Executive Summary

Deduplication asks whether two records point to the same thing. Corporate-family resolution asks whether two records sit under the same owner. The two questions look alike, but the evidence lives in different places. For the first, how similar two strings are already carries part of the answer. For the second it does not. Heico Corporation and Blue Aerospace LLC really are parent and subsidiary, and no amount of staring at the two names produces that fact. The relationship sits outside both records, written into a filing the company made with the securities regulator.

The industry has long treated this as a branch of entity resolution and entity matching. Pebblous covered the diagnosis that unstructured data pipelines break at resolution and provenance earlier. This paper steps one stage in front of that diagnosis. Instead of asking what breaks, it splits the data by stratum to measure where the break happens, and releases the result as a benchmark.

Grouping records into families supports more than spend consolidation. Credit exposure aggregation, beneficial-owner and sanctions screening, and supplier risk consolidation all rest on the same grouping, and on the revenue side the account hierarchy in a customer system has the same structure. The paper's related-work section explains why the task has not been measured in this shape before. A long line of research matches company names across sources, running through patent data, financial identifiers and learned name representations, but its concern is recognising the same company under spelling variation. Family resolution begins where that ends. Ownership itself has been studied too, in economics and network science, in bank holding structures, and in knowledge graphs of European business registers, and hierarchical linkage has been treated as link prediction over enterprise data. To the author's knowledge, none of that work released a reproducible public benchmark with held-out splits, and none split pairs by whether the relationship is recoverable from the records at all. The closest public resource the author names is CompanyKG, a graph of 1.17 million companies as nodes and 51.06 million edges across 15 types of inter-company relation. Its tasks are similarity prediction, competitor retrieval and similarity ranking. Because its nodes are already-resolved company entities, the linking problem this article is about is assumed solved before those tasks begin.

The raw material is the full-year archive of US federal contract award records for fiscal year 2025. It holds 6,638,350 rows covering 104,459 distinct entities. The ground truth is neither hand annotation nor model inference. It is the Unique Entity Identifier and name of the ultimate parent that each supplier declared for itself when registering for federal procurement. That this is self-reporting with legal liability for misstatement sets the character of the label. It has force behind it, and it also survives unchanged when the filer is careless. A sense of scale helps here. Aggregating the same API directly, Pebblous found $778.5 billion in federal contract obligations for fiscal year 2025. The 6.63 million rows in this paper are the ledger of where that money went.

1.186.3% of registrations that named a parent named themselves

Open the archive and the first trap shows up immediately. Of the entities that populated a parent field, 89,962 of them, or 86.3%, entered themselves as the ultimate parent. In a separately retrieved API sample of 4,806 records, 82.8% of child-level records pointed at themselves, and only 760 genuine parent–child links survived. With the self-references stripped out, 14,288 genuine links remain. Hand-adjudicating the largest families out of that population is what produces the benchmark's 13,716 positive pairs. The two numbers count different things and cannot be used interchangeably.

The finished benchmark consists of 54,864 candidate pairs over 10,307 corporate groups. Three negatives accompany each of the 13,716 positives, for 41,148 in total, and the negatives come in three grades: an unrelated family's parent drawn at random, an unrelated parent that shares a common token, and a parent falling into the same blocking key. That last grade is what a deployed pipeline actually adjudicates. Splits are drawn at the family level and checked for leakage along four axes, covering families, entities, normalised names and duplicate pairs, with a failed check aborting the build rather than quietly patching it.

1.2Three strata, defined by how visible the name is

The design decision that shapes the benchmark is how to divide the positive pairs. Rather than lumping them under a label like difficulty, the author splits them into three strata by how many distinctive tokens the child's name shares with the parent's. A distinctive token is a word left after removing the boilerplate that attaches to any company: inc, holdings, international, services. Defining the strata this way means that which stratum is hard is fixed by definition rather than discovered by analysis.

Composition of the benchmark's name-visibility strata. Source: arXiv:2609.04269v1, Table 1.

More than half, 55.0%, are pairs whose names become identical once normalised. The commercial value of data integration sits in the bottom row. That row is 23.5% of the total, 3,222 pairs, and they share not a single meaningful word between the two names. Heico and Blue Aerospace from the previous section live in this stratum, and so does Aerojet Rocketdyne under L3Harris Technologies. A real acquisition, entirely invisible in the names, and confirmable only by filing.

An entity resolution pipeline runs in two stages. First it picks out the pairs worth comparing, then it adjudicates only the pairs it picked. The front half is candidate generation, or blocking. Arithmetic is why the stage exists. The recipient register the paper measured blocking against holds 114,230 entities, and pairing all of them gives 6,524,189,335 pairs. Six and a half billion pairs cannot go through a matcher, so blocking keeps a small fraction. Blocking is graded on two numbers: pair completeness, meaning how many true links survive into the candidate set, and reduction ratio, meaning how much of the comparison space was cut away. The author measured these against the whole recipient register rather than against only the entities appearing in the pair file. Narrowing to the pair file would mean measuring against a register already filtered down to entities of interest, which flatters both reduction ratio and candidate quality.

The author writes that the table below is the most consequential result in the paper. It runs seven blocking schemes over the same register and puts overall pair completeness next to per-stratum pair completeness. Summarised as one average, it swallows this article's argument whole.

Pair completeness by blocking scheme (%). Measured over the 114,230 entities of the recipient register, against a naive comparison space of 6,524,189,335 pairs. Source: arXiv:2609.04269v1, Table 4.
† The 0.00% on the two daggered rows is an identity, not an experimental result. The invisible stratum is defined as exactly the case where that token function's intersection is empty, so a blocking key built from the same function has no way to catch it. The author claims no credit for those entries.

Read the rightmost column top to bottom and the point of this article is there. Name-keyed schemes catch 60 to 72% overall and never clear 3% on that stratum. Character q-grams drop from 71.4 to 2.79, sorted neighbourhood from 71.2 to 2.05, phonetic keys from 61.3 to 0.25. Drop the two identity rows entirely and the conclusion holds. Even with the key detached from that token function, not one scheme cleared 3%.

2.1Abandoning the name added 2.95 percentage points

Two schemes in the table never look at the name at all: the attribute key built from ZIP and city–state, and nearest neighbours over sentence-encoder embeddings. The attribute key is the one scheme whose hard-stratum score, 2.39%, exceeds its own overall score of 1.9%. It never looks at the name, so it cannot be penalised when names fail to overlap. The absolute level, though, is 2.39%.

Embedding nearest neighbours has the highest overall pair completeness of any single scheme, 72.5%, ahead of character q-grams. On the hard stratum it brings back 2.89%. The author reads that number as a statement about knowledge. MiniLM does not place Blue Aerospace anywhere near Heico because the encoder is weak; it does so because nothing in its training signal connects them. Adding both name-blind schemes to the name-keyed union moves the number from 3.82 to 6.77, which is 2.95 percentage points.

2.2Those 2.95 points cost 8.5 times as many candidate pairs

Producing more candidates raises pair completeness. The question is the price. Plain token blocking, the most standard scheme, proposes 1,534,063 pairs. The union of all seven proposes 13,074,120. That is about 8.5 times as many pairs, in exchange for 2.95 points on the stratum that matters. The author's own phrasing is that a practitioner is being asked to adjudicate roughly an order of magnitude more pairs for those 2.95 additional points. And the stratum still stops at 6.77%.

The paper leaves a concrete bar for later work. Hold the candidate budget near 13,074,120 out of 6,524,189,335 possible pairs, and beat 6.8% on the hard stratum. Any proposal that widens the candidate set until reduction ratio collapses has relocated the problem rather than solved it. Trading candidate budget against recall is a familiar tension elsewhere in data integration. Pebblous covered the early-stop rule that made training data deduplication 8x faster, which works the same trade-off from the other end.

Before accepting that candidate generation is the bottleneck, the later stage has to be checked. If the matcher had been good enough, the story would read differently. The paper ran five matchers over the same benchmark: exact match on normalised strings, Jaccard overlap of distinctive tokens, a character sequence ratio, character 3-gram TF–IDF cosine, and sentence-encoder embeddings. Thresholds were selected on the validation split, and the table below also carries a floor: the constant classifier that answers yes to every pair.

Matching baselines. The three right-hand columns are per-stratum recall (%). Source: arXiv:2609.04269v1, Table 5.

On the identical stratum, four of the five recover 100.0 and token Jaccard follows at 99.2. At the right edge of the same table, no method clears 4.7%. The paper's abstract quotes 4.2% for its strongest matcher, and the difference is a matter of which metric is doing the ranking. TF–IDF leads on average precision at 78.7; MiniLM leads on F1. Under either yardstick, that stratum does not reach 5%. Confidence intervals do not change the picture. The 4.2% for TF–IDF carries a 95% interval of [2.9, 6.1], the same method's 49.9% on the visible stratum carries [45.8, 54.0], and its 100.0% on the identical stratum carries [99.8, 100.0]. The intervals do not come near one another.

The aggregate scores alone read entirely differently. TF–IDF character 3-gram earns F1 76.8, precision 89.6, recall 67.3 and average precision 78.7. Put the average in a report and the task looks close to solved. The 0.0% that exact match and token Jaccard record on the hard stratum is likewise a consequence of the definition rather than of performance. The stratum has no shared tokens, so methods that count shared tokens score zero by construction.

3.1On the hard stratum the constant classifier outscores every matcher

Answering yes to every pair on the hard stratum yields F1 29.0. On that same stratum the best of the five matchers reaches 9.0 and the worst reaches 0.0. All of them sit below the floor. When five methods line up beneath a rule that exercises no judgement at all, the metric is not measuring the methods. This is why the author reports recall rather than F1 at the stratum level.

Turning this into a case against the sentence encoder would weaken the argument. The encoder is the strongest matcher overall. Its F1 of 78.5 beats the best string method's 76.8, and on the visible stratum it leads on F1 by better than eight points, 64.3 against 56.3. It handles abbreviation and rephrasing, so it catches pairs that token overlap misses. On the identical stratum the two tie on F1 at 98.7, because string equality has already saturated that stratum. The encoder wins where there is something to win.

On this stratum the sentence encoder gains 1.0 point of F1 over the best string method, from 8.0 to 9.0. Moved to the earlier stage and used as a blocker, the same encoder returns 2.89%. The same representation, dropped into two different positions in the pipeline, lands near zero in both. That symmetry is the strongest support for the author's claim that the missing ingredient sits outside the embedding.

3.2Why "just use the address" runs into a wall

If the name is useless, why not use the address or the phone number? The paper ran that experiment too. It is restricted to the 822 test pairs that carry attributes on both sides, and the base rate of that subset differs from the main split. The attribute-only model scores 59.9 on the hard stratum, half a point above that subset's floor of 59.4, and it gets there by firing yes at nearly every pair. The author's verdict is that at n=822 these differences do not count as results. One qualitative finding survives: name features score 31.2 on this stratum, far below the floor, which makes them worse than useless rather than merely unhelpful.

More decisive is the reason attributes cannot rescue this stratum in principle. Of the benchmark's 10,307 distinct parents, only 608, or 5.9%, appear as recipients in their own right. The remaining 94.1% have no address, no phone number and no place of business anywhere in the source. Holding companies exist to hold, and a parent that does not transact has no site to record. This is not a gap a better vendor feed fills. There is nothing on the other side to fill it with.

The structural hole in attribute coverage. Address agreement is computed over true pairs with an address on both sides, on samples of 77, 110 and 130 pairs respectively. Source: arXiv:2609.04269v1, §6.6.

The last row runs against intuition. Address agreement is highest on the hardest stratum. Registrations sharing a name are usually separate sites scattered under one brand, so their addresses differ, while an acquired subsidiary is sometimes administered from the parent's building. The sample is small, so the author draws no strong inference from the ordering. The level is the part that matters. Address agreement never exceeds 10.0% anywhere, so even a matcher that resolved addresses perfectly would barely touch this stratum.

It is also worth asking what population that experiment measured. Keep only the pairs with attributes on both sides and what remains are the families whose parent happens to transact on its own account. Those are the parents furthest from being holding companies. The author writes as much: the multi-attribute baseline is measured on a subset that does not represent the task. Neither the finding that attributes did not help nor the hope that attributes might help extends beyond that subset.

So where does the answer come from? The paper's conclusion is that this stratum measures knowledge rather than similarity. Whatever supplies the answer has to come from outside the pair, which turns corporate-family resolution into a retrieval and evidence-aggregation problem. That is why the author files the task alongside work on grounded factual verification instead of the entity-matching literature it usually sits in. It is a proposal to change the drawer the task has been kept in.

The benchmark's second contribution is not a number but a way of scoring. Grade the same data with a single F1 in the conventional way and the gap from the previous section vanishes from the report. The author gives three reasons for that. A fourth is how the field has been scoring this same stage.

4.1Per-stratum F1 measures the base rate, not the method

The constant classifier that answers yes to everything scores F1 98.6 on the identical stratum and 18.5 on the visible stratum. No method was applied, and 80 points of difference opened between two strata. Lining up per-stratum F1 scores for comparison means reading differences in that stratum's positive rate rather than differences in method. For the record, the positive rates in this benchmark are 97.3% on the identical stratum, 10.2% on the visible stratum and 16.9% on the invisible stratum. That the lowest of the three does not belong to the hardest stratum is further evidence that this metric is not measuring difficulty.

The second entanglement is nastier. The grade of a negative pair is structurally tied to the stratum. A negative built from an unrelated parent sharing a common token falls, by definition, into the visible stratum, and a randomly drawn negative almost always falls into the invisible one. The hardest stratum is issued the easiest negatives, which biases precision in the direction opposite to the effect being measured. So the author reports recall per stratum, which depends only on that stratum's positives, and reports precision and average precision globally only.

Reporting negatives by grade also exposes what precision really is. Measured against random negatives alone, all five methods have a false positive rate of 0.0%. Against same-blocking-key negatives, the ones a deployed pipeline actually adjudicates, the rate rises to 0.5–3.2%, and against shared-token negatives to 1.0–6.5%. Write the report on random negatives alone and you publish a precision no practitioner will ever experience.

4.2A pipeline that does well by count can do badly by dollars

Procurement spend is extremely concentrated. Across the benchmark's 13,716 links, the top 1% carry 77.4% of obligated dollars and the top 10% carry 96.8%. Under spend weighting, TF–IDF character 3-gram recall falls from 67.3 unweighted to 60.1 weighted. A method that catches many small suppliers while missing a few large ones is not at all the same thing in practice as its opposite, and F1 grades the two identically.

This concentration figure carries a correction history the author applied himself. An earlier version computed it from a per-entity API sample, and the collection had been cut off mid-sort, leaving the sample filled almost entirely with identifiers beginning with one particular letter. He flags it as not a population sample and recomputes over the full link set, which is where the 77.4% above comes from. Read alongside the F1 88 from the previous section, the pattern is that the repairs in this paper cluster around what the denominator was rather than around the method.

4.3Pair scores and the deliverable do not move together

Procurement and credit systems do not take delivery of a pair verdict. They take a partition that assigns every supplier record to a family. The paper compared two conditions over the 902 families with more than one child: a condition applying blocking exactly as deployed, and an oracle condition scoring every pair within the split.

Family-level clustering. Thresholds were selected on the validation split. Source: arXiv:2609.04269v1, Table 8.

Remove blocking and pairwise F1 rises from 32.2 to 39.4 while the share of families recovered exactly falls from 16.6% to 14.9%. The extra candidates bring in false links, and transitive closure breeds each one into a merger of two separate families. The author warns against overstating the contrast. The comparison rests on 181 test families, and the confidence intervals on exact recovery overlap, so neither condition dominates. The defensible sentence is the narrow one. Pairwise F1 and exact partition recovery are not monotonically related, so a pipeline tuned on pair quality can move the deliverable backwards.

The two conditions also agree on one thing. Split B-cubed into precision and recall and the blocked condition reads 85.8 against 45.4, the oracle condition 84.3 against 45.1. Failing to merge what belongs together is far more common than merging what does not. Exact recovery therefore stays in the minority under either condition, and consolidating spend in a ledger depends on that recovery figure rather than on a pair score.

4.4The field has been reporting this stage as nearly solved

Only next to neighbouring benchmarks does it become clear how unusual a number 6.8% is. MaDI-Bench, an end-to-end data integration benchmark released in June 2026, evaluates blocking on the same two metrics, pair completeness and reduction ratio, and reports 94.37 to 100.00% across five tasks and three pipelines. For the Companies task alone the figures are 94.37, 97.73 and 100.00%. The stage that benchmark identifies as having room left is not blocking but data fusion, whose accuracy it puts between 40.20 and 84.87%. SC-Block, a recent blocking-specific paper, fixes pair completeness at 99.5% by default and competes on pipeline execution time instead, reporting itself 1.5 to 2 times faster than eight recent blockers and 8 times faster on large datasets. The field had moved on to racing on speed, treating candidate generation as settled.

The difference comes from what was designated a hard case. Both benchmarks grade blocking on the same two metrics. MaDI-Bench synthesises its hard cases with difficulty knobs. One knob is the strength of surface variation, rewriting values with abbreviations, token reordering, rephrasing and token dropping, and that document states explicitly that the knob erodes the surface overlap blocking and matching depend on. Difficulty manufactured out of string corruption leaves signal in the string, which is what makes blocking look solved. The strata in this benchmark, by contrast, occur naturally and are certified by external legal filings. Blocking research was not lazy. The measurement design was different.

Subgroup disparity in blocking was first raised to a first-class metric in the fairness literature. A study published in September 2024 splits records into majority and minority groups by protected attributes such as gender or race, defines the between-group difference in reduction ratio and pair completeness, and measures that gap across seven standard entity matching datasets. Its conclusion is that even assuming a perfect matcher, the disparity at the blocking stage carries straight through to the final result. On the Amazon–Google dataset the XSuffix blocker showed 18.16% and QGram 1.01%. This article's central claim, in other words, was already confirmed by an independent prior experiment.

The two gaps should not be subtracted from one another, though, because the populations differ. The prior work divides by demographic group; this benchmark divides by name-visibility stratum. On magnitude alone the comparison runs as follows. In the prior work's table of pair completeness gaps across all seven datasets, values ran from −6.13 to +11.79 percentage points, and even the worst-off subgroup never fell below 67.62% pair completeness. The 18.16% in the previous paragraph was measured on a single dataset, so it is aggregated differently from that table. In this benchmark the two strata read 100.00 and 6.77. The prior numbers lend support to the author's description of the disparity here as near-total.

The author himself writes that this failure reaches beyond corporate families. A defensible aggregate concealing near-zero performance on the subset that motivates the task arises whenever a benchmark's positives are heterogeneous in difficulty and the easy majority correlates with a surface feature. So benchmark builders should report a stratification along whatever axis makes the easy cases easy, and reviewers should ask for one. The earlier F1 88 is the same recommendation seen from another side. When the two sides of a relation are different kinds of object, a model can learn the object type instead of the relation, and an aggregate metric will not reveal it.

A thing that is never found is never evaluated, and that structure shows up elsewhere too. Pebblous has covered the case where AI agents find fewer than half the columns a research question needs and the case where changing the output format moved the data quality score. A retrieval stage that bottlenecks while only the later stage is scored, and a metric that fails to measure what it set out to measure, are both observed here inside a single dataset.

If those 3,222 pairs with no name in common were really registration errors, then nobody finding them would be the expected outcome rather than a failure. The paper answers that objection with a document that shares no provenance at all with a procurement registration: Exhibit 21, the schedule of subsidiaries of the registrant that a public company attaches to its annual report.

5.1The corroboration design did not trust filenames

How the documents were selected is what determines whether this check can be trusted, and selecting by filename fails. ex2101.htm could be a sub-exhibit of Exhibit 21 or one of Exhibit 2, and some registrants file the schedule under a name carrying no exhibit number at all. The only selection criterion, then, is the exhibit type that EDGAR declares for each document in the filing's own index. Two secondary signals, a filename pattern and a content test for a jurisdiction-keyed list of company names, agreed with the declared type on 92.6% of documents, but agreement was deliberately not made a selection condition, because requiring it would discard 12 schedules the registrant itself declares to be Exhibit 21. This yields 160 usable filings, against which 1,575 declared links were checked.

Corroboration against SEC Exhibit 21 subsidiary schedules. Source: arXiv:2609.04269v1, Table 3.

On the stratum where matchers recovered no more than 4.7%, 510 of 794 links were written down as subsidiaries in the parent's own filing. The connection is not missing from the data. The pipeline does not go looking for the evidence.

That the 64.2% is not an accident of rummaging through documents is established by control conditions. There are three null conditions, and each rules out a different kind of coincidence.

The three null conditions, against a true-condition rate of 64.2%. Source: arXiv:2609.04269v1, §5.

The first two nulls share no machinery whatsoever. One randomises the company and holds the document type fixed; the other holds the company fixed and swaps the document type. They landed 0.25 points apart and are not separable by a two-sided Fisher exact test (p=0.34). The true condition sits 64.1 points above them. That two unrelated designs settled on the same floor identifies that floor as a property of the matcher rather than an artifact of either construction. The third condition is a harder variant that removes any advantage from filing size, and it still gives 5.79%. The second condition is conservative rather than a pure null, though: a benefit plan or a credit agreement can legitimately list a subsidiary as a participating employer or a guarantor, and the one observed hit was exactly that case.

5.2Why that document holds the answer, and why 64.2% is a lower bound

Why the evidence collects in this particular document is set out in the regulation. 17 CFR 229.601(b)(21) specifies what a registrant must file.

Because trading names are what the rule asks for, this is precisely where a subsidiary doing business under a name unlike its registered one leaves a trace. Clause (ii) then fixes the size of the caveat. The omission threshold hangs on the definition of significant subsidiary elsewhere in the same regulations, which applies a 10% test on investment, assets and income. Take every unnamed subsidiary together as a single subsidiary, and if the aggregate falls short of that 10%, the names need not appear. Formatting is unregulated as well.

So 64.2% is the confirmed rate, not the real rate. Three reasons make it a lower bound. Confirmation correlates with how much text the parser recovered (Spearman ρ=0.35), so the figure is discounted by parser recall. Documents were obtained by matching parent names against the list of securities registrants, so the family sample is not random. And the 284 unconfirmed links cannot be read as counter-evidence: the regulation above permits omitting immaterial subsidiaries, so absence from the list leaves the relationship undecided. The caveats attached to this paper are not the author's modesty. The regulation set their size.

5.3This conclusion was not built by discarding the hard cases

A self-reported archive carries noise. It contains, for instance, a claim that an Australian subsidiary is the ultimate parent of Raytheon Company, and a claim that a moving company is the parent of 103 waste-management businesses. An automatic rule can be tried. Flagging any family whose parent lacks the dominant token its children share catches both of those. It also catches Arctic Slope Regional Corporation, whose subsidiaries are all genuine. That is not a tuning failure. A real conglomerate looks identical, from the outside, to a mislabelled family. Apply the rule aggressively and Heico, TransDigm, Berkshire Hathaway and Republic Services all disappear, and those are precisely the families that make the benchmark worth building.

So the author separated out the large families and adjudicated them by hand. He reviewed 28 families, excluded 8 and kept 20, recording reasons on both sides and publishing the full log. Exclusions were decided on entity identifiers rather than name strings, the only defensible choice in a paper about name instability. That adjudication removed 458 links, and another 114 came out under sovereign umbrella entities.

This is where a suspicion of bias arises. Of the excluded links, 84.7% happen to belong to the stratum this paper's argument rests on, so it is fair to ask whether the gap was manufactured by throwing away the hard cases. The author reran every experiment on a build with no exclusions at all: 14,288 links, of which 3,619 are invisible. The result went the other way. On the unfiltered build the best recall on the hard stratum is 0.9%, below the filtered build's 4.2%. Removing the exclusions makes the task harder. Both builds are released, small families carry no automatic filter in either, and rather than claiming to have removed label noise the author reports it as bounded.

5.4The ground truth has a ceiling of its own

The most data-centric fact in this paper is not 93.2% but 18.5%. The same registration, read through two independent channels, gives diverging answers. Across the 248 entities for which both the per-entity API and the bulk award archive report a parent, the parent identifier matches exactly for 64.9% and the normalised name matches for 73.8%. In 18.5% of cases, roughly one in five, the two channels name substantively different parents.

The instability shows up inside a single channel too. Within the archive alone, 1,005 entities carry several different parents across their own award rows. In the API, 1,065 of 4,424 child records hold more than one parent in their history, with up to nine stacked on a single record, because a change of ownership adds a value rather than replacing one. The causes split three ways: genuine ownership change between snapshots, registrations that never caught up with a completed acquisition, and outright error. The author does not arbitrate among the three. He takes the most recent value and publishes the list of the 46 entities where the channels disagreed.

The paper's prescription fits in one line. The evidence lives outside the records, so candidate generation has to go outside and fetch it. Whether the prescription is right and whether it can be carried out today are separate questions. Answering the second means checking how wide the available registries of ownership relationships are, and the paper does not go that far. This section is what Pebblous found by going to the regulations and the agencies' published files at source. All queries were made on 8 September 2026.

6.1The US beneficial ownership registry took domestic entities out of scope

Beneficial ownership information reporting under the Corporate Transparency Act is the first candidate that comes to mind. A final rule published in the Federal Register on 14 August 2026 narrowed the reporting scope. FinCEN, the Treasury's financial crimes unit, finalised its interim final rule of March 2025 with amendments, additionally exempting the reporting of information on US person beneficial owners and US person company applicants. The agency's own guidance page states that US companies are exempt from the beneficial ownership information reporting requirement and therefore no longer need to file reports. What remains in scope is entities formed under foreign law that have registered to do business in the United States.

The population the paper studies is US domestic entities registered for US federal procurement. There is now no beneficial ownership registry covering them. The registry has not been abolished, and this article takes no position on the direction of the regulation. One fact was established. The widest-looking candidate registry for the paper's prescription does not cover the paper's population.

6.24.02% of filers in the global identifier system name an ultimate parent

The next candidate is the global Legal Entity Identifier system, which carries Level 2 data on who owns whom. Issuance stands at 3,423,173 records in total and 3,162,582 active. Sources commonly describe Level 2 reporting as 99% complete. A direct count over the published golden copy files shows what that 99% is actually counting.

Direct count over the GLEIF golden copy relationship record file and reporting exception file. Files published 7 September 2026 at 16:00 UTC, counted 8 September 2026. Naming and exception filings do not intersect, since a filer submits one or the other. Against active LEIs as the denominator the share is 4.20%.

Reading the 96% exception rate as negligence would be wrong. Level 2 of this system works on accounting consolidation rather than ownership, and a direct parent is defined as the lowest-level legal entity that prepares consolidated financial statements consolidating that entity. In the distribution of exception reasons, most are honest answers that no parent exists under that definition. Natural persons in control account for 37.1% (1,175,644 filings), no consolidating parent for 34.6% (1,096,733), and an unknown controlling party for 21.0% (666,312).

Viewed as a registry to plug into a blocker, though, the conclusion converges. Across the entire global identifier system, 132,777 entries name an ultimate parent, and they gather into fewer than 40,000 corporate groups. The paper's single benchmark holds 10,307 groups on its own. One exception reason is different in kind: 118,686 filings, or 3.7%, report that a parent exists but has no identifier, so there is no counterparty in the registry to record the relationship against. That is nearly as many as the 132,777 relationships actually filed. And a simpler reason keeps this registry away from the paper's population. US federal procurement registration carries no obligation to report this identifier. The paper's population sits outside this registry to begin with.

6.3Commercial registries exist. Their recall is not published

If the public registries are narrow, commercial ones remain, and they do exist. Dun & Bradstreet states that its corporate linkage data holds roughly 18 million linked records and about 4 million global ultimate parents, attaching four identifiers to each subsidiary for itself, its parent, its domestic ultimate and its global ultimate, and generally applying a threshold of more than 50% ownership. Moody's Orbis reports roughly 193 million active ownership links across more than 635 million companies. Both figures are vendor self-reported and the units differ: one counts linked records, the other counts individual ownership links. They are not values that can be placed side by side to rank one above the other.

The number that would actually settle the question is published by neither: recall against a held-out ground truth, and specifically per-stratum recall restricted to pairs whose names do not overlap. So the claim that commercial registries have already solved this problem can be made, and it cannot be checked from outside. This is where the article's loop closes. The paper records that 52.5% of its benchmark's positive pairs may fall under a data redistribution restriction in the procurement system, and the source of that restriction is data supplied by the vendors in the previous paragraph. The author deliberately set 52.5% as an upper bound. The restriction is scoped to records under base contracts that began before 4 April 2022, and because the field designated for making that determination is absent from the award data altogether, he counted by the earliest performance start date among the transactions supporting each link. A 2025 order under an old master contract inherits that contract's original start date, so the figure can only be inflated. Under the opposite reading, in which every transaction here counts as a fiscal 2025 action, the exposure is zero. The author released a conservative subset of 6,522 positive pairs restricted to the period after the cutoff alongside the full benchmark. The loop itself remains. The parties holding the data that would solve the linking problem are also the reason a public benchmark has to treat nearly half its positive pairs conditionally.

6.4Korea groups by corporate registration number rather than by name

One jurisdiction runs the opposite design, and it is worth reading as a contrast case. Where US procurement relies on self-reporting, Korea determines group membership by a statutory control test. Article 4 of the Enforcement Decree of the Monopoly Regulation and Fair Trade Act treats a company as an affiliate when a designated controlling person, together with related parties, holds 30% or more of total issued shares and is the largest shareholder, and it adds a separate control test asking whether that person in fact controls the company's business regardless of shareholding. Names are not part of the test. This registry therefore does not, in principle, drop affiliates whose names fail to overlap.

The scale of designation and the publication format are confirmable from primary sources. For 2026, 102 business groups subject to disclosure were designated, covering 3,538 member companies, up from 92 groups and 3,301 companies in 2025 and 88 groups and 3,318 companies in 2024. Of those, 47 groups covering 2,088 companies are subject to cross-shareholding restrictions. The Korea Fair Trade Commission's business group portal exports this list through a public open API whose returned fields include the group name, the member company name, the corporate registration number, the representative, the date of establishment and the date of admission to the group. A registry keyed on identifiers rather than strings is already available in machine-readable form.

The gap this registry leaves is defined just as explicitly. Designation is limited to groups with total assets of 5 trillion won or more, and no official registry was found covering affiliate relationships below that line. Updates run once a year, as of 1 May, following submission and review of filings. Nor is the list exhaustive: the enforcement decree carries separate grounds for exclusion, such as a deferral for small and medium enterprises with a high ratio of research spending, or companies meeting an independent-management test for their officers. The low-visibility subsidiary layer this paper studies generally sits below that asset threshold. Pebblous mapped the layers of domestic standards and registries separately in an earlier report on Korea's AI-ready data standards. As for how Korean companies actually consolidate affiliates inside their own procurement and purchasing systems, this investigation found no published case.

6.5All the parts exist, and nobody has fitted them to this task

The same question has to be put to the methods side as well as the registry side. Has anyone built a blocker that generates candidates from external evidence? The paper offers this only as future work. The survey found that the architecture already exists, and that no published case applies an ownership registry as evidence to this task.

Lines of work that come close to external-evidence candidate generation. Survey as of 8 September 2026.

No study was found that implements a blocker querying an ownership registry to propose candidates with no string evidence and reports per-stratum recall for it. That does not mean nobody thought of it. Every part exists. The missing pieces are an implementation that fits those parts to this task, and a yardstick to score it once fitted. This paper built the second one.

It is better to settle up front how much authority to place on this result. The paper has a single author, whose affiliation is independent researcher. It is version 1, posted to arXiv on 2 September 2026, and it has not been peer reviewed. Twenty-one pages, eight tables. There is no research group or joint team to refer to here, and no university or company name to attach.

In place of review, the paper has reproduction machinery. Every figure in the manuscript is generated from a results file by a script, and a separate script verifies the manuscript against those results. The seed is fixed at 20260827 and the build is deterministic. The author says no figure is transcribed by hand. The benchmark, the full hand-adjudication log and the code that reproduces every number are all in a public repository. Reasons are recorded for the families kept and the families excluded alike, and the 46 entities where the ground truth diverged can be opened and inspected.

The scope the paper draws around itself is narrow too. A single jurisdiction and a single fiscal year. Multinational structures appear only through their US-registered entities. The parent relation as recorded is one hop, so it evaluates child-to-ultimate-parent linkage and not intermediate holding chains. The Exhibit 21 corroboration covers SEC registrants only. The multi-attribute baseline is measured on the minority subset with attributes on both sides. Label noise is bounded but real, and the hand adjudication covered large families while leaving small families untouched entirely. And the baselines here establish the shape of the problem and a floor rather than the state of the art. They do not answer the question of whether a better matcher exists.

On one point the author explicitly declines to answer. He did not test whether a pretrained model already holds these ownership facts, and he makes no claim either way, because the filings are on the open web and that experiment carries its own contamination problem. So no conclusion about whether a language model knows or does not know these relationships can be drawn from this result.

Section 5 of the paper cites the prior work that began treating subgroup disparity in blocking as a first-class property. That bibliography entry merges two different papers into one line. The five authors listed are the authors of a 2022 technical report on meta-blocking, while the title, identifier and year alongside them belong to the September 2024 paper on evaluating blocking bias. We opened all three abstract pages and checked. The substantive claim does not fall. The disparity measurement cited in section 4 exists, and its authors are Moslemi, Balamurugan and Milani. Only the attribution is wrong. That an entry like this survived in a paper whose reference annotation is unusually careful says something about division of labour. A numeric reproduction script cannot catch this class of error, and peer review can. That is what settles where a reader of an unreviewed version 1 has to check by hand.

With DataClinic, Pebblous has been opening datasets and counting what is wrong with them. This paper says the act of counting itself has a missing column. That is why it does not read as somebody else's problem.

8.1The metric grading the cleanup cannot validate itself

Matching accuracy grades only the pairs the matcher was shown. Pairs it was not shown do not register even as errors. If AI-ready data means data organised so a model can use it directly, and the metric grading that organisation does not count the relationships that never reached the candidate set, then the definition cannot validate itself. What entity matching failures cost downstream is covered separately in our report on the six data defects that stall AI agents.

8.2Quantifying the limit is more useful than asserting quality

Section 5.4, which records how far the ground truth disagrees with itself and posts that as the benchmark's upper bound, overlaps with a problem Pebblous runs into every time it issues a diagnostic report. The author did not arbitrate the cases where the ground truth diverged. He published the list. Quantifying the limit instead of asserting quality is the posture Pebblous has taken in its diagnostic reports. For the same class of problem in a different domain, see our report on data quality in a scholarly graph that turns on author identity.

8.3Three things an organisation with a supplier master can check today

First, does our integration metric measure recall at the candidate generation stage separately? If all we have is matching F1, it is a metric that does not count what was never seen. Second, have we weighted the missed links by amount? A pipeline that does well by count may be doing badly by dollars, which is the content of section 4.2. Third, have we broken attribute coverage down by the two sides of the relationship? A coverage figure computed per record hides the one-sided hole that section 3.2 exposed.

8.4The same problem at a different point

Carrying out the paper's prescription means reading filings, building relationships out of them, and proposing candidates from those relationships. Extracting structure from documents into a graph and using that graph to link data puts it on the same layer as the unstructured pipeline and ontology work Pebblous has done. The deliverable differs, though. It is not a knowledge graph for answering questions but a registry for producing candidates that link records. How a wrongly connected node contaminates everything downstream is covered in our report on what happens when the graph is wrong, and this paper points to one more place where such a graph pays off.

Every benchmark figure in the body was checked directly against the full text of the paper. The registry figures in section 6 were counted by Pebblous on 8 September 2026 from the regulatory texts, the agencies' published files and their open APIs, with the query time and the file publication time recorded on the relevant line. Vendor self-reported figures are marked as such.

Academic

• 1.Harshit Gupta. "Corporate-Family Resolution Is Not a String-Matching Problem: A Public Benchmark Stratified by Name Visibility." arXiv:2609.04269v1 [cs.DB], 2026-09-02, 21 pages, 8 tables. doi:10.48550/arXiv.2609.04269 · arXiv — single author, affiliation independent researcher, not peer reviewed. The benchmark, the full hand-adjudication log and the code reproducing every figure are in a public repository. Tables 1, 3, 4, 5, 6, 7 and 8 and the discussion in §1, §2, §3.4, §4.1, §4.3, §4.4, §5, §5.1, §6.2, §6.4, §6.6, §7, §8, §9 and §10 were all verified in the full text.
• 2.Mohammad Hossein Moslemi, Harini Balamurugan, Mostafa Milani. "Evaluating Blocking Biases in Entity Matching." arXiv:2409.16410, 2024-09-24. arXiv — the subgroup pair completeness disparity and the perfect-matcher experiment cited in section 4.4 (XSuffix 18.16%, QGram 1.01%), together with the −6.13 to +11.79 percentage point range across seven datasets and the minority-group minimum of 67.62%, were verified in the full text of this paper. The 18.16% and 1.01% are values for the Amazon–Google dataset condition, so they are aggregated differently from that table. The bibliography entry in §5 of reference 1 attaches the author list of reference 5 to this paper's title, identifier and year. We opened all three arXiv abstract pages and compared them (2026-09-08).
• 3.Aaron Steiner, Ralph Peeters, Christian Bizer. "MaDI-Bench: An End-to-End Data Integration Benchmark." arXiv:2606.30371, 2026-06-29. arXiv — blocking pair completeness of 94.37 to 100.00% (Companies task 94.37 / 97.73 / 100.00), data fusion accuracy of 40.20 to 84.87%, and the description of the surface variation knob were verified in the full text. Reference 1 states that it checked this work only at the metadata level, so the comparison in the body is Pebblous re-verifying against the original.
• 4.Alexander Brinkmann, Roee Shraga, Christian Bizer. "SC-Block: Supervised Contrastive Blocking within Entity Resolution Pipelines." arXiv:2303.03132. arXiv — a design that fixes pair completeness at 99.5% by default and competes on execution time. The result cited in section 4.4 is that it runs 1.5 to 2 times faster than eight recent blockers, and 8 times faster on large sets.
• 5.Luca Gagliardelli, George Papadakis, Giovanni Simonini, Sonia Bergamaschi, Themis Palpanas. "Generalized Supervised Meta-blocking (technical report)." arXiv:2204.08801, 2022-04-19 — used to check the author attribution in entry 2.
• 6.Saravanan Thirumuruganathan et al. "Deep Learning for Blocking in Entity Matching: A Design Space Exploration." PVLDB 14(11):2459–2472, 2021. doi:10.14778/3476249.3476294 — the representative study for the learned blocker line in section 6.5.
• 7.Lele Cao et al. "CompanyKG: A Large-Scale Heterogeneous Graph for Company Similarity Quantification." arXiv:2306.10649, 2023-06-18. arXiv — the work reference 1 names as the closest public resource. The 1.17 million companies, 15 relation types and 51.06 million edges in section 1, and the three evaluation tasks (similarity prediction, competitor retrieval, similarity ranking), were verified directly in this paper's abstract (2026-09-08). The bibliography of reference 1 records this work's tasks and author list differently, so the body follows the original.

Policy, statistics and primary sources

• 8.17 CFR 229.601(b)(21) — Exhibits, subsidiaries of the registrant. The significant subsidiary definition that governs the omission threshold is at 17 CFR 210.1-02(w). Text verified at Cornell LII. The quotation in section 5.2 is clauses (i) and (ii) of that provision, verbatim.
• 9.FinCEN. "Beneficial Ownership Information Reporting Requirement Revision." Final rule, 91 FR 52508, published and effective 2026-08-14, document number 2026-16576 — retrieved directly through the Federal Register API. The abstract states that it finalises the interim final rule of 2025-03-26 with amendments and narrows the reporting scope.
• 10.FinCEN. Beneficial Ownership Information guidance page, fincen.gov/boi, retrieved 2026-09-08 — the statement that US companies are exempt from the reporting requirement and no longer need to file reports was verified on this page.
• 11.GLEIF. Golden copy relationship record file 20260907-1600-gleif-goldencopy-rr-golden-copy.csv and reporting exception file 20260907-1600-gleif-goldencopy-repex-golden-copy.csv, published 2026-09-07 16:00 UTC (goldencopy.gleif.org) — the 132,777, 126,605, 3,167,134, 3,299,911 and 38,828 in the section 6.2 table, and the distribution of exception reasons, were counted directly from these two files. A reproducible first-party calculation.
• 12.GLEIF LEI Records API (api.gleif.org), retrieved 2026-09-08 — 3,423,173 LEIs in total, 3,162,582 active.
• 13.Korea Fair Trade Commission. Press release on the 2026 designation of business groups subject to disclosure, 2026-04-30 — 102 groups and 3,538 member companies subject to disclosure; 47 groups and 2,088 companies subject to cross-shareholding restrictions; 92 groups and 3,301 companies in 2025, 88 groups and 3,318 companies in 2024.
• 14.Korea Public Data Portal. Open API specification for the KFTC business group portal service returning member companies of designated large business groups — returned fields include group name, member company name, corporate registration number, representative, date of establishment and date of admission to the group. The reference date for publication is 1 May each year.
• 15.Enforcement Decree of the Monopoly Regulation and Fair Trade Act, Articles 4 and 5 (Korean Law Information Center) — the shareholding test for affiliate determination (30% or more and largest shareholder), the control test, and the grounds for exclusion from a group.
• 16.USAspending.gov API v2 (api.usaspending.gov), retrieved 2026-09-08 — used to confirm the scale of the paper's source population. Fiscal year 2025 contract obligations came to $778,489,275,685 by direct aggregation. Not mixed with third-party figures aggregated on a different basis.
• 17.Dun & Bradstreet corporate linkage product description · Moody's Orbis product description — the 18 million, 4 million, 193 million and 635 million figures in section 6.3 are all vendor self-reported and are aggregated on different bases. Neither publishes recall against a held-out ground truth.

Related Pebblous reading

• 18.Unstructured Data Pipelines Break at Resolution and Provenance (2026-08-06) · The Six Data Defects That Stall AI Agents (2026-07-03)
• 19.300 Million Papers, Now Free. Should You Swallow Them Unchecked? (2026-07-23) · When the Graph Is Wrong, RAG Is Wrong (2026-04-17)
• 20.AI Agents Find Fewer Than Half the Columns a Research Question Needs (2026-08-09) · The Early-Stop Rule That Made Training Data Deduplication 8x Faster (2026-08-10)
• 21.Korea's AI-ready data standards are scattered across catalogs and DataOps (2026-09-01) · The Output Format Moves the Data Quality Score (2026-09-07)