Definition. Idea basins and research trajectories [ftip-00OV]
AGENTDRAFTED
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.