Controlled reset of search state [ftip-00P0]
AGENTDRAFTED
A lifecycle comparison must distinguish the state that proposes a candidate
from the state that stores a candidate, its workspace, and its evaluation
history. Fix an immutable verifier law/configuration \(\mathcal V\in \mathbf V\).
Write \(s_t\in \mathcal S\), \(h_t\in \mathcal H\), \(w_t\in \mathcal W\),
\(b_t\in \mathcal B\), \(q_t\in \mathcal Q\), and \(\rho _t\in \mathcal G\). Let
\(\mathcal J\) be a finite set of lifecycle boundaries, with a recorded state
\(Z_r\) at every \(r\in \mathcal J\) at which an arm may act. Let \(\mathcal A\)
be a finite arm-label set with maps \(r:\mathcal A\to \mathcal J\) and
\(M:\mathcal A\to \mathcal P(\{s,h,w\})\).
Fix baseline coordinates \((s_0,h_0,w_0,b_0,q_0,\rho _0)\) in these spaces.
The declared endowment \(E_0\) from § [ftip-00OY] fixes the baseline
implementation, split, permission, and initial-source state. The comparison
also declares its verifier configuration, task law, and budget below; an arm is
admissible only when its retained-best record \(b_0\) and initial source
\(\rho _0\) are included in the declared endowment. A search state at round \(t\)
is
\[
Z_t=(s_t,h_t,w_t,b_t,q_t,\rho _t;\mathcal V),
\]where \(s_t\) is the session context visible to the proposer, \(h_t\) is the
candidate-history record, \(w_t\) is the workspace and filesystem snapshot,
\(b_t\) is the retained best candidate together with its score, artifact digest,
and required verifier status, \(q_t\) is mutable reducer state, and \(\rho _t\)
is the random-source state. The reset recomputes \(q_0\) rather than carrying
mutable reducer pointers. Candidate visibility and reducer behavior are part of
the record: a candidate that is scored but not shown to a later proposer is not
the same state as a candidate that remains in its context.
Let \(\mathcal R\) be the declared joint paired randomization law. For every
\(r\in \mathcal J\) and nonempty mask \(M\subseteq \{s,h,w\}\), \(\mathcal R\)
determines a measurable Markov kernel \(K_{r,M}(\mathord \cdot \mid \rho _r)\) on
\(\mathcal G\); write \(\rho '_r\sim K_{r,M}(\mathord \cdot \mid \rho _r)\) under
that joint law and record the draw in the run receipt. The continue arm uses
\(\rho _r\) itself.
For each arm, the protocol declares a workspace materialization map
\(\operatorname {mat}:\mathcal B\to \mathcal W\) for the verified retained-best
artifact. For a reset mask \(M\subseteq \{s,h,w\}\), define the typed transition
at boundary \(r\) by
\[
\mathsf {Reset}_{r,M}(Z_r)=
(s^M_r,h^M_r,w^M_r,b_r,q^M_r,\rho ^M_r;\mathcal V),
\]For \(x\in \{s,h\}\), set \(x^M_r=x_0\) when \(x\in M\) and
\(x^M_r=x_r\) otherwise. Set \(w^M_r=\operatorname {mat}(b_r)\) when \(w\in M\)
and \(w^M_r=w_r\) otherwise. Set \(q^M_r=q_0\) and \(\rho ^M_r=\rho '_r\) when
\(M\ne \varnothing \), and \(q^M_r=q_r\), \(\rho ^M_r=\rho _r\) for the continue
mask \(M=\varnothing \). Thus session-only and history-only arms preserve
\(w_r\). For a workspace reset, \(w^M_r\) is the declared materialization of
\(b_r\).
It also requires the precondition \(\operatorname {NoOverlap}(h_0,b_r)\) for each
arm, meaning that the history namespace contains neither discarded history nor
retained-best metadata duplicated in \(b_r\); an arm that fails this predicate
is inadmissible. The transition retains the declared best candidate \(b_r\) and
its content-addressed artifact. For a training-script task, runtime checkpoints
and other generated outputs remain in \(w_t\) and are cleared unless the protocol
explicitly declares them part of \(b_r\). The retained artifact and its
materialization are counted explicitly as retained storage. The transition records the
parent and child hashes, the discarded bytes and tokens, the reducer and
visibility rules, and the random-source change. It does not erase the rejected
proposals or their execution and evaluation costs from the lifecycle vector in
Definition [ftip-005H]. A reset is therefore an intervention on state lifecycle, not
evidence that the solver or proposer learned a new general algorithm.
The source observation in [tan2026forgetting, Abstract; Sections 3-5 and Tables 1-3]
uses the Pi agent with DeepSeek V4.1 Flash on four bounded tasks spanning
heuristic programming, kernel optimization, and model training, with the same
budget in a single-agent run, four parallel agents, and a four-agent team that
forgets three times; it reports three runs per task and configuration. Its
session-and-history intervention carries forward the best candidate. That
observation motivates, but does not test, the following paired FTIP decomposition
arms:
- continue all declared state;
- clear session context only (new FTIP arm);
- clear candidate history only (new FTIP arm); and
- clear session, candidate history, and workspace state while retaining the
best candidate, score, status, and artifact digest (new FTIP arm).
Use the scalar evaluation convention of Convention [ftip-005D]; write
\(Q:=Q_{\rm ev}\) and \(\Lambda :=\Lambda _{\rm ev}\) for its fixed task and
evaluation kernels. \(U\) denotes the measurable scalar
random variable obtained by evaluating the retained candidate with the declared
inference protocol and evaluator draw. Higher \(U\) is better; a minimization
cost is negated before comparison, and incompatible task coordinates are kept
as separate contrasts rather than silently pooled.
For each \(a\in \mathcal A\), define
\(\mathsf {Reset}_a:=\mathsf {Reset}_{r(a),M(a)}\) and
\(\mathsf {Continue}_a:=\mathsf {Reset}_{r(a),\varnothing }\). Let
\(\mathbb P^{\rm pair}_a\) be the declared joint paired law induced by the fixed
endowment \(E_0\), verifier law \(\mathcal V\), componentwise budget
\(\mathbf B\in \mathbb R_+^7\) from Definition [ftip-005H], task law and evaluation law
\(Q,\Lambda \), and \(\mathcal R\). The declared measurable run/evaluation kernel
\(\mathsf K^{\rm run}_a\) maps each reset or continue state and its random-source
draw to the final candidate, costs, and evaluation outcome; \(\mathbb P^{\rm pair}_a\)
is the joint law obtained by applying this kernel to the paired arms. Its reset
and continue marginals are \(\mathbb P^{\rm reset}_a\) and
\(\mathbb P^{\rm cont}_a\). Require \(\mathbb E_{\mathbb P^{\rm reset}_a}|U|<\infty \)
and \(\mathbb E_{\mathbb P^{\rm cont}_a}|U|<\infty \); the primary finite
estimand is
\[
\Delta _a=\mathbb E_{\mathbb P^{\rm reset}_a}[U]
-\mathbb E_{\mathbb P^{\rm cont}_a}[U].
\]The joint law \(\mathbb P^{\rm pair}_a\) assigns paired runs, their
random-source draws, and the declared coupling; it is not defined by the
informal instruction to reuse a seed. The estimand is a marginal contrast, while
the joint law supplies a paired estimator. A run reports the best-candidate
utility, proposal and verifier outcomes, realized token/tool/storage cost, and
the complete state and artifact hashes. A noisy or deceptive verifier is a
future stress arm for this estimand; it is not an assumption that the reset is
beneficial.
The source does not identify whether its gain comes from session length,
candidate visibility, filesystem persistence, proposal diversity, or an
interaction among them. The four-arm decomposition is an FTIP protocol proposal.
Without the isolated arms, the source supports a bounded reset observation but
not a theorem that memory is harmful, a monotone law for forgetting, or a
general self-improvement claim.
Existing lifecycle, replay, and evaluation declarations cover subcomponents
only; this typed reset transition remains an evaluation protocol proposal and
does not claim a corresponding formal theorem.