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Excerpt/Description:
"We introduce contextual finiteness: the mechanism by which an unbounded quantity becomes strictly bounded when evaluated on a conserved partition constraint surface a + b = 1. The Thales altitude h = √(ab) is confined to [0, 1/2], and the three classical mean differentials inherit this boundedness as exact closed forms. The harmonic mean of the Dirac spinor partition, evaluated at the Schwarzschild innermost stable circular orbit with post-Newtonian velocity β² = 1/6, equals exactly 1/12 — the same constant from Ramanujan summation ζ(−1) = −1/12 and the Casimir effect — derived here in three lines from HM = β²/2 with no analytic continuation. The algebraic decomposition h⁴ = a² − 2a³ + a⁴ identifies the cubic correction −2a³ as the leading-order term at which the constraint modifies unbounded estimates, structurally parallel to the Bernoulli corrections producing −1/12 in the Euler–Maclaurin formula. An appendix shows that the coherence corridor width 7/4 − √e matches 1/π² to 0.042%, with the gap explained to 0.24% by the self-coupling cost (√2−1)·(GM−HM)²·(1/π²), built entirely from the framework's own diagnostic constants. No new physics is proposed. All results are algebraic consequences of the Pythagorean constraint, the Schwarzschild metric at the ISCO, and standard Dirac kinematics.
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Title Contextual Finiteness on the Thales Constraint Surface: Boundary-Induced Finite Values at Distinguished Orbital Points
Excerpt/Description:
"We introduce contextual finiteness: the mechanism by which an unbounded quantity becomes strictly bounded when evaluated on a conserved partition constraint surface a + b = 1. The Thales altitude h = √(ab) is confined to [0, 1/2], and the three classical mean differentials inherit this boundedness as exact closed forms. The harmonic mean of the Dirac spinor partition, evaluated at the Schwarzschild innermost stable circular orbit with post-Newtonian velocity β² = 1/6, equals exactly 1/12 — the same constant from Ramanujan summation ζ(−1) = −1/12 and the Casimir effect — derived here in three lines from HM = β²/2 with no analytic continuation. The algebraic decomposition h⁴ = a² − 2a³ + a⁴ identifies the cubic correction −2a³ as the leading-order term at which the constraint modifies unbounded estimates, structurally parallel to the Bernoulli corrections producing −1/12 in the Euler–Maclaurin formula. An appendix shows that the coherence corridor width 7/4 − √e matches 1/π² to 0.042%, with the gap explained to 0.24% by the self-coupling cost (√2−1)·(GM−HM)²·(1/π²), built entirely from the framework's own diagnostic constants. No new physics is proposed. All results are algebraic consequences of the Pythagorean constraint, the Schwarzschild metric at the ISCO, and standard Dirac kinematics.
Work type Technical Documentation
Tags black holes, casimir effect, contextual finiteness, isco, corridor width, ramanujan summation, dirac spinor, partition geometry, zeta regularization, mean differentials, bernoulli numbers, self-coupling cost, harmonic mean, constraint surface, thales theorem
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Identifier 2603154937062
Entry date Mar 15, 2026, 3:13 PM UTC
License Creative Commons Attribution 4.0
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Author. Holder Elias DeJesus. Date Mar 15, 2026.
Information available at https://www.safecreative.org/work/2603154937062-contextual-finiteness-on-the-thales-constraint-surface-boundary-induced-finite-values-at-distinguished-orbital-points
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