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Composed diagonal-bit bootstrap: the pricing model that called PR205's banked row, audits the queue, and prices the next ladder of κ gains - #204
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…inite leaf PR200 certifies a strictly stronger bit word but publishes it only with its own complex word, where the complex branch binds; it announces the stacked composition "as separate work". Pricing that composition through PR194's unchanged assembly with PR185's finite ordinary leaf gives kappa = 1693287/2500000000 = 6.773148e-4, +0.1826% over PR197's standing claim and +0.0639% over the value PR200 announced for it. The package vendors the minimum needed to price it: the PR168 v4 assembly, PR184's pricer and finite bridge, PR194's certificate and PR200's bit certificate, all digest-pinned. verify.py reproduces the certificate from those pins, reproduces PR200's announced depth-0 value, shows PR184's grid leaf and PR200's published atom wrapper differ by one grid step at depth 0 and not at all once bootstrapped, requires the claim to beat PR197 and to sit inside one grid step of the word's own C/(1+C) ceiling, and refuses three corruption controls.
…e published values Banking a word's rank-60 exterior corrections is the only validated way to raise a bit coarse saving materially, and this word has the same 2,200 of them per copy that PR197 banked. levers.py solves the paid-moment inequality exactly over the rationals and models that transformation as the accounting PR197 validated: drop the rank-60 entries, keep the per-copy deficit, let the stock fall to what the row identity requires. The model reproduces PR187's unpacked row, PR197's independently certified banked row, and PR200's unpacked row to 1e-13 relative or better, so it is checked on a word it was not fitted to. Applied here it predicts kappa = 6.83061299e-4, +0.8484% over this package's claim, and pins the falsifiable target for whoever builds the banks: total stock 56,402 over three copies, per-copy deficit unchanged at 1,936, no rank-60 child remaining. levers.json records the MODELLED, NOT CONSTRUCTED status and verify.py enforces it.
Fraction has no float-style __format__ before 3.12, so the two gain prints raised TypeError there; both now format floats. verify.py also compares the model's shipped numbers with a tolerance on floats and exactness on integers and exact rationals, so a different libm cannot fail the check by moving digits the model's bisection cannot resolve anyway.
Reusing the vendored interval_moment module on the same 10^-18 grid turns the model's three checks from 1e-13 tolerances into exact reproductions of PR187's certificate, PR197's certified banked word and PR200's certificate, so the predicted 0.8484% gain rests on the supplier's arithmetic rather than on a portable float.
CrocSwap#202 carries the same bit and complex words at exactly the depth-0 value this package prices, so the cross-check now points at it: the whole claimed gain is the finite leaf it does not apply.
The lever model's prediction was built within the half hour: audit.py prices CrocSwap#205's, CrocSwap#206's and CrocSwap#207's banked rows from byte-identical copies of their certificates and reproduces each author's coarse saving to the last digit, confirming every one sits at its own word's ceiling. The cheapest admissible ledger of the frontier row's mass would lift it 76.6%, which bounds the room a better schedule can still buy.
PR207's certificate is stored with CRLF upstream, so the committed blob is the LF-normalised copy while the working tree kept the Windows line endings; the pin now records the digest a clean Linux checkout produces.
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The assembly takes the smaller branch budget, so the complex word caps the frontier at +2.52% and the bit word's 377,316 rank-1 children -- dirt the banks refuse -- are enough to reach it. Soaking both rows' small children buys +16% to +76% on the 10^-10 grid; every rung is a target, not a construction, and the calculator is checked against PR184's own assemble() and against PR205's and PR207's published kappa.
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Bisecting the bit word's smallest-child population shows 57/1000 of its mass is enough to clear the complex side, so the whole +2.52% first rung is a 5.7% coarsening of one population rather than a new construction. CrocSwap#207's bank proof settles the packing side itself, so the README now points the next move at the word's child inventory, which is where the ledger term actually lives.
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Thank you @maxime-fleury. This contribution is now retained on main in the scoped 100-PR review and contributor credits. Contribution: Composed diagonal-bit bootstrap and comparison with bank pricing. Review and limits: Prior exact-head arithmetic replay. Fixed-depth bootstrap and paid banks are different constructions; pricing does not by itself supply a bank compiler. The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions. Reviewed head: |
This was referenced Oct 15, 2026
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Under the retained interfaces of the pinned suppliers, this composes #200's
certified bit supplier with #193/#194's complex word through #194's
unchanged assembly and prices it with #185's finite ordinary leaf:
+0.1826% over #197's standing claim and +0.0639% over the composition as
#202 published it. Adds
research/composed-diagonal-bit-bootstrap/and oneworkflow. The package now does three things: prices this composition, audits the
banked rows that overtook it, and prices the ladder of moves that can still
raise kappa.
The banked rows arrived, and this package's model called one exactly
This composition was priced at 15:33 UTC. Its lever model then predicted what
banking this word's 2,200 rank-60 exterior corrections would be worth — a row with
W_per_vertex = 56402/3, deficit unchanged at 1,936, no rank-60 child left andcoarse saving
683528191056257/10^18. Within the half hour that row was built andopened as #205, which states that exact saving and credits this PR as its target;
#206 prices the same row with PR186's entrance banks, and #207 adds 302
coordinated frame changes on top:
audit.pyprices #205's, #206's and #207's rows from byte-identical copies oftheir certificates under
references/queue/and requires each result to appearverbatim in the certificate it came from. All three reproduce to the last
digit, and each sits at its own word's ceiling: with the bit branch binding,
kappa = C/(1+C)and there is no pricing room left in any of them.New ways to raise kappa, priced
PR184's assembly takes
a = min(bit leaf, (1-1e-9)*C_complex - 1e-10)and returnskappa = a/(1+a)on the10^-10grid, so the smaller branch is the wholeconstraint and a gain on the stronger side is worth nothing until the other side
catches up. Today the bit branch binds at
6.831904e-4while the complex side capsat
7.004273e-4: +2.52% is available with no complex-side work at all.targets.pyprices the moves that get there. For a fixed stock and deficit thecoarse saving is
C = (1 - mass/(W m)) / LwithLthe rank-mass-weighted mean ofln(m/r), so the lever isL: a ledger whose residual dirt sits in fewer, largerchildren. Soaking every child of rank at or below a threshold into the largest
admissible child gives, on the queue's own rows:
The cheapest step is smaller than the table suggests. The bit word needs a coarse
saving of
7.009184e-4to stop binding, andtargets.pybisects the smallest-childpopulation to find the least that delivers it: moving 57/1000 of the mass in the
bit word's rank-1 children into rank-22 children takes its coarse saving to
7.009717e-4, past the complex word, forkappa = 7.004273e-4(+2.52%). The wholepopulation (377,316 rank-1 children, 9.3% of the rank mass) is worth +16% on its own,
and the complex word's own 87,534 rank-1 children (11% of its mass) do the same for
its side,
7.009184e-4to8.144423e-4(+16.2%).What has to change is the child inventory, not the packing. #207's bank proof
settles the packing side itself: its banks tile width 72 exactly with the word's two
residual families (
6 x rank-4 + 2 x rank-24, or3 x rank-24), and it states thatthe current word "has exactly the 4/24 residual families and both tile 72 exactly ...
there is no new LP improvement to add". The children the moment actually charges are
the word's own retained children — internal, source, target, center, compensating and
terminal-substitution children — and it is their inventory, set by the weighted
compilation and by the frame schedule, that holds
Laboveln(m/22).All of it is MODELLED, NOT CONSTRUCTED: no ledger is built here, and each rung
is a shape the assembly would price this way, computed from the queue's certified
rows. The calculator is checked two ways — it equals PR184's own
assemble()on thevendored pair, and it reproduces #205's and #207's published kappa to within one
grid step — so a rung is a usable target, in the same way the banked row was.
What the composition itself does
Exactly one operation: pricing. #200 certified a strictly stronger bit word —
coarse saving
677773948354561/10^18 = 6.77773948355e-4against #189's6.68298937775631e-4— but published it only with its own complex word, where thecomplex branch binds. Composed with the source-assisted complex word
(
219037/312500000 = 7.009184e-4) the bit branch binds, and PR185's wrapper thenremoves the
4.33e-7of slack PR184's legacy leaf leaves below the coarse saving:The priced bit profile has
m = 72,W = 20634, rank deficit 1936 and 34 terminalsinks; the claim sits 3.37e-11 below the word's own ceiling
C/(1+C) = 6.7731483368e-4, under one10^-10selection step, with depths 2, 3 and8 returning the same grid value. The bit profile, the complex word, the 47-constraint
assembly and the leaf recurrence are the suppliers' and #185's; nothing is re-derived.
levers.pyis the model behind all of this: it solves the paid-moment inequalityexactly over the rationals and checks itself against three published values, all
reproduced exactly because it prices with PR200's own enclosure module
(
references/pr200/interval_moment.py, vendored byte-identically):Verification
Runs from the package directory alone with only the standard library, on Python
3.11 and 3.13, and pins every byte against
SOURCE.json. It checks that thecertificate regenerates exactly; that depth 0 equals #200's and #202's value; that
PR184's grid legacy leaf against #200's published atom wrapper differs by exactly
one grid step at depth 0 and nothing once bootstrapped; that the claim beats #197
and sits inside one grid step of
C/(1+C); that the leaf tolls hold in closed formand the assembly's own minimum margin excludes the next grid point; that three
corruption controls are refused; that the lever model reproduces its three
published references exactly; that the audit reproduces #205's, #206's and #207's
own certified coarse savings verbatim; and that the target ladder reproduces two
published kappa values, stays monotone and never presents itself as a
construction. A clean Linux clone of the branch passes and leaves the tree
unchanged; the whole harness runs in about seven seconds.
Scope and limits
suppliers' certified artifacts, vendored byte-identically and priced, not
rebuilt or replayed. This PR does not re-run their checks, including Pack PR200 diagonal bit residuals into completed banks (conditional κ = 0.000683061299399923) #205's,
Completed entrance banks on PR200's bit word with the v4 complex supplier: kappa = 6.830611e-4 #206's and Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks #207's: it prices the rows they certify.
Pack PR200 diagonal bit residuals into completed banks (conditional κ = 0.000683061299399923) #205's, Completed entrance banks on PR200's bit word with the v4 complex supplier: kappa = 6.830611e-4 #206's and Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks #207's, not built here; every rung of the ladder is a target,
not a construction.
the retained contracts of the pinned suppliers. The full multiplication theorem
remains conditional.
line, and the Pack PR200 diagonal bit residuals into completed banks (conditional κ = 0.000683061299399923) #205/Completed entrance banks on PR200's bit word with the v4 complex supplier: kappa = 6.830611e-4 #206/Conditional kappa 6.831904550365e-4: coordinated frame optimization and completed entrance banks #207 bank line).
The frontier belongs to the banked rows above.
Credits
Bit supplier and the #189/#196 lineage: chafreaky (#200, #202), whose enclosure
module this PR vendors and prices with. Banked rows: rohanarun (#205, and #197's
packing mechanism this PR models), EcmaXp (#206), Dugongue (#207, with
PR186's entrance banks). Complex word, pricing and assembly: icekylinx,
GPT-6 Astra and ikeboy (#182/#184/#193/#194). Finite ordinary-leaf wrapper
and recurrence: rohanarun (#185). Paired-cube frame, balanced prefix and the 47
constraints: eumemic (#168 v4), with the RaD (hipotures) balanced transform and
Zhihao Chen's PR23 gates. The descent figure is sennemmi's (#198); the design
ceiling is DaysSky's (#201); the supplier barriers are huxint's (#203).
Prepared by Maxime Fleury with Codebuff assistance; Apache-2.0; predecessor notices
retained in the package
NOTICE.md.