Research: selected m=73 row-ledger terms do not bind rho (no new kappa)

[Mainzu]

Change and scope

Card selected-stock-envelope, priority revision 6, scope refined to
rho. #3113 bound B = 2642 and #3421 proved A = 0 for the selected
m=73 complex producer in

sigma <= (43/26)*(1-s)*(A+B) + rho

Both left rho, the leaf reserve, unbound. This package traces the
non-complex terms of the selected row ledger to their sources. It then reads
the merged selected complex layer to settle rho.

Result

Package: research/selected-stock-rho-ledger/. Base:
20ecf2891d80b5acf18d980b2164fb44ea7faa90.

• The ledger terms are not rho. 9909 = 367·27 (historical coarse
  bit), 252 = 9·28 (old leaf) and 1024 = 2·512 (prefix) are w-free degrees of
  the fixed external reserve. So Selected stock envelope at m=73: bound quantities and the exact missing shape lemma #3113's 16469/15555 readings do not bind
  rho.
• The selected layer gives rho = 0, conditionally.
  • PR2287's m=73 layer, implemented by PR3385, has one row stock: its own
    divisor L^D0(d), with L = 14336·|O(73,2)| and
    ceil(log2 L) = 2642 = B. Its three H-bit compact fields are reserved
    separately and are not row stock.
  • Its peeled axes and leaves use the elementary C kernel.
  • Its only BIT calls are inside PR2250's adapters, which give the callee
    "no external row stock". That callee (PR2234 §8, B1 in PR2899) borrows
    its own K(w)^D(e) stock.
  • So S_leaf = 1 and sigma <= 4362.14.
• The "reserved simultaneously" sentence was mis-cited. The previous
  version cited it from structured-bulk-assembly.tex for the alternative
  rho >= 8194. It concerns fixed-wire external factors (W_b,W_c<2^43), so
  that alternative is now kept only as a counterfactual (12556.14).
• All fourteen recorded stages pass both values. Stage 1 is the
  tightest, at H = 6,562,783, with guards 16 and 17.
• The 9909/252 slots are slack in the selected layer, which gives a lean
  row of 6308.
• The q-adic BIT the adapters call cannot sit in the row cap. With
  q > 2^80, its row term is at least 655,356 at w = 1, against a cap
  of 20161. So that stock is borrowed inside the call.
• Conditional. The PR ledger records PR2287, PR2250, PR2234 and PR2899
  as incorporated after a scoped review of written constructions. PR3385,
  Selected stock envelope at m=73: bound quantities and the exact missing shape lemma #3113 and Research: selected m=73 complex stock shape A=0 under finite-stock-as-C (no new kappa) #3421 are partially reviewed. No physical O(73,2)/GL64 payload
  has been run.

Partial. No new kappa. No change to any supplier, cutoff, frontier or
the selected record.

Validation

python3.12 -I -B research/selected-stock-rho-ledger/verify.py
python3.12 scripts/research_package.py --package research/selected-stock-rho-ledger

• Marker: PASS_SELECTED_STOCK_RHO_LEDGER ... L_bits=2642 S_leaf=1 guard=16,17<=6562783 stages=14 H_min=6562783 lean_row=6308 qadic_bit_row>=655356>20161 controls=16 checks=62.
• Every constant and quoted sentence is parsed from pinned source.
• Sixteen mutation controls must each be rejected. Each rejects at its
  intended check.
• Local runs: Python 3.13 and 3.14 on Windows, also under -O. Metadata
  --check-only passes.
• Registered replay: passes on Python 3.12.10 with -Werror at 2b4a97e
  (PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=partial).
• Not run locally: --check-source-history, which needs a full clone.

Overlap and credit

• Checked against open and closed PRs and package READMEs. Discussion search
  covered the TASK.json terms, Discussions FINDING / HANDOFF: selected complex compact adapters with sequential repair #2238 and Selected BIT first-node caller and recursive-return handoff #2319 in full, and the
  latest 100 comments of Handoffs and requests for independent checks #1166.
• Multiply the published row-ledger terms #3670 repeats this package's first-version arithmetic. It does not
  classify callee modes.
• Credit: Aaron Wang, Wentao Li, Sricharan Vagvala, Adam Gall, Josie
  Elliston, ToikY, Jeremy Kothe and Rohan Arun. Also Jose Manuel (PR2234,
  PR2250, PR2287, PR2899, PR3385), Douglas Colkitt (compact-control method,
  via PR2250) and Nick Petalas (PR2808 wrapper, via PR2899).
• Prepared by Mainzu with substantial Claude Code (Anthropic) assistance. No
  independent human review is claimed. Apache-2.0.

🤖 Generated with Claude Code

[Mainzu]

Update: open question 1 is now settled from merged sources. The selected
m=73 layer (PR2287/PR3385) has one row stock, its own divisor
L^D0(d) (ceil(log2 L) = 2642 = B). Its compact fields are not row
stock and its leaves are elementary. Its only BIT callee borrows
internally (PR2250 → PR2234 §8 / PR2899 B1). So rho = 0 and
sigma <= 4362.14, conditional on that chain: PR3385 has only had
archival intake.

The structured-bulk "reserved simultaneously" sentence I cited before
concerns fixed-wire external factors, so rho >= 8194 is now only a
counterfactual. Both values pass all fourteen stage guards. The 9909/252
row slots are slack in the selected layer. Marker
... controls=16 checks=62.

[Mainzu]

Update: open question 2 is answered from source, and no selected step
bootstraps the m=73 complex layer. The assembler has one seven-step chain
per branch, the bit chain, and its end goes into the outer assembly as
bit_saving (PR1087 assemble.py L205–214, engines/outer.py L16–17).
The complex root bb enters as a fixed complex_saving and only caps s,
because the outer slacks need the chain to stay below it (assemble.py
L206; outer.py L27, L29). The layer's own fallbacks are elementary kernels with no stage
cutoff (PR2287 L139, L424), so this package's m=73 sigma is a consistency
bound, not an obligation. philippeVV's #1166 handoff (comment 18932239)
named the PR589 BIT as the stopped producer back on 2026-10-14, alongside
PR2084. The README and
TASK.json are updated, one provenance pin is added, and verify.py's marker
is unchanged (... controls=16 checks=62).

[Mainzu]

Update: open question 1 is answered, with local evidence. PR3385's
registered replay fails on Windows only, because the frozen PR2753 verifier
(inputs/pr2753/verify.py L72–75, inside
physical-ordinary-interchange/inputs/pr2809.tar) compares
str(path.relative_to(...)), which uses \ on Windows, with
/-separated names. That likely affects any package that loads PR2809's
loader on Windows, though I only ran PR3385. With a local relative-path
shim, which is not the registered replay, all three suites pass on Python
3.12.10, and all nine receipt hashes in PR3385's EVIDENCE.md match. B1
runs its fitted branch only when the compact width (f-1)G is at least
27,312,693 bits at q* (bitlength(q*^311310)). That bound comes from
the 311311 cutoff in bit2234-stock-threshold, plus a local
exact-integer check that no smaller width fits. Below that it is
elementary, and
neither branch takes row stock from the caller, so rho = 0 is
unaffected; the README, TASK.json and six new provenance pins record this,
and verify.py's marker is unchanged (... controls=16 checks=62).

[Mainzu]

Update: the last open question is answered from source, and no construction step of the selected layer uses the 1024 = 2·512 term. The 512 is the invoice's precision reserve (397 bits needed). Dugongue's PR514 added it to the row when it replaced the 192-bit local prefix allowance, with "an additional 2*512 enters the two-level physical row bound". The same sentence appears earlier in the closed PR505. So the factor 2 is the halving depth, as for the stock bits (73² > 2·48²). No source I found says why a precision reserve should be billed as rows. PR2287 reserves only L^D0(d) rows and supplies precision with Δ = ⌈C0·d⌉ guard bits per component (L136–147, L374–380), and PR3385 does the same physically (L190–201). So 1024 is inherited slack like 9909 and 252, and κ is unchanged. The README and TASK.json are updated (TASK.json now has no open questions, with the reason recorded), three provenance pins are added, and verify.py's marker is unchanged (... controls=16 checks=62).