Recorded Riccati context continuation

Recorded Riccati context continuation

Status: released and deployment-verified in PR120. The general geometric-language research program remains active.

Problem and representation

The existing recorded context frame for JacobiData.slope_bound_abs stopped after six introductions. A source-level local definition can be visible without having a checked construction record. Its name or position does not justify extending a typed frame.

Eighteen additional exact native queries supply six local-definition records for each of the published-15 and working-26 packet identities, and six introduction records for the working packet. The same existing frame rule now retains twelve source constructors: six introductions followed by hz, hD, hds, hprod, amgm and hsum. No theorem-specific drawing rule is added.

For member i, its domain/type and local-definition value use Γi; its original body uses Γ(i+1). The AM–GM value is original source node 1227 at Γ10. Source selection and computed-type selection retain separate identities. The frame retains twelve occurrences and represents 165,582 hidden header/body occurrences, accounting for all 165,594 occurrences below its original root.

The published packet’s next body has a recorded Π-application. The working packet’s next body has a recorded type but no construction record. The latter therefore stops with no-construction-record; an available type does not imply an available rule or recursive proof-step coverage.

Native and publication provenance

The queries were executed in one existing, pinned compiled project environment and matched against the two immutable packet identities. The selected source module and compiled modules were unchanged. This is not an independent reconstruction of both historical snapshot environments or a portable kernel certificate.

Only compiled native judgments, their packed type/reduction data and derived delivery pages are public inputs. Original private source projects, proof scripts and execution logs are excluded. publish_native_contexts.cjs appends profiles, refuses replacement, validates source/context attachments and records this environment scope. Its compiled input archives permit deterministic projection checks without importing private mathematical modules.

The canonical projection excludes gzip-size measurements: recompressing identical JSON can produce different sizes under different zlib versions. It records decoded size instead. Delivery-pool sizes describe the retained gzip artifacts; the publisher compares every decoded byte before retaining their stored sizes. The explicit --reproject command changes packing metadata only and refuses any change to the source, environment, expressions or contextual judgments. Original input archives and preceding packed archives remain available.

A construction can own a different shared type table from an overlapping older position observation. Page production retains the construction’s original table identity without replacing the position observation or inventing another query.

Checks

From the repository root:

node scripts/test-proof-atlas-native-context-publication.cjs
node research/proof-atlas/publish_let_pools.cjs --check
node scripts/test-proof-atlas-construction-owner-tables.cjs
node scripts/test-proof-atlas-riccati-context-continuation.cjs
node scripts/test-proof-atlas-riccati-context-continuation-browser.cjs

The publication check reconstructs three new compiled-input projections and rejects 26 changed provenance/context/conversion controls. Six alternate gzip encodings must preserve the same canonical descriptors and decoded data. The projection and delivery-page checks also pass under Node 22 and Node 23. The targeted page check compares both twelve-member frames and all 62 selected recorded type views with the complete reference, independently walks source fields and binder depths, and rejects foreign packet attachments. The normal production browser compares the same 62 views, follows both AM–GM source focuses, checks the explicit working-packet boundary, and runs four accessibility checks at phone/desktop widths in both themes. These interactions fetch no complete source/native archive.

The refreshed structural source-cut summary covers 41 requests, 3,222 cuts and 3,087 binding appearances, including the working Riccati packet. Its native execution and independent target audit were completed in CI. Fresh local core Lean runs for both Riccati packets and the shared-binder control additionally match the CI native output hashes: 450 cuts and 227 binding appearances. These checks reconstruct source syntax and lexical targets; they do not type-check the original mathematical proofs.

The normal paged-browser audit compares 26 extraction profiles and 269 recorded chain starts after this extension. These are finite occurrence checks, not whole-proof coverage. PR120 supplied the contextual records; it did not evaluate mathematical readability, semantic compression or human comprehension. The subsequent bounded caption rule is described in the caption method.