Skip to content

MPA-RFC-S_Scale-Management.md

Latest commit

 

History

History
187 lines (123 loc) · 15.8 KB

MPA-RFC-S_Scale-Management.md

File metadata and controls

187 lines (123 loc) · 15.8 KB
Raw

MPA-RFC-S: Scale Management

Status: Draft v0.2 — first thin-RFC pass. (v0.1 preserved at MPA-RFC-S_Scale-Management_Block-In.md as honest-scope reference; not authoritative.) Targets: mpav1 (compressed, operational). Compression Axiom + operator algebra are the load-bearing imports. Companion: Architectural Block-In v0.2, RFC-1 v0.2, RFC-2 v0.1, RFC-RI v0.1

0. Foundational principles

This RFC inherits five principles from the Architectural Block-In, declared (not re-derived):

  1. Color-management discipline. Three layers (substrate-native / canonical / realizer-output); transforms declared, named, versioned, swappable.
  2. Observer-driven scale management. $\tau_{obs}$ is the camera; canonical representation is observer-relative.
  3. Demand-bounded sufficiency. Canonical representation sized to declared demand. The MPA is not the bottleneck.
  4. Singular working-space path. Within an RFC version, exactly one shape. Plurality lives in drivers, intent flags, and version succession.
  5. Thin-RFC discipline. It was never brittle if it never broke.

RFC-S adds one principle, internal to scale management:

  1. RG flow as foundational structure. Scale-management semantics derive from the renormalization-group flow defined by mpav1's Compression Axiom (Wilson–Kadanoff + Banach contraction at $\epsilon < 1$). The canonical representation, substrate gamut, intent operations, and behavior at boundary points are positions in or trajectories under this flow, not finite-engineering analogs reconstructed from color management. Color management is a finite discipline; MPA scale management is infinite. Infinity-machinery is imported directly, not patched on case-by-case.

1. Canonical representation (at observer position $p$)

The canonical representation at $p = \tau_{obs}$ is the fixed-point set of the Compression Axiom's RG flow at level $n$, restricted to the substrate's reachable trajectory.

Object Reading under RG flow
Vertex regime ${c, s, r}$ Fixed-point structure: $c$ and $r$ stable; $s$ metastable.
Edge $\gamma$ sign Cooperativity class; preserved at fixed $\tau_{obs}$.
Subgraph $k_{\text{frust}}$ RG-invariant on substrates carrying it; topological.
Trail-class equivalence Equivalence classes under the flow; cardinality $\tau_{obs}$-dependent.

Cross-position structure (auto-remap as $\tau_{obs}$ moves) is the flow trajectory itself; the driver supplies the rule that realizes it (form open — see Appendix B). Specifying the canonical representation at one $p$ plus the contraction $\mathcal{C}_n$ specifies it everywhere along the trajectory.

Pointer: mpav1 §Compression Axiom; §Three typed objects; §Boolean section.

2. Substrate gamut

A substrate's gamut is the image of its RG trajectory in canonical-representation space, parametrized by $(\tau_{obs}, D)$ — the locus the substrate's flow can traverse. Characterized by trajectory shape, not by multi-dimensional region enumeration.

Axis Substrate-declared content
$D$-range $[D_{\min}(p), D_{\max}(p)]$ at each $p$, from the substrate's $(\Phi^*, \kappa)$ envelope.
$\tau_{obs}$-range $\Pi(S)$, observer positions yielding valid canonical readings.
Persistence depth $N(S)$, maximum measurable ascent before $\epsilon \to 1$ or signal floors.
Reachable trail-class structure Which fixed-point patterns the trajectory visits.

A spec is in-gamut at operating $(\tau_{obs}, D)$ iff its $(V, E, \Gamma, D, \tau_{obs}, P)$ corresponds to points along the substrate's trajectory. Out-of-gamut handling is intent-determined (§3).

Pointer: mpav1 §Setting; §Capacity; §Falloff profile; Appendix G (Convergent Tower).

3. Intents

Five intents enumerate which canonical-representation invariants are preserved when a spec is out-of-gamut. The intent determines the mapping operation: scale uniformly along the gamut to fit, preserving the named invariant. (Rule, not per-intent operation table.)

# Name Preserves Sacrifices Color analog
I1 Regime-preserving Vertex regime partition; edge-type partition; $k_{\text{frust}}$; persistence-profile shape Absolute $D$, $\gamma$, $\lambda$ Perceptual
I2 Drive-faithful Exact $D$, $\gamma$, $\lambda$ on in-gamut content Completeness (out-of-gamut rejected, diagnostic-listed) Absolute colorimetric
I3 Capacity-preserving $|\Gamma^*|$ and structural pattern of sustainable subgraphs Absolute drive level; non-sustained regime relationships Saturation
I4 Persistence-preserving ${\varepsilon_n}$ shape; ${S_n}$ survival declarations; contraction ordering Absolute drives; single-position regime relationships (none — MPA-unique)
I5 Signature-preserving FDR-signature universality class (per regime / subgraph) Exact signature parameters Relative colorimetric

Where intents are declared. At type-changing junctions (driver, auto-remap, realizer). Operator actions ($C, S, K, R$) inside canonical space are intent-neutral by construction — they preserve canonical-representation invariants because the algebra is closed (RG-flow associativity).

Composition. Two adjacent intents compose iff their preserved-invariant sets union without conflict. I2 (drive-faithful) does not compose with adjusting intents. Composition algebra beyond this rule is deferred (Appendix B).

Pointer: mpav1 §Operators; §FDR signatures (I5 universality classes); Appendix F (substrate-conditional reading).

4. Driver profile

The artifact a driver produces. Field enumeration here; machine-readable schema in Appendix A. Operating envelope is folded in as a driver-profile section, not its own RFC section.

Section Content
header profile_version, target_rfc_versions, substrate_class, characterization_date, authority, validation_history
operating_envelope initial_conditions, parameter_ranges, measurement_protocol — what calibration must verify
gamut $D$-range; observer-range $\Pi(S)$; shear-profile envelope; trail-class support; persistence depth $N(S)$; contraction-rate fit
translation_field substrate-to-canonical and canonical-to-substrate maps, parametrized by $\tau_{obs}$; auto-remap rule (form open — Appendix B)
intents per-intent: supported (bool); gamut-mapping operation; sacrifice declaration; use cases
reference_outputs canonical test inputs with expected substrate responses + tolerance, for round-trip validation
metadata methodology; known limitations; versioning history

Characterization vs. calibration. Characterization produces the driver profile (one-time per substrate class). Calibration verifies the substrate is in the declared operating_envelope (per-experiment). A characterized-but-uncalibrated substrate has a profile that cannot be trusted on the current measurement; a calibrated-but-uncharacterized substrate has no profile at all.

Pointer: mpav1 §Substrate-conditional reading rules; Architectural Block-In §"What this means for drivers."

5. Round-trip validation

A driver is accepted iff forward and round-trip errors fall below intent-specific thresholds on every reference dataset the driver claims to support.

Protocol:

  1. Reference. Canonical reference dataset for the substrate class. (Surface-code QEC and habit-extinction are the proposed first two; see Architectural Block-In §"Reference substrates.")
  2. Forward. Driver under test produces canonical representation from reference substrate-native data.
  3. Forward comparison. Driver output vs. known-correct canonical representation, intent-specific metric.
  4. Backward. Reference realizer applied to driver's canonical output, producing predicted substrate-native data.
  5. Round-trip comparison. Predicted vs. original substrate-native data, intent-specific metric.
  6. Acceptance. Forward and round-trip errors both below thresholds, for every supported intent / dataset.

Per-intent metric (forward and round-trip share the metric):

Intent Metric
I1 regime-preserving Hamming distance on regime partition; agreement on edge-type partition
I2 drive-faithful $L^2$ on drive vector; $\max$ deviation on $\gamma$
I3 capacity-preserving $|\Gamma^*|$ deviation; structural-pattern similarity (graph-isomorphism family)
I4 persistence-preserving Sequence distance on ${\varepsilon_n}$; survival-declaration agreement
I5 signature-preserving Universality-class agreement; intra-class parameter distance

Reference-substrate bootstrap. First reference per substrate domain is hand-built from mpav1 by-hand reading (mpav1 §5 + Appendix F for surface-code QEC). Subsequent drivers are validated against it. Multi-driver agreement supersedes single-reference validation once multiple drivers exist.

Pointer: mpav1 §5 (surface-code identification); Appendix F (substrate-conditional reading); RFC-2 v0.1 canonicalizes I5 metrics.

6. Behavior at compactification points

Boundary parameter values are points in the compactified parameter space, not separate edge cases per intent. Behavior is specified once per point; the intent's preserved invariant fixes its action at the point.

Point Physical reading Default policy
$\epsilon \to 1$ Complexity Wall (mpav1 Appendix G). Tower fails to converge; further ascent thermodynamically forbidden. Spec must declare wall-acceptance (terminal level) or fail. I4 extrapolates with growing $\sigma_n$; others reject.
$D \to \infty$ Boolean limit. Canonical representation collapses to $\mathcal{M}_2 \cong \mathbb{B}$. Specs reduce to classical propositional logic; full operator algebra unnecessary. Recommend Boolean export.
$D = 0$ No drive. Only $\mathcal{M}_2$ subset admissible (no $s$-regime). Reject specs with $s$-regime vertices at $D = 0$.
$\tau_{obs} \to 0$ Microscopic limit. Substrate-native granularity dominates; $\Pi(S)$ floor governs. Below the driver's stated floor, the driver is invalid.
$\tau_{obs} \to \infty$ Fully coarse-grained. All structure migrates to $r$. Spec's persistence profile must terminate; else flag as exceeding $N(S)$.
$\lambda = \pm D$ Regime-transition boundary. Reading ambiguous within transition zone of substrate-characterized width $\delta$. Zone reading undefined. I1 widens to next category; I2 reports ambiguous; substrate declares $\delta$ in its driver profile.
$\gamma_{AB} > 0 \wedge D < \gamma_{AB}$ Theorem-9 boundary. Joint commitment infeasible. RFC-1 mechanical check flags. Intent-determined: I2 hard-flags, I1 scales, I3 redistributes $\gamma$.

Pointer: mpav1 Theorem 9 (joint-commitment threshold); Appendix G (Convergent Tower / Complexity Wall); §Boolean section.

Appendix A: Schema

Driver-profile schema is the canonical exchange shape. Machine-readable schema at schema/driver-profile.v0.2.json. §4 mirrors the schema's field structure as a reading aid; v0.1's YAML sketch (v0.1 §6) remains a non-authoritative reference.

Appendix B: Open

Items the next revision absorbs as needed:

  1. Auto-remap form: function vs. generator. v0.1 specifies auto-remap as a finite remap function. RG-thinking suggests the infinitesimal (tangent-flow) form: drivers specify the rule for small $\tau_{obs}$ changes; finite remaps are integrated. Open whether all substrate classes admit clean infinitesimal rules and whether integration is tractable. v0.2 admits both forms; v0.3 may canonicalize.
  2. Intent composition algebra past the union rule. §3 declares "union of preserved invariants without conflict." Whether this rule covers all admissible compositions is unverified at v0.2. If v0.3 needs a small composition table, that is the place a debt-marker would land — and the place sheaves (handoff Tier 3) might earn their weight.
  3. Lower-bound $\varepsilon_n$. $\varepsilon = 0$ is non-physical (information must be lost across real-scale coarse-graining). Substrate-specific $\varepsilon_n^{\min}$ declared in driver profile; form of declaration open.
  4. Observable sufficiency in round-trip validation. §5 assumes the backward map is invertible enough to validate; §4's reference_outputs are the inputs that drive it. Neither states which observables jointly constrain which canonical-representation axes. Concrete force: an inversion against a single-mode gFDR locus constrains the vertex regime but is rank-deficient on the edge $\gamma$ — the round-trip would pass while leaving an axis untouched. v0.3 should add an observable-coverage obligation: a driver's reference_outputs must jointly constrain every canonical axis it claims to support. (Surfaced by the mpa-auditor mock-dataset slice; see that repo's docs/rfc-s-integration-notes.md.)

(Trail-class metric and per-regime universality invariants closed in mpav1 between v0.2 and the next RFC-S revision: $\rho$ in §Compression Axiom, ${X_c, \alpha_s, P_s, X_r, N_f}$ in §FDR signatures. RFC-S §3 I5's intra-class metric and §5 round-trip per-intent metrics now reference these directly; v0.3 will tighten the §3 / §5 wording to point at the mpav1 invariants by name.)

Appendix C: What this RFC does not specify (deferred)

  • Behavioral / evolving substrates. Substrates whose operating envelope evolves during measurement (training neural networks, evolving biological systems) do not admit a static driver profile. Out of scope. Future RFC-Beh or extension axis.
  • Sheaf-theoretic pipeline composition. Tier-3 import (handoff §"Infinity-machinery available, ranked by fit"). Not earning weight at v0.2; reserve for v0.3 if §3's union rule proves insufficient.
  • Coalgebraic trail-class equivalence. Reserve for when mpav1's open trail-class metric question becomes blocking.
  • Reference-target standardization governance. Who declares which substrates are reference targets, on what criteria — operational, not protocol-layer.

Versioning

Version Status Change
v0.1 (Block-In) preserved as honest-scope reference Standards-body weight; ~5,800 words; 170–200-page projection.
v0.2 current Thin-pass rewrite. RG flow as foundational structure (§0 principle 6). Six body sections at half-page weight. Edge cases collapsed under compactification.

Compatibility. Within v0.x: schema additions only. Removal of intents or change to compactification-point semantics requires v1.0+ revision. Drivers declare which RFC-S version they target.

Page-budget self-check

Target: ≤5 pages including appendices (handoff §"What success looks like").

Body §0–§6 ≈ 3 pages; appendices A–C ≈ ½ page; versioning + self-check ≈ ¼ page. Total ≈ 4 pages. Pass.

For comparison: v0.1 ran ~620 lines of body and projected 170–200 pages at full ICC-v4-comparable resolution. The thin pass collapses 13 v0.1 sections to 6 active sections + 3 appendices. Compression mechanisms: RG flow + Banach contraction handle infinite coarse-graining as a single import (§0.6); compactification handles boundary behavior as points-in-space (§6); the five-intent table (§3) and round-trip protocol (§5) are preserved at full weight as the load-bearing exchange artifacts.

Debt-markers. None at v0.2. Pipeline composition — the handoff's flagged candidate to break the budget — was held to §3's intent-composition union rule plus deferral in Appendix C. If that rule proves insufficient against actual stress, v0.3 will carry a debt-marker naming the break and may import sheaves.