Lorentz spin lift; do not replace those by
000067 | the failed constant rescaling.