A registered result in its source context
Original ledger classification: Identity [I] (exact heat-kernel arithmetic both routes + numerics) + Physical [P] (route reading + remaining shares)
Recorded statement: THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not - the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S^2 x S^2,…
Statement, assumptions and sources
Paper context: Horizon readouts
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HOR.CLOCK.10
Original ledger classification: Identity [I] (exact heat-kernel arithmetic both routes + numerics) + Physical [P] (route reading + remaining shares)
Original claim text
THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not - the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S^2 x S^2, so the temporal dS2 sector continues to the SAME unit sphere and both candidate routes are exactly computable. (1) THE REDUCED ROUTE [I]: each 2d sector carries the HOR.CLOCK.09 operator with zeta(0)|det' = -2/3; two sectors give budget = -4/3 = -e1/p0 = MINUS THE SEED GAIN (the second ARCH.TRIAD.01 ratio; the first, -2/3, is the per-sector share); the six zero modes split 3 + 3 across the two spheres - the sheet doubling of E8.GRADE.01/HOR.CLOCK.07 IS the two-sphere structure of Euclidean Nariai (= the horizon pair, HOR.NARIAI.01). (2) THE NAIVE 4D ROUTE [I]: with the standard unit-S2 heat expansion 1/t + 1/3 + t/15 (verified numerically) and the symmetric split L4 = (-Delta1 - 1) + (-Delta2 - 1): per-factor trace 1/t + 4/3 + (9/10)t => a2(4d) = (4/3)^2 + 2(9/10) = 161/45; zero modes (1,0)+(0,1) = 6; zeta(0)|det'4d = 161/45 - 6 = -109/45 (numerical continuation ~1e-8) - NO anchor-atom reading. (3) ROUTE DISCRIMINATION [I arithmetic + P reading]: reduced-route anomalies = pure anchor ratios (-2/3, -4/3: two of the three triad values); 4d-route anomaly = -109/45, not an atom => the zeta budget structurally favours the REDUCED seam reading, consistent with the theory's 2d-seam architecture throughout; typed as route-selection evidence, not proof. (4) REMAINING [P] (recorded): the graviton/ghost shares on S^2 x S^2 (Volkov-Wipf-class computation, external standard) complete the budget; both scalar-sector shares pinned exactly - the remaining work is a finite list of known heat coefficients
Original classification detail
Identity: reduced budget = -4/3 = -seed gain (per sector -2/3); 4d route = -109/45 no atom; zero modes 3+3 = horizon pair; route selection -> reduced seam reading
Dependencies as recorded
HOR.CLOCK.09; ARCH.TRIAD.01 (triad); E8.GRADE.01; HOR.NARIAI.01
Open the original ledger source, row 218Location recorded in the ledger
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- Horizon readouts
Navigation through a shared verification script
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- The closure ledger: what is done, and what genuinely remainsTFPT — Introduction and reading guide
- Honest statusinput 4 origin theory
- Honest statusorigin theory
- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- Honest statusOrigin Theory
- 2026-06-12Research changelog; TFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Honest statusinput 4 origin theory
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Registered verification modules
- v133_zeta_budget.pyRegistered verification module · registry
Read the description recorded in the module registry
THE ZETA BUDGET, BOTH ROUTES COMPUTED EXACTLY (the reduced seam route carries pure anchor-ratio anomalies; the naive 4d route does not — the budget computation structurally selects the reduced seam reading): Euclidean Nariai = S²×S², so the temporal dS₂ sector continues to the SAME unit sphere; THE REDUCED ROUTE [I]: each 2d sector carries the v132 operator with ζ(0)|det′ = −2/3; two sectors give budget = −4/3 = −e₁/p₀ = MINUS THE SEED GAIN (the second v119 triad ratio; the first, −2/3, is the per-sector share); the six zero modes split 3+3 across the two spheres — the sheet doubling IS the two-sphere structure of Euclidean Nariai (= the horizon pair, v101); THE NAIVE 4D ROUTE [I]: standard unit-S² heat expansion 1/t + 1/3 + t/15 (verified numerically), symmetric split ⇒ a₂(4d) = (4/3)² + 2·(9/10) = 161/45, six zero modes, ζ(0)|det′,4d = 161/45 − 6 = −109/45 (continuation ~1e−8) — NO anchor-atom reading; ROUTE DISCRIMINATION [I+P]: reduced-route anomalies = pure anchor ratios (two of the three triad values), 4d-route anomaly is not an atom ⇒ the ζ budget structurally favours the REDUCED seam reading, consistent with the 2d-seam architecture (route-selection evidence, not proof); remaining [P]: graviton/ghost shares on S²×S² (Volkov–Wipf class) — a finite list of known heat coefficients
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