research: add observer-driven scale compiler S0–S2 (NARROW)

sonnet/README.md

@@ -82,6 +82,7 @@ deferred until its next oracle/evidence gate is affordable.
 | [`stochastic-feedback-trap-first-passage/`](stochastic-feedback-trap-first-passage/) | current calibration closed | exact Itô task quotient plus independent first-passage and reset-Bellman covariance across 242 monotone charts | [Phase-4 results](stochastic-feedback-trap-first-passage/09-phase4-reset-bellman-results.md); further work requires a new Sonnet or governed extraction proposal |
 | [`pcr3bp-history-cost/`](pcr3bp-history-cost/) | Phases 0–1 complete; Phase 2 frozen | lifted topology and scale-jet reconstruction separate word, clock, deck, and hyperbolic costs; no Bellman/Huffman source is yet justified | [Phase-2 contract](pcr3bp-history-cost/02-return-partition-holonomy-contract.md); next run the frozen two-gate covariance and convergence gates |
 | [`am-conformal-chart-normal-forms/`](am-conformal-chart-normal-forms/) | T0/T1; Phase 1 mechanism calibrated | exact Riccati lift, Möbius covariance, scalar-gauge invariance, cubic no-go, and eight-axis Pareto accounting; no discovery or economy theorem | [Phase-1 results](am-conformal-chart-normal-forms/02-phase1-riccati-results.md); next freeze a blind low-height grammar and run bounded recovery |
+| [`observer-driven-scale-chart-compiler/`](observer-driven-scale-chart-compiler/) | S2 local-chart gate passed; disposition narrow | exact backward task-repair semantics plus frozen Airy, held-out cusp, and registered raw-Bessel-to-local-chart certificates; no uniform integral, comparative novelty, or economy theorem | [S2 Newton/Bessel result](observer-driven-scale-chart-compiler/03-analytic-germ-newton-bessel.md); next require a second representation family and executable same-information Wolfram comparison before any claim expansion |
 | [`s6-complex-arithmetic-tower/`](s6-complex-arithmetic-tower/) | T0 initialization | auditable two-question research contract only; neither the manuscript nor an arithmetic interface is verified | [problem frontier](s6-complex-arithmetic-tower/00-problem-frontier.md); next archive/checksum the source and reproduce its matrix/topology certificate |
 | [`boltzmann-bbgky-h-theorem/`](boltzmann-bbgky-h-theorem/) | Phase 1I charted fibre-response calibration passed | 47 exact certificates through Phases 1C and 1E–1I; target Lyapunov decrease need not survive continued fibre response; contrast/odds expose a chart-relative dynamics/composition tradeoff; no continuum response theorem, fibre objectification, or generic entropy claim | [Phase 1I result](boltzmann-bbgky-h-theorem/18-phase1i-charted-fibre-calculus-results.md); next run the separate finite collision-covector and continuum fibre-response gates |
 

sonnet/observer-driven-scale-chart-compiler/00-problem-frontier.md

@@ -0,0 +1,168 @@
+# Observer-driven scale and chart compiler — problem frontier
+
+**Issue:** [#140](https://github.com/mountain/process-geometry/issues/140)  
+**Date:** 2026-08-27  
+**Status:** T1/local research target; Sonnet-local; no Experimental or Public API
+
+## 0. Research question
+
+Can a task-relative compiler propagate an output observer backwards through a
+finite expression DAG, retain scale information that downstream operations can
+amplify, and discover a distinguished monomial chart with an exact replayable
+certificate and explicit failure semantics?
+
+The larger motivation is that an observer sees only a bounded window of a
+scale ensemble. Surreal numbers, Hahn fields, transseries, valuations, and
+nonstandard structures are relevant semantic comparison models. They are not
+assumed to be the runtime representation, and no computational advantage is
+credited to surreal arithmetic in this phase.
+
+## 1. Frozen problem contract
+
+The first prototype receives:
+
+~~~text
+finite exact expression DAG
+one large parameter N -> +infinity
+dimensionless regime
+output observer and requested residual order
+unknown variable scales and fixed scales
+finite monomial-chart grammar and resource budget
+~~~
+
+It returns one of:
+
+~~~text
+certified finite series and residual ledger
+certified unique monomial chart and normalized phase
+unsafe within Taylor budget
+outside the implemented scale/domain grammar
+underdetermined or inconsistent balance
+resource budget exceeded
+~~~
+
+Expected exponents, named normal forms, target special functions, and
+case-specific rules are forbidden discovery inputs.
+<code>prototype/FROZEN_CONTRACT.json</code> is the machine-readable S0
+contract.
+
+## 2. Mathematical seam
+
+For a current task quotient \(q:H\twoheadrightarrow B\), a downstream operator
+\(U:H\to H'\), and an output task \(q':H'\twoheadrightarrow B'\), exact descent
+exists iff
+
+\[
+\ker q\subseteq\ker(q'\circ U).
+\]
+
+When descent fails, the information-minimal exact task repair is the joint
+image
+
+\[
+q^*_{U,q'}:h\longmapsto(q(h),q'(U(h))).
+\]
+
+Equivalently, output predicates pull back contravariantly through the DAG and
+branch obligations meet by intersection. This is the mathematical core of the
+backward observer pass. It does not imply that the information-minimal quotient
+has the cheapest encoding.
+
+The non-Archimedean exponent example supplies a sharp amplification witness.
+For positive infinite \(Y\), the near-unit elements
+
+\[
+x_a=\exp(a/Y)
+\]
+
+have the same standard part \(1\), but
+
+\[
+x_a^Y=e^a.
+\]
+
+The response coordinate \(b_Y(x)=\operatorname{st}(Y\log x)\) is the minimal
+exact repair inside the critical response window. This is mainly a valuation
+and exponential-field consequence, not a new surreal-specific theorem.
+
+## 3. Initial compiler mechanism
+
+The evaluator uses a finite log-exp-power IR and exact rational powers of
+\(N\). Intermediate terms are propagated through the whole expression before
+the output observer truncates them. A noninteger power is lowered locally as
+
+~~~text
+pow(base, exponent) -> exp(exponent * log(base)).
+~~~
+
+Thus a locally hidden \(N^{-1}\) perturbation in
+\((1+N^{-1})^N\) is retained because the exponent amplifies it to order
+\(N^0\).
+
+For polynomial exponential phases, chart discovery distributes exact
+monomials and solves one rational order equation per active term. The initial
+task requires every nonzero phase monomial to be \(O(1)\). Candidate subset
+search, competing balances, and chart ranking are outside this frozen phase.
+
+## 4. Calibration and evidence firewall
+
+The public calibration is
+
+\[
+S_N(t,z)=N\left(\frac{t^3}{3}-zt\right).
+\]
+
+The solver must derive
+
+\[
+1-3a=0,\qquad 1-a-b=0
+\]
+
+and hence \(t=N^{-1/3}u,\ z=N^{-2/3}\xi\) without receiving the exponents or
+the word “Airy”.
+
+A strict held-out is selected by commit--reveal. Compiler source, tests,
+grammar, scoring, and failure semantics are hashed before the held-out preimage
+is disclosed. Any post-reveal grammar or implementation edit receives no
+discovery credit.
+
+## 5. Baseline discipline
+
+Every system receives the same raw expression/equation, regime, task
+neighborhood, requested order/error, and allowed grammar when its interface
+accepts one. Unhinted discovery and hinted verification are separate rows.
+
+Required pressures include:
+
+- SymPy one-variable exp/log and cancellation controls;
+- Sage growth-group and asymptotic-ring comparison;
+- Wolfram asymptotic-scale, WKB, boundary-layer, and steepest-descent
+  comparison;
+- automatic asymptotics and transseries work by Richardson and van der Hoeven;
+- a non-toy coalescing-saddle pressure case;
+- at least one correct refusal or ambiguity result.
+
+## 6. Acceptance and kill conditions
+
+The initial phase passes only if it provides exact replayable certificates,
+typed failure, a strict held-out run without grammar edits, and honest total
+cost ledgers. It must be narrowed or stopped if:
+
+- expected scales or solved charts leak into discovery;
+- the carrier stores the complete source expression as a disguised residual;
+- branches, cancellation, or competing balances are resolved by undeclared
+  backend heuristics;
+- reparameterization changes the result with no typed transport or ambiguity;
+- an equal-information baseline matches the capability with no weaker
+  certificate and lower total cost;
+- surreal arithmetic changes vocabulary but no theorem, algorithm,
+  certificate, or reachable workload;
+- a held-out result requires post-reveal grammar changes.
+
+## 7. Claim ceiling
+
+This work does not claim a general asymptotic or Process Geometry compiler, a
+surreal runtime, a new arithmetic rank, effective V5 closure, a complexity
+breakthrough, or leverage on 3D Ising. A successful S0/S1 prototype is at most
+a bounded research-local certificate generator and a future extraction
+candidate after independent-domain pressure.