Lean4 axiomatic kernel for the legal domain. RICO + Title VI + §§ 1981/1983/1985(3). Predicates return ⟨bool, evidence, citation⟩; the kernel does no I/O. Each verifier run produces a per-predicate report.json + proof-DAG graph.json + intro-rule loci.json — surfaced here as the recent-runs table + latest-run diagram + predicate roster.
What we found. Our own adversarial review lane found leak channels in the cross-axis agreement oracle that classifies our Tier-A/B/C figures. The fan-out agents that are supposed to agree independently could, in principle, see each other's work — so blind agreement was never established for any wave.
What survives. Kernel soundness is unaffected and mechanically re-checked: every lake build, every sorry-free proof still stands. You cannot leak your way into a green build — the encoded work is real. Only the agreement-based confidence is in question.
What is withdrawn. The agreement-based tier counts (proving's Tier-A/B/C and accounting's) are withdrawn — shown as "withheld", restated provisional as of 2026-07-14. Sections-encoded, universe %, sector census and the soundness panels are mechanical and remain.
The schedule. Re-earning a tier means a fresh blind re-slice under the now-closed contracts, not a re-score of the old one. It is sequenced cheapest-first: the operational axis re-attacks first, the financial axis re-slices next, and the textual re-slice is a multi-week program. This notice updates as each axis re-earns its figure.
Frameworks — module readiness
One node per Lean module. Focused = predicates + axioms compile under the current toolchain.
Verifier-run statistics
Aggregate over all examples/<id>/report.json artefacts.
Verifier runs
2
Complaints elaborated against the kernel.
Accepted
OK
2
Kernel verdict: ACCEPTED — the validity theorem elaborates.
Rejected
OK
0
Kernel verdict: REJECTED — at least one element disproved.
Latest run
13.8d ago
M.G. v. Springfield Public Schools — toy Title VI sample
Axiomatize-U.S.-Code program
Corpus-wide coverage from proving/coverage.json (dau-cross rollup).
Sections encoded
388
Operative U.S. Code sections encoded across all axes.
Tier-A
withheld
Agreement-tier confidence withdrawn 2026-07-14 — the cross-axis agreement oracle is under re-verification (blind re-slice pending). Sections-encoded and soundness figures are unaffected.
Titles touched
11/58
Distinct U.S. Code titles with at least one encoded section.
Of USC universe
0.62%
Share of the 62,831-section operative universe encoded so far.
Recent verifier runsOne row per complaint elaborated against the kernel. Verdict pill reflects whether the validity theorem type-checks; the expand row enumerates each kernel rejection's locus.
ID
Complaint
Framework
Predicates
Verdict
Failures
Run at
titlevi_sample
M.G. v. Springfield Public Schools — toy Title VI sample
titlevi § 601 / § 602 / retaliation
17 / 17 True
ACCEPTED
0
2026-07-10T14:54:17Z
Verdict accepted — no kernel rejections recorded for this run.
sample
Doe v. Acme — toy § 1962(c) sample
rico § 1962(c)
19 / 19 True
ACCEPTED
0
2026-07-10T14:54:12Z
Verdict accepted — no kernel rejections recorded for this run.
Sorted by runFinishedAt, descending.
§ 601 / § 602 / retaliation intro-rule shape — M.G. v. Springfield Public Schools — toy Title VI sample
One node per kernel-required element, coloured by per-element verdict. Round nodes are derived structures/theorems; rectangles are predicate slots. The top-level disjunction is focused.
ValidTitleVIJudicialClaim
top-level inductive — disjunction across § 1962 subsections
directed
✓ True · Low
ActionDirectedAtPerson
intentional
✓ True · Medium
4 of 5 Arlington Heights factors pled (impact, historical background, substantive departure, administrative history); procedural irregularity absent. The Feeney 'because of' / 'in spite of' line is the contested edge: ¶10 alone establishes
officialCap
✓ True · Low
DefendantSuedInOfficialCapacity
personInUS
✓ True · Low
M.G. is pleaded as a natural person, a minor, physically enrolled at a school in Springfield, Massachusetts. No extraterritoriality question is raised, and the plaintiff is plainly not a state instrumentality (the District is the *defendant
notInstrumentality
✓ True · Low
NotAStateInstrumentality
recipient
✓ True · Low
IsRecipient
receivesFFA
✓ True · Low
ReceivesFederalFinancialAssistance
programOfRecipient
✓ True · Low
IsProgramOfRecipient
underProgram
✓ 2 of 2
2 positional applications of OccursUnderProgram
Predicate roster — M.G. v. Springfield Public Schools — toy Title VI samplePer-predicate atomic view of the most recent run. Each row is one Bool the kernel consumed via Facts.lean; expand the row for evidence and uncertainty rationale.
#
Predicate
Args
Value
Uncertainty
Evidence
Cite
Kernel locus
§ 601 / § 602 / retaliation
1
IsPersonInUS
mg titleviComplaint
True
low
¶1 — Plaintiff M.G. is a 14-year-old Latino student enrolled at Lincoln Middle School, a public middle school operated by Defendant Springfield Public Schools, in Springfield, Massachusetts.
Uncertainty: M.G. is pleaded as a natural person, a minor, physically enrolled at a school in Springfield, Massachusetts. No extraterritoriality question is raised, and the plaintiff is plainly not a state instrumentality (the District is the *defendant*, sued in its governmental capacity per ¶20). The suit is brought by M.G.'s mother on M.G.'s behalf (¶1), which is a capacity/next-friend question under Fed. R. Civ. P. 17(c), not a personhood question — the named plaintiff for § 601 purposes remains M.G.
¶1 — Plaintiff M.G. is a 14-year-old Latino student enrolled at Lincoln Middle School, a public middle school operated by Defendant Springfield Public Schools, in Springfield, Massachusetts. — M.G. is a natural person physically present in Massachusetts — a State of the United States — at the time of the alleged discrimination, satisfying rubric prong 1.
¶12 — M.G. applied to the Magnet in 2023. M.G. ranked in the top 25% of test-takers but did not reach the top 10% cutoff. — Confirms M.G. was a present applicant/participant in the District's program during the operative period, not a foreign or absent claimant.
¶13 — M.G. is a member of an identifiable protected class — Latino students of Mexican national origin — who were disproportionately excluded from the Magnet by the 2022 Policy. — National origin is the protected ground, not a bar to personhood; under Plyler and Mathews, citizenship and immigration status are irrelevant to "person in the United States" under § 601.
42 U.S.C. § 2000d — No person in the United States shall, on the ground of race, color, or national origin, be excluded from participation in . . . any program or activity receiving Federal financial assistance. — Operative statutory text; M.G. falls squarely within the class of covered "persons."
¶1: "Plaintiff M.G. is a 14-year-old Latino student enrolled at Lincoln Middle School... M.G.'s mother, MARIA GUTIERREZ, brings this action on M.G.'s behalf." — plaintiff is a natural person (a minor suing through a parent as next friend…
¶1: "Plaintiff M.G. is a 14-year-old Latino student enrolled at Lincoln Middle School... M.G.'s mother, MARIA GUTIERREZ, brings this action on M.G.'s behalf." — plaintiff is a natural person (a minor suing through a parent as next friend), not an entity of any kind.
¶13: "M.G. is a member of an identifiable protected class — Latino students of Mexican national origin" — an individual beneficiary of the federally funded program, precisely the class of claimant for whom the Title VI private right of action exists (Alexander v. Sandoval, 532 U.S. 275, 279-80 (2001), recognizing a private right to enforce § 601).
¶2 + ¶12: the plaintiff is the applicant denied admission by Defendant Springfield Public Schools; the school district is the *defendant*, not the plaintiff. The United States v. Alabama / DeKalb Cty. Sch. Dist. v. Schrenko, 109 F.3d 680, 689 (11th Cir. 1997) bar runs against a state instrumentality *as plaintiff* suing the state — the posture here is inverted.
42 U.S.C. § 2000d (verbatim): "No person in the United States shall, on the ground of race, color, or national origin, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under any program or activity receiving Federal financial assistance." M.G. is a "person" within the plain text; the instrumentality-standing cases construe "person" to exclude state-created entities, not natural persons.
¶20: "The District is sued in its official, governmental capacity." No state agency or the Commonwealth appears as a party at all, so the suit-against-the-state predicate of the Schrenko/Alabama bar is absent on both ends.
¶2. Defendant SPRINGFIELD PUBLIC SCHOOLS ("the District") is a Massachusetts public school district. The District operates 28 schools serving approximately 24,000 students.
¶2. Defendant SPRINGFIELD PUBLIC SCHOOLS ("the District") is a Massachusetts public school district. The District operates 28 schools serving approximately 24,000 students.
¶3. The District has received federal financial assistance from the U.S. Department of Education since at least 2010, including approximately $4.2 million annually in Title I grants for the 2022-23 and 2023-24 school years.
¶3. The District signed Title VI assurance documents as a condition of receiving these funds.
¶1. ... Lincoln Middle School, a public middle school operated by Defendant Springfield Public Schools
34 C.F.R. § 100.13 (ED): "recipient" means any State, political subdivision ... public or private agency, institution, or organization ... to whom Federal financial assistance is extended, directly or through another recipient
¶3: "The District has received federal financial assistance from the U.S. Department of Education since at least 2010, including approximately $4.2 million annually in Title I grants for the 2022-23 and 2023-24 school years."
¶3: "The District has received federal financial assistance from the U.S. Department of Education since at least 2010, including approximately $4.2 million annually in Title I grants for the 2022-23 and 2023-24 school years."
¶3: "The District signed Title VI assurance documents as a condition of receiving these funds." — voluntary entry into the federal relationship (Paralyzed Veterans, 477 U.S. at 605-06).
¶2: "Defendant SPRINGFIELD PUBLIC SCHOOLS ('the District') is a Massachusetts public school district. The District operates 28 schools serving approximately 24,000 students." — the recipient entity itself is the fund recipient, not a mere sub-unit.
Continuity through the operative period: the 2022 Policy (¶7) and the 2023 suspension (¶15) both fall within the pleaded 2022-23 / 2023-24 funding years.
¶5: "The District operates the Lincoln STEM Magnet (“the Magnet”), a competitive academic program housed at Lincoln Middle School."
¶5: "The District operates the Lincoln STEM Magnet (“the Magnet”), a competitive academic program housed at Lincoln Middle School."
¶5: "Admission is by application; selection criteria are set by the District's Board of Education."
¶2: "Defendant SPRINGFIELD PUBLIC SCHOOLS (“the District”) is a Massachusetts public school district. The District operates 28 schools serving approximately 24,000 students."
¶1: "Lincoln Middle School, a public middle school operated by Defendant Springfield Public Schools"
¶3: "The District has received federal financial assistance from the U.S. Department of Education since at least 2010, including approximately $4.2 million annually in Title I grants" — satisfies § 2000d-4a's trailing "any part of which is extended Federal financial assistance"
¶5 — The District operates the Lincoln STEM Magnet ("the Magnet"), a competitive academic program housed at Lincoln Middle School. Admission is by application; selection criteria are set by the District's Board of Education.
¶5 — The District operates the Lincoln STEM Magnet ("the Magnet"), a competitive academic program housed at Lincoln Middle School. Admission is by application; selection criteria are set by the District's Board of Education.
¶7 — In January 2022, the Board of Education adopted a new admissions policy ("the 2022 Policy"). Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test ("SHSAT"), with admission limited to applicants scoring in the top 10% of test-takers.
¶17 — The District, acting through its Board of Education, intentionally adopted the 2022 Policy
¶12 — M.G. applied to the Magnet in 2023. M.G. ranked in the top 25% of test-takers but did not reach the top 10% cutoff. ... M.G. was denied admission solely because of his SHSAT score under the 2022 Policy.
¶9 — Following implementation of the 2022 Policy, Latino enrollment in the Magnet dropped to 9% in the 2022-23 admitted class and 8% in the 2023-24 admitted class.
42 U.S.C. § 2000d (legal/uscode/md/42/ch21/2000d.md) — No person in the United States shall, on the ground of race, color, or national origin, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under any program or activity receiving Federal financial assistance.
¶15: "Lincoln Middle School Principal SARAH BRENNAN moved to suspend M.G. from Lincoln's after-school enrichment activities, citing \"attendance concerns\" that had not previously been raised."
¶15: "Lincoln Middle School Principal SARAH BRENNAN moved to suspend M.G. from Lincoln's after-school enrichment activities, citing \"attendance concerns\" that had not previously been raised."
¶20: "Principal Brennan is named as defendant only in her official capacity as the District's agent."
¶2: "Defendant SPRINGFIELD PUBLIC SCHOOLS (\"the District\") is a Massachusetts public school district."
¶3: "The District has received federal financial assistance from the U.S. Department of Education since at least 2010"
¶5: "The District operates the Lincoln STEM Magnet (\"the Magnet\"), a competitive academic program housed at Lincoln Middle School."
¶16: "M.G. has not been re-admitted to the after-school enrichment activities. The suspension has impaired his academic record and chances of future Magnet admission."
42 U.S.C. § 2000d-4a: "the term \"program or activity\" and the term \"program\" mean all of the operations of— ... (2)(B) a local educational agency (as defined in section 7801 of title 20), system of vocational education, or other school system; ... any part of which is extended Federal financial assistance."
¶2 — Defendant SPRINGFIELD PUBLIC SCHOOLS ("the District") is a Massachusetts public school district. The District operates 28 schools serving approximately 24,000 students.
¶2 — Defendant SPRINGFIELD PUBLIC SCHOOLS ("the District") is a Massachusetts public school district. The District operates 28 schools serving approximately 24,000 students.
¶20 — The District is sued in its official, governmental capacity. Principal Brennan is named as defendant only in her official capacity as the District's agent.
¶1 — a public middle school operated by Defendant Springfield Public Schools
¶17, ¶19 — The District, acting through its Board of Education, intentionally adopted the 2022 Policy … The District retaliated against Plaintiff …
¶15 — Lincoln Middle School Principal SARAH BRENNAN moved to suspend M.G. …
¶12: "M.G. applied to the Magnet in 2023. M.G. ranked in the top 25% of test-takers but did not reach the top 10% cutoff."
¶12: "M.G. applied to the Magnet in 2023. M.G. ranked in the top 25% of test-takers but did not reach the top 10% cutoff."
¶12: "M.G. was denied admission solely because of his SHSAT score under the 2022 Policy."
¶12: "Under the pre-2022 composite formula, M.G.'s strong grades (3.8 GPA) and four teacher recommendations would have placed him among the admitted students."
¶13: "M.G. is a member of an identifiable protected class — Latino students of Mexican national origin — who were disproportionately excluded from the Magnet by the 2022 Policy."
¶16: "The suspension has impaired his academic record and chances of future Magnet admission."
¶9. Following implementation of the 2022 Policy, Latino enrollment in the Magnet dropped to 9% in the 2022-23 admitted class and 8% in the 2023-24 admitted class. Over the same period, Latino representation in the District-wide eligible …
Uncertainty: 4 of 5 Arlington Heights factors pled (impact, historical background, substantive departure, administrative history); procedural irregularity absent. The Feeney 'because of' / 'in spite of' line is the contested edge: ¶10 alone establishes only knowledge of foreseeable adverse effect, which Feeney holds insufficient. Intent is inferred from the conjunction of ¶10's rejected equally-predictive alternative with ¶11's unsupported and self-contradicting ('traditional') justification. ¶17's assertion of purpose is conclusory under Iqbal and was given no weight. A court could plausibly dismiss Count I while permitting the § 602 disparate-impact theory.
¶9. Following implementation of the 2022 Policy, Latino enrollment in the Magnet dropped to 9% in the 2022-23 admitted class and 8% in the 2023-24 admitted class. Over the same period, Latino representation in the District-wide eligible applicant pool remained at approximately 30%.
¶6. From 2010 through 2021, Magnet admissions were determined by a composite formula ... Latino enrollment in the Magnet during this period averaged 28% — closely tracking the District-wide Latino enrollment of 31%.
¶7. Under the 2022 Policy, the sole admissions criterion is performance on the [SHSAT] ... Grades and teacher recommendations are no longer considered.
¶10. The District's own 2021 internal pilot study ... projected that this formula would maintain academic predictive value while admitting Latino students at approximately 25% of the admitted class — within 5 percentage points of white-student admission rates.
¶11. The District has stated, in public Board meetings, that the SHSAT-only criterion was selected because it is "objective" and "traditional." The District has not produced data demonstrating that the SHSAT cutoff outperforms the prior composite formula at predicting student success in the Magnet curriculum.
¶13. M.G. is a member of an identifiable protected class — Latino students of Mexican national origin — who were disproportionately excluded from the Magnet by the 2022 Policy.
¶7: "In January 2022, the Board of Education adopted a new admissions policy ("the 2022 Policy"). Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test ("SHSAT"), with admissi…
¶7: "In January 2022, the Board of Education adopted a new admissions policy ("the 2022 Policy"). Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test ("SHSAT"), with admission limited to applicants scoring in the top 10% of test-takers."
¶8: "The 2022 Policy is facially neutral as to race, color, and national origin."
¶18: "The 2022 Policy is a facially neutral admissions criterion that has an adverse disparate impact on Latino applicants..."
¶5: "Admission is by application; selection criteria are set by the District's Board of Education." — Board-adopted, generally applicable selection rule, not an ad-hoc decision.
¶12: "M.G. was denied admission solely because of his SHSAT score under the 2022 Policy." — application of the standing criterion to plaintiff, confirming policy-not-one-off.
¶7: "Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test (\"SHSAT\"), with admission limited to applicants scoring in the top 10% of test-takers."
¶7: "Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test (\"SHSAT\"), with admission limited to applicants scoring in the top 10% of test-takers."
¶8: "The 2022 Policy is facially neutral as to race, color, and national origin." — establishes the facially-neutral predicate for a disparate-impact (as opposed to disparate-treatment) analysis.
¶6: "Latino enrollment in the Magnet during this period averaged 28% — closely tracking the District-wide Latino enrollment of 31%." — pre-policy baseline showing near-parity.
¶9: "Following implementation of the 2022 Policy, Latino enrollment in the Magnet dropped to 9% in the 2022-23 admitted class and 8% in the 2023-24 admitted class. Over the same period, Latino representation in the District-wide eligible applicant pool remained at approximately 30%." — the disparity, measured against the eligible applicant pool.
¶12: "M.G. was denied admission solely because of his SHSAT score under the 2022 Policy." — adversity: denial of a benefit (admission to a competitive academic program).
¶13: "M.G. is a member of an identifiable protected class — Latino students of Mexican national origin — who were disproportionately excluded from the Magnet by the 2022 Policy." — group-level pleading, not an isolated individual.
42 U.S.C. § 2000d (verbatim): "No person in the United States shall, on the ground of race, color, or national origin, be excluded from participation in, be denied the benefits of, or be subjected to discrimination under any program or activity receiving Federal financial assistance."
Four-fifths computation: Latino share of admitted class (9%, 8%) against Latino share of the eligible applicant pool (~30%) yields a selection-rate ratio of ~0.30 and ~0.27 — far below the 0.80 threshold of 29 C.F.R. § 1607.4(D). The pre/post comparison (28% → 9% with the applicant pool flat at ~30-31%) isolates the 2022 Policy as the intervening cause.
¶10: the District's own 2021 pilot study projecting ~25% Latino admission under a hybrid formula corroborates that the disparity is an artifact of the SHSAT-only criterion rather than of the applicant pool.
¶7. Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test ("SHSAT"), with admission limited to applicants scoring in the top 10% of test-takers. Grades and teacher recommendat…
¶7. Under the 2022 Policy, the sole admissions criterion is performance on the Springfield High Schools Admissions Test ("SHSAT"), with admission limited to applicants scoring in the top 10% of test-takers. Grades and teacher recommendations are no longer considered.
¶6. From 2010 through 2021, Magnet admissions were determined by a composite formula combining (a) standardized test scores (40%), (b) middle-school grades (40%), and (c) teacher recommendations (20%). Latino enrollment in the Magnet during this period averaged 28%.
¶9. Following implementation of the 2022 Policy, Latino enrollment in the Magnet dropped to 9% in the 2022-23 admitted class and 8% in the 2023-24 admitted class. Over the same period, Latino representation in the District-wide eligible applicant pool remained at approximately 30%.
¶10. The pilot study projected that this formula would maintain academic predictive value while admitting Latino students at approximately 25% of the admitted class.
¶12. Under the pre-2022 composite formula, M.G.'s strong grades (3.8 GPA) and four teacher recommendations would have placed him among the admitted students. M.G. was denied admission solely because of his SHSAT score under the 2022 Policy.
The District has stated, in public Board meetings, that the SHSAT-only criterion was selected because it is "objective" and "traditional."
The District has stated, in public Board meetings, that the SHSAT-only criterion was selected because it is "objective" and "traditional."
The District has not produced data demonstrating that the SHSAT cutoff outperforms the prior composite formula at predicting student success in the Magnet curriculum.
From 2010 through 2021, Magnet admissions were determined by a composite formula combining (a) standardized test scores (40%), (b) middle-school grades (40%), and (c) teacher recommendations (20%).
The pilot study projected that this formula would maintain academic predictive value while admitting Latino students at approximately 25% of the admitted class
¶14: "On 2023-09-15, MARIA GUTIERREZ filed a written Title VI complaint with the District's Title VI Coordinator alleging that the 2022 Policy discriminated against Latino applicants. She also filed a parallel complaint with the U.S. Dep…
¶14: "On 2023-09-15, MARIA GUTIERREZ filed a written Title VI complaint with the District's Title VI Coordinator alleging that the 2022 Policy discriminated against Latino applicants. She also filed a parallel complaint with the U.S. Department of Education's Office for Civil Rights."
¶1: "M.G.'s mother, MARIA GUTIERREZ, brings this action on M.G.'s behalf."
¶19: "The District retaliated against Plaintiff for the protected activity of filing a Title VI complaint by suspending M.G. from after-school enrichment activities, in violation of 42 U.S.C. § 2000d as construed in Jackson v. Birmingham Bd. of Educ., 544 U.S. 167 (2005)."
¶15: adverse action dated 2023-09-29, two weeks AFTER the 2023-09-15 protected activity — activity precedes retaliation.
¶13: "M.G. is a member of an identifiable protected class — Latino students of Mexican national origin" — establishes the race/national-origin nexus of the complaint's subject matter.
¶15: "On 2023-09-29 — exactly two weeks later — Lincoln Middle School Principal SARAH BRENNAN moved to suspend M.G. from Lincoln's after-school enrichment activities, citing 'attendance concerns' that had not previously been raised."
¶15: "On 2023-09-29 — exactly two weeks later — Lincoln Middle School Principal SARAH BRENNAN moved to suspend M.G. from Lincoln's after-school enrichment activities, citing 'attendance concerns' that had not previously been raised."
¶16: "M.G. has not been re-admitted to the after-school enrichment activities. The suspension has impaired his academic record and chances of future Magnet admission."
¶15: "Internal email correspondence obtained through a public-records request shows that Principal Brennan circulated a memo on 2023-09-22 (one week after the Title VI complaint) discussing 'the Gutierrez family's complaint' and asking whether 'consequences' should follow."
¶14: "On 2023-09-15, MARIA GUTIERREZ filed a written Title VI complaint with the District's Title VI Coordinator..." (establishes the protected activity the action followed)
¶3: "The District has received federal financial assistance from the U.S. Department of Education since at least 2010..." (recipient status — the actor is the recipient, acting through its principal)
¶14: 'On 2023-09-15, MARIA GUTIERREZ filed a written Title VI complaint with the District's Title VI Coordinator alleging that the 2022 Policy discriminated against Latino applicants.'
¶14: 'On 2023-09-15, MARIA GUTIERREZ filed a written Title VI complaint with the District's Title VI Coordinator alleging that the 2022 Policy discriminated against Latino applicants.'
¶15: 'Internal email correspondence obtained through a public-records request shows that Principal Brennan circulated a memo on 2023-09-22 (one week after the Title VI complaint) discussing "the Gutierrez family's complaint" and asking whether "consequences" should follow.'
¶15: 'On 2023-09-29 — exactly two weeks later — Lincoln Middle School Principal SARAH BRENNAN moved to suspend M.G. from Lincoln's after-school enrichment activities, citing "attendance concerns" that had not previously been raised.'