A registered result in its source context
Original ledger classification: Identity [I] (model theorem + det'-clean bend + localisation) + [P] (measure identification)
Recorded statement: THE CLOCK IS A GAUSSIAN ZERO-MODE INTEGRAL AND THE BEND IS DET'-CLEAN (R1's derivation structured to its floor): (1) GAUSSIAN MODEL THEOREM - for p2 modes with per-mode variance ratio (1-alpha) (FORCED by norm = area, v131), the…
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HOR.CLOCK.13
Original ledger classification: Identity [I] (model theorem + det'-clean bend + localisation) + [P] (measure identification)
Original claim text
THE CLOCK IS A GAUSSIAN ZERO-MODE INTEGRAL AND THE BEND IS DET'-CLEAN (R1's derivation structured to its floor): (1) GAUSSIAN MODEL THEOREM - for p2 modes with per-mode variance ratio (1-alpha) (FORCED by norm = area, v131), the Born-squared partition ratio is (1-alpha)^{p2}, i.e. rate = -p2 ln(1-alpha) EXACTLY = the v124 closed form, and the ln series IS the v127 ring sum term by term: the 'one-loop = ring sum' job discharged at the Gaussian-zero-mode-model level; (2) THE BEND IS DET'-CLEAN - weights n = 1,2 are bookkeeping levels of ONE Euclidean geometry (Nariai S2 x S2, v101), so det'_1 = det'_2 IDENTICALLY and the bend log_{3/2}3 (v107 target) carries NO determinant correction; (3) the single across-topology step is the alpha = 0 reference (round dS vs Nariai), where the v132/v133 budgets and the v144 6->14/3 obstruction live - the quantum content is clean, the classical side of the reference is matched (v126 slope 2 = |Z2|); (4) kappa_seam = 1/(3pi) = alpha_1/pi re-pinned. RESIDUE [P]: the measure identification (gravitational zero-mode measure = this Gaussian model) + the reference normalisation only
Original classification detail
Identity [I]: ring sum = Gaussian zero-mode integral; bend det'-clean; residue = measure + reference
Dependencies as recorded
HOR.CLOCK.12; HOR.CLOCK.07; HOR.CLOCK.08; v101; v126; v127; v131
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- 2026-06-12 (R1–R5 second round: every class at its floor, v145– v148)Research changelog; TFPT — Introduction and reading guide
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- The hard reduction: the live residual as typed interfacesTFPT — Introduction and reading guide
- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
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Registered verification modules
- v147_clock_gaussian.pyRegistered verification module · registry
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clock = Gaussian zero-mode integral (R1): variance ratio (1−α) (norm=area, v131) ⇒ Born² Γ-ratio (1−α)^{p₂}, rate = −p₂ln(1−α) = the v127 ring sum term by term; the BEND log_{3/2}3 lives between the two Nariai levels of ONE geometry ⇒ det′-clean; obstruction localised to the α=0 reference
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