Construction (no κ claim): PR2226 low anticipatory aliases on the T74 borrow words — 400 helpers, mass 5264, packing ceiling 0.0017179→0.0017480

[thakrarsagar]

Status: construction (local, verified), plus exact packing ceilings and model prices. No κ claim. This is not an admitted supplier, and the selected record is unchanged.

What is new

Every open record on the T74 borrow line uses only high borrowed-helper aliases from #2226. That includes #2269, #2281, #2288, #2302, #2309, #2312 and #2322; #2260 does the same on T8. None uses #2226's 32 low (anticipatory) aliases.

This PR builds those 32 low aliases, with their 64 initial compensation terms, on both record T74 pivot-566+554 words of #2269 (head b479fc55). It also builds the 5 high aliases #2269 omitted. Their T8 lenders are blocked on T74 by a paid 5→4 drop. An exhaustive search found rank-zero lenders among the retired X fields 12, 6, 31, 4 and 1.

word	aliases	helpers	local paid profile	local mass
gauge44, #2269	43	437	{1:2351,2:501,3:414,4:129,5:42,8:8}	5385
gauge44, this PR	80	400	{1:2303,2:527,3:386,4:125,5:37,8:8}	5264
extra, #2269	43	437	{1:2339,2:509,3:418,4:125,5:42,8:8}	5385
extra, this PR	80	400	{1:2287,2:535,3:386,4:125,5:37,8:8}	5264

That is −121 rank units per call: −96 from the low aliases and −25 from the 5 highs. Cleanup needs 44 private zero buffers, against 76 before.

The other 16 low helpers (blocks 632, 640, 648 and 656) are lender-blocked. At every handoff, exactly the 32 #2226 low lenders qualify, and every low alias saves the same 3 units.

Evidence

Build (build_ext.py --controls). It uses #2226's replay and operators and #2269's emitter and auditor, with credit. Checks:

• an exact free-operator replay over all 624 dirty inputs, giving Y+=X, with everything else and the buffers restored;
• each low lender exactly equals its initial input at its handoff;
• the 64 compensation terms equal Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226's T8 terms (only the operator ids differ);
• dropping the compensation or flipping a sign fails;
• the exact Gaussian handoff and exit products for all 80 warps (512 columns each);
• Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269's audit_local.py passes in both orientations;
• all 23 of its borrow_controls mutations are rejected.

Independent check (check_ext.py). It is our own standard-library code with no PR or construction imports. It repeats the warp algebra, the anticipatory-term structure, the frame recount and the exact forward/dual replay. It has 28/28 negative controls per word. Positive controls: the canonical words and #2269's words.

Exact fixed-word packing ceiling (cap_ext.py). This uses the merged research/complex-local-word-ceiling/ceiling.py. The cap is an upper bound on b for any hosting or idle refill of the fixed words. With R = 48 (T74's maximum child) it rises from 0.0017179 (#2269) to 0.0017480, which is +1.75%.

#2269 realizes 98.74% of its own cap, and #2322 reports 98.66%. At the same fraction, the new words give b ≈ 0.0017259. That is an estimate, not a claim. It is ≈ +1.7% over the top open claim, #2322 (0.001697060).

Model prices (price_ext.py, idle refill modelled, not built).

model	b	vs #2269
favourable	0.0017255	+1.73%
calibrated on #2269's realized refill	0.0017127	+0.97%
calibrated on T8	0.0017141	+1.05%
pessimistic	0.0016871	−0.54%

The calibrated rules overshoot their out-of-sample controls by about 2·10⁻⁶.

What is NOT done (needed before any κ)

1. Native lowering in both orientations. This means the 64 frame-zero compensation reads, the reflected handoffs with exact Gaussian phases, and the X-register lenders. No PR has natively lowered anticipatory compensation yet.
2. Owner fill. A window-exact owner fill at 400 helpers per call is needed, including ownership of X fields 1, 4, 6, 12, 31 and 73, and owner lifetimes covering the 32 start-of-call reads.
3. Charges. The 44 buffers and the 64 terms still need charges.
4. The rest of the pipeline. PLAN/SPEC refreeze, the certified price, and the outer assembly (Conditional kappa = 0.001677160151714381 via capped phase-cell fusion #1673 et al.) remain.

Reproduce

python3 -I -B research/t74-low-alias-borrowing/run_all.py --fetch
python3 -I -B research/t74-low-alias-borrowing/cap_ext.py

This takes about 25 s with the standard library. The expected last lines begin with PASS_T74_LOW_ALIAS_RUN_ALL check=PASS price=PASS crosscheck=PASS and PASS_T74_LOW_ALIAS_PACKING_CAPS cap48_high43=0.001717935929 cap48_ext80=0.001747958372.

The rebuild needs numpy: run_all.py --build --numpy-site DIR. It reproduces words/ and witness/ byte for byte.

Checks run locally:

• the package metadata check passes;
• the 65 test_research_* tests pass;
• the scripts parse under the 3.10 grammar;
• the registered Python 3.12 replay was not run (it is not installed).

Provenance and credit

• Base: 0fdd7d82 (priority revision 4), unchanged at submission.
• Track and claim: 20–39 (complex supplier), OS seed 35. Card: complex-new-helper-inventory, refined. No sprint coordination issue exists, so the claim was recorded locally.
• Predecessors:
  • Cinna Davis / 1337isnot1337 (Research: 80-helper anticipatory borrowing component and exact price rejection (no new kappa) #2226): the mechanism, the 80-alias witness, replay and operators.
  • Jeremy Kothe (Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269): T74 words, the 43-alias witnesses, the emitter, auditor and controls (vendored).
  • Dugongue (Improve conditional κ to 0.0016805 with selective dirty borrowing and physical owner repacking #2260): high aliases on T8.
  • Vlado Vojdanovski (Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting #2322): found independently and concurrently that retired source fields can be rank-zero lenders for high roles. Our 5 extra high lenders use the same idea.
  • Douglas Colkitt et al.: the merged ceiling tool.
• Related: our own independent check of Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269 is Independent verification (no new κ): record candidate #2269 T74 borrow43 — words, 437-helper fill and moment root reproduce; stale evidence, unpriced buffers, X2 open #2315.

Prepared for Sagar Thakrar with substantial AI assistance (Claude Code, Anthropic): one subagent built the construction, others wrote the independent checker and pricing harness, and another reviewed it adversarially. The main session reran the checks and computed the caps. Apache-2.0.

🤖 Generated with Claude Code

[thakrarsagar]

Correction (author). The "≈ 0.0017259" estimate in this PR is wrong, and so are the model prices F/C/C8 (0.0017255 / 0.0017127 / 0.0017141). None of them is attainable on the PR2269 T74 template with unsplit helpers. The width-blind R = 48 cap here (0.0017480) is still a valid upper bound, but a loose one.

• An actual legal 400-helper owner fill of these words reaches b = 0.00168654323627, which is 0.57% below Conditional κ = 0.001696247139058474: capped phase-cell fusion outer (PR1673) on the T74 supplier with anticipatory dirty borrowing (PR2226, 43 high-helper aliases) on the T74 pivot-566+554 supplier: conditional kappa 0.0016962471390584742… #2269.
• An exact width-aware LP-dual certificate shows that every legal whole-helper fill has b < 0.0016867. The width-9 low lenders fragment the rank-16/32 bins, which costs more than the 121 freed rank units.
• The "+5 high" variant gives exactly zero gain.

Details, fill, checks and certificate: #2387. #2360 (Jeremy Diviney) independently certifies b < 0.0016870. The local construction in this PR is unaffected; it should be read as a no-gain inventory for this template.