Sufficient Statistics
B_H values horizon progress, B_F values reliability in unforgiving environments, and C measures the value mass where both constraints bind.
Main Intuition
AI progress is not one scalar quality ladder. Tasks fail for different reasons. Some tasks require long chains of coordinated action. Other tasks can be short but unforgiving because a local error is costly or irreversible. The model turns that distinction into sufficient statistics for valuing frontier movement and firm races.
Race Inversion
The same economy can race on runtime in one task region and on base reliability in another. The regional ratio B_H^R/B_F^R determines the direction.
Data Flywheels
Deployment scale creates productive tipping only when served tasks produce usable traces that move the scarce boundary. Otherwise scale can be pure lock-in.
Revision Plan & Today's Learning
Current Plan
- Keep future changes selective: tighten the theory contract without expanding the mechanism set.
- Use each new pass to remove ambiguity in the main restriction, not to add new examples.
- Keep the first read centered on one primitive: horizon times forgiveness, expressed through coordinate fragility.
- Protect the main theorem as the paper's spine: task-side project value equals regional scarcity times effective project direction.
- Preserve the current packaging: the compressed abstract should hand the reader to the Introduction quickly.
Today's Learning: All June 28 Rounds
- Round 54 compressed the Introduction and added guardrails on iso-fragility comparisons and region-specific effective steps/costs.
- Round 55 moved private-payoff and deployment-scale propositions to the appendix, leaving the main text focused on the inversion theorem.
- Round 56 moved infrastructure into the project-map appendix: GPUs, energy, interconnect, inference, and financing shift feasible projects, costs, or effective steps.
- Round 57 compacted routine proof algebra and renamed it Proofs and Algebraic Details, reducing page pressure without changing theory.
- Round 58 compressed the pre-theorem technology map into a value-index bridge, so the main theorem appears earlier and the engineering mechanisms no longer crowd the theory.
- Round 59 rewrote the conclusion as a compact synthesis around the task-frontier state variable, boundary scarcity, project-value inversion, and the main extensions.
- Round 60 moved empirical discipline into the first read: task families and measured project steps now anchor the sign and rank restrictions upfront.
- Round 61 strengthened the sequential microfoundation by showing the horizon gate multiplied by the forgiveness-adjusted reliability gate before the common-kernel benchmark.
- Round 62 compressed the abstract so the first page now reaches the Introduction while retaining the puzzle, primitive, theorem, scalar restriction, rank restriction, and saturation implication.
- Round 63 sharpened the Introduction's theory contract: the empirical object is a constructed region-by-project value matrix with sign and rank restrictions under independently measured coordinates, steps, and costs.
- Round 64 sharpened the contribution positioning: the paper is about the remaining AI task frontier and the project-value restrictions it imposes, not a task-substitution taxonomy or a diffusion-level story.
- Round 65 cleaned up the main theorem's comparison object: project rankings are now explicitly task-side frontier-value rankings, with private rent and outside-return margins handled later.
- Round 66 aligned the Introduction and appendix proof with that theorem object, making the headline cutoff explicitly about task-side frontier value per dollar.
- Round 67 aligned the abstract, Introduction definition, and technology bridge with the theorem's task-side frontier-value-per-dollar object, replacing informal ranking language with the precise cost-normalized comparison.
- Round 68 moved the local scope and overidentifying content of the theory into the first read: the result ranks task-boundary movement after project steps, costs, and payoff wedges are fixed or measured.
- Round 69 polished the main theorem and proof by replacing the narrow same-cost-unit wording with same-cost wording and making equality/tie cases explicit.
- Round 70 aligned the project-selection proposition and proof with the theorem's task-side frontier-value-per-dollar object, avoiding a switch to private-return language.
- Round 71 aligned Observable Restrictions and the conclusion with that same task-side frontier-value object, separating model-implied rankings from adoption and investment choices.
- Round 72 aligned the measurement table itself with the task-side frontier-value object, so its violations no longer read like raw adoption predictions.
- Round 73 aligned the rank-minimality explanation with the task-side local project-value matrix, keeping the scalar-rank result tied to the theorem's object.
- Round 74 harmonized the first-read and measurement language around the local project-value matrix, making clear its entries are per-dollar task-side frontier values.
- Round 75 clarified the horizon-forgiveness primitive at the front door: serial depth compounds the residual failure risk left after retry, observability, rollback, and tolerance.
- Round 76 aligned the remaining ranking language with the task-side frontier-value object, including the mapping from task-side frontier-value rankings to choices.
- Round 77 clarified that the scalar benchmark is generous: regions may have different scalar marginal values, while scalar project increments and costs remain common.
- Round 78 aligned the Introduction's value-index notation with the formal Lambda_aR object, leaving V_i(R) for delivered task value.
- Round 79 clarified that forgiveness is a task-side property, while q_F is the system reliability capability whose marginal value is highest in low-forgiveness tasks.
- Round 80 brought that task-side primitive discipline into the abstract, clarifying horizon and forgiveness as task-side coordinates.
- Round 81 harmonized the measurement section's terminology by replacing the lone product-kernel phrase with the established common-kernel benchmark.
- Round 82 replaced the buzzword-like one-dimensional agentic frontier wording with the clearer one-dimensional horizon-frontier special case.
- Round 83 replaced the conclusion's old race-reversal wording with task-side project-value reversals.
- Round 84 cleaned up the first-read reliability phrase by replacing low irreversible error with low irreversible-error rates.
- Round 85 clarified the abstract's boundary-value sentence as horizon movement, fragility relaxation, and complementarity.
- Round 86 aligned the finite-step inversion wording with the task-side frontier-value object.
- Round 87 made the rank restriction operational with two-by-two minors, admissible task families, and a minimum held-out rejecting design.
- Round 88 consolidated scope conditions into affirmative design language so the paper reads less like a referee response.
- Round 89 repackaged the appendix as optional extensions using the same boundary objects, protecting the main theory spine.
- Round 90 aligned the abstract with the operational rank/minor and pre-ranking measurement discipline.
Open full learning log from today
This panel is synced from the project-level learning.md log for the June 28 revision sequence.
Task Regions
High forgiveness
Low forgiveness
Low horizon
Product recommendation, ad copy, search help. Low-cost systems and imitation can be strong.
Driving maneuvers, medical dosage, payments control. Reliability and verification dominate.
High horizon
Coding, debugging, data analysis, research assistance. Runtime, tools, retries, and workflow integration matter most.
Drug discovery, critical infrastructure, autonomous organizations. Full-stack frontier advantages can persist.
Paper
The compiled PDF, LaTeX source, and math checker in this folder are synchronized with the current revision.