A registered result in its source context
Original ledger classification: Identity [E] (tree 3/4 + over-determination) + physical bridge [C] (the kappa^2 ansatz)
Recorded statement: GRAVITATIONAL 3/4 OVER-DETERMINATION (2026-06-15, archive integration of the old Eliminating-K note): the torsion-compression ansatz kappa^2 = xi phi0/c3^2 with the Einstein limit kappa^2=8 pi G fixes xi = 8 pi c3^2/phi0 = c3/phi0 (since 8…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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GRAV.XI.01
Original ledger classification: Identity [E] (tree 3/4 + over-determination) + physical bridge [C] (the kappa^2 ansatz)
Original claim text
GRAVITATIONAL 3/4 OVER-DETERMINATION (2026-06-15, archive integration of the old Eliminating-K note): the torsion-compression ansatz kappa^2 = xi phi0/c3^2 with the Einstein limit kappa^2=8 pi G fixes xi = 8 pi c3^2/phi0 = c3/phi0 (since 8 pi c3^2 = c3), and at tree level phi_tree=1/(6 pi) this is EXACTLY 3/4. (1) [E] tree identity xi = c3/phi_tree = (1/8pi)/(1/6pi) = 3/4. (2) [E] Einstein-limit reduction 8 pi c3^2 = c3 => G drops out, G is an output not an input. (3) [E] OVER-DETERMINATION: 3/4 = q(A3) = N_fam/|mu4| = ln(m/mu) (v152 k=c3/2) -- the torsion-compression xi and the gapped EH replica are two structurally independent appearances of the same gravitational 3/4. (4) [N] with the retained seed xi=c3/phi0=0.748303 (-0.226%). (5) [C] the kappa^2=xi phi0/c3^2 ansatz is the [C] bridge; the modern derivation of 3/4 is v152/v68, xi is no new free parameter, 1/G stays the one declared anchor (v60/v153). Wolfram-mirrored (tree identity + over-determination exact)
Original classification detail
Identity [E]: xi = c3/phi_tree = 3/4 = q(A3) = ln(m/mu) -- an independent route to the gravitational 3/4; the kappa^2=xi phi0/c3^2 ansatz is the [C] bridge, G is a metrology output, 1/G the one anchor
Dependencies as recorded
v152_norm_is_anchor.py; v68_seeley_dewitt_residual.py; v60_lambda_metrology_branch.py
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- Frontier and open physical interfaces
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- 2026-06-15 (archive integration \#5: six dormant results revived from the old papers)Research changelog; TFPT — Introduction and reading guide
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Full quantum gravity — induced from the boundary kernelFrontier and open physical interfaces
Registered verification modules
- v205_xi_threequarter.pyRegistered verification module · gravity
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ξ=c₃/φ_tree=3/4: an INDEPENDENT route to the gravitational 3/4 (archive integration of the old Eliminating-K note). The torsion-compression ansatz κ²=ξφ₀/c₃² with the Einstein limit κ²=8πG fixes ξ=8πc₃²/φ₀=c₃/φ₀ (since 8πc₃²=c₃), and at tree level φ_tree=1/(6π) this is EXACTLY 3/4. [E] tree identity ξ=c₃/φ_tree=(1/8π)/(1/6π)=3/4; [E] Einstein-limit reduction 8πc₃²=c₃ ⇒ G is an output, not an input; [E] OVER-DETERMINATION 3/4=q(A₃)=N_fam/|μ₄|=ln(m/μ) (v152 k=c₃/2) — the torsion-compression ξ and the gapped EH replica are two independent appearances of the same gravitational 3/4; [N] with the retained seed ξ=c₃/φ₀=0.748303 (−0.226% from 3/4); [C] the κ²=ξφ₀/c₃² ansatz is the [C] bridge, the modern derivation is v152/v68, 1/G stays the one anchor (v60/v153).
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