Typed harness adaptation and total lifecycle accounting [ftip-00OY]
AGENTDRAFTED
A harness adaptation claim must keep the executable solver, the proposer
that edits its harness, the retained harness state Definition [ftip-00C8], and the
evaluator Definition [ftip-001T] as
different objects. A change in one object is not evidence that the others
changed. The stateful-search convention already records durable
research state and replay; the comparison therefore fixes an adaptation and
accounting boundary for interpreting evidence.
Typed roles and declared endowment. Let \(M\) be a fixed solver
artifact, \(\theta \) the parameters of a proposer, \(h_t\in \mathcal H\) the
versioned harness state after inner round \(t\), and \(q\in \mathcal Q\) a task.
The proposer is a revision policy
\[
\pi _\theta :\mathcal Q\times \mathcal H\times \mathcal R
\longrightarrow \mathsf {Dist}(\mathcal Y),
\]where \(\mathcal R\) is a typed execution-report space and \(\mathcal Y\)
contains candidate edits. Applying an edit to a parent state produces a
candidate \(\widetilde h_t\); a validation and selection rule either commits
\(h_t=\widetilde h_t\) or retains \(h_t=h_{t-1}\). The solver \(M\) and final
proposer parameters \(\theta _*\) are fixed during this inner loop.
For the declared outer training, define
\[
O_{\rm outer}=(\theta _0,\ldots ,\theta _K,D_{\rm train},\xi _{<K},
L_{\rm outer},C_{\rm outer}),
\]The final proposer is \(\theta _*:=\theta _K\), and \(L_{\rm outer}\) records
prompts, generated and failed revisions, and teacher filtering. The declared
endowment for an inner-loop comparison is
\[
E_0=(M,\theta _*,h_0,\kappa _0,\mathcal Q_0,\mathcal P_0,\rho _0,O_{\rm outer}),
\]where \(\kappa _0\) contains implementation and harness versions,
\(\mathcal Q_0\) the task and split laws, \(\mathcal P_0\) permissions and
available tools, and \(\rho _0\) seed, API, tokenizer, and evaluator state.
Existing solver code, seed harnesses, accessible examples, and checker
interfaces are part of \(E_0\); if an arm constructs any of them, that
preparation is a charged outer operation recorded in \(C_{\rm outer}\). An
adaptation result is therefore conditional on the same declared endowment,
including its outer-training trace, event reports, and cost, even when the
retained state is later changed.
Outer training and inner adaptation. Outer training updates only
the proposer, for example
\[
\theta _{k+1}=U(\theta _k;D_{\rm train},\xi _k),
\]using proposer or teacher data and execution feedback. Its outer-training
trace is included in \(E_0\); at test time the inner loop starts from the
declared seed \(h_0\). For a finite nonempty
candidate index set \(J_t\), it repeatedly records
\[
R_t=\operatorname {report}(M,h_{t-1},q_{\rm fb,t},\xi _t),\qquad
\{y_{t,j}\}_{j\in J_t}\sim \pi _{\theta _*}^{\otimes J_t}(q,h_{t-1},R_t),\qquad
h_t=\operatorname {select}\bigl (h_{t-1},
\{\operatorname {apply}(h_{t-1},y_{t,j})\}_{j\in J_t};q_{\rm score,t}\bigr ).
\]An outer teacher, when used for supervised initialization, is a separate
role from the proposer and solver. Its prompts, generated revisions, failed
revisions, and filtering work remain in \(L_{\rm outer}\). Neither an outer
weight update nor an inner harness edit may be described as a model-weight
capability change.
Leakage controls. A reported comparison declares pairwise-disjoint
sets \(Q_{\rm train}\), \(Q_{\rm fb}\), \(Q_{\rm score}\), \(Q_{\rm dev}\), and
\(Q_{\rm eval}\) (or records the exact exception). Feedback and score questions
may select or reject a candidate during adaptation; development questions may
select a frozen proposer or protocol. Final evaluation questions are revealed
only after the adapted state and its configuration are frozen, and their
outcomes cannot revise that state in the same run. The task family, solver,
proposer, seed harness, checker, and split law are reported with every score.
Provenance and rollback. Each committed state carries a record
\[
V_t=(\operatorname {digest}(E_0,M,\theta _*,h_t,\kappa _t),
E_0,
L_t,\{y_i,R_i,d_i\}_{i<t},C_{\leq t}),
\]where the digest also covers the declared endowment \(E_0\), including its
task and split laws, permissions, tools, and seed and evaluator state. \(L_t\)
is the event prefix, \(d_i\) records validation and commit
decisions, and \(C_{\leq t}\) is the cumulative cost record. A rejected edit
leaves the parent state in place but remains in the event log. A proposed
rollback, as specified in Definition [ftip-00D7], to \(V_j\) restores the complete named snapshot and its configuration;
it cannot erase the proposal, execution, storage, or evaluator costs already
incurred. Rollback is an FTIP protocol proposal, not a result established by
the source papers.
Total accounting. Refine the lifecycle vector
\(C(P)=(C_{\rm data},C_{\rm feedback},C_{\rm rollout},C_{\rm env},
C_{\rm update},C_{\rm storage},C_{\rm eval})\) from
Definition [ftip-005H] by recording a role-indexed vector for
\[
\mathbf C_{\rm total}
=\sum _{r\in \{\rm teacher,prop_{outer},prop_{inner},solver,tool,evaluator\}}
\mathbf C^{r}.
\]Every component keeps its declared unit. The account includes initial
endowment preparation when it is arm-specific, proposer and teacher calls,
solver and tool executions, evaluator calls, context and artifact storage,
retries, invalid edits, rejected candidates, failed experiments, and any
development work. Cached and uncached tokens, wall time, FLOPs, bytes, and
calls are not silently converted into one scalar. A price or scalar utility
may be reported only after this typed vector and the split of each role are
available.
Finite typed example. Fix \(M\), \(\theta _*\), and \(h_0\) in the
endowment. In round one, the proposer emits an invalid edit \(y_1^a\) and a
valid edit \(y_1^b\); the first execution and rejection are charged, while
selection commits \(h_1=\operatorname {apply}(h_0,y_1^b)\). In round two, noisy
feedback produces \(y_2\); an adversarial score check rejects it, so
\(h_2=h_1\). A later audit may restore \(V_1\), but the costs of \(y_1^a\),
\(y_1^b\), \(y_2\), their executions, and the checks remain in
\(\mathbf C_{\rm total}\). Evaluating \(h_1\) on fresh \(Q_{\rm eval}\) tests the
frozen state; it does not prove that the proposer learned a general solver.
Source observations. Harness Learning defines a harness as the
executable program that organizes solver calls, tools, and information flow,
trains a proposer in an outer loop, and uses execution feedback to revise a
fixed solver harness in an inner loop. Its test-time proposer and solver stay
fixed while the harness changes; the paper reports Reasoning Gym and
multi-hop question-answering experiments, including held-out and unseen-task
comparisons ([zhang2026harnesslearning, Sections 3-4.3 and 5-6]).
ReHarness reports a different intervention: under a strictly online stream,
forward read and write are coupled with backward revision of reflections using
the current trajectory. Its three continual-learning benchmarks and three
backbones report source-grounded revisions and failures under distribution
shift, but the result remains a benchmarked online protocol
([xiao2026reharness, Sections 3-5]). Stateless Language Agents likewise
place durable research state in the harness and reconstruct role-specific
contexts for stateless calls; their protected evaluation and token records
motivate the provenance fields, while their mostly single-run settings and
omitted experiment/evaluation compute limit the cost conclusion
([zhang2026statelessagents, Sections 3-5, Appendix B.1, and limitations]).
FTIP deduction and boundary. These observations support separating
outer training, inner adaptation, state provenance, feedback, and lifecycle
costs. The conceptual-discovery boundary in § [ftip-00MH] remains separate:
these results do not establish a universal self-improvement law, transfer to
frontier reasoning, or a monotone relation between more revisions and
capability. The source results are finite empirical observations; the typed
state record, leakage controls, complete cost decomposition, and rollback
test are FTIP protocol proposals. The checked Forest, formal-math,
TauCetiReview, and TauCetiWorker sources contain no declaration corresponding
to these empirical harness mechanisms or their total-cost record; existing
Forest state, replay, version, and lifecycle conventions are reused without
adding a formalization claim.
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.