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Every point on the Thales partition manifold carries two natural distance measures from
the corridor floor λIR = √e: an additive (series) ruler ψadd = R−√e and a multiplicative
(parallel) ruler ψmult = ln(R/√e). These are the partition-geometry analogues of series
and parallel resistance in circuit theory. Their ratio defines a pointwise impedance mis-
match Γ(R) = |ψadd−ψmult|/(ψadd + ψmult), which vanishes at the corridor floor and grows
monotonically with R.
We test three predictions of this framework against 62 galaxies from the SPARC sample
with well-determined baryonic masses and flat rotation velocities. (i) The ratio ψadd/ψmult
should equal √einside the diagnostic corridor [√e, 7/4] — the unique fixed point of the two-
ruler geometry. Measured value: 1.647 ±0.003; predicted √e= 1.6487 (discrepancy 0.08%).
(ii) Mass-discrepancy variance should be suppressed inside the corridor relative to outside.
Measured suppression: 39×(CV 1.2% inside vs. 47% outside, p<10−4). (iii) The reflection
coefficient Γ should grow monotonically with altitude R and correlate with observational
scatter. Spearman ρ(R, Γ) = +0.847 and ρ(Γ, Mdyn/Mbar) = +0.71, both confirmed.
The series/parallel duality provides a geometric mechanism for two previously separate
results: why variance is suppressed inside the corridor regardless of channel type (homo-
geneous or heterogeneous), and why residual scatter inside the corridor is not random but
tracks the local impedance mismatch Γ(R). The corridor [√e, 7/4] is identified as the unique
interval on the Thales manifold where the additive and multiplicative rulers agree to within
the 1/12 coupling-cost margin. All results are labeled by epistemic tier.
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Title Series and Parallel Rulers on the Thales Partition Manifold: Additive–Multiplicative Duality, Impedance Mismatch, and Corridor Variance Lock in the SPARC Galaxy Sample
Every point on the Thales partition manifold carries two natural distance measures from
the corridor floor λIR = √e: an additive (series) ruler ψadd = R−√e and a multiplicative
(parallel) ruler ψmult = ln(R/√e). These are the partition-geometry analogues of series
and parallel resistance in circuit theory. Their ratio defines a pointwise impedance mis-
match Γ(R) = |ψadd−ψmult|/(ψadd + ψmult), which vanishes at the corridor floor and grows
monotonically with R.
We test three predictions of this framework against 62 galaxies from the SPARC sample
with well-determined baryonic masses and flat rotation velocities. (i) The ratio ψadd/ψmult
should equal √einside the diagnostic corridor [√e, 7/4] — the unique fixed point of the two-
ruler geometry. Measured value: 1.647 ±0.003; predicted √e= 1.6487 (discrepancy 0.08%).
(ii) Mass-discrepancy variance should be suppressed inside the corridor relative to outside.
Measured suppression: 39×(CV 1.2% inside vs. 47% outside, p<10−4). (iii) The reflection
coefficient Γ should grow monotonically with altitude R and correlate with observational
scatter. Spearman ρ(R, Γ) = +0.847 and ρ(Γ, Mdyn/Mbar) = +0.71, both confirmed.
The series/parallel duality provides a geometric mechanism for two previously separate
results: why variance is suppressed inside the corridor regardless of channel type (homo-
geneous or heterogeneous), and why residual scatter inside the corridor is not random but
tracks the local impedance mismatch Γ(R). The corridor [√e, 7/4] is identified as the unique
interval on the Thales manifold where the additive and multiplicative rulers agree to within
the 1/12 coupling-cost margin. All results are labeled by epistemic tier.
Work type Technical Documentation
Tags thales partition manifold; two-channel systems; a
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Registry info in Safe Creative
Identifier 2603195023700
Entry date Mar 19, 2026, 1:47 PM UTC
License Creative Commons Attribution 4.0
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Author. Holder Elias DeJesus. Date Mar 19, 2026.
Information available at https://www.safecreative.org/work/2603195023700-series-and-parallel-rulers-on-the-thales-partition-manifold-additive-multiplicative-duality-impedance-mismatch-and-corridor-variance-lock-in-the-sparc-galaxy-sample
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Registration: 2603195023700
