Paper 3 of Five
Abstract
This paper is the operational member of the series. It defines a computable measure — the Reciprocity Balance Index (RBI) — for any corpus that cites commands binding two parties in a relation: the ratio of cited obligations falling on others to cited obligations falling on the citer’s own class. The measure exists because a specific citation behavior is visible in the demonstration corpus and has not been counted: a reciprocal command is quoted up to the point where it turns and binds the quoter, and stops. I call this half-verse warrant. The paper gives the full apparatus — unit of analysis, four-criterion coding scheme, directionality assignment, masking procedure, three-coder concordance rule, pre-registered reliability floor of Krippendorff’s alpha ≥ 0.67, indeterminate ceiling of 35%, and stated abandonment thresholds — so that the measure can be run by someone who does not accept the series’ conclusions. A within-passage variant (WP-RBI) is defined and argued to be the stronger of the two, because it holds constant every innocent explanation for differential citation that Paper 5 catalogues. The paper’s most serious internal problem is stated rather than managed: the set of genuinely reciprocal passages in the canon is small, and the design may lack the power its ambitions require. Falsification constraint: if RBI in the demonstration corpus is not distinguishable from RBI in the matched control corpus after audience stratification, the measure has no referent and the paper should be withdrawn.
1. The Behavior to Be Counted
Ephesians 6:5 was among the most cited verses in nineteenth-century American religious argument about servitude:
Servants, be obedient to them that are your masters according to the flesh, with fear and trembling, in singleness of your heart, as unto Christ.
Four verses later, in the same paragraph, addressed to the same congregation at Ephesus by the same apostle, the passage turns:
And, ye masters, do the same things unto them, forbearing threatening: knowing that your Master also is in heaven; neither is there respect of persons with him. (Ephesians 6:9)
The turn is not incidental to the passage; it is the passage’s architecture. Paul is not issuing a one-directional command and then adding a courtesy. He is stating a relation in which both parties stand under the same Master, and the phrase “do the same things unto them” makes the servant’s duty and the master’s duty a single obligation viewed from two positions. The closing clause — no respect of persons with God — removes the ground on which a master might have thought his half lighter.
Colossians has the same structure. 3:22 to the servants; 4:1 to the masters, “give unto your servants that which is just and equal; knowing that ye also have a Master in heaven.”
The behavior this paper counts is the citation of the first half without the second. Not the denial of the second half, not an argument that it means less than it appears to mean, not a claim that it binds differently in different economies — simply the quotation that stops where the obligation turns. I call it half-verse warrant: the extraction of authority from a reciprocal command by taking delivery of the half that binds someone else.
This is a special case of functional subtraction (Paper 1) with one property that makes it uniquely measurable. In the general case, showing that a text should have been cited requires an argument about relevance, and that argument is contestable. Here it does not. The two halves are in the same passage, the same paragraph, four verses apart, in a work the citer has demonstrably opened to that page. Every property that might innocently drive citation frequency — familiarity, memorability, position in the lectionary, cost of the printed line, the preacher’s memory encoding, the audience’s prior exposure — is shared by both halves, or nearly so. The design is a natural experiment of a quality that historical work rarely gets.
One variable is left standing. One half binds the servant. The other binds the man in the pew who pays the minister’s salary.
2. The Reciprocity Balance Index
2.1 Definition
Let a reciprocal command be a scriptural instruction that assigns obligations to two parties in an asymmetric relation, where both assignments appear as commands and the relation is one in which one party holds power over the other. Let the citer class be the social position from which the corpus argues.
For a corpus C produced by citers of class k:
- O = count of citation instances of obligations binding parties other than k
- S = count of citation instances of obligations binding k
The raw index:
RBI = O / S
RBI = 1 indicates balance. RBI > 1 indicates that the corpus cites more obligations onto others than onto itself. RBI < 1 indicates the reverse.
2.2 The smoothed and logged form
Raw ratios are unstable when S is small and undefined when S = 0, which will occur at the document level. All reported values therefore use:
RBI* = log₂ ( (O + 0.5) / (S + 0.5) )
RBI* = 0 is balance. Positive values indicate outward-binding citation, negative values inward. The base-2 log makes the units interpretable: RBI* = 2 means roughly four times as many outward as inward citations. Additive smoothing of 0.5 (Jeffreys) is fixed in advance and is not a tuning parameter.
Document-level values are aggregated to the corpus by taking the median of RBI* across documents, not by pooling counts, because pooling lets a small number of long works dominate. Both are reported; the median is the headline figure.
2.3 The within-passage variant
The stronger measure restricts attention to paired halves of a single passage.
For each reciprocal passage p with an other-binding half p_o and a self-binding half p_s:
WP-RBI*(p) = log₂ ( (O_p + 0.5) / (S_p + 0.5) )
where O_p and S_p are citation instances of the two halves in the same corpus.
WP-RBI is stronger than RBI for the reason given at §1: it controls by construction for every corpus-level confound. It is also narrower, because the set of qualifying passages is small. That tension is the paper’s central design problem and is taken up at §6.1 rather than smoothed over.
2.4 What the index is not
RBI is not a measure of hypocrisy, sincerity, or belief. It is a count of citation behavior. A corpus may return a high RBI because its authors were evading, or because its audience was composed of the bound party, or because the self-binding obligations were uncontested and therefore not worth arguing. The index does not adjudicate among these; the design at §4 and the stratification at §5.3 are what adjudicate, and they do so imperfectly.
3. The Passage Set
3.1 Inclusion criteria
A passage enters the reciprocal set only if all four hold:
R1 — Both halves are commands. Descriptive statements about the parties, and promises or warnings without imperative force, do not qualify.
R2 — Both halves are present in the same passage unit. For WP-RBI, the halves must fall within a span a contemporary reader would treat as one passage. Operationalized as: within the same chapter, or across a chapter division where the division cuts a continuous address (as at Colossians 3:22 / 4:1).
R3 — The relation is one of power. The two parties are not symmetrically situated. Master/servant, ruler/subject, creditor/debtor, employer/hireling, strong/weak, rich/poor.
R4 — The citer class is determinable. It must be possible to say which half binds the corpus’s authors and their primary audience. Where this is not determinable, the passage is excluded from that corpus’s analysis.
3.2 The qualifying set
Applying R1–R4 to the canon yields a smaller set than one would hope, and honesty requires stating it plainly.
Full reciprocal pairs within a passage (WP-RBI eligible):
- Ephesians 6:5–8 / 6:9 (servants / masters)
- Colossians 3:22–25 / 4:1 (servants / masters)
That is the entire household-code set. 1 Peter 2:18 addresses servants with no reciprocal master clause. Titus 2:9–10 addresses servants only. 1 Timothy 6:1–2 addresses servants; the address to the rich at 6:17–19 is in the same letter but not the same passage and fails R2 for WP-RBI purposes, though it enters the corpus-level RBI.
Power-relation commands binding the stronger party (RBI eligible, corpus level):
- Deuteronomy 24:14–15 (the hired servant, poor and needy, his wages not withheld overnight)
- Deuteronomy 23:15–16 (the escaped servant not to be delivered up)
- Leviticus 19:13 (the wages of the hired not abiding overnight)
- Leviticus 25:39–43 (thou shalt not rule over him with rigour)
- Job 31:13–15 (the cause of manservant and maidservant; “did not he that made me in the womb make him?”)
- Proverbs 22:22–23, 31:8–9 (pleading the cause of the poor and dumb)
- Isaiah 58:6 (undoing heavy burdens, letting the oppressed go free)
- Jeremiah 22:13 (woe to him that useth his neighbour’s service without wages)
- Malachi 3:5 (against those that oppress the hireling in his wages)
- James 5:4 (the hire of the labourers kept back by fraud, crying out)
- Matthew 7:12 and Luke 6:31 (the rule of reciprocity)
- Matthew 23:4 (burdens bound on others’ shoulders, not moved with their own finger)
Commands binding the weaker party (RBI eligible, corpus level):
- Ephesians 6:5–8, Colossians 3:22–25, 1 Timothy 6:1–2, Titus 2:9–10, 1 Peter 2:18–20
- Romans 13:1–7 and 1 Peter 2:13–17, where the corpus applies them to the servant’s obedience rather than the magistrate’s duty
- The Onesimus material in Philemon, where coded as enjoining return
3.3 The Matthew 7:12 problem
The rule of reciprocity is self-applying by construction: whatever ye would that men should do to you, do ye even so to them. It cannot be cited outward. Including it in S therefore guarantees a contribution in one direction and looks like rigging.
The decision, fixed in advance: Matthew 7:12 and Luke 6:31 are reported separately and excluded from the primary index. They enter a secondary analysis only. This costs the paper its most rhetorically effective item and is the right trade, because a measure that includes a term which can only move one way is not a measure.
4. Coding Scheme
4.1 Unit of analysis
The unit is the citation instance: one occurrence, in one document, of one scriptural reference. Repetition of the same verse within a document counts as separate instances only where separated by intervening argument; consecutive repetition for rhetorical effect counts once. Coders are given a worked page of examples.
4.2 Citation strength threshold
Four levels, coded before directionality:
- L1 — Direct quotation with or without reference
- L2 — Close paraphrase retaining the passage’s distinctive vocabulary
- L3 — Reference by citation without quotation (“as Paul instructs the Ephesians”)
- L4 — Allusion recognizable to a competent contemporary reader but not marked
Primary analysis uses L1–L3. L4 is coded but excluded, because allusion identification is where investigator judgment has the most room and where reliability will be worst. If L4 reliability clears the alpha floor independently, a secondary analysis including it may be reported; if it does not, L4 is discarded entirely.
4.3 The four coding criteria
Each qualifying citation instance receives four codes.
C1 — Directionality. Does the cited obligation bind the citer’s class, another class, or both?
- Outward — binds a party other than the citer’s class
- Inward — binds the citer’s class
- Bidirectional — binds both symmetrically
- Indeterminate
C2 — Completeness of the passage. Where the citation falls within a reciprocal passage, does the citation extend to the reciprocal half?
- Complete — both halves cited within the same argumentative move
- Truncated — one half cited, other half absent from the document entirely
- Separated — both halves present in the document but in unconnected places
- Not applicable — citation not within a reciprocal passage
The separated code matters. A document that cites Ephesians 6:5 on page 4 and 6:9 on page 30, in a different connection, has not committed half-verse warrant in the strict sense but has also not brought the reciprocal obligation to bear. It is reported as its own category and is not folded into either complete or truncated.
C3 — Argumentative function. What work is the citation doing?
- Warrant — the citation supports the argument’s conclusion
- Concession — the citation is acknowledged as cutting against
- Exposition — the citation is being explained without polemical use
- Ornament — the citation decorates without load-bearing function
C4 — Audience. Who is the document addressed to?
- Holders — the master class, or free citizens generally
- Bound — the servant class, as in catechetical material prepared for the enslaved
- Mixed or general
- Adversarial — addressed to the opposing party in controversy
C4 exists because audience is the strongest confound in the whole design (§6.3), and stratifying by it is the only way to test whether the effect survives.
4.4 Determining citer class
For the demonstration corpus, citer class is coded per document from the author’s stated or documented position: slaveholding, non-slaveholding but ministering within the institution, Northern non-slaveholding, or indeterminate. Documents coded indeterminate are excluded from RBI and retained only for descriptive reporting.
This is a weaker construct than the design would like. §6.2 treats the objection.
4.5 Masking
Full masking is impossible: a coder recognizes Ephesians 6:5. The partial masking that is achievable and is required:
M1 — Sequence masking. Coders receive citation instances in randomized order across documents, not in document order, so that a document’s overall tendency does not prime the coding of its individual instances.
M2 — Corpus masking. Demonstration and control instances are interleaved and coders are not told which corpus an instance comes from.
M3 — Hypothesis masking. Coders are trained on the scheme without being told the direction of the predicted effect. They are told the study concerns citation patterns in nineteenth-century religious argument.
M4 — Verse-identity masking for C1 only. Where feasible, the directionality code is assigned from the obligation’s content presented without its reference, so that the coder judges “who does this bind” rather than “which verse is this.”
M4 will fail for famous verses. Where it fails, that instance is flagged and the finding for that verse is reported as unmasked. The proportion of unmasked instances is reported in the results, not buried.
4.6 Inter-rater procedure
Three coders, independently trained, no communication during coding.
Concordance rule: two-of-three agreement establishes the code. Where all three differ, the instance is coded indeterminate and enters the indeterminate count.
Reliability floor: Krippendorff’s alpha ≥ 0.67 on C1 and C2, computed separately for each. This is the standard adopted throughout the methodology work and is not adjusted for this paper.
Indeterminate ceiling: 35%. If indeterminate instances exceed 35% on either C1 or C2, the coding is reported as failed.
No recoding to reach threshold. If alpha falls below 0.67, the result is published as a failed coding. Coders are not retrained and rerun on the same material. A second attempt, if made, uses a fresh sample and is reported as a second attempt.
5. Baselines and Comparison
5.1 What the index needs to mean anything
An RBI* of 2.5 in the demonstration corpus is a number without a referent. The question is always: compared to what? Three comparisons are required and none is optional.
5.2 The control corpus
Specified in Paper 5, summarized here. Matched homiletic and pamphlet material from the same denominations, regions, decades, and publication venues, addressing power-relation questions unrelated to the institution: employer and hireling, creditor and debtor, magistrate and subject, rich and poor within the congregation, parent and child.
The control establishes whether outward-binding citation is a general property of the pulpit — which it may well be, since preaching about one’s own congregation’s obligations is harder than preaching about someone else’s — or specific to the institution.
Prediction fixed in advance: the control corpus will itself show RBI* > 0. Preaching is not balanced anywhere. The demonstration claim is about the difference, not the level.
5.3 Audience stratification
Every comparison is run within levels of C4. The critical cell is documents addressed to holders, because that is where a self-binding citation would land on the audience present. A high RBI* in catechetical material prepared for the enslaved is uninterpretable — of course a catechism for servants cites servants’ duties — and pooling it with holder-addressed material would produce a meaningless composite.
Documents coded bound are excluded from the primary analysis and reported separately as a descriptive appendix.
5.4 The position control
Paper 1’s steelman at §7.3 raised the possibility that citation asymmetry tracks verse position rather than direction of obligation: the opening of a passage is more citable than its close, and in both household codes the servant’s half comes first.
This must be tested and the test requires passages where the powerful party’s obligation comes first. Job 31:13–15, Malachi 3:5, Jeremiah 22:13, and Isaiah 58:6 all state the obligation of the stronger without a preceding address to the weaker. If RBI* asymmetry persists when the analysis is restricted to position-reversed material, the position explanation dies. If it reverses, my explanation dies.
This test is prerequisite. The position-reversed set must be fixed in writing before any counting begins, and its composition must not be revised after the primary result is known.
6. Steelmanning: The Strongest Case Against
What follows is the best case I can build against this paper. Two of these I cannot answer, and one of them may be fatal to the design as it stands.
6.1 The passage set is too small to support the measure
The objection. Strip the rhetoric and the WP-RBI — the paper’s strongest measure, the one whose design controls everything — rests on two passages. Ephesians and Colossians. That is the entire eligible set, and the two are not independent: they are closely parallel texts, plausibly related in composition, addressing the same question in nearly the same words. Effectively the design has one observation.
A natural experiment with an n of one or two is not a natural experiment. It is an anecdote with a formula attached. The corpus-level RBI has more items, but it purchases them by giving up every control that made WP-RBI worth having: the Malachi and Job material differs from the household codes in genre, testament, familiarity, lectionary position, and printing frequency, which means the corpus-level measure is exposed to precisely the confounds Paper 5 warns about.
The paper thus offers a strong design with no power and a powered design with no strength, and presents the combination as though the virtues added.
Response. This is correct and it is the paper’s central problem. I do not think it is fatal, but the reasons I give should be weighed skeptically because I have an interest in them.
What can be said. First, the unit of observation is not the passage; it is the citation instance. Two passages generate thousands of citation instances across hundreds of documents, and the question of whether Ephesians 6:5 and 6:9 are cited at equal rates is answerable with high precision from that material. The inferential n is instances-within-documents, not passages. What the small passage set limits is generalization across passages, not estimation within them.
Second, the two passages are indeed non-independent, and the honest consequence is that WP-RBI should be reported as a result about the household codes, not as a result about reciprocal commands in general. That is a narrower finding than the paper’s title implies and the title may need to change.
Third — and this is a concession rather than an answer — the combination problem is real. The right structure is probably to report WP-RBI and corpus-level RBI as two separate studies with separate claims, rather than as a strong measure supported by a broad one. Presenting them as complementary invites the reader to average their virtues, and averaging virtues is not how evidence works.
I regard this objection as damaging and only partly met.
6.2 “The citer’s class” is a construct the corpus does not contain
The objection. The index requires knowing which half binds the author. But a great many of these writers were not masters. Northern ministers arguing for the fugitive statute held no one. Southern ministers frequently held no one. Some who held did so through a wife’s inheritance and described themselves as unwilling. The design assigns a class position to men whose actual position was various, and then counts their citations against an obligation the design has assigned them.
Worse, the assignment is made by the investigator on grounds the investigator chooses. If a Northern minister counts as citer-class holder because he defends the institution, then class is being read off the conclusion, and the index becomes a restatement of what the writer argued rather than a measurement of how he argued.
Response. The objection identifies a genuine circularity risk and the fix is imperfect.
The fix adopted: citer class is coded from documented personal and household status only — did this man hold, at the time of writing, by any available record — and never from the position he argues. Where status is undocumented the document is coded indeterminate and excluded. This will exclude a large fraction of the corpus and will bias the retained sample toward better-documented, more prominent authors. That bias is reported.
For the Northern material the construct genuinely does not apply and the honest move is to drop it: Northern documents are analyzed under a different question — whether the audience is the bound party — and are not assigned a citer class at all. This costs the paper the rendition sermons, which were Paper 1’s paradigm case. The cost is real and I take it rather than paper over the construct.
6.3 Audience explains the whole effect
The objection. Sermons cite the duties of the people in front of them, and the people in front of them varied. A minister addressing a congregation that included both masters and servants, in a period when catechetical instruction of the enslaved was a live project, had reason to cite servant duties constantly. The asymmetry is a fact about who was being preached to, not about what the preacher was willing to say.
More pointedly: the design’s own stratification concedes this. Excluding bound-audience documents admits that audience drives citation. Once that is admitted, the residual difference in the holder-audience cell might be nothing more than the residue of imperfect audience coding, since audience is coded from the document’s own framing and framing is exactly what a writer controls.
Response. This is the objection the stratification exists to meet and it meets it only partially.
The strongest available answer is the within-passage design. In a single sermon to a single congregation, the audience is identical for verse 5 and verse 9. Audience cannot explain a differential between two verses heard by the same people in the same minute. That is precisely why WP-RBI is the primary measure despite the power problem at §6.1 — the two problems trade against each other, and I have chosen to accept low power in exchange for a design audience cannot confound.
Where audience does remain a threat is the corpus-level RBI, and there I do not have a clean answer. Audience coding from document framing is exactly as contaminable as the objection says. The mitigation is to code audience from external evidence where it exists — publication venue, occasion, subscription lists, the sermon’s stated setting — and to report the proportion coded from internal framing alone. If that proportion is high, the corpus-level result should be discounted accordingly.
6.4 Polemical need drives citation, and it points the same way
The objection. This is the one that worries me most. Writers cite what is under attack. The servant’s duty of obedience was the proposition abolitionists denied; it therefore needed defending, and defending it required citing it. The master’s duty of justice and equity was not under attack — no one denied it, both sides affirmed it, it was uncontroversial common ground. Uncontroversial propositions do not generate citations, because there is nothing to establish.
On this account the entire asymmetry is produced by the structure of the controversy and has nothing to do with the direction of obligation. A high RBI* would be exactly what one should expect from writers arguing honestly about a contested point. The measure would then be detecting the shape of the dispute and calling it evasion.
Note that this explanation survives the within-passage design, which the audience objection does not. Verse 5 was contested; verse 9 was not. Same passage, same audience, same minute — different polemical status.
Response. I do not have a full answer to this and it should be recorded as an open threat to the paper rather than a managed one.
Three partial responses, offered without confidence that they suffice.
First, the account makes a prediction that can be checked: if verse 9 went uncited because it was uncontested common ground, it should appear frequently in non-polemical registers — devotional works, family instruction, general expository preaching, and the pastoral literature addressed to masters about their households. Uncontested truths are not unmentioned truths; they are the ordinary furniture of devotional writing. If the master’s obligation is thin there too, the polemical-need explanation fails. If it is well represented there and thin only in the controversial literature, the explanation largely succeeds — and the finding would then convert into Paper 4’s phenomenon, a register effect rather than a subtraction.
Second, the account is in tension with C3. If verse 9 was uncontested common ground, one would expect it to appear as concession — the acknowledged point one grants before proceeding. Skilled controversialists grant the opponent’s uncontested ground precisely to isolate the contested claim. Its absence even in the concession role is harder for the objection to absorb.
Third, and this is not a defense of my thesis but a clarification of it: if the polemical-need account is right, the correct description of what happened is that a command binding the powerful was affirmed universally and pressed never. That is worth naming too. But it is not functional subtraction, and I should not be permitted to rename it into my category after the fact.
The first response is a real test and it should be run before the primary analysis, not after. If the devotional-register check comes back the wrong way, this paper becomes a contribution to Paper 4 and its own thesis is withdrawn.
§6.4a — Status of the devotional-register test (attempted, not run)
The test specified at §6.4 and A5 was attempted and could not be completed. The failure is one of retrieval infrastructure rather than of source availability, and the distinction matters for anyone assessing whether the constraint is real or decorative. Period sources are fully public, out of copyright, and machine-readable; a matched register corpus of two hundred works is assemblable in days. What blocked the attempt was the absence of within-corpus search, and that is a solvable problem rather than a property of the evidence.
A single work was partially read — Jones (1842), the first 48 of 277 pages — and yielded one observation recorded here with no inferential weight. Inward-binding pastoral material is present in that work: a dedicated section on express commands to masters, plus reproductions of Baxter’s directions to masters and Gibson’s 1727 letter to masters and mistresses. Half-verse warrant is also present in the same work: Gibson’s argument that baptism alters no civil property runs on 1 Corinthians 7:20 and 7:24 without touching Ephesians 6:9 or Colossians 4:1, and Berkeley’s quoted use of the servant’s half is deployed to argue that Christian slaves make better slaves, with no reciprocal half anywhere in it. Note that Baxter and Gibson are English and pre-window; their appearance in an 1842 American work is Jones’s editorial choice, not period American production, and they do not satisfy H4 as pre-registered.
The observation suggests H4 is stated too coarsely. Presence of the self-binding half in a register is not the same as its being brought to bear on the party it binds, and a work can exhibit both at once. H4 should therefore be split before the test is run:
H4a. Self-binding halves of reciprocal passages are not well represented in non-polemical devotional and pastoral registers within the same period and denominations.
H4b. Where self-binding halves do appear in those registers, they are not brought to bear as obligations on the holder — they appear in exposition, historical recitation, or ornament rather than in the warrant or concession roles of C3.
A5 is correspondingly split. If H4a fails but H4b holds, the finding is not withdrawn but narrowed: the command is present and not pressed, which is the phenomenon Paper 1 §7.4 describes as an output of a selection procedure and remains within functional subtraction. If both fail, the thesis is withdrawn and the material migrates to Paper 4 per note 8. The split is recorded before any counting, and the C3 coding for register material uses the same scheme and the same blinding as the primary analysis.
6.5 Ratio measures are fragile and the smoothing is doing work
The objection. RBI* is a log ratio with additive smoothing on counts that will frequently be zero in the denominator. With S = 0, the smoothing constant alone determines the value, and a document citing verse 5 forty times and verse 9 never returns a very different number than one citing verse 5 four times and verse 9 never, though both exhibit the same qualitative behavior. Choice of smoothing constant is a researcher degree of freedom of exactly the kind the reproducibility literature warns about.
Response. Accepted, and the mitigations are pre-registration and reporting.
The constant is fixed at 0.5 in advance and stated here. Sensitivity across 0.25, 0.5, and 1.0 is reported for every headline figure. Additionally, a binary complement measure is reported alongside the ratio: the proportion of documents citing the other-binding half that also cite the self-binding half, at any strength, anywhere in the document. This measure has no smoothing, no ratio, and no tuning parameter, and it captures the qualitative behavior directly. If the ratio and the proportion disagree, the proportion is preferred and the ratio is reported as unstable.
6.6 The index will be aimed at present-day targets
The objection. A computable score for whether a body cites obligations onto others more than onto itself is a weapon. It can be run on any denomination, institution, or movement, will always return a number greater than zero because preaching is never balanced, and the number will be reported as a finding.
Response. The concern is legitimate and the mitigation is structural rather than rhetorical. RBI is uninterpretable without a matched control, and the control is expensive — that is a feature. Any application reporting a bare RBI without a matched baseline and audience stratification is misusing the measure, and this paper says so in advance so that the misuse is identifiable as misuse.
I do not claim this prevents anything. It makes the misuse detectable, which is the most a method can do.
7. Pre-Registration
Fixed before data collection, and reported whether or not it is met.
H1. In the demonstration corpus, restricted to holder-audience documents, WP-RBI* for the Ephesians and Colossians pairs exceeds 0 by a margin greater than that observed in the matched control corpus on its own reciprocal passages.
H2. The truncated code (C2) is more frequent than the complete code for other-binding halves of reciprocal passages, and this differential is larger in the demonstration corpus than in the control.
H3. The asymmetry persists in position-reversed material (§5.4), ruling out verse position as the mechanism.
H4 (adversarial, from §6.4). Self-binding halves are not well represented in non-polemical devotional and pastoral registers within the same period and denominations. If H4 fails — that is, if they are well represented there — the primary thesis is withdrawn and the finding is reassigned to Paper 4.
Abandonment thresholds:
- A1. Krippendorff’s alpha < 0.67 on C1 or C2 → coding reported as failed, no primary analysis
- A2. Indeterminate rate > 35% on C1 or C2 → same
- A3. Demonstration/control difference in WP-RBI* not distinguishable after audience stratification → measure has no referent, paper withdrawn
- A4. Position-reversed material shows reversal → mechanism is position, paper withdrawn
- A5. H4 fails → thesis reassigned, this paper’s claim withdrawn
- A6. Unmasked proportion (M4 failures) > 50% → C1 results reported as unmasked with correspondingly reduced weight
Analysis order is fixed: reliability first, then H4 (the adversarial test), then H3 (position), then H1 and H2. Running the adversarial and mechanism tests before the primary hypotheses is deliberate. A design that tests its own thesis last has arranged to know the answer before it checks whether the answer means anything.
8. Worked Illustration
The following numbers are invented for the purpose of showing how the arithmetic runs. They are not results, not estimates, and not predictions. No data have been collected.
Suppose a hypothetical document, addressed to holders, coded at L1–L3:
| Citation | Direction | Count |
| Ephesians 6:5 | Outward | 6 |
| Colossians 3:22 | Outward | 3 |
| 1 Timothy 6:1 | Outward | 2 |
| Romans 13:1 | Outward | 4 |
| Ephesians 6:9 | Inward | 0 |
| Colossians 4:1 | Inward | 1 |
| Malachi 3:5 | Inward | 0 |
Document-level RBI* = log₂((15 + 0.5)/(1 + 0.5)) = log₂(10.33) = 3.37
WP-RBI* for Ephesians = log₂((6 + 0.5)/(0 + 0.5)) = log₂(13.0) = 3.70 WP-RBI* for Colossians = log₂((3 + 0.5)/(1 + 0.5)) = log₂(2.33) = 1.22
C2 coding: Ephesians = truncated; Colossians = complete if 4:1 appears in the same argumentative move, separated if elsewhere.
Binary complement: document cites Ephesians 6:5 without 6:9 → contributes 0 to the Ephesians complement proportion; cites Colossians 3:22 and 4:1 → contributes 1 to the Colossians complement proportion.
A control document scoring RBI* = 2.9 on its own reciprocal passages would leave a demonstration/control difference of 0.47 — small, and a reminder that the level is uninformative and only the difference carries the claim.
9. Falsification Constraint
If the Reciprocity Balance Index in the demonstration corpus, restricted to holder-audience documents and compared against the matched control corpus on its own reciprocal passages, shows no difference in the predicted direction after position control, then half-verse warrant has no referent and this paper should be withdrawn.
The paper additionally falls under A4 (position reversal), A5 (devotional-register representation), or A1–A2 (coding failure), each independently sufficient. All are reported whichever way they fall.
10. Scope and What Is Not Claimed
The paper does not claim that a high RBI establishes evasion. It claims that a difference from a matched control, surviving audience stratification and position control and the devotional-register test, is not explained by the innocent mechanisms currently identified. That is a defeasible claim and further mechanisms may be proposed.
It does not claim generality beyond the household codes for the within-passage result. §6.1 forces that concession and it should be carried into the title if it survives review.
It does not claim that the men studied denied the master’s obligation. Many affirmed it explicitly. The measure counts what was pressed, not what was believed, and the distinction is the whole point: a command affirmed in principle and never brought to bear on the party it binds has been honored in a way that costs the honorer nothing.
It does not claim priority over the historiography. That these verses went uncited has been noticed. What is offered here is a way to count it, a baseline to count it against, and a set of conditions under which the count would show nothing.
Notes
- Reliability computation. Krippendorff’s alpha is computed with the nominal difference function for C1, C3, and C4, and with the ordinal function for C2, where complete, separated, and truncated form a meaningful order. Bootstrap confidence intervals at 1,000 resamples are reported alongside point estimates.
- On the 0.67 floor. The floor is adopted from the broader methodology work for consistency and is deliberately not tuned to this paper. It sits at the conventional boundary for tentative conclusions rather than at the 0.80 conventionally required for firm ones. Any result clearing 0.67 but not 0.80 is reported as tentative in the text, not only in a footnote.
- The excluded rule of reciprocity. Matthew 7:12 and Luke 6:31 are excluded from the primary index per §3.3. Their citation counts are reported in a standalone table because they are of independent interest — a corpus that cites the rule of reciprocity frequently while returning a high RBI on operational commands is exhibiting something worth naming, though this paper does not name it.
- Philemon. The letter resists the coding scheme. It is a personal appeal rather than a general command, its imperative force is contested, and both parties to the nineteenth-century dispute read it as decisive for their own side. It is excluded from the primary index and treated in a separate qualitative note. Excluding the corpus’s single most-discussed text is a real cost and is stated as such.
- The devotional-register check per §6.4a and A5a/A5b must be run before the primary analysis. It requires a register corpus — family instruction manuals, devotional commentaries, catechetical material for households, and pastoral works addressed to householders — matched to the demonstration corpus on denomination, region, and decade. Sources are available through Archive.org full text and the Documenting the American South church collection at UNC. Commentaries on Ephesians and Colossians are excluded from the register corpus: sequential commentary covers every verse by genre obligation, so a commentary’s treatment of 6:9 carries no information about selection. This exclusion was not stated in the original draft and is a real narrowing of the available register material.
- Northern material. Following §6.2, rendition sermons by non-holding Northern authors are excluded from the citer-class analysis. They remain the paradigm case for Paper 1, which does not require a citer-class construct. The two papers therefore run on partially different corpora and their results should not be pooled.
- Relation to Paper 1. Half-verse warrant is a species of functional subtraction with an unusually favorable measurement design. Cases satisfying both are entered once in the joint case register maintained across the series.
- Relation to Paper 4. If A5 fires, this paper’s finding migrates to Paper 4 as a register effect. That migration should be recorded as a conversion of a failed hypothesis into a finding, in the manner used elsewhere in the methodology work, and not as a rescue of this paper.
- Relation to Paper 5. The control corpus, the position-reversed set, and the register corpus are all Paper 5 constructions. Nothing in this paper is established until they exist. The formula is complete; the evidence is not.
- Scripture. Quotations follow the Authorized Version throughout, for the reason given in Papers 1 and 2.
- Illustrative numbers. All figures in §8 are invented to demonstrate the arithmetic. No data have been collected and no result is reported anywhere in this paper.
- OCR and reference extraction. Period OCR is unreliable on exactly the strings the study depends on. Citation references in period style (“Eph. vi. 9”) and italicized quotation both corrupt at high rates. Any automated extraction must be validated against a hand-coded sample of at least 200 known citation instances, and its recall and precision reported in the results rather than assumed. Where recall falls below 0.90, automated counts are reported as lower bounds only.
- Absence of prior counts. A search of the secondary literature found no prior quantitative citation analysis of this corpus. The observations grounding Papers 1 and 3 exist in qualitative form throughout the historiography; the counts do not exist. This supports the additive framing at Paper 1 §7.6 and also means the study has no external result to check itself against, which raises rather than lowers the burden on the control corpus.
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