research: backlog Otto-287 Noether-style formalization (P3, L)

docs/BACKLOG.md

@@ -10146,6 +10146,29 @@ systems. This track claims the space.
 
 ## P3 — noted, deferred
 
+- [ ] **Otto-287 Noether-style formalization — quantify
+  cognitive Lagrangian + identify continuous symmetries +
+  derive conserved currents.** Aaron 2026-04-25 directive:
+  *"backlog ongoing research here to formalize this
+  conservation law analogously."* Source: Otto-287
+  (`memory/feedback_finite_resource_collisions_unifying_friction_taxonomy_otto_287_2026_04_25.md`)
+  proposed all friction sources are finite-resource
+  collisions; Aaron asked whether this generalizes to a
+  physics-style conservation law analogous to Noether's
+  theorem. Soft analogy is substantive (constrained-
+  optimization-produces-structure shape, meta-conservation
+  of rule-form, cognitive-effort-redirection); strict
+  Noether-style derivation is open research. Four steps
+  owed: (1) define cognitive action $S = \int (W - F) \, dt$
+  with quantified work-output and friction-cost rates;
+  (2) identify continuous symmetries (time-translation,
+  reader-identity, resource-type); (3) derive Noether
+  currents; (4) symmetry-breaking analysis. Effort L,
+  research-grade. **Acceptance signal:** new substrate
+  rules become DERIVABLE from the formalism rather than
+  intuited. Per-row file: `docs/backlog/P3/B-0002-otto-287-noether-formalization.md`.
+  Research direction: `docs/research/otto-287-noether-formalization-2026-04-25.md`.
+
 - [ ] **Local-DB shortlist for factory indexing / search
   (code, docs, skills, memory) — research-lane, pick the
   two-to-three bets we'd actually integrate.** Human

docs/backlog/P3/B-0002-otto-287-noether-formalization.md

@@ -0,0 +1,90 @@
+---
+id: B-0002
+priority: P3
+status: open
+title: Otto-287 Noether-style formalization — quantify cognitive Lagrangian + identify continuous symmetries + derive conserved currents
+tier: research-grade
+effort: L
+directive: maintainer Otto-287/Aaron 2026-04-25 ("backlog ongoing research here to formalize this conservation law analogously")
+created: 2026-04-25
+last_updated: 2026-04-25
+composes_with: []
+tags: [otto-287, formal-methods, physics, cognitive-substrate, research-grade, noether]
+---
+
+# Otto-287 Noether-style formalization
+
+Push the Otto-287 finite-resource-collisions taxonomy from
+**substantive analogy** toward **rigorous formalization**
+in the style of Noether's theorem (continuous symmetries
+→ conserved quantities).
+
+Source: Aaron 2026-04-25 directive *"backlog ongoing
+research here to formalize this conservation law
+analogously."*
+
+## What's owed
+
+Per the research direction in
+`docs/research/otto-287-noether-formalization-2026-04-25.md`,
+four steps:
+
+1. **Define the cognitive action $S = \int (W - F) \, dt$.**
+   Quantify productive work output rate $W$ and friction cost
+   rate $F$ for the factory's collaboration loop. Some are
+   already measurable (CI minutes, decisions queued); some
+   are subjective and need a measurement scheme.
+2. **Identify continuous symmetries of $S$.** Candidates:
+   time-translation, reader-identity, resource-type. Test
+   each against observed factory behaviour.
+3. **Derive Noether currents.** For each symmetry, the
+   corresponding conserved quantity. Three candidates:
+   factory-energy, semantic charge, rule-form
+   (Otto-287's externalize-compress-preallocate template).
+4. **Symmetry-breaking analysis.** Identify enduring
+   modes (memory entries, decision records) as Goldstone-like
+   massless modes from broken symmetries.
+
+## Acceptance signals
+
+The formalization succeeds (and graduates from research-
+grade to production substrate) when:
+
+- A quantitative metric for $W$ and $F$ exists and runs
+  per-tick.
+- At least one continuous symmetry of $S$ is verified
+  empirically over multiple sessions.
+- At least one conserved current is derived, and its
+  conservation is observable in factory data.
+- New substrate rules can be DERIVED from the formalism
+  rather than just intuited.
+
+## Why P3 (not higher)
+
+The operational substrate (Otto-281..287) works as a
+practical discipline regardless of whether the
+formalization succeeds. The formalization is upside, not
+load-bearing. Existing factory output is unchanged
+whether or not we ever derive a Noether current.
+
+## Why open (not closed)
+
+Indefinite research direction. May never close fully;
+incremental progress per session deepens the analogy.
+First milestone is Step 1 (quantification) — anything
+beyond is upside.
+
+## Composes with
+
+- `memory/feedback_finite_resource_collisions_unifying_friction_taxonomy_otto_287_2026_04_25.md`
+  — the substrate captured this observation
+- `docs/research/otto-287-noether-formalization-2026-04-25.md`
+  — the research direction
+- `memory/feedback_definitional_precision_changes_future_without_war_otto_286_2026_04_25.md`
+  — Otto-286 precision discipline enables Step 1
+  quantification
+- `memory/project_precision_dictionary_evidence_backed_context_compressor_2026_04_25.md`
+  — the precision-dictionary makes formal cognitive-
+  Lagrangian definitions AI-consumable
+- `docs/VISION.md` — the Z-set/DBSP operator algebra sits
+  one level below; cognitive-Noether may compose downward

docs/research/otto-287-noether-formalization-2026-04-25.md

@@ -0,0 +1,228 @@
+# Otto-287 → Noether-style formalization — research direction (2026-04-25)
+
+**Status:** open research. Not committed work; not blocking
+operational substrate. Captured per Aaron's 2026-04-25
+directive: *"backlog ongoing research here to formalize this
+conservation law analogously."*
+
+**Source:** Otto-287 (memory entry
+`feedback_finite_resource_collisions_unifying_friction_taxonomy_otto_287_2026_04_25.md`)
+proposed that all friction sources in the factory's
+collaboration loop are finite-resource collisions. Aaron asked
+whether this generalizes to a physics-style conservation law
+analogous to Noether's theorem.
+
+## The question
+
+> *"ALL FRICTION SOURCES ARE FINITE-RESOURCE COLLISIONS — do
+> you think this generalizes to physics invariant / symmetry
+> or reason for symmetry breaking?"* (Aaron, 2026-04-25)
+
+> *"is there some new conservation law we have exposed now
+> too because of this?"* (Aaron, 2026-04-25, follow-up)
+
+## The honest answer
+
+**The strict version (Noether-style):** No. Physics
+conservation laws come from continuous symmetries of an
+action principle (Noether's theorem). Cognition does not have
+a clean Lagrangian or continuous symmetry group in the same
+sense, so we cannot derive a rigorous conservation law
+analogously. Yet.
+
+**The soft analogy (substantive):** Yes, with caveats. Three
+candidate "conservation-adjacent" structures live here:
+
+### 1. Constrained-optimization produces structure (same shape, both domains)
+
+- **Physics:** minimize energy under finite-resource
+  constraint → symmetry-breaking ground states (Higgs vacuum
+  expectation value, crystal lattice formation, magnetic
+  domains, superconducting Meissner state).
+- **Cognition:** minimize friction under finite-cognitive-
+  resource constraint → externalization / compression /
+  pre-allocation rules (Otto-281..287 substrate).
+
+In both domains the **constraint is what produces the form**.
+This is a deep similarity, but it's a similarity of
+methodology (constrained optimization), not of mathematical
+structure.
+
+### 2. Meta-conservation of rule-form
+
+Otto-287 itself IS what's conserved across the substrate.
+Each Otto-NNN rule is a "Noether-current-like" instance of
+the same conserved structure: take a finite resource, apply
+externalize / compress / pre-allocate, get a discipline.
+The rule-form persists invariantly across all applications.
+
+| Otto-NNN | Conserved meta-structure (the form) | Local "current" (the resource) |
+|---|---|---|
+| Otto-281 | externalize-compress-preallocate | flake-investigation budget |
+| Otto-282 | externalize-compress-preallocate | reader's working memory |
+| Otto-283 | externalize-compress-preallocate | maintainer's context-switch budget |
+| Otto-284 | externalize-compress-preallocate | agent's session-time budget |
+| Otto-285 | externalize-compress-preallocate | test-coverage budget |
+| Otto-286 | externalize-compress-preallocate | argument-resolution context window |
+
+This is more like a **symmetry principle** than a
+conservation law strictly. But it has teeth — predicting
+that any newly-identified finite resource will admit a
+rule of the same form.
+
+### 3. Cognitive-effort redirection (closest to a conserved quantity)
+
+Total cognitive effort over a fixed time window isn't
+created or destroyed; substrate rules shift its
+allocation between two buckets:
+
+- **Wasted on friction** (re-derivation, context-switches,
+  bottleneck waits, calcification, fake-green CI tax,
+  flake-rerun cycles)
+- **Available for productive work** (substrate building,
+  research, code, decisions, communication that lands)
+
+Substrate rules apply *transformations* that move effort
+from the first bucket to the second. The total capacity is
+finite (Otto-287 physics layer), but the productive
+fraction grows as friction is externalized.
+
+This is **not strict conservation** (capacity is bounded
+above, not invariant in the strict sense), but it is a
+**redistribution principle** that has measurable
+consequences. If we could *quantify* per-tick cognitive
+budget and per-rule friction-removal magnitude, we'd have
+a quantitative law.
+
+## What a real formalization would need
+
+To push from analogy to rigor, the research owes:
+
+### Step 1 — define the cognitive "action" $S$
+
+Action principles in physics: $S = \int L \, dt$ where $L$
+is a Lagrangian (kinetic - potential energy).
+
+Cognitive-substrate analogue: $S = \int (W - F) \, dt$
+where:
+
+- $W$ = productive work output rate (information produced,
+  problems solved, substrate captured)
+- $F$ = friction cost rate (re-derivation, bottleneck waits,
+  flake reruns, etc.)
+
+This requires *quantifying* both $W$ and $F$ for the factory.
+Some are measurable (CI minutes, tokens consumed, decisions
+queued); others are subjective (re-derivation effort, debate
+exhaustion). The first research milestone is a quantitative
+metric for both.
+
+### Step 2 — identify continuous symmetries of $S$
+
+Candidates:
+
+- **Time-translation symmetry**: $S$ invariant under $t \to t
+  + \delta t$. If true, conserves something like
+  "factory-energy" (productive-work-minus-friction). But the
+  factory has explicit time-dependence (sessions, fatigue,
+  context-window decay), so time-translation symmetry may be
+  broken.
+- **Reader-identity symmetry**: $S$ invariant under
+  exchange of readers (Aaron, agent, future-contributor,
+  external-AI). If true, conserves "semantic charge" — the
+  meaning of substrate is the same regardless of who reads
+  it. Otto-282 + the precision-dictionary direction
+  *enforce* this symmetry.
+- **Resource-type symmetry**: $S$ invariant under exchange
+  of one finite resource for another (working-memory ↔
+  test-budget). If true, conserves the rule-form (Otto-287).
+  This is the meta-conservation already identified.
+
+### Step 3 — derive conserved Noether currents
+
+For each symmetry, the corresponding conserved quantity:
+
+- Time-translation → factory-energy (analog of physical
+  energy)
+- Reader-identity → semantic charge (the meaning preserved
+  across readers)
+- Resource-type → rule-form (the externalize-compress-
+  preallocate template)
+
+Whether these are *useful* conserved quantities (i.e., the
+formalization predicts something we couldn't predict
+without it) is the third research milestone.
+
+### Step 4 — symmetry-breaking analysis
+
+If the cognitive Lagrangian has more symmetry than the
+factory's actual ground state, then symmetry-breaking
+mechanisms would explain WHY the factory exhibits less
+symmetry than its action principle would suggest. Candidates:
+
+- The maintainer's specific identity breaks reader-identity
+  symmetry.
+- Session-boundary effects break time-translation symmetry.
+- The specific algebra (Z-set, DBSP) breaks resource-type
+  symmetry.
+
+Each broken symmetry produces a "Goldstone-like" massless
+mode — the analogue would be the *enduring narrative* that
+persists across substrate captures. Empirical observation:
+the factory's running narrative (memory entries, decision
+records) IS such a persistent mode.
+
+## Why this matters operationally
+
+If the formalization succeeds, three concrete benefits:
+
+1. **Quantitative substrate-rule predictions.** A new
+   finite resource → predicted friction-reduction rule
+   shape derivable from the symmetry, not just intuited.
+2. **Conservation-law-driven design.** New factory features
+   could be evaluated against whether they preserve or break
+   the substrate's symmetries. Same way physicists use
+   conservation laws to constrain new theories.
+3. **Cross-domain transferability.** A formal
+   correspondence with physics opens applications to other
+   constrained-optimization domains (economics, ecology,
+   distributed systems). The factory's substrate becomes
+   exportable substrate for any system facing
+   finite-resource collisions.
+
+## What this doesn't claim
+
+- This is *not* a claim that cognition is physics. Reduction
+  is not the goal; analogy with operational utility is.
+- This is *not* a claim that we've solved or will solve the
+  formalization soon. It's a research direction with
+  significant gaps (especially Step 1 quantification).
+- This is *not* a substitute for the operational substrate.
+  Otto-281..287 work as practical disciplines regardless of
+  whether the formalization succeeds.
+
+## Backlog tracking
+
+A BACKLOG row owes (P3 research-grade, L effort): **"Otto-287
+Noether-style formalization — quantify cognitive Lagrangian,
+identify continuous symmetries, derive conserved currents,
+analyze symmetry-breaking modes."**
+
+Filed under research-grade because the operational substrate
+is independent of the formalization's success. The
+formalization is upside, not load-bearing.
+
+## Composes with
+
+- `memory/feedback_finite_resource_collisions_unifying_friction_taxonomy_otto_287_2026_04_25.md`
+  — the source observation.
+- `memory/feedback_definitional_precision_changes_future_without_war_otto_286_2026_04_25.md`
+  — the precision discipline that makes Step 1
+  quantification possible.
+- `memory/project_precision_dictionary_evidence_backed_context_compressor_2026_04_25.md`
+  — the precision-dictionary IS the substrate that would
+  make formal cognitive-Lagrangian definitions
+  AI-consumable.
+- `docs/VISION.md` — the Z-set/DBSP operator algebra is
+  the formal foundation; cognitive-Noether sits one level
+  above and may compose downward.