deterministic OCaml engine to compute and validate liturgical calendars for multiple rites, template-driven output to year 9999 https://git.labunix.xyz/colitur.git/atom?h=v0.2.0 2026-08-17T12:13:02Z 2026-08-17T12:13:02Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-17T12:13:02Z urn:sha1:3565ebd1608a7d87e0d890f9953845efcfe743ca A live-missalemeum sweep over a full liturgical year (2028, 364 days) returned 333 matching and 31 differing days: 17 already-known or pure notation, 3 new. All three now adjudicated against the photographic scans of the 1962 Missal. The Assumption's Epistle reads "Iudith 13, 22-25; 15, 10" (scan1:35357). Both engines carried "Judith 13:22-25; 13:15; 13:10" -- a chapter carry-over defect that re-applied chapter 13 to the second citation and so invented two verses the Missal never cites. The Seven Sorrows reads "Iudith 13, 22 et 23-25" (scan1:36938, corroborated at 28468); both carried "Judith 13:22; 13:25", dropping the range. The third, St Monica, resolves the other way: the Missal gives 1 Timothy (scan2:32679, heading and incipit both legible; scan1:29524 agrees) where missalemeum serves the Common of Holy Women's Proverbs -- colitur is right, no change. Layer 3 could not have found either citation defect. colitur's data is bootstrapped from lectio, and lectio is the other side of that differential, so while both engines produced the identical wrong answer the comparison held it against itself and reported agreement -- the shared-lineage blindness CLAUDE.md names, now with a second live witness beside Holy Thursday's colour. Only an external oracle could see it, and only outside the committed fixture's own window. Fixed upstream in lectio, re-bootstrapped here (provenance SHA-256 moved to 54f6bfc5, verified against the source), fixture regenerated. The upstream fix inverted layer 3 from blind to load-bearing here: reverting the Assumption citation now reddens both layers, where before it would have reddened neither. Verified by mutation, both directions. Allow-lists: - C22 closed and removed (128 rows -> 0), not re-adjudicated -- the other engine was fixed to agree, the same shape as the C2-C5/C7/C9-C13/C21 closures. Its own note had already flagged the Lenten Ember dead-key bug for upstream; lectio now also fails its build on any unreachable lectionary key rather than serving a plausible wrong Mass. - M28 opened (3 rows, verdict colitur), pinning both sides' citation text rather than the date and diff shape alone, so a different divergence landing on the same date cannot be swallowed. - M8's gate widened, expected_rows unchanged at 2: 2027-08-15 carries both its cause and M28's, and one entry is admitted per day. It stays under M8, which now requires its own commemoration difference to be present and admits the citation difference only when it satisfies M28's two-sided predicate. Neither cause absorbs the other. layer_m_reason's oracle-row parameter, kept named since M2 closed for exactly such a future reader, is live again. Register: docs/research/rules-register.md section 6.6. 2026-08-17T11:02:39Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-17T11:02:39Z urn:sha1:5d236c75c557a7e9ed4a8a852b8089aca48b594e Three Important findings from coordinator review of 8d1eb25, all fixed. 1. C30's own note claimed its 91-row population "is C25's OWN former population, before this task narrowed it" -- false. Independently re-derived against the real resolver (pre-fix vs post-fix binary) and the lectio fixture: only 44 of the 91 rows were ever in C25 (Wed 6/ Thu 19/Fri 19, matching C25's own fix-round-3 breakdown exactly); the other 47 (all of Monday/Tuesday, plus part of Wednesday/Friday) previously matched lectio outright -- both engines independently landing on the same wrong value -- and are newly allow-listed only because colitur is now right. Rewritten to the same "both engines silently agreed on the wrong answer" pattern C33/C34 already used. 2. "Diebus ferialibus" is not RG 17(a) -- RG 17(a) states only the day-identity privilege; the ferial-Mass rubrics are Mass-propers rubrics, a distinction the register's own §6.3 already drew before this task's first pass blurred it in code/allow-list comments. A further slip: C31/C32 called their own rubric "RG 17(a)'s own next/ third sentence" when it is a different rubric block ~230 lines away, in Holy Family's (not Holy Name's) own feast propers. Fixed the attribution chain throughout tools/bootstrap_lectionary.ml, data/ef/expected-divergences.sexp's C29-C34, and (gitignored, outside this commit) docs/research/rules-register.md -- closed the §6.3 park, added §6.5 recording all four citations with corrected attribution. Quotes and line numbers were already right; only the chain of custody to RG 17(a) was wrong. 3. M26's own 30 rows classify into two nameable shapes, not "three confirmed shapes" with an unexplained 23-row residue that was in fact empty: 21 rows are RG 78's own already-documented BVM votive-Mass gap; 9 rows are a second, distinct gap -- a week whose own Sunday was displaced by a movable named feast (Trinity->Corpus Christi, "Missa Dominicae I post Pentecosten"; Christ the King), where the Missal requires the displaced Sunday's own Mass to keep informing that week's ferias but step 3 walks back to the displacing feast's citation instead -- proven directly by colitur's own citation on the Christ- the-King rows being literally that feast's own Gospel. verdict open unchanged (not fixed here); the shape is now named instead of buried. Minors: section count corrected 1458->1456 (four places); "exactly one candidate, zero ambiguous" corrected to "correctness rests on ordering, not uniqueness" (2 of 1456 sections genuinely yield two candidates, Holy Saturday's own Lectio, both years); the stale "nothing in layers 3-5 compares citations" claim corrected (only layer 5 still doesn't); M18's note corrected (five new entries not six; ~18 of its remaining 352 rows only agree now because of this task's own fixes, not "already" before it); "five" corrected to "six" otherwise-unoccupied Saturdays in bootstrap_lectionary.ml; scan2 quotes softened where OCR-garbled. Also done outside the git-tracked files: the step-4 (Commons) coverage gap is now recorded in data/ef/expected-divergences-missalemeum.sexp's own header, not only the commit body and the (gitignored) report. dune test: 358 tests green. COLITUR_EXHAUSTIVE_SWEEP=1 dune test --force: 359 tests green, 95.7s. 2026-08-17T10:28:03Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-17T10:28:03Z urn:sha1:8d1eb25a311e16ddb7bf89d2b21fb1ca0aa058a7 Layer 4 (test_oracle.ml) now extracts and compares the Epistle/Gospel citation for every one of the 730 days in the 2026-2027 fixture, the same axis Task 8 already added to layer 3. tools/ extract_missalemeum_oracle.py gained a structural citation-span detector (the first "*...*"-wrapped span under 40 chars containing a chapter:verse-shaped digit pair), verified exhaustively over all 1 458 Lectio/Evangelium sections. 728 of 730 days are comparable; the 2 that are not (Good Friday, both years) have no such section in missalemeum's own JSON at all -- a structural limit on the oracle's own side (M23), not a colitur gap. 451 of 730 days differ and are all explained across 19 cited entries; 0 unexplained. Chain step 4 (the Commons) has no layer-4 witness: confirmed empirically (a scratch sweep, not merely re-asserted from Task 6's own report) that none of the 15 Commons/proper saints is ever the observed office in this window. The comparison surfaced three genuine colitur bugs in data/ef/lectionary.sexp, all fixed at the source in tools/bootstrap_lectionary.ml: 1. Holy Name of Jesus (ef-holy-name-sunday/ef-holy-name) carried a mis-derived citation, borrowed by analogy from an unrelated ini section ("ef-christmas-sunday-0", the Sunday-within-the-Octave's own Mass) on the wrong assumption the two share a Mass. Disproved by missalemeum's own extraction for both real Holy Name Sundays in its window, confirmed against the Missal itself, twice, both scans (Acts 4:8-12/Luke 2:21, not Gal 4:1-7/Luke 2:33-40). 2. RG 17(a)'s own "diebus ferialibus" rubric (immediately following the Holy Name heading, both scans) was never implemented: 2-5 January ferias repeat 1 January's Mass, 7-12 January ferias before Holy Family Sunday repeat Epiphany's, and Holy Family's own week has a named formula ("Missa Dominicae Primae post Epiphaniam"). All three fell to step 3's undifferentiated Sunday walkback instead. Fixed for three 5-weekday families, deliberately excluding Saturday from all three -- RG 78's BVM Saturday Office wins there unconditionally, confirmed against missalemeum's own title on this window's own such Saturdays. 3. Corpus Christi and Sacred Heart (both real, never-impeded I-class movable feasts) had no lectionary entry at all. Both engines independently fell back to Trinity Sunday's own citation and silently agreed on the wrong answer -- the "Holy Thursday violet in both" shape CLAUDE.md names for exactly this reason. Because lectionary.sexp is shared with layer 3 (the lectio differential, 2005-2050), these fixes changed colitur's output for the whole domain, not only 2026-2027. data/ef/expected-divergences.sexp and test_differential.ml needed matching updates: C1 narrowed 361->173 and C25 narrowed 57->13 (rows that now resolve correctly moved to new entries), C16's note corrected (count unchanged), and six new entries added (C29-C34, 397 rows total, all verdict colitur). test_lectionary.ml and test_lectionary_ef.ml's own pins were updated to match (entry count 131->148; one step-3 regression test re-pointed to a date that still genuinely exercises that step). One entry, M26 (30 rows, verdict open), is a genuine unfixed gap: colitur's step-3 "resume the preceding Sunday" fallback is its only ferial-Mass mechanism, and missalemeum's own selection is more granular in three confirmed ways (a rotating votive Mass of the BVM, a named weekly formula for at least one week, and later Time-after-Pentecost weeks this task's own investigation did not narrow to a single rule) -- the same "needs a season-keyed selection mechanism, new behaviour not new data" shape data/ef/expected-divergences.sexp's own C6/C25 and Task 6's own residual concern already name, out of this task's own scope to build. dune test: 358 tests green. COLITUR_EXHAUSTIVE_SWEEP=1 dune test --force: 359 tests green, 89.5s. 2026-08-14T10:40:24Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-14T10:40:24Z urn:sha1:112781d6e3b92310d9d657c53a7e0fc789aefdfb The sanctoral audit set chair-of-st-peter (22 Feb), conversion-of-st-paul (25 Jan) and peter (25 Jan, commemoration) to Red on RG 124(b). All three are reverted to White. RG 120(f), fifteen lines above RG 124(b) in the same column of the same page, names two of them in its enumeration of white: "Cathedrae S. Petri (22 februarii); Conversionis S. Pauli (25 ianuarii)". RG 124(b)'s own qualifier "in eorum die natalicio" independently excludes them, and RG 475(e) confirms it a third time by naming the Chair separately from "natalician feasts of Apostles". lectio and missalemeum both said white because both were right. peter rested on "match the host day's Red", whose host is white by that same clause, so the precedent inverts. Root cause: the audit's page-image method, its real advance, was applied to the calendarium and not to the rubric. RG 124 was read from the OCR text layer, where the two-column interleave shreds RG 120(f) across rows belonging to RG 115 and hyphen-splits Cathedrae, so a text-layer grep for it returns nothing while RG 124's enumeration survives cleanly. That read finds 124 and structurally cannot find 120(f). Two sentinels had been reporting this correctly and were overridden. The golden pin at 1902-02-22 asserted colour=white, was changed to red, and had its comment rewritten to guard against "a regression back to the old one" -- the only pin asserting a colour for any of the 21 slugs. And C18 and M21 both listed the two slugs under an RG 124(b) citation where both oracles were right. Pin restored; slugs dropped; C18 re-derived 526->450 from the observed-day counts, M21 20->18, M15 17->18. The audit's own discriminator would have isolated these. Its stated corroboration was that lectio's name.pl contradicts lectio's colour; run as a gate across all 21 that splits 17 genuine defects from 4 needing adjudication, and three of those four are these. It was quoted as illustration rather than used as a gate. 18 of 21 corrections stand, and the twelve whites are recited to RG 120(e) "Sanctorum non Martyrum" rather than to RG 117's negative residual. Also records Anastasia's deliberate non-fix in the tracked tree beside barbara, where the next auditor will be standing. 2026-08-14T10:00:24Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-14T10:00:24Z urn:sha1:bf326ab963f46c42dc1a3b5141f2022bed81756d Full re-extraction of the primary CALENDARIUM (both photographic scans, missale-romanum-1962.pdf and Missale Romanum 1962_text.pdf, rendered page images read directly rather than trusting either PDF's own OCR text layer) against all 327 base sanctoral entries plus the two prior overlay Adds. Both scans agree throughout; no OCR ambiguity required adjudication this round. Add `barbara` (4 December): both scans carry a Commemoratio nested under Peter Chrysologus's own entry, absent from data/ef/sanctoral.sexp AND from lectio's own tridentine-calendar.ini (confirmed directly) — the same upstream-gap shape as the five entries the ef-rebootstrap task already added (agnes-secundo/boniface-martyr/eusebius-confessor/evaristus/ theodore). Correct 21 sanctoral colours against RG 124 ("De coloribus paramentorum"), scan-verified word for word: 124(b) red for an Apostle/Evangelist's own feast day except John's (27 December, already correct); 124(e) red for a Martyr's own martyrdom; RG 117's five-colour residual otherwise white. Every one of the 21 is a confirmed lectio/missalemeum bootstrap defect — checked individually against lectio's own ini, several of whose Polish name fields already contradict that same record's own colour tag (e.g. `martha`: "Dziewicy", Virgin, no "Męczennicy", yet `colour = red`) — the identical root cause and mechanism the `eusebius-confessor` fix already established. Colour is confirmed read nowhere in Precedence_ef's resolution logic (grep), so these are output-correctness fixes with zero observed-office blast radius; three (apollinaris/josaphat/chair-of-st- peter) additionally disagree with missalemeum's own oracle, not only with lectio, so they are adjudicated from RG 124's text directly rather than by which engine happens to agree. Both corrections applied via data/ef/adjustments.sexp's established Overlay mechanism (data/ef/sanctoral.sexp stays generated, untouched). Pinned: test_rite_ef.ml (two new tests, verified to fail against the pre-fix data); test_differential.ml's new C18 predicate (526 rows, 2005-2050) and test_oracle.ml's new M21/M22 predicates (20 + 2 rows, 2026-2027), each with data/ef/expected-divergences{,-missalemeum}.sexp entries citing RG124 or the matching upstream-gap precedent; test_golden.ml's 1902-02-22 pin corrected (chair-of-st-peter was white in the stale pin, RG124(b) makes it red). All 329 tests green, including the full 1583-9999 exhaustive sweep. Full method, per-entry adjudication table and corrected bucket counts: docs/research/rules-register.md (gitignored) and .superpowers/sdd/2026-08-12-colitur-rg16a/sanctoral-audit-report.md (gitignored). 2026-08-13T19:18:58Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-13T19:18:58Z urn:sha1:72b19098905cd609d87783f6e68311de4f1b61a0 Five follow-ups from the fix-round re-review, none touching a computed result. M20's note had said "moderate-high, not certain" with a specific revisit trigger attached. The fix round raised the label to "near-certain" and deleted the trigger in the same edit. Upgrading a confidence while removing the condition that would lower it again is the one move this record must not make, so the trigger is restored alongside the higher label: no primary text anywhere names the Major Litanies in a Mass-orations-count worked example, only the general II-class-Sunday rule twice over. RG 434(b) closes the Office-shaped doubt and nothing further. "WORD-IDENTICAL" overstated the relation between RG 111(b) and n. 434(b). Only the trailing "quae tamen omittitur si commemoratio privilegiata facienda sit" is verbatim in both; the openings differ, n. 434(b) recasting the rule into the orations register. The claim was self-refuting -- both texts are quoted adjacent to it -- and the argument never depended on it. Now "identical in its operative clause". And n. 434 is not "a different part of the same document": the running heads put RG 111 under Rubricae generales and n. 434 under Rubricae generales Missalis Romani, two distinct corpora bound in one volume, which is the entire force of the corroboration. The code comment had understated its own point. Also corrects the register's LT line range for n. 434(b) (3574-3576, not 3564-3570; the (b) clause is not in the cited range), and records in calendar.ml the diagnostic that channel (3) trades away: a rite whose transfer_target names a date its own disposition omits used to raise a loud, mislabelled Validate failure and is now silent at the origin. The kernel cannot distinguish that from a deliberate omission without rite knowledge it must not have, so accepting it is right -- but the signal is gone, and that should be written down rather than discovered later. 2026-08-13T18:55:43Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-13T18:55:43Z urn:sha1:cbf6826edc77e3ad5a813237bae27e367221452c F2: the task report's "colour/subject/names on the Litanies entry are currently inert" was false for names -- test_oracle.ml's identity axis reads Names.find on every commemoration, and the invented English name is exactly why 2026-04-25 registers as a Comm_identity_mismatch, the reason M5 had to be re-gated. Corrected precisely, field by field, in the report. F3: Easter 2027 is 28 March, not 18 April, as previously stated in the report's own "layer 4 is blind to the transfer" reasoning. The conclusion survives (28 March is not 25 April); the date is corrected. F4: "the exhaustive property sweep caught this immediately" was a wrong attribution, in the report, the register, and calendar.ml's own comment. The committed exhaustive sweep walks 1583-9998 in order and aborts at the first failure; the years actually reported (5700, 4747) were draws from prop_invariants, the default dune test run's 200-year random sample. Corrected in all three places. F5: the Litanies' privileged commemoration is due in the MASS specifically (RG 108 + RG 81), never a separate Office answer -- colitur emits one resolved day, and the M20 adjudication rests on that being the Mass reading. Stated explicitly now in M20's own note, the register, and precedence_ef.ml's own RG111(b) comment. Also added to M20 and the register: Rubricae Generales Missalis Romani n. 434(b) ("VIII - De diversis Missae partibus", "D) De orationibus", "I - De orationibus in genere"), verified word for word against all three documents -- word-identical to RG 111(b) but explicitly scoped to the Mass ("post orationem Missae"), answering the objection that RG 111 (Caput XVI, which RG 106 says governs both Office and Mass) might be read as Office-shaped. Moves the M20 adjudication from "moderate-high, not certain" to near-certain. 2026-08-13T18:15:56Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-13T18:15:56Z urn:sha1:81c72ce9fc4b769be19e6373ce66852acd5b3425 M5 (the pre-existing register-cited gap this task closes) had a genuine backwards claim in its own note: it said missalemeum's single admitted commemoration on 25 April 2027 (the Sunday-conflict year) was "the Major Litanies". Checked directly against the raw fixture row while adjudicating this task's own new divergence -- missalemeum's own commemorations field there is "St. Mark"; "Pro rogationibus" (the Litanies) is the one listed as displaced. Corrected in place, both the .sexp entry and this file's own header note. M5 itself now covers only the ordinary case (25 April 2026): presence agrees now that the entity is built, identity does not (colitur's own English name vs missalemeum's Latin-ish descriptive string), the same declared comparator limit M15/M18 already document, hit here for a different reason. The real, substantive divergence the correction exposes: colitur now admits the Litanies on 2027-04-25 where missalemeum admits Mark. New entry M20, adjudicated colitur -- RG 109(f) places the Litanies in the same closed privileged list as (a)-(e), and RG 111(b)'s own text is unconditional ("the II-class commemoration is dropped if a privileged one is due", no table-order qualifier). The same mechanism already primary-source-verified and used for other RG 109 categories elsewhere in this codebase; honestly flagged as the first real, non-synthetic test of this specific admit clause, consistent with this oracle's own already-documented pattern of RG 108-111 gaps (M1, M8, M10). M18's own count moves 395 -> 394 (2027-04-25 no longer falls into "observed- identity-unresolved alone"; it moved into M20), traced to the specific date and mechanism, not merely re-baselined. data/ef/expected-divergences.sexp (the lectio allow-list) needed no change: lectio computes no Major Litanies at all, and its own row type carries no commemorations field -- layer 3 is entirely blind to this change, confirmed rather than assumed. 2026-08-13T13:57:26Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-13T13:57:26Z urn:sha1:957a6d88ed447be16aa8c7e71250f4c9b87a832b The BVM Saturday office is now genuinely correct, so both comparators' allow-lists move -- every count derived from the harnesses' own failure output, never transcribed or guessed. lectio differential (data/ef/expected-divergences.sexp, C17, new, colitur): lectio builds no equivalent office at all, so it keeps showing the plain season colour on every otherwise-unoccupied Class4 Saturday where colitur now shows white. Season, slug and rank all still agree (the office deliberately reuses the ordinary ferial slug), so Colour_f alone is the complete diff set -- gated on colitur's own rank/weekday/colour rather than a date list, the same shape M2 used, at 416 rows over 2005-2050. missalemeum oracle (data/ef/expected-divergences-missalemeum.sexp): M2 is CLOSED, REMOVED, the same shape as this file's own M4/M6/M7/M9/M12/ M14/M17 precedents -- not re-adjudicated to a different verdict, gone because the colour divergence it named no longer occurs on any of its former 22 dates. What is left on all 22 is Observed_identity_unresolved alone (colitur's BVM-Saturday candidate is temporal-origin and deliberately carries no English name) -- exactly M18's own shape, not a distinct citation any more. Keeping M2 as a separate id would have kept silently absorbing these rows under a stale "colour differs" citation whose own reason had stopped firing (subset's own diff-set test admits a SMALLER set than the one named) -- the same "count proving cardinality where identity was required" trap this project's review process watches for. M18's own expected_rows moves 373 -> 395 accordingly. 2026-08-13T09:19:19Z Lukasz Kasprzak lukas@labunix.xyz 2026-08-13T09:19:19Z urn:sha1:ee5c81e70adcd2ce6cecc57da4c416d482c187ca RG 110 (Caput XIV): "In Officio et Missa S. Petri semper fit commemoratio S. Pauli, et vicissim... pro unica habeantur" -- in the Office and Mass of either Peter or Paul, a commemoration of the other is always made, uncapped by RG 111's own admission count. Both photographic scans, full text including sub-clause (c) (a separate trigger this register previously had not transcribed: the same rule also fires when one Apostle's oration is admitted merely as an ordinary/privileged commemoration, not only when it is the day's own office). Three real pairs in the 1962 calendar, all confirmed on both scans: 25 January (conversion-of-st-paul + peter), 22 February (chair-of-st-peter + paul), 30 June (in-commemoratione-sancti-pauli-apostoli + a new commemoration-of-st-peter). The first two already existed as ordinary sanctoral candidates but were wired into RG 111's ordinary, capped admission contest instead of this rule's own uncapped one -- the defect this closes. 30 June had no companion at all: a genuine gap in lectio's own source data (confirmed directly against tridentine-calendar.ini) and in missalemeum's own oracle output for both fixture years, not only a colitur bootstrap miss, so colitur is now uniquely correct on this date among the three engines compared. Added via data/ef/adjustments.sexp's own Add directive, the architecture's existing extension point for exactly this shape of gap, since data/ef/sanctoral.sexp is generated and lectio must not be touched. Precedence_ef.admit gained rg110_additions/rg110_companion_slug, layered on after admit's own four ordinarily-capped branches decide their normal result: checks both the observed candidate and every already-admitted candidate against the three-pair lookup and prepends any companion found, uncapped and additional, never competing for RG 111's own slot. Measured full blast radius (1583-9999, pre-change binary from git archive at 59fbda8 vs the fixed binary, 3,074,246 days each side, 14,627 differing days, all four predicted shapes, zero unclassified): 3,619 Holy Name fallback days (previous commit), 3,533 days Paul was wrongly excluded from Chair of St Peter's own day by a competing privileged feria, 593 days Chair of St Peter itself was admitted only as an ordinary commemoration with Paul entirely absent, and 6,882 days the new 30 June companion is added. The 3,533+593 figure supersedes an earlier, narrower 852-day estimate that measured only the delta between two older code commits, not the rule's full scope. The lectio differential needed no change: it does not compare commemorations at all, and this fix never touches season, slug, rank, or colour. The missalemeum oracle allow-list needed three changes: M12 removed (22 February 2027 no longer diverges in commemoration count), M15's date list gained 2027-02-22 (now reaching identity comparison for the first time, where it lands on that entry's own pre-existing, unrelated limit -- one of the two commemorations is temporal-origin and unnamed), and a new M19 for the 30 June gap. Mutation-tested, both halves separately: disabling the admit-level addition reddens the two new unit tests, the oracle's own M12-shaped checks, and an existing golden pin (updated to expect the Paul companion); removing only the 30 June data entry reddens solely the oracle's new M19 count, confirming the code and data halves are independently load-bearing.