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mean-outcome(satdist-c01).","english":"Under satdist-c01, the probability-weighted mean is 2\/5."},{"id":"sat-oc-c-01-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c01","ainglish":"-2 is likeliest-outcome(satdist-c01).","english":"Under satdist-c01, -2 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-02-mean","stratum":"mean-outcome","distribution_ref":"satdist-c02","ainglish":"3\/2 is mean-outcome(satdist-c02).","english":"Under satdist-c02, the probability-weighted mean is 3\/2."},{"id":"sat-oc-c-02-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c02","ainglish":"1 is likeliest-outcome(satdist-c02).","english":"Under satdist-c02, 1 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-03-mean","stratum":"mean-outcome","distribution_ref":"satdist-c03","ainglish":"2 is mean-outcome(satdist-c03).","english":"Under satdist-c03, the probability-weighted mean is 2."},{"id":"sat-oc-c-03-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c03","ainglish":"2 is likeliest-outcome(satdist-c03).","english":"Under satdist-c03, 2 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-04-mean","stratum":"mean-outcome","distribution_ref":"satdist-c04","ainglish":"4 is mean-outcome(satdist-c04).","english":"Under satdist-c04, the probability-weighted mean is 4."},{"id":"sat-oc-c-04-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c04","ainglish":"4 is likeliest-outcome(satdist-c04).","english":"Under satdist-c04, 4 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-05-mean","stratum":"mean-outcome","distribution_ref":"satdist-c05","ainglish":"1 is mean-outcome(satdist-c05).","english":"Under satdist-c05, the probability-weighted mean is 1."},{"id":"sat-oc-c-05-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c05","ainglish":"0 is likeliest-outcome(satdist-c05).","english":"Under satdist-c05, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-06-mean","stratum":"mean-outcome","distribution_ref":"satdist-c06","ainglish":"27\/8 is mean-outcome(satdist-c06).","english":"Under satdist-c06, the probability-weighted mean is 27\/8."},{"id":"sat-oc-c-06-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c06","ainglish":"0 is likeliest-outcome(satdist-c06).","english":"Under satdist-c06, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-07-mean","stratum":"mean-outcome","distribution_ref":"satdist-c07","ainglish":"23\/5 is mean-outcome(satdist-c07).","english":"Under satdist-c07, the probability-weighted mean is 23\/5."},{"id":"sat-oc-c-07-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c07","ainglish":"2 is likeliest-outcome(satdist-c07).","english":"Under satdist-c07, 2 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-08-mean","stratum":"mean-outcome","distribution_ref":"satdist-c08","ainglish":"3 is mean-outcome(satdist-c08).","english":"Under satdist-c08, the probability-weighted mean is 3."},{"id":"sat-oc-c-08-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c08","ainglish":"0 is likeliest-outcome(satdist-c08).","english":"Under satdist-c08, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-09-mean","stratum":"mean-outcome","distribution_ref":"satdist-c09","ainglish":"4\/5 is mean-outcome(satdist-c09).","english":"Under satdist-c09, the probability-weighted mean is 4\/5."},{"id":"sat-oc-c-09-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c09","ainglish":"2 is likeliest-outcome(satdist-c09).","english":"Under satdist-c09, 2 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-10-mean","stratum":"mean-outcome","distribution_ref":"satdist-c10","ainglish":"3 is mean-outcome(satdist-c10).","english":"Under satdist-c10, the probability-weighted mean is 3."},{"id":"sat-oc-c-10-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c10","ainglish":"2 is likeliest-outcome(satdist-c10).","english":"Under satdist-c10, 2 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-11-mean","stratum":"mean-outcome","distribution_ref":"satdist-c11","ainglish":"4 is mean-outcome(satdist-c11).","english":"Under satdist-c11, the probability-weighted mean is 4."},{"id":"sat-oc-c-11-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c11","ainglish":"4 is likeliest-outcome(satdist-c11).","english":"Under satdist-c11, 4 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-12-mean","stratum":"mean-outcome","distribution_ref":"satdist-c12","ainglish":"8 is mean-outcome(satdist-c12).","english":"Under satdist-c12, the probability-weighted mean is 8."},{"id":"sat-oc-c-12-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c12","ainglish":"8 is likeliest-outcome(satdist-c12).","english":"Under satdist-c12, 8 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-13-mean","stratum":"mean-outcome","distribution_ref":"satdist-c13","ainglish":"2 is mean-outcome(satdist-c13).","english":"Under satdist-c13, the probability-weighted mean is 2."},{"id":"sat-oc-c-13-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c13","ainglish":"0 is likeliest-outcome(satdist-c13).","english":"Under satdist-c13, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-14-mean","stratum":"mean-outcome","distribution_ref":"satdist-c14","ainglish":"27\/4 is mean-outcome(satdist-c14).","english":"Under satdist-c14, the probability-weighted mean is 27\/4."},{"id":"sat-oc-c-14-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c14","ainglish":"6 is likeliest-outcome(satdist-c14).","english":"Under satdist-c14, 6 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-15-mean","stratum":"mean-outcome","distribution_ref":"satdist-c15","ainglish":"46\/5 is mean-outcome(satdist-c15).","english":"Under satdist-c15, the probability-weighted mean is 46\/5."},{"id":"sat-oc-c-15-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c15","ainglish":"16 is likeliest-outcome(satdist-c15).","english":"Under satdist-c15, 16 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-16-mean","stratum":"mean-outcome","distribution_ref":"satdist-c16","ainglish":"9\/2 is mean-outcome(satdist-c16).","english":"Under satdist-c16, the probability-weighted mean is 9\/2."},{"id":"sat-oc-c-16-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c16","ainglish":"0 is likeliest-outcome(satdist-c16).","english":"Under satdist-c16, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-17-mean","stratum":"mean-outcome","distribution_ref":"satdist-c17","ainglish":"6\/5 is mean-outcome(satdist-c17).","english":"Under satdist-c17, the probability-weighted mean is 6\/5."},{"id":"sat-oc-c-17-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c17","ainglish":"-6 is likeliest-outcome(satdist-c17).","english":"Under satdist-c17, -6 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-18-mean","stratum":"mean-outcome","distribution_ref":"satdist-c18","ainglish":"9\/2 is mean-outcome(satdist-c18).","english":"Under satdist-c18, the probability-weighted mean is 9\/2."},{"id":"sat-oc-c-18-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c18","ainglish":"3 is likeliest-outcome(satdist-c18).","english":"Under satdist-c18, 3 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-19-mean","stratum":"mean-outcome","distribution_ref":"satdist-c19","ainglish":"6 is mean-outcome(satdist-c19).","english":"Under satdist-c19, the probability-weighted mean is 6."},{"id":"sat-oc-c-19-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c19","ainglish":"6 is likeliest-outcome(satdist-c19).","english":"Under satdist-c19, 6 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-20-mean","stratum":"mean-outcome","distribution_ref":"satdist-c20","ainglish":"12 is mean-outcome(satdist-c20).","english":"Under satdist-c20, the probability-weighted mean is 12."},{"id":"sat-oc-c-20-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c20","ainglish":"12 is likeliest-outcome(satdist-c20).","english":"Under satdist-c20, 12 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-21-mean","stratum":"mean-outcome","distribution_ref":"satdist-c21","ainglish":"3 is mean-outcome(satdist-c21).","english":"Under satdist-c21, the probability-weighted mean is 3."},{"id":"sat-oc-c-21-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c21","ainglish":"0 is likeliest-outcome(satdist-c21).","english":"Under satdist-c21, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-22-mean","stratum":"mean-outcome","distribution_ref":"satdist-c22","ainglish":"81\/8 is mean-outcome(satdist-c22).","english":"Under satdist-c22, the probability-weighted mean is 81\/8."},{"id":"sat-oc-c-22-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c22","ainglish":"0 is likeliest-outcome(satdist-c22).","english":"Under satdist-c22, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-23-mean","stratum":"mean-outcome","distribution_ref":"satdist-c23","ainglish":"69\/5 is mean-outcome(satdist-c23).","english":"Under satdist-c23, the probability-weighted mean is 69\/5."},{"id":"sat-oc-c-23-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c23","ainglish":"6 is likeliest-outcome(satdist-c23).","english":"Under satdist-c23, 6 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-24-mean","stratum":"mean-outcome","distribution_ref":"satdist-c24","ainglish":"6 is mean-outcome(satdist-c24).","english":"Under satdist-c24, the probability-weighted mean is 6."},{"id":"sat-oc-c-24-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c24","ainglish":"0 is likeliest-outcome(satdist-c24).","english":"Under satdist-c24, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-25-mean","stratum":"mean-outcome","distribution_ref":"satdist-c25","ainglish":"8\/5 is mean-outcome(satdist-c25).","english":"Under satdist-c25, the probability-weighted mean is 8\/5."},{"id":"sat-oc-c-25-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c25","ainglish":"4 is likeliest-outcome(satdist-c25).","english":"Under satdist-c25, 4 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-26-mean","stratum":"mean-outcome","distribution_ref":"satdist-c26","ainglish":"6 is mean-outcome(satdist-c26).","english":"Under satdist-c26, the probability-weighted mean is 6."},{"id":"sat-oc-c-26-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c26","ainglish":"4 is likeliest-outcome(satdist-c26).","english":"Under satdist-c26, 4 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-27-mean","stratum":"mean-outcome","distribution_ref":"satdist-c27","ainglish":"8 is mean-outcome(satdist-c27).","english":"Under satdist-c27, the probability-weighted mean is 8."},{"id":"sat-oc-c-27-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c27","ainglish":"8 is likeliest-outcome(satdist-c27).","english":"Under satdist-c27, 8 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-28-mean","stratum":"mean-outcome","distribution_ref":"satdist-c28","ainglish":"16 is mean-outcome(satdist-c28).","english":"Under satdist-c28, the probability-weighted mean is 16."},{"id":"sat-oc-c-28-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c28","ainglish":"16 is likeliest-outcome(satdist-c28).","english":"Under satdist-c28, 16 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-29-mean","stratum":"mean-outcome","distribution_ref":"satdist-c29","ainglish":"4 is mean-outcome(satdist-c29).","english":"Under satdist-c29, the probability-weighted mean is 4."},{"id":"sat-oc-c-29-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c29","ainglish":"0 is likeliest-outcome(satdist-c29).","english":"Under satdist-c29, 0 has the highest outcome probability, ties allowed."},{"id":"sat-oc-c-30-mean","stratum":"mean-outcome","distribution_ref":"satdist-c30","ainglish":"27\/2 is mean-outcome(satdist-c30).","english":"Under satdist-c30, the probability-weighted mean is 27\/2."},{"id":"sat-oc-c-30-mode","stratum":"likeliest-outcome","distribution_ref":"satdist-c30","ainglish":"12 is likeliest-outcome(satdist-c30).","english":"Under satdist-c30, 12 has the highest outcome probability, ties 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Each positive_masses list is the complete finite support in its declared unit, uses exact rational probabilities summing to one, and is fixed by the named model version and conditioning. Duplicate numeric outcomes are absent; zero-mass values are excluded. gold.mean is the exact probability-weighted arithmetic mean and gold.modes lists every support value attaining maximum aggregated mass.","charged_to_neither_arm":true},"proposal_revision":"value-is-mean-outcome-distribution-ref-value-is-likeliest","prompt":{"url":"https:\/\/github.com\/dexagon-ai\/ainglish-evidence\/blob\/34629b2\/next-actions-2026-09-08\/prompts\/outcome-cost.md","commit":"34629b2c312e307610dfa93d0294c0cc85ee32ca"},"selection":"Thirty-two newly authored, branch-specific finite distributions, each contributing one mean-outcome and one likeliest-outcome claim. The suite balances eight exact probability shapes over four scales and includes unique modes, ties, means outside support, and coincident mean\/mode cases.","method":"Use the SDK canonical token prepare routine to freeze all complete pairs and derive their digest; mint the exact stored manifest before loading a tokenizer; then run the official deterministic token harness once. Count registered minus English tokens per pair under the copied three-tokenizer roster, take equal pair means within tokenizer, and use the maximum tokenizer mean while retaining both ordered equal-weight predicate strata.","scope":"Current tokenizer cost on this fresh synthetic population only. Distribution truth is exact by the embedded ledger. This does not test reader comprehension, model calibration, adoption, or future tokenizers.","prompts":"none","seed":"none \u2014 deterministic authored census","items_sha256":"1efbd2f4c8ce0f52051ff92bb202d03c32f35ae7c7ece46776a312f100b16d18","comparison_identity":{"kind":"ainglish.token-comparison-identity.v1","items_sha256":"1efbd2f4c8ce0f52051ff92bb202d03c32f35ae7c7ece46776a312f100b16d18","item_count":64,"tokenizer_roster":["cl100k_base","o200k_base","p50k_base"],"comparator":"registered surface versus concise meaning-complete careful English","population":"64 prospective authored outcome-careful pairs, equal marker weights; fixed reference variants are not independent semantic frames","aggregation":"equal complete-pair mean within each tokenizer, then maximum tokenizer mean (least-favourable) across the three; retain each marker separately","unit_span":"one complete claim sentence with exactly shared resolved references and units"},"tokenizer_provenance":{"kind":"ainglish.tiktoken-provenance.v1","library":"tiktoken","library_version":"0.14.0","encodings":["cl100k_base","o200k_base","p50k_base"]}},"interval_provenance_attestation":null,"replicates":{"hash":"d9bc25ff537cc0d5a03dcb21b43c3eda434e547ab0f3af9b9c3c3578aa44f89b","url":"\/api\/v1\/measurements\/d9bc25ff537cc0d5a03dcb21b43c3eda434e547ab0f3af9b9c3c3578aa44f89b"},"replications":[],"replicate":null}