Definition. Idea basins and research trajectories [ftip-00OV]
Definition. Idea basins and research trajectories [ftip-00OV]
Fix a task family, an initial endowment, an interaction protocol, a resource cap and a state descriptor. Use the active research state as the base record; for this assay, a trajectory state records the current representation, proposed method, open obligations, retained artifacts and charged resource ledger. A research trajectory is a finite sequence of such states together with each operation, observation, failure or acceptance, provenance record and cost. Rejected directions remain in the trajectory because they show which work was attempted and why the method changed.
To make an idea basin testable, declare before the run a finite set of local operators, a canonicalization or equivalence test for states, a step horizon and a resource budget. The local state graph has an edge between canonical state classes when a declared operator changes one representative to another while passing the fixed protocol and checks. The basin of an initial state is the set of canonical state classes reachable by at most the declared number of local steps and within the declared budget. It is therefore relative to the chosen descriptor and local operators: a different neighborhood or horizon defines a different basin. Similar wording, more sampling or a longer trace does not by itself define a new basin.
A basin escape is a trajectory transition whose resulting state lies outside that declared reachable set and whose witness names the changed representation, decomposition, invariant, objective or search operator. The claim is supported only when the changed state passes an independent check and solves withheld or fresh tasks under the predeclared accounting. A local baseline with matched seeds and resources must be run in parallel, and failed escape attempts are retained as evidence. Escape is a claim relative to the declared neighborhood and horizon, not a proof of global mathematical novelty.
The [cai2026forkflush, Sections 3-4] study reports that independent runs on the same task can plateau in localized idea basins, and evaluates fork-and-flush interventions that preserve the workspace while starting a fresh chat context. The [zhang2026statelessagents, Section 2.2] study reports replayed histories, repeated work, premature stopping and continued token use without new experiments; its stateless, harness-reconstructed contexts and explicit assignments improve long-horizon progress in the tested software and systems tasks ([zhang2026statelessagents, Sections 3.1-3.2 and 4.2-4.3]). This supports the qualified inference that persistent conversational state can reinforce a decision or search basin, while harness-controlled reconstruction can expose alternative directions. Most configurations in that paper use one run ([zhang2026statelessagents, Section 4.1]), and it does not directly measure FTIP idea-basin membership.
The trajectory record separates discovery from evaluation. It records when the escape witness was proposed, which information was available, which checks rejected alternatives and which artifact was frozen for acquisition. Fresh-task transfer and retention are measured after the contributor, search aid and temporary context are removed. The semantic discovery records provide the evidence slots; this convention adds the locality and path conditions needed to interpret a claimed change of idea basin.