Research: enforce Brownian A/M/P generator semantics

docs/RESEARCH_STATUS.md

@@ -159,7 +159,7 @@ Process Geometry solver or independent adoption.
 | [`am-conformal-chart-normal-forms`](../sonnet/am-conformal-chart-normal-forms/00-problem-frontier.md) | Phase 1 exact Riccati lift, Möbius covariance, scalar gauge, cubic no-go, and eight-axis cost accounting | run oracle-isolated bounded discovery (1B) before the pendulum atlas search; no economy theorem yet |
 | [`moving-am-observer`](../sonnet/moving-am-observer/README.md) | static-observer no-go followed by blind moving-frame recovery, held-out family selection, task-equivalence quotient, blind morphism discovery, grammar stability, and dimensionful Bellman covariance | broader non-affine/multi-family or stochastic pressure, now separated into its own Sonnet |
 | [`stochastic-feedback-trap-first-passage`](../sonnet/stochastic-feedback-trap-first-passage/README.md) | bounded grammar census, exact Itô task quotient, independent BVP/Monte Carlo first-passage comparison, and reset Bellman value/policy covariance complete | calibration is closed; new discovery or API incubation requires a new contract |
-| [`brownian-scale-fibre`](../sonnet/brownian-scale-fibre/README.md) | S0/S1 initialized: blind centered finite-law scale balance, typed drift refusal, exact endpoint fibres, and concatenation pushforward | separate lattice point return, continuum neighbourhood recurrence, and singleton hitting before authorizing a Brownian/heat-kernel lowering |
+| [`brownian-scale-fibre`](../sonnet/brownian-scale-fibre/README.md) | S0/S1 corrected to PRE-AMP; executable A/M/P gate finds a global positive-position obstruction and an exact ensemble A/M/integer-P adapter with infinite-closure and path residuals | freeze a task that resolves one declared residual before recurrence or Brownian/heat-kernel lowering resumes |
 | [`lonely-runner`](../sonnet/lonely-runner/README.md) | exact upstream pruning transfer and bounded K4/K5 contact mechanisms; Phase 15A global audit complete | lift-aware initial search on solved cases, then frozen K13 validation; `LRC(13)` remains open |
 | [`hidden-am-noether`](../sonnet/hidden-am-noether/README.md) | bounded static-observer route reached a structural no-go; the viable moving-observer continuation is tracked separately | do not reopen static conjugation without new grammar or task semantics |
 | [`pcr3bp-history-cost`](../sonnet/pcr3bp-history-cost/README.md) | Phase 0/1 history, scale-jet, topology, and coding audit complete; Phase 2 contract frozen | execute converged return/absorbing ensemble and twisted partition audit; no numerical result yet |

sonnet/README.md

@@ -80,7 +80,7 @@ deferred until its next oracle/evidence gate is affordable.
 | [`hidden-am-noether/`](hidden-am-noether/) | static branch closed negatively | a frozen observer in the same product-affine group cannot reveal a missing stabilizer dimension | [static-observer no-go](hidden-am-noether/03-static-observer-no-go-and-schedule-split.md); continuation moved to `moving-am-observer/` |
 | [`moving-am-observer/`](moving-am-observer/) | affine deterministic phase closed | bounded blind observer discovery, task-equivalent minimum slice, and dimensionful Bellman covariance on the declared family | [study ledger](moving-am-observer/README.md); stochastic continuation moved to its own Sonnet |
 | [`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 |
-| [`brownian-scale-fibre/`](brownian-scale-fibre/) | S0/S1 active | blind centered finite-law scale balance and exact endpoint-fibre concatenation; no continuum limit or heat-kernel lowering yet | [problem frontier](brownian-scale-fibre/00-problem-frontier.md); next separate recurrence observers, then certify the continuum lowering |
+| [`brownian-scale-fibre/`](brownian-scale-fibre/) | A/M/P correction gate active | S0/S1 relabelled PRE-AMP; positive position chart fails globally, while the ensemble chart gives exact A shift, M scale, and integer-P replicas with closure/path residuals | [AMP chart gate](brownian-scale-fibre/01-amp-generator-chart-gate.md); recurrence and heat-kernel continuation paused |
 | [`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 |
 | [`effective-scale-carrier-ladder/`](effective-scale-carrier-ladder/) | T1 / NARROW | finite syntax decision eliminates a surreal runtime; symbolic height is a real C2 obstruction, but semantic evaluation and C3/C4 separation remain open | [results](effective-scale-carrier-ladder/01-results.md), [compiler](../workstreams/carrier_ladder/compiler/), and [commit--reveal audit](../workstreams/carrier_ladder/redteam/); next implement an effective normalized hyperiteration fragment, not a general surreal runtime |

sonnet/brownian-scale-fibre/00-problem-frontier.md

@@ -1,10 +1,22 @@
 # Problem frontier: recalculate Brownian motion from process fibres
 
-Status: frozen S0/S1 contract for
-[#158](https://github.com/mountain/process-geometry/issues/158), downstream of
+Status: frozen `PRE-AMP` S0/S1 discrete control for
+[#158](https://github.com/mountain/process-geometry/issues/158), corrected by
+[#160](https://github.com/mountain/process-geometry/issues/160), downstream of
 [#140](https://github.com/mountain/process-geometry/issues/140) and the
 native-method firewall merged in
-[#157](https://github.com/mountain/process-geometry/pull/157).
+[#157](https://github.com/mountain/process-geometry/pull/157).  Recurrence and
+heat-kernel continuation is paused pending the A/M/P chart gate.
+
+## 0. Correction boundary
+
+The finite-history calculation below is mathematically valid, but it is not an
+AMP-native calculation.  Its executable grammar contains only `A-step`:
+addition is active, while population size and probe scale are external
+parameters.  It contains neither finite M/P flows nor their infinitesimal
+generators and brackets.  The result is therefore retained as a discrete
+control, not promoted by changing its vocabulary.  The corrected AMP gate is
+recorded in [`01-amp-generator-chart-gate.md`](01-amp-generator-chart-gate.md).
 
 ## 1. Primitive process before the continuum answer
 
@@ -82,17 +94,19 @@ This phase certifies a necessary nontrivial scale and its local response
 coefficient.  It does **not** yet prove convergence to a Gaussian law or a
 continuum path process.
 
-## 3. Method firewall
+## 3. PRE-AMP method firewall
 
-S0/S1 have no allowed lowering witness.  The native source contains only the
+The discrete S0/S1 control has no allowed lowering witness.  Its source contains only the
 finite increment law, exact centered response, chronological histories,
 endpoint fibres, and their composition.  Classical local expansion,
 transform, continuum PDE, and simulation routes are declared separately in
 `phase0_contract.py` and cannot enter a native trace without a later
-task-adequacy witness.
+task-adequacy witness.  Its method events are now required to name `A-step`,
+and its contract explicitly says that M, P, and AMP brackets are absent.
 
 This is deliberately stronger than asking an agent not to use an oracle in
-prose: the merged method tool rejects the corresponding event in a native lane.
+prose: the method tool rejects both classical oracle entry and an AMP claim
+whose native evidence omits any task-required generator.
 
 ## 4. Held-out and red-team cases
 
@@ -109,15 +123,16 @@ prose: the merged method tool rejects the corresponding event in a native lane.
 
 ## 5. Relation to the larger programme
 
-This is the first independent scale/fibre family after the Bessel-based draft
+This is the first independent discrete scale/fibre control after the Bessel-based draft
 in PR #141.  It pressures U1, U2, U3, U4, and Effective Analysis because the
 same construction connects raw histories, scale, measured fibres, a continuum
 lowering, and later physical response.  At S0/S1 it remains T1 and leaves the
 Mathematical Core, Engineering Architecture, Theory Map, dependencies, and API
 unchanged.
 
-Surreal numbers are not needed for this finite-height task.  That is a negative
-runtime result, not an argument against later AMP or higher-height uses.
+Surreal numbers are not needed for this finite-height control or the first
+exact integer-replica AMP adapter.  That is a negative runtime result, not an
+argument against later AMP closure or higher-height uses.
 
 ## 6. Claim ceiling
 

sonnet/brownian-scale-fibre/01-amp-generator-chart-gate.md

@@ -0,0 +1,138 @@
+# Brownian A/M/P generator and chart gate
+
+Status: executable correction for
+[#160](https://github.com/mountain/process-geometry/issues/160).  This gate
+precedes recurrence, continuum, and heat-kernel work.
+
+## 1. What changed
+
+The first Brownian phase derived a correct discrete scale balance and exact
+endpoint fibres, but the computation had only an additive step process.
+Population (N) and probe contraction (N^{-a}) were external parameters.
+Calling that calculation AMP would therefore confuse an answer expressed with
+three letters with a calculation generated by three processes.
+
+The corrected method contract requires every AMP grammar to declare all of
+
+
+\[
+A_t(x)=x+t,\qquad
+M_s(x)=e^s x,\qquad
+P_r(x)=\exp(e^r\operatorname{Log}x),
+\]
+
+their infinitesimal actions
+
+\[
+A=\partial_x,\qquad
+M=x\partial_x,\qquad
+P=x\log(x)\partial_x,
+\]
+
+and the three relation witnesses
+
+\[
+[A,M]=A,\qquad [M,P]=M,\qquad
+[A,P]=(1+\log x)\partial_x.
+\]
+
+The last bracket is not in the constant span of (A,M,P).  Full A/M/P is not
+one three-dimensional Lie group.  Its closure generates further
+logarithmically weighted vector fields, represented at this gate by the
+residual family
+
+\[
+V_{m,n}=x^m(\log x)^n\partial_x.
+\]
+
+The software now rejects an AMP contract that omits a generator or relation,
+hides the A/P escape, or claims a task without trace evidence for every
+generator that task requires.
+
+## 2. Competing chart I: physical position
+
+The positive real chart is faithful to a physical position state and supports
+the real logarithm used by P.  M preserves positivity.  A does not: the exact
+symmetric history
+
+\[
+1\xrightarrow{A_{-1}}0\xrightarrow{A_{+1}}1
+\]
+
+leaves the common A/M/P domain at its first step.  The executable audit returns
+the first exit index, value, and offending increment as a typed obstruction.
+
+This is not a proof that no atlas can represent Brownian position.  It is a
+proof that the single real positive chart is not global, so any continuation
+must submit branch/gluing semantics rather than silently applying Log across
+zero.
+
+## 3. Competing chart II: positive ensemble observer
+
+For a finite law (mu), take the positive real observer
+
+\[
+Z_\mu(s)=\mathbb E_\mu[e^{sX}].
+\]
+
+The executable finite carrier stores exact atoms
+
+\[
+E_q(s)=e^{qs},\qquad E_pE_q=E_{p+q},
+\]
+
+with rational exponents and coefficients.  It is exponential-polynomial-like;
+it is not lowered to an ordinary polynomial, Taylor series, matrix, or Fourier
+basis.  The three process roles become
+
+\[
+Z_{X+t}=E_tZ_X,\qquad
+Z_{\lambda X}(s)=Z_X(\lambda s),\qquad
+Z_{X_1+\cdots+X_N}=Z_X^N.
+\]
+
+Thus A shifts atom exponents, M rescales them, and the nonnegative-integer
+slice of P composes independent replicas.  For the symmetric unit law the
+fifth replica is computed exactly as
+
+\[
+\left(\tfrac12E_{-1}+\tfrac12E_1\right)^5
+=\tfrac1{32}E_{-5}+\tfrac5{32}E_{-3}
++\tfrac5{16}E_{-1}+\tfrac5{16}E_1
++\tfrac5{32}E_3+\tfrac1{32}E_5.
+\]
+
+An independent comparison certifies coefficient-by-coefficient equality with
+the PRE-AMP endpoint-fibre law at horizon five.
+
+## 4. What the ensemble chart does not solve
+
+Two residuals remain explicit.
+
+First, the continuous P flow (Z\mapsto Z^{e^r}) is pointwise meaningful for
+positive real (Z), but a noninteger power generally exits the finite
+exponential-atom carrier.  The current exact implementation therefore claims
+only the integer replica slice; it does not replace the missing closure by a
+series expansion.
+
+Second, the endpoint observer identifies histories such as
+((+1,-1)) and ((-1,+1)).  They have the same terminal observer but different
+running maxima and chronological order.  The ensemble chart is exact for the
+declared endpoint-law task, not for path-space tasks.
+
+## 5. Result and next authorization gate
+
+The first nontrivial result is a separation, not a Brownian theorem:
+
+| Candidate | Exact gain | Blocking residual |
+| --- | --- | --- |
+| positive position | direct A/M/P state semantics | A crosses zero; P needs branch/gluing data |
+| positive ensemble observer | exact A shift, M scale, integer-P replicas; exact endpoint-law certificate | noninteger P leaves finite atoms; paths are forgotten |
+
+This is enough to correct the software method and expose a usable
+polynomial-like calculation at the AMP level.  It is not enough to authorize
+recurrence, a continuum Brownian law, a heat kernel, a speedup claim, or
+surreal arithmetic.  The next task must be frozen around one residual—either a
+branch-aware position atlas, a P-closed observer enlargement, or a
+path-sensitive fibre—and must beat the declared discrete control on that same
+task before the broader Brownian narrative resumes.

sonnet/brownian-scale-fibre/README.md

@@ -1,7 +1,9 @@
 # Sonnet — Brownian scale and endpoint fibres
 
 Research-local calibration for
-[#158](https://github.com/mountain/process-geometry/issues/158).
+[#158](https://github.com/mountain/process-geometry/issues/158), corrected by
+the A/M/P method gate in
+[#160](https://github.com/mountain/process-geometry/issues/160).
 
 This Sonnet recalculates the entrance to Brownian motion from raw increment
 histories.  It does not begin with the continuum process, a Gaussian density,
@@ -11,25 +13,36 @@ Read in order:
 
 1. [`00-problem-frontier.md`](00-problem-frontier.md) — primitive histories,
    tasks, scale argument, held-outs, and claim ceiling;
-2. [`phase0_contract.py`](phase0_contract.py) — frozen executable method lanes;
-3. [`brownian_native.py`](brownian_native.py) — exact scale and endpoint-fibre
-   calculations;
-4. [`test_brownian_scale_fibre_phase0.py`](../../tests/research/test_brownian_scale_fibre_phase0.py)
-   — independent certificates and source firewall.
-
-Current S0/S1 result:
+2. [`phase0_contract.py`](phase0_contract.py) — frozen `PRE-AMP` discrete-control
+   lanes;
+3. [`brownian_native.py`](brownian_native.py) — exact discrete scale and
+   endpoint-fibre controls;
+4. [`01-amp-generator-chart-gate.md`](01-amp-generator-chart-gate.md) — the
+   corrected A/M/P grammar, competing charts, and result boundary;
+5. [`phase1_amp_contract.py`](phase1_amp_contract.py) and
+   [`brownian_amp.py`](brownian_amp.py) — executable grammar audit and exact
+   exponential-observer adapter;
+6. the two research tests in [`tests/research`](../../tests/research/) —
+   independent certificates and fail-closed method checks.
+
+Current corrected boundary:
 
 ```text
-raw centered finite law -> active response order 2 -> scale balance a=1/2
-finite histories -> endpoint fibres -> exact concatenation pushforward
-biased law -> typed centering-required refusal
-continuum / heat-kernel lowering -> not yet authorized
+PRE-AMP: centered finite law -> response order 2 -> scale balance a=1/2
+PRE-AMP: finite histories -> endpoint fibres -> exact pushforward
+AMP position chart -> typed obstruction at zero / negative states
+AMP ensemble chart -> exact A shift, M scale, integer-P replicas
+full A/M/P closure -> infinite-dimensional residual retained
+recurrence / continuum / heat-kernel -> paused and unauthorized
 ```
 
-The scale result is narrower than a central-limit theorem.  The endpoint result
-is narrower than path equivalence.  S2 must next separate lattice point return,
-continuum neighbourhood recurrence, and singleton hitting before S3 authorizes
-a Brownian/heat-kernel lowering.
+The earlier scale and endpoint results remain valid controls, but they are not
+AMP results: only a discrete additive step was active.  The corrected gate
+shows that the positive position chart is not global for a symmetric process,
+while the positive ensemble observer supports exact A/M and the integer
+replica slice of P.  Noninteger P generally leaves the finite atom family, and
+the observer still forgets paths.  S2 recurrence and S3 heat-kernel work remain
+paused until one of those residuals is resolved for a frozen task.
 
 This task is the second independent representation family requested in
 [#140](https://github.com/mountain/process-geometry/issues/140).  Draft
@@ -39,4 +52,4 @@ while it remains unmerged.  The completed stochastic feedback-trap Sonnet is
 an independent downstream Itô/first-passage calibration and is not duplicated
 here.
 
-No Experimental or Public API pressure follows from S0/S1.
+No Experimental or Public API pressure follows from this gate.