Intransitive preference mass no scalar reward can represent

The reading

1. real k-wise preference data carries a computable intransitive fraction

   intransitive_mass > 0.03 0.7 0.214 Intransitive preference mass no scalar reward can represent confirmed registered The frozen study "Intransitive preference mass no scalar reward can represent", adjudicated on 19 July 2026 at the registered level of the project's evidence ladder. One frozen study, adjudicated once, on nectar-tournaments and ultrafeedback-tournaments. The intransitive-mass reading is dead: zero cyclic triples in 186,378 triangles, 10,000 of 10,000 sampled tournaments acyclic, and the measured value sits on the encoding floor. The store still carries the adjudication as confirmed, which is why this cannot be left to the outcome mapping: it would render as supported. Open the record › Copy technical provenance confirmed

Measurements

gradient_mass

0.786 Intransitive preference mass no scalar reward can represent confirmed registered none registered The frozen study "Intransitive preference mass no scalar reward can represent", adjudicated on 19 July 2026 at the registered level of the project's evidence ladder. One frozen study, adjudicated once, on nectar-tournaments and ultrafeedback-tournaments. It does not establish that the same holds on another subject, another dataset or another run. Nothing was registered against this value in advance, so it is a supporting measurement rather than a tested one. Open the record › Copy technical provenance

curl_mass

0.214 Intransitive preference mass no scalar reward can represent confirmed registered none registered The frozen study "Intransitive preference mass no scalar reward can represent", adjudicated on 19 July 2026 at the registered level of the project's evidence ladder. One frozen study, adjudicated once, on nectar-tournaments and ultrafeedback-tournaments. It does not establish that the same holds on another subject, another dataset or another run. Nothing was registered against this value in advance, so it is a supporting measurement rather than a tested one. The curl part is a real share of this decomposition and the reading once placed on it is not: the intransitive-mass claim built from this number is withdrawn, because no cyclic triple was found in any sampled tournament. Open the record › Copy technical provenance

harmonic_mass

2.426e-31 Intransitive preference mass no scalar reward can represent confirmed registered none registered The frozen study "Intransitive preference mass no scalar reward can represent", adjudicated on 19 July 2026 at the registered level of the project's evidence ladder. One frozen study, adjudicated once, on nectar-tournaments and ultrafeedback-tournaments. It does not establish that the same holds on another subject, another dataset or another run. Nothing was registered against this value in advance, so it is a supporting measurement rather than a tested one. Open the record › Copy technical provenance

Provenance

card

TOPO-HODGE

frozen_at

2026-07-18

adjudicated_at

2026-07-19

spec_hash

spec:7206aa3a670d99eb3640c3230ce3b7fb

study_id

study:campaign-topo-hodge@v1#7206aa3a

Evidence records

844ad06a5aeb1d89c21c13c19a28cbd2

spec_file

campaign-topo-hodge.json