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A successor topology rule may resemble the retired rule yet still require its own qualification. New thresholds, filtrations, labels or stopping logic change the claim, and evidence tuned on the old failure can create a contaminated lineage. Clean-lineage qualification separates development material from decisive evaluation. Cap-inheritance prohibition then prevents a new rule from automatically receiving the authority earned by its predecessor. This article makes the handover concrete through a persistent-homology example and a changed-context transfer.
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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 successor rule as a new claim
State the input space, filtration, summary, decision threshold, stopping condition, target use and failure boundary. A rule that replaces maximum persistence with a persistence ratio is not merely a software revision; it can rank shapes differently and needs a new validity argument.
Preserve the predecessor’s record for comparison, but assign the successor a new identifier, evidence ledger and authority decision. Similar names or shared code do not make their claims interchangeable.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Build a clean evidence lineage
Separate development examples, threshold-selection data, debugging cases and decisive qualification cases. Freeze the successor rule before opening the decisive set, and record every later change as a new version that may require fresh evidence.
Clean lineage does not mean the developers know nothing about the domain. It means the final evaluation was not repeatedly mined to repair the same rule, and that any reused evidence is labelled with the purpose it already served.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. Work a persistent-homology qualification register
A quality-control system classifies a scanned ring as intact when one prominent one-dimensional feature persists across a locked filtration range. The retired rule used maximum persistence; successor S2 uses the ratio of the longest bar to the second longest so that duplicated cracks do not mimic one stable hole.
| Qualification stratum | Cases | S2 correct | Necessary limit | Result |
|---|---|---|---|---|
| Clean intact rings | 80 | 79 | At least 77 | Pass |
| Single breaks | 70 | 68 | At least 66 | Pass |
| Double-edge artefacts | 50 | 48 | At least 46 | Pass |
| Uneven sampling | 50 | 45 | At least 46 | Fail |
| Scanner noise shift | 40 | 39 | No more than 2 false intact | Pass |
Developers may repair sampling robustness, but the changed S3 rule must be frozen and evaluated on fresh decisive cases. Reusing the failed forty-five successes as if unseen would contaminate the new claim.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Commission authority without inheriting the old cap
The predecessor could automatically release low-risk rings after years of monitored performance. The successor does not inherit that authority merely because it addresses the same product.
| Decision item | Predecessor state | Successor evidence | Commissioning result |
|---|---|---|---|
| Advisory flag | Qualified | Fresh strata pass after repair | Grant |
| Automatic low-risk release | Previously granted | No live successor evidence | Prohibit |
| High-risk rejection | Human confirmation required | Same safeguard tested | Retain safeguard |
| Uneven-sampling cases | Restricted after old breach | Fresh S3 set passes | Grant advisory only |
| Authority expansion | Old cap allowed 20% auto-release | No independent expansion study | Do not inherit |
The cap belongs to a rule-and-evidence lineage, not to a project name. A successor may inherit safeguards and documentation obligations, but not unearned decision authority.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Qualify topology, computation and decision mapping
Check the mathematical construction: metric, filtration, coefficient field, persistence calculation and stability assumptions. Then test the implementation with known shapes, perturbations and versioned outputs.
Finally qualify the decision mapping. Even a correct persistence diagram can support an unsafe rule if the threshold, class label or stopping condition was tuned to a narrow sample or used outside its intended shape family.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Monitor the successor as a distinct family
Track input geometry, sampling density, noise, barcode summaries, abstentions, overrides and downstream outcomes. Separate warnings caused by measurement drift from those caused by a mathematical or implementation defect.
Predefine stop, repair and expansion rules. If a clean-lineage breach is discovered later, freeze authority that depends on the affected evidence and open a successor review rather than silently relabelling the same result.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Changed-context transfer: network-loop detection
Transfer the method to a sensor network that uses a topological rule to flag persistent coverage holes. A successor changes the complex construction to reduce false loops near the boundary and performs well on development simulations.
Because the old simulations shaped the repair, qualification uses independently generated layouts and field traces. The successor receives advisory authority first; it does not inherit the predecessor’s automatic dispatch cap until live evidence supports that separate decision.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect stopping rules, family limits and retirement
Begin with authority-cap monitoring, breach escalation and rule-family retirement. Use family-wide stopping rules and independent audit when evidence reuse affects a broader claim family.
Continue through restart-family limits, repair-sequence dependence and global evidence budgets when repeated successor attempts draw on related evaluation material.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and common misconceptions
Clean lineage does not guarantee generalisation, and persistent homology does not make a decision rule immune to sampling, noise, metric choice or domain shift. A mathematically stable summary can still be paired with an unstable operational threshold.
Cap-inheritance prohibition is not a claim that predecessor evidence is useless. It can justify design choices, safeguards and candidate plausibility. It cannot substitute for decisive evidence supporting the successor’s own authority.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Practical evidence and commissioning checks
Retain the mathematical specification, code and dependency versions, data lineage, development and qualification partitions, freeze time, threshold rationale, perturbation tests, failed attempts, decisive outputs, reviewer independence and commissioning vote.
The decision record should name granted and prohibited roles, monitoring measures, stop triggers, fallback, evidence owner and next review. Record which predecessor materials were reused and why that reuse does or does not affect the successor claim.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Can the successor use the predecessor’s data?
Yes for documented development or contextual evidence, but decisive qualification should account for prior use and rely on fresh or otherwise independent evidence for the new claim.
Why not inherit an authority cap after a small rule change?
Because a small formula or threshold change can alter errors and stopping behaviour. The successor should earn the authority affected by that change.
Does one failed stratum invalidate the topology?
Not necessarily. It may reveal a decision boundary, sampling limitation or implementation problem. The response depends on the locked necessary gate and intended use.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Sources and next reading
The Statistical Science article on safe anytime-valid inference develops evidence processes designed for decisions at data-dependent times. The W3C PROV Data Model represents provenance through entities, activities and agents. This article uses those ideas as evidence-governance support; the ring and network examples are original teaching cases, not claims that provenance alone proves a topological classifier.
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