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Read the result in its research context.

Follow the published construction into its registered claims, then explore reviewed research questions, attempts and the connections that remain open.

Established in scope

Normalization invariant matter coupling and original nonlinear source map

In the question: Recursion, hypergraphs and mirroring at the original joint source

Explicit geometric Lorentz source identities,no automatic transport into primitive Euclidean beta_new pairing. Canonical matter coefficient fixes neither the entire photon coupling nor global periods. Retain whole regulated anomaly,mass terms,pairing,reference,domain,contour and original state/time;do not integrate the same Jacobian fermions twice. Ordinary eta is not axial sea trace and gamma5 trace is not assumed zero on arbitrary APS domains. No entire quantum positivity,complete S_adm,H_tr,pos or common interacting spectrum claimed. Preserve previous results and F1 owner.

Read the exact result, assumptions and evidence

Result

The same Lorentz spin lift source fixes (c/f)^2=3*kappa_phys^2/8 and for theta=2*c*a exactly F_theta^2=2/(3*kappa_phys^2) after canonical normalization,without choosing lambda. The full auxiliary equation yields S=(2/3)dtheta-(kappa_phys^2/2)J5. Only S_hat=S+(kappa_phys^2/2)J5 is locally a gradient; the original Hodge field map explicitly needs the matter current. The finite triangular shift has unit Berezinian while full weights,auxiliary sources and contacts are transported. P25-L:196-205 explicitly calls its photon term a Fujikawa Jacobian;L218 has a factor two conflict under its own phase definition. Reinterpreting it as an independent bare term would change the original source.

Required assumptions

  • Do not identify source types

    Observable algebra, OS reflection, state, collar operator, time evolution, carrier connection, family holonomy, and readout are distinct data until an original map relates them.

  • Actual historical axial action with its own conventions

    P25-L explicitly uses torsionless hats,signature(+---),dimensionless a and kappa=mu*kappa_phys,K=epsilon S/2,and its complete algebraic S terms. Evaluate that supplied historical action only,no whole current primitive Sadm identity. Classical a/Maxwell positivity only on supplied fixed background with constant real nonzero coefficients and actual Gauss reduction. Quantum elimination retains full reference,boundary,contour and prefactors.

  • Explicit Lorentz geometric spin lift with actual matter pairing

    The geometric step uses P25 signature (+---),K=epsilon*S/2,and ordinary minimal Spin(1,3) lift of the metric-compatible connection. Define axial matter source by actual fermionic variation with its Dirac/Majorana prefactors. No automatic identity with present Euclidean Spin4 chart or beta_new,or selection of this lift from all primitive TFPT principles.

  • Actual earliest trace ansatz and complete later axial action

    J25-TRACE supplies d^[m(phi*g^n]r), J25-CURRENT the quoted local current. P25-L supplies K=epsilon*S/2, its auxiliary equation, epsilon_lower0123=+1, dimensionless phase and C=epsilon*A*F. The original field maps and local action are evaluated in their actual scope; no new physical model is chosen.

Original evidence

finding:hist20261103n-normalization-invariant-nonlinear-source-map