Math dependency graph

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Catalog: research; topics: mathematical-reasoning, visualization, scholarly-documents; visibility: featured Activation: user-request, skill-workflow; persistent modifier: no

Skill Version: 69

Uses Interfaces:

• math-dependency-graph.source.gateway -> math-dependency-graph._rtx.interface.scripts-advance-extraction-phases@23
• math-dependency-graph.source.gateway -> math-dependency-graph._rtx.interface.scripts-record-run-diagnostics@5
• math-dependency-graph.source.gateway -> math-dependency-graph.interface.extract@26
• math-dependency-graph.source.gateway -> math-dependency-graph.interface.inventory@29

Public Interfaces:

• math-dependency-graph.interface.default
• math-dependency-graph.interface.extract
• math-dependency-graph.interface.inventory

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Generated from blueprint.yaml. Do not edit this block by hand.

Instruction Interfaces:

These interfaces are documented prompt surfaces. They are not executed through dispatcher:

• math-dependency-graph.interface.default — Orchestrate a measured inventory, extract, compile, and render run.
• math-dependency-graph.interface.extract — Reconcile pooled inventory and the retained entrypoint into final notation-faithful entities and direct relationships, or author one returned narrow repair.
• math-dependency-graph.interface.inventory — Author one concise recall-first graph inventory fragment through one bounded-unit, signal-complete, validated forward loop.

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Mathematical Dependency Graph

The gateway orchestrates one canonical semantic pipeline: inventory -> extract -> compile -> render. It invokes interfaces and schedules workers; it does not restate or perform the mathematical judgments owned by inventory and extract.

Use a fresh empty run directory and never reuse an earlier inventory, semantic IR, graph JSON, or HTML artifact. Use only absolute paths returned by process-interface reports. A worker writes its assigned JSON directly; the gateway never generates semantic records with code or bulk transformations.

Gateway algorithm

1. Prepare. Resolve the TeX entrypoint and invoke math-dependency-graph._rtx.interface.scripts-advance-extraction-phases prepare <entrypoint> --run-dir <run-dir>. This operation prepares the complete reachable source, creates the minimum safe ordered inventory jobs, and performs the required diagnostics initialize event. Require its report to name an absolute diagnostics path and retain that exact path for the whole run. Do not issue a second initialize event.

2. Inventory. Schedule every reported next_jobs item through a fresh worker. Pass its returned instruction, schema, packet, progress, and output paths exactly. Require one recall-first monotone source loop. At each bounded source unit—one prose paragraph, one display, one complete delimited theorem-like environment, or one paragraph/display inside a proof—the worker must, in order: identify the owning object; make the bounded-formal-block decision; check all six formal-claim, reusable-setup, assumption, named-tool, proof-use, and exposition/application slots; emit every direct prerequisite-to-dependent lead; account for the observed signals; validate and checkpoint when due; then advance. Section and subsection commands and Markdown headings supply context only; they are not graph-reading units. Theorem-like and definition-like TeX or Markdown blocks default to candidates, while technical wrappers never duplicate their inner statements. Require one-sentence node summaries and one-clause edge explanations when first recorded, a schema-valid cumulative fragment at every bounded cursor, and complete explanations before appending matching cursor/counter progress; never dispatch a later compaction or wording-rewrite job. Retries reuse both paths only to repair validation or coverage failures. Immediately before a job waits for or requests a worker, invoke math-dependency-graph._rtx.interface.scripts-record-run-diagnostics worker-queued <run-dir> <job-id> --phase inventory --model <exact-model-id>. Immediately after successful worker creation, invoke math-dependency-graph._rtx.interface.scripts-record-run-diagnostics worker-started <run-dir> <job-id>. After the worker terminates, invoke math-dependency-graph._rtx.interface.scripts-record-run-diagnostics worker-finished <run-dir> <job-id> --status success --output <output> or the same operation with --status failure --error-code <code>. If worker creation itself fails, omit worker-started and close the queued attempt with the failure event. The gateway is the sole writer of the shared diagnostics report: serialize these diagnostics calls even while the inventory workers themselves run concurrently and write separate fragment and progress paths.

   Fill available worker slots and launch the next queued job as capacity opens. A retry uses the same job id, records a new worker-queued event, and must include exactly one --retry-code: worker-failed, validation-failed, timeout, capacity, or transient. Failure events use the matching allowlisted error code. Record the worker's actual model identifier, never a model tier or alias. After all inventory jobs succeed, write their fragment paths in reported order to the manifest.

3. Pool. Invoke math-dependency-graph._rtx.interface.scripts-advance-extraction-phases advance-inventory <inventory-manifest> --run-dir <run-dir>. Require its report to name the same diagnostics path. Pooling authenticates source ownership and records exact local and aggregate inventory-size ratios as controller-facing quality diagnostics. Size never rejects a fragment and never causes a worker compaction job. During skill evaluation, compare the ratios with the 50% local and 35% aggregate reference thresholds to decide whether the general inventory instruction needs improvement. Retry only the rejected inventory job when schema, ownership, anchor coverage, or record accounting identifies one; do not replace valid fragments or broaden their source assignments.

4. Extract. Launch exactly one fresh worker from the returned next_job, passing its instruction, schema, base, packet, sidecar, immutable source snapshot, retained entrypoint, progress, and output paths exactly. Require every attempt to append bounded actual-clock milestones to the stable progress_path; full retries reuse it. Record worker-queued, worker-started, and worker-finished as above with --phase extract, the exact model identifier, and an allowlisted retry code on every later attempt. Write the successful output path to the extract manifest.

5. Finalize. Invoke math-dependency-graph._rtx.interface.scripts-advance-extraction-phases finalize-extract <extract-manifest> --run-dir <run-dir> [--html <path>] and require the report to name the same diagnostics path. A successful final report validates, compiles, renders, and performs the sole diagnostics finish event; do not issue another finish event. If the report instead has status: "correction-required", the run remains open: schedule only its returned next_job, pass the diagnostic, persisted repair base, pooled inventory, immutable extract inputs, entrypoint, repair schema, progress, and output paths exactly, and record the same queued/started/finished lifecycle with --phase extract. The correction appends to the same stable progress sidecar. Submit that output in a new manifest to finalize-extract. If the diagnostic is not record-local, rerun the single extract job from its immutable inputs instead of submitting a repair.

6. Verify and report. Require nonempty semantic IR, graph JSON, and HTML artifacts and a schema-valid diagnostics report with final status success. Report the diagnostics path and its latest-stage summary; inventory and extract job counts; exact models; retries and retry codes; queue, worker, stage, initialization, and total durations; artifact paths, sizes, hashes, and counts; every per-fragment ratio, the aggregate canonical-fragment ratio, and the remaining physical/pipeline ratios; final entity, relationship, exclusion, unresolved, and gap counts; represented source scope; and genuine unresolved gaps. Never conflate the aggregate canonical-to-owned ratio with physical pooled-inventory-to-active-source bytes. Use the durable report rather than reconstructed console timing.

If a diagnostics update fails, stop: an unmeasured run is not a successful run. Invalid semantic output never reaches compile or render, and deterministic finalization never supplies missing mathematical content.

Maintainer evaluation

When explicitly constructing or revising benchmark truth, follow references/gold-standard-extraction.md. When explicitly improving this skill through measured subagent trials, follow references/experimental-improvement.md. These are controller-only references: never include either file, gold artifacts, benchmark scores, or prior-pass findings in an inventory or extract worker's context.