NOTE-1091: Aevyra — The Ledger of Will

Contribution

The paper organizes known ideas (sufficient statistics, predictive state representations, truth maintenance, AGM, Moore–Nerode refinement, successor features) around one requirement for the memory of a persistent agent: that what is kept still supports the revisions the agent may later need, not only today’s answers. It gives that requirement a definition, “revision sufficiency”, relative to a declared family of future demands, and proves elementary finite results about it. It then proposes an architecture and a protocol for testing one. Its own framing: “The contribution is a testable synthesis of established ideas and explicit design proposals, rather than a new criterion of consciousness or a claim of demonstrated behavioral superiority” (Abstract).

Key insight

“A record that reconstructs yesterday’s answer perfectly can nevertheless prevent tomorrow’s appropriate revision if it has retained the conclusion and discarded its conditions” (§1). Whether a memory is adequate is not a property of the memory alone but of the memory and a declared family of future demands, and “Declaring a restricted demand family is therefore part of the scientific claim, not administrative metadata” (§4.2).

Assumptions

• Finite histories, and a deterministic reduction ρ from histories to retained states (§4.1). A “state” in §4.4 includes any law or status needed to make revision Markovian.
• A declared demand family D: each demand fixes context, question, actions or interventions and the evaluative or revision law (§4.1). Nothing is promised outside it.
• Total, deterministic revisions J_z on a finite state set closed under them, for the repeated-revision result (§4.4). Partial revisions need a further convention, which is not given.
• Commuting updates at reachable states for replay invariance (Prop. 1), or “swap closure” for partial operators.
• Linear evaluation, bounded weights and bounded feature error for the regret bound (Prop. 5).
• Causal targets presuppose an identified model: “writing a do-operator does not identify a causal effect from a log” (§4.1).

Key results

• Prop. 1 (interleaving-invariant replay). Replay of a finite record DAG gives one result for every topological order if the update operators of incomparable events commute at every reachable state. For partial operators, agreement where both orders are defined is not enough; A.10 is a counterexample, and swap closure is the fix.
• Def. 1 and Prop. 2 (fibre criterion). ρ is exactly sufficient for D iff ρ(h) = ρ(h′) implies T_d(h) = T_d(h′) for all d. The quotient by agreement of all targets is the coarsest exact representation. “This is an information characterization, not an efficient construction” (§4.1).
• Prop. 3 (capacity). K classes need at least K states, ⌈log₂K⌉ bits; if any of n observed bits may be asked for, n bits. A content hash does not evade this: hash plus archive is the representation.
• §4.3, revision after compression. A retained-state update matching full-history revision exists exactly when the post-revision target is constant on ρ’s fibres. “Adding an instruction to reconsider cannot reconstruct a distinction that was irreversibly merged.” The three responses are to keep more, promise less, or reacquire evidence; “Treating a plausible reconstruction as recovered evidence is not a fourth solution.”
• Prop. 4 (revision closure). h ≈ h′ when all targets agree after every finite word of revisions. ≈ is the coarsest equivalence refining target agreement that is invariant under every revision; a representation supports exact decoded outputs after any revision word iff its fibres lie within ≈-classes; K* ≥ K, and at most K* − K extra revision words distinguish all classes. The exact-update identity Ĵ∘ρ = ρ∘J holds only when ρ’s own fibres are invariant (A.9). It is “a finite-machine refinement construction in the tradition of Moore and Nerode”, and “efficient selection for open-ended agents remains unresolved” (§4.4).
• §5.1, the counterexample. Two histories with the same current best action and current values but different feature vectors; after the weights change, any decoder of the merged state has expected regret 1/2. In a four-state law-indexed extension, K = 2 and K* = 3.
• Prop. 5 (revaluation regret). With feature reconstruction error ε and ‖w‖ ≤ W, regret ≤ 2Wε, tight (A.3).
• §5.2, two resources. R*(H) ≤ R*(S) always, but “a fixed bounded model may perform better with a well-designed summary than with an entire history. Information availability and computational accessibility are different resources.”
• §5.4, narrowing. Further reduction can only shrink the set of evaluative laws recoverable without new evidence. The authors propose that a narrowing be “attributable, justified, and recorded”, and add: “A party’s technical ability to delete does not itself establish its entitlement to do so.”
• §6.2, repeated interpretation. With a fixed evidence evaluator, adding a derived note does not change support; a rephrasing must not “acquire the likelihood weight of a second independent measurement”. A.5: one likelihood ratio of 3 gives 3/4; counting four copies as independent gives 81/82.
• Prop. 6 (forgetting). Exact reconstruction of Z from accessible S implies I(Z;S) = H(Z) > 0, so it is incompatible with I(Z;S) = 0.
• §7, commitments. A commitment has an owner, content, activation predicate, deadline, completion condition, scope, revision authority and state; “Delivery of a reminder does not establish completion, and failure to retrieve an intention does not establish cancellation.”
• §9, the protocol. Four separately failing stages (formation, access, uptake, durable revision), eight matched scenario families, fibre-paired trials with an error floor of 1/2, budget accounting, and stated rejection conditions. “The following study is a proposal, not a completed benchmark.”

Claims

id	claim	strength	support
C1	A deterministic retained state is exactly sufficient for a declared demand family iff every target is constant on its fibres	strong (elementary)	Prop. 2, proof; checked
C2	Exact decoded outputs after any finite word of declared total revisions are possible iff the fibres lie within the coarsest revision-invariant refinement of target agreement, reachable with at most K* − K extra revision words	strong (elementary, classical)	Prop. 4, proof; exhaustive and seeded checks in the archive
C3	A memory that keeps only the current conclusion can be adequate now and fail after a change of evaluative law, with regret 1/2 in the stated example	strong for the example	§5.1; A.1
C4	Exact sufficiency over unrestricted future questions admits no nontrivial lossless compression	strong	Prop. 3
C5	Rederived or rephrased records must not count as independent evidence, and provenance can itself be a revision witness	strong as a stipulated design invariant; the arithmetic is trivial	§6.2; A.5, A.6
C6	Exact recoverability and perfect statistical forgetting from the same accessible state are incompatible	strong (elementary)	Prop. 6
C7	A memory architecture keeping grounds, counterevidence and commitment status in bounded bundles will improve durable revision at equal budget	untested; a proposal	§6, §9

Concepts

• Revision sufficiency: a reduction ρ is sufficient for D if each demand’s target factors through it, T_d = g_d ∘ ρ, where D includes “specified changes to questions, circumstances, or evaluative laws”.
• Revision witness: a record or feature that distinguishes cases needing different responses under a chosen revision family; in §5.1, the sign of the second feature.
• Authored (memory): “a memory belongs to a continuing organization insofar as that organization can attribute its acquisition, assess its grounds, adopt or contest its evaluative use, and answer for commitments carried through it” (§1). Structural and normative, compatible with external storage; exclusive possession is “neither necessary nor sufficient”.
• Three relations: occurrence precedence, derivational dependence and semantic relation (§3.1), so that a contradiction between claims does not make the occurrence graph cyclic.
• Observation, appraisal, recognition: what was encountered, how it mattered under a law, and another party’s response; “Neither positive valence nor recognition is a probability that a claim is true” (§3.3).

Connections

The paper names its precedents: predictive state representations and the ε-transducer for memory defined by future tests; Moore and Nerode for the refinement; successor features for transfer under reward change; Doyle’s truth maintenance and AGM for revision; synaptic tagging, reconsolidation and Mattar & Daw as motivation only; and Generative Agents, MemGPT, A-MEM, AgeMem and five memory benchmarks for language-model agents. “We do not claim priority for sufficient statistics, dependency maintenance, or agent-controlled memory” (§1). The word “will” appears only in the title, which is the name of a six-paper series about “a portable synthetic subject”.

Bearing on the record

• CLAIM-295, QUESTION-112. The exchange’s judgement (A15, A16) that this is the closest outside predecessor is right. CLAIM-295’s three values have exact counterparts: informational value is §5.2’s R*(H) ≤ R*(S) with sufficiency making it zero; computational value is “Information availability and computational accessibility are different resources”; option value is §5.4’s shrinking set of recoverable laws. A5’s mechanism, targeted reconsideration after a premise is challenged, is §6.3 and A.6. The paper adds what the record lacked: an exact answer to QUESTION-112 for one case, a finite family of total deterministic revisions declared in advance (Prop. 4), and A10’s robust objective as a minimax over demands (§6.4). It does not answer the question’s hard part, a family that changes in response to findings: “An agent cannot infer that its future concerns are exhausted by its current ontology. The response is explicit scope and retained routes to reacquisition” (§10). Filed as THEORY-884, Proposed.
• CLAIM-350. Prop. 2 is CLAIM-350, stated for histories and a family of targets, with the same remark that it is elementary. A second, independent statement of it, not a test.
• CLAIM-294, CLAIM-300. §5.1 is a decision-valued twin of CLAIM-294’s construction (two histories, one current conclusion, different revisions), and the paper agrees with CLAIM-300 that a sufficient state leaves nothing for history to add for that family.
• CLAIM-293. Agrees: §6.3 asks for support sets or “another representation of alternative justifications, rather than propagating a Boolean invalid flag indiscriminately”, and says literal identifiers are “not universally necessary”.
• CLAIM-303. §6.4’s budgeted objective and §9.3’s resource accounting are the cost side the record’s claim states; the paper offers no break-even.
• CLAIM-250. The paper’s distinctions between historical attribution and active status, and between declared grounds, evidence of influence and later reconstruction (§5.3, §6.3), are the accountability structure CLAIM-250 wants preserved, argued from revisability rather than from fidelity.
• CLAIM-342. §3.3 (“Algebraic scale invariance is not immunity to self-confirmation”) and §6.2 (derived notes are not new evidence) are safeguards against the loop CLAIM-342 describes, and §9.2’s strongest test, where “the agent’s own initial choice produces the observation later requiring correction”, is its case.
• The will-organization material (TERM-023, TERM-047, TERM-067, CLAIM-122, CLAIM-407, the essay The Organization of Will). The shared word is the series title only. The paper has no counterpart of TERM-023’s will-organization, the organization of the conditions under which action-generating regimes gain or lose efficacy. Its subject is memory, and its agent is whatever revises through it. There are two real points of contact. (1) Form: revision sufficiency and TERM-067’s governance-response sufficiency are the same factorization criterion (CLAIM-350) applied to different target families. TERM-067’s targets are responses to interventions on governance; the Ledger’s include changes of evaluative law. Neither paper’s family contains the other’s. (2) Authority: §7’s “authority boundary” (who may propose, endorse, revise or terminate a commitment, with delegation scoped and revocable) is close to TERM-047’s jurisdiction, and §5.4’s “technical ability to delete does not itself establish its entitlement” echoes CLAIM-416’s and CLAIM-190’s line that competence does not certify authority. The paper does not define authority and does not study how it changes, so it gives the will line no test of CLAIM-122 or CLAIM-407.
• THEORY warranted? One, THEORY-884, for Prop. 4 with its scope. The rest the record already holds (CLAIM-350, CLAIM-294, CLAIM-300) or are design proposals.
• Anthology. The flag stands: the paper’s subject is memory for language-model agents and it names their systems and benchmarks. It gives no instruction for practice that it claims to have shown; §6 is offered as proposals to be tested.

Limitations

• The results are elementary and, by the paper’s account, not new; the contribution is their arrangement. Prop. 4 is Moore–Nerode refinement applied to an expanded target family.
• Everything formal needs a declared, finite demand family and enumerated revisions. For an open-ended agent the paper offers no way to choose witnesses: “Selecting useful, inexpensive witnesses for an open-ended environment remains an optimization and empirical problem” (§5.3).
• No experiment was run. “this paper offers no new human-subject study, no large-model performance result, and no experimental demonstration of subjecthood” (§10). The architecture of §6 is unevaluated, and the protocol of §9 is unexecuted.
• Authorship is by first names under a project name, with no affiliation, venue or review; versions 1–3 are not on the site.
• “Authored” memory and “authority” are used normatively and not analysed; the paper says its framework leaves “phenomenal remembering” outside its tests.

Open questions

• How should a revision family be chosen when the agent cannot list its future concerns? A robust objective over an uncertainty set of families (A10’s proposal, §6.4’s minimax) needs that set to be declared too.
• Does keeping revision witnesses improve durable revision at equal budget over plain retrieval with status metadata? §9’s protocol would decide it; it has not been run.
• Is there a governance-response analogue of Prop. 4: a coarsest representation invariant under interventions on what governs efficacy, for TERM-067’s targets after sequences of such interventions?