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A successor topology rule begins with its own evidence lineage and bounded authority, but monitoring may later reveal that decisive cases influenced development after all. That clean-lineage breach does not have one automatic meaning. The affected claim, version and authority must be traced before action is chosen. Cap reassignment then asks whether any automation can remain, move to a narrower role or return only after fresh evidence. This article uses a persistent-homology classifier to make those governance choices concrete.
Open the chapter contents · Topology root · Gold Standard of Education · How X Works
Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the decision
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE DECISION
1. Define the monitored successor claim
Record the rule version, input space, filtration, persistence summary, threshold, decision role, authority cap, abstention, fallback and monitoring strata. The claim includes the implementation and decision mapping, not only the mathematical idea.
Link every live decision to the version and evidence ledger that authorised it. Otherwise a later threshold or preprocessing change can inherit authority without a visible review.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Recognise a clean-lineage breach
A breach occurs when supposedly decisive evidence influenced rule design, threshold choice, debugging or repeated selection in a way not accounted for by the qualification claim. Accidental preview, label leakage and post-freeze tuning are different mechanisms but share the same independence problem.
Do not assume that every breach makes the rule false. It weakens what the affected evaluation can establish and requires a new boundary decision.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work a successor-rule monitoring register
Successor S3 classifies scanned rings from a persistence ratio and holds a 20% automatic-release cap for low-risk lots.
| Monitoring stratum | Exposure | Necessary limit | Observed result | Action |
|---|---|---|---|---|
| Clean intact rings | 620 | False reject at most 3% | 2.1% | Continue |
| Single breaks | 410 | False intact at most 1% | 0.7% | Continue |
| Uneven sampling | 180 | False intact at most 2% | 1.7% | Continue |
| New scanner firmware | 95 | Advisory only until 150 cases | 95 cases | Keep advisory |
| Operator override | 1,305 | Review above 8% | 9.4% | Investigate |
The review discovers that several qualification images appeared in a development presentation and were later used to tune the sampling repair. The decisive-set independence claim is no longer clean.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Trace the breach and reassign the cap
The board maps which versions, strata and authority decisions depended on the affected evidence.
| Claim component | Breach exposure | Independent support | Cap decision |
|---|---|---|---|
| Clean intact performance | None identified | Fresh holdout remains | Retain advisory |
| Uneven-sampling repair | Direct tuning exposure | No clean decisive set | Remove auto-release |
| Single-break safeguard | Threshold unchanged; fresh field cases | Adequate for human-confirmed use | Retain safeguard |
| New firmware | Not yet qualified | Insufficient exposure | Advisory only |
| 20% global cap | Depends partly on contaminated stratum | Not separable | Reassign to 0% |
Cap reassignment follows evidence dependence. It is neither punishment nor a negotiated compromise; it states what the remaining evidence can still support.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Design fresh evidence after the breach
Freeze the candidate before collecting or opening fresh decisive cases. Use independently generated shapes, field scans or a protected future stream whose selection was not driven by the failed examples.
Prespecify strata, necessary limits, minimum exposure, stopping rules and who may view outcomes. A new file name does not create independence if the same cases or labels continue to guide repairs.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Monitor mathematical and operational drift together
Track sampling density, metric scale, filtration parameters, barcode summaries, threshold distance, abstentions, overrides and downstream outcomes. These signals help distinguish input drift from implementation change or an unsuitable decision threshold.
Include known shapes and perturbation tests after dependency or firmware changes. A stable topological summary can still be paired with a changed operational consequence if the cap, class definition or fallback moves.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Changed-context transfer: coverage-hole alerts
Transfer the method to a sensor network that flags persistent coverage holes. A successor rule gains capped automatic dispatch after clean qualification.
Later, engineers learn that several field layouts in the decisive set were shown during parameter tuning. The operator removes automatic dispatch, keeps advisory alerts supported by unaffected regions and rebuilds the cap from a protected future deployment stream.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect commissioning, cap monitoring and family limits
Begin with successor-rule commissioning, clean-lineage qualification and cap-inheritance prohibition. Use authority-cap monitoring, breach escalation and rule-family retirement for the operating boundary.
Continue through family-wide stopping rules, independent audit capital and claim retirement when the same evidence influenced several successors.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and common misconceptions
A lineage breach is not the same as a data fabrication finding, and it does not automatically invalidate every unaffected result. It means the claimed independence or evidence role was wrong and the supported boundary must be reassessed.
Fresh evidence cannot erase the historical breach. It can support a new version and authority decision when its selection, access and analysis are properly separated.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Practical evidence and governance checks
Retain dataset roles, access logs, presentations, code versions, threshold history, freeze times, monitoring outputs, breach discovery, dependency map, cap decision, fresh-evidence protocol and reviewer approvals.
After reassignment, verify that automation is actually disabled, cached rules are withdrawn and operators understand the remaining role. Link any later cap increase to the fresh evidence that earned it.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Does viewing one decisive case always contaminate the set?
Its effect depends on what was seen and how it influenced design or selection. Record the exposure and assess the affected claim rather than assuming either harmlessness or total collapse.
Can a narrower role remain after a breach?
Yes, when independent evidence supports that role and the contaminated component is separable. Make the boundary explicit.
Who should approve cap reassignment?
Use the named authority with enough independence to review evidence lineage, operational consequence and the proposed fallback.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Sources and next reading
The Statistical Science article on safe anytime-valid inference explains evidence processes designed for data-dependent stopping. The W3C PROV Data Model represents entities, activities, agents and derivations. These sources support evidence and provenance concepts; the ring and network cases are original teaching examples rather than claims that provenance alone validates a classifier.
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