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

research/t74-low-alias-borrowing/.gitattributes

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+# Preserve exact PR2269 bytes (CRLF) so the pinned git blob ids in SOURCES.json stay valid.
+vendor/pr2269/*.py -text

research/t74-low-alias-borrowing/README.md

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+# PR2226 low (anticipatory) aliases on the T74 pivot-566+554 borrow words
+
+**Construction (local, verified) plus exact packing ceiling and model prices. No kappa claim.** PR2269 (Jeremy Kothe) put
+43 **high** PR2226 aliases on both T74 local words (`gauge44` "base" and `extra`). This
+package adds PR2226's **32 low (anticipatory) aliases** and the **5 high aliases that PR2269
+omitted** to both words. Each word now has 80 aliases. The 32 low aliases come with the
+64 initial compensation terms `c K_G z`.
+
+| word | aliases | helpers | local paid profile | local mass |
+|---|---|---|---|---|
+| gauge44, PR2269 (43 high) | 43 | 437 | `{1:2351,2:501,3:414,4:129,5:42,8:8}` | 5385 |
+| gauge44 + 32 low | 75 | 405 | `{1:2303,2:527,3:386,4:125,5:42,8:8}` | 5289 |
+| gauge44 + 5 high | 48 | 432 | `{1:2351,2:501,3:414,4:129,5:37,8:8}` | 5360 |
+| **gauge44, this package (80)** | 80 | **400** | **`{1:2303,2:527,3:386,4:125,5:37,8:8}`** | **5264** |
+| extra, PR2269 (43 high) | 43 | 437 | `{1:2339,2:509,3:418,4:125,5:42,8:8}` | 5385 |
+| extra + 32 low | 75 | 405 | `{1:2287,2:535,3:386,4:125,5:42,8:8}` | 5289 |
+| extra + 5 high | 48 | 432 | `{1:2339,2:509,3:418,4:125,5:37,8:8}` | 5360 |
+| **extra, this package (80)** | 80 | **400** | **`{1:2287,2:535,3:386,4:125,5:37,8:8}`** | **5264** |
+
+Change per call: −121 rank units, i.e. −96 from the low aliases and −25 from the five high
+aliases. COPY64 is still included. Each word has 624 independent input columns and 44 private
+FULL-cleanup zero buffers (PR2269 had 76). The identity `mass = 1856 + sum of helper widths`
+still holds: width inventory `{4:4,5:4,7:36,8:84,9:272}`, sum 3408.
+
+All 16 low helpers that were not aliased are blocked by one exact condition: no lender is
+left (see below). There is no second construction choice that would avoid it.
+
+## What was checked
+
+`python3 -B build_ext.py --controls` is deterministic. Run it with
+`PYTHONPATH` pointing at a numpy install; numpy is needed only for the Gaussian products. It
+does the following:
+
+1. Checks the git-blob pins of every input. The inputs are copied from PR2269 head `b479fc55`
+   and PR2226 head `dacaf3d8`.
+2. Replays PR2269's shipped 43-pair witnesses with `replay_core.py` and reproduces its
+   recorded profiles exactly. `replay_core.py` is PR2226's `replay.py` in function form. Its
+   semantics are unchanged; only the `80 pairs / 32 low` assertion is now a parameter.
+3. Builds the low and high pairs. The initial corrections are read off the residual of an
+   exact diagnostic replay. Every residual term must have the form `(lender, (op,))` for a
+   low operator, with a dyadic coefficient. No other term is allowed.
+4. Re-runs the full exact replay for all three variants: free noncommutative operator
+   algebra over all 624/629/656 independent inputs, `Y'=Y+X`, nested frame chronology,
+   cold restoration, inverse cleanup at FULL with private zero buffers, and the
+   omitted-inverse-warp control. It also confirms that dropping the compensation fails, and
+   so does flipping one coefficient's sign.
+5. Runs PR2226 `operators.py` on all 80 warps per word: exact Gaussian handoff and FULL-exit
+   products, all 512 columns, phases included. The 43 inherited records are reproduced
+   byte-for-byte.
+6. Emits `words/BORROW-WORD-80{base,extra}.json.gz` with PR2269's unchanged emitter, then
+   runs PR2269's independent `audit_local.py` as a subprocess. It passes in both
+   orientations (`PASS_INDEPENDENT_EXACT_BORROWING_WORD`: 80 warps, 64 corrections, profile
+   and width inventory re-derived from the word alone).
+7. With `--controls`, runs PR2269's `borrow_controls.py`. All 23 mutations are rejected for
+   the expected reason, including the four initial-correction controls, which are not
+   vacuous here (`receipts/CONTROLS-80*.json`).
+
+Receipts: `receipts/BUILD.json` (per-candidate decisions and blockers),
+`receipts/AUDIT-80*.json` and `receipts/CONTROLS-80*.json`.
+
+## Independent check and model prices
+
+- `python3 -I -B check_ext.py --out` (standard library only; imports no PR or construction code;
+  reads the reference inputs as git blobs at the PR2269/PR2226 heads) prints
+  `PASS_T74_LOW_ALIAS_WORDS_INDEPENDENT`: warp algebra, anticipatory-term structure (frame-zero
+  source = lender of its own operator), frame recount, exact forward and dual replay, links to
+  the canonical words, and 28/28 negative controls per word (`check_ext.receipt.json`).
+- `python3 -I -B run_all.py --out` re-runs the check, then prices the recounted profiles with
+  `price_ext.py` (`price_ext.ext80.receipt.json`). E = 80586 extra freed mass versus PR2269.
+  These are **model prices of an idle refill that was not built**:
+
+| model | b (floor, 1e-22) | vs PR2269 b |
+|---|---|---|
+| F | 0.0017255088890837212072 | +1.725% |
+| C | 0.0017126737497248571464 | +0.968% |
+| C8 | 0.0017140567316684824711 | +1.050% |
+| P | 0.0016871233700042746562 | −0.538% |
+
+Model caveats. F keeps PR2269's realized idle remnants fixed and caps idle children at rank 48;
+it is not a ceiling (fully repacking all idle mass into rank 48 would give about 0.001748).
+P is not a floor for a real supplier, because hosting may add paid adapters. C reproduces
+PR2269's own refill exactly by construction. Out of sample, both calibrated rules overshoot
+the realized record they were not fitted to: C on T8 by 2.0e-6 and C8 on T74 by 2.3e-6.
+C8 is not exact even in sample; it is 5.2e-6 above PR2260's realized b (`price_ext.py controls`).
+
+## Packing ceiling for the new local words (exact, any hosting)
+
+`python3 -I -B cap_ext.py` evaluates the merged fixed-word packing ceiling
+(`research/complex-local-word-ceiling/ceiling.py`) on the call-weighted local profile. It uses
+m = 73, 896 families per nine-stage replica and centre 64, with the largest idle child R = 48
+(T74's maximum child) or 51. Each cap is an upper bound on b for **any** hosting, owner packing or
+idle refill of that fixed local word under the coverage law.
+
+| local words | cap, R = 48 | cap, R = 51 |
+|---|---|---|
+| PR2269 (43 high) | 0.001717935928829 | 0.001727257612832 |
+| **this package (80)** | **0.001747958371974** | **0.001758245201617** |
+
+The ceiling rises by +1.75%. PR2269's claimed b realizes 98.74% of its own R = 48 cap. PR2322
+reports 98.66% of a 0.001720061 cap for its profile. At the same 98.74%, the new words would
+give b ≈ 0.0017259. **This is an estimate, not a bound or a claim.** It sits above every open
+T74 claim (top: PR2322, 0.001697060296). It needs every obligation under *Scope and limits*.
+
+## Reproduce
+
+From the repository root, with the standard library and `git`. It takes about 25 s and fetches
+the pinned PR heads if they are absent:
+
+```sh
+python3 -I -B research/t74-low-alias-borrowing/run_all.py --fetch
+python3 -I -B research/t74-low-alias-borrowing/cap_ext.py
+```
+
+Expected final lines: `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`.
+`run_all.py` rewrites its receipts. Repeated runs differ only in elapsed-time fields.
+
+Rebuilding the words needs numpy, which is used only for the Gaussian products:
+`python3 -B research/t74-low-alias-borrowing/run_all.py --build --numpy-site DIR`. It
+reproduces `words/` and `witness/` byte for byte.
+
+## How PR2269 derived its T74 witnesses from PR2226 (reconstructed)
+
+PR2269 ships its T74 witnesses as inputs; the derivation script is not in the PR. Diffing
+`witness_43_*.json` against PR2226 `WITNESS.json` shows how they were made:
+
+- The 43 kept high pairs keep the PR2226 register and lender.
+- Each handoff index is the T74 block `first_input`, which is the T8 index + 7.
+- `retirement_B_event` is moved to the T74 index.
+- `handoff_basis` is recomputed as the first `dim(lender)` vectors of the echelon basis of the
+  helper's first post-handoff frame.
+- The 48 early-tail gates are unchanged, with `before_B` moved to T74 indices.
+- `initial_corrections = []`, and every low pair is dropped.
+- High pairs 606, 635, 637, 638 and 639 are dropped.
+
+## Low aliases: conditions and outcome
+
+These are the PR2226 low-pair conditions as enforced here:
+
+- **(a)** The lender is retired before the handoff. It has no B, deferred or early-tail touch
+  after the handoff.
+- **(b)** At the handoff, the lender is exactly its own initial dirty input (asserted in the
+  replay).
+- **(c)** The lender's entrance frame has dimension 0. Every compensation term
+  `c K_op z_lender` then reads a frame-zero helper input, so the monomial `K_G` is free. The
+  auditor also requires that the source is the lender of its operator.
+- **(d)** The handoff has rank zero: `E` is the first `dim(lender)` vectors of the helper's
+  first post-handoff frame.
+- **(e)** Every pre-handoff event on the low helper, other than the deferred helper-only
+  corrections, is either an echo (`target += c L`, which is deleted) or a temporary
+  external addition (`L += a ext`) with zero net change. An echo that reads a nonzero
+  temporary part is rewritten as direct reads `target += c a ext` at the same index and frame.
+- **(f)** The residual target response is exactly `-sum c K_op z_lender`, with dyadic `c`.
+
+**32 transfer, with PR2226's own lenders.** The 64 corrections form the same
+`(target, source, coefficient)` multiset as PR2226's 64 T8 terms; only the operator ids
+differ. The prefix rewrites come from the T74 pivot kernels:
+
+- 628 gets two rewrites, because the kernel inserts a temporary `±2·567` pair.
+- 672 gets two, because the kernel's `B[6]` donates `−2·566` until `B[232]`.
+- 676 gets one, as in T8.
+
+The exact replay accepts all five rewrite gates (`add 214 566 -1`, `add 151 567 1`,
+`add 117 566 1`, `add 181 566 -1`, `add 181 566 1`, all at frame 3).
+
+**16 are blocked:** low helpers 632, 633, 634, 636, 640, 641, 642, 644, 648, 649, 650, 652,
+656, 657, 658 and 660. Each one has a legal prefix plan. The blocker is lender supply. At
+every one of the 12 handoffs, exactly 32 registers satisfy (a)–(c): the PR2226 low lenders
+273…394, all at dimension 4. No other register qualifies, including registers that B never
+touches. All 32 are used. Every low alias saves the same 3 units
+(the lender is at dimension 4, the helper enters at dimension 1), so choosing a different 32
+cannot help.
+
+The other 16 cold registers with entrance dimension 0 are 311, 327, 498, 500, 501, 510,
+512, 513 (final dimension 8) and 572–575, 580–583 (final dimension 7). Restoring them early
+by moving more tail gates would hand off at dimension 7–8 into first frames of dimension 4–5.
+That is a paid dimension-drop handoff. It is outside PR2226's rank-zero scope, and it costs
+more mass than it saves.
+
+## The five omitted high aliases
+
+In T74, helpers 606, 635, 637, 638 and 639 enter at dimension 4. Their first frame after the
+handoff is also dimension 4, because the pivot kernels re-solved those frames. The PR2226
+lenders 395, 363, 530, 331 and 299 are at dimension 5 at the handoff. Using them would need
+a paid 5→4 drop. That is why PR2269 dropped these aliases.
+
+An exhaustive search over retired, unused, non-target registers found rank-zero lenders at
+dimension 4: the X registers 12, 6, 31, 4 and 1. They retire in B between 732 and 862, and
+their final frame is FULL. Each alias saves 5 units because the climbs to FULL merge.
+Precedent: PR2226 and PR2269 already lend X register 73 to helper 653. The only other
+rank-zero dimension-4 lenders are the 32 low lenders, and using them would give up a low
+alias for no saving.
+
+## Scope and limits
+
+This covers the local scalar/frame construction plus exact Gaussian handoff products. It
+does **not** include any of the following:
+
+- native lowering of the new words in either orientation (PR2269 `run_native_borrow.py`
+  chain, warp recipes, the Lemma G stage);
+- a window-exact owner fill for 400-helper words;
+- a refreeze of PLAN/SPEC;
+- a certified price (only the model prices above), outer assembly or a kappa.
+
+Hosting caveats:
+
+- The five new high aliases lend X-register fields.
+- The 64 compensation terms read 32 frame-zero helper inputs before the preconditioner.
+
+Whole-call ownership of these must be re-checked in the hosted owner map. A naive
+per-call-type difference, `249·Δgauge44 + 417·Δextra`, gives
+`{1:−33636, 2:+17316, 3:−20316, 4:−996, 5:−3330}` (mass −80586). That figure is only
+arithmetic: how the freed units fill idle depends on a new fill.
+
+## Open next questions
+
+1. Run PR2269's native chain (`bw_transport`, `bw_emit`, warp recipes, LOCAL-PROGRAMS, Lemma G
+   labels) on `BORROW-WORD-80*`. Do the 64 frame-zero compensation reads and the X-register
+   lenders lower without paid adapters in both orientations?
+2. Build a window-exact owner fill at 400 helpers per call, then price it. The model prices
+   above (-0.54% to +1.73% on b; calibrated about +1%) stay unverified until that fill exists.
+3. Is there a rank-zero source of extra low lenders for blocks 632, 640, 648 and 656? One
+   option is a dimension-4 cold register with entrance dimension 0 created by re-solving a
+   pivot-kernel frame. The 16 remaining helpers would save at most 48 more units per call.
+
+## Credit
+
+- PR2226, anticipatory dirty borrowing (Cinna Davis, @1337isnot1337, with OpenAI Codex): the
+  mechanism, the alias rule, initial compensation, `replay.py` (adapted here as
+  `replay_core.py`) and `operators.py` (vendored).
+- PR2269 (Jeremy Kothe, `research/gmx-t74-borrow43`): the T74 canonical words, the 43-alias
+  witnesses, and the BORROW-WORD emitter, auditor and controls (vendored byte copies).
+- PR2260 (Dugongue): concurrent application of high aliases to the T8 parent.
+- PR2322 (Vlado Vojdanovski) found concurrently and independently that retired source fields
+  can serve as rank-zero lenders for high roles: 619/621/622/623 to X fields 1/4/6/12 at a
+  common rank-4 chart. This package's five extra high lenders (X 12, 6, 31, 4, 1) use the same
+  idea. Its owner exchanges and the other open records (PR2302, PR2309, PR2312) use high aliases
+  only. None of them adds the 32 low (anticipatory) aliases.
+
+The full predecessor lineage is in `vendor/*/NOTICE*` and `SOURCES-PR.json`. Prepared with
+substantial AI assistance (Claude Code, Anthropic); Apache-2.0. No independent human review
+is claimed.

research/t74-low-alias-borrowing/SOURCES-PR.json

@@ -0,0 +1,96 @@
+{
+ "heads": {
+  "PR2269": "b479fc5567bc09ab9185bffe89b62594f36d74e5",
+  "PR2226": "dacaf3d81f1936bb55b8454b1244e5d014272754",
+  "PR2260": "fde6b107e26a14da5bac5b66913c914708ea6901"
+ },
+ "base_main": "0fdd7d82d",
+ "files": {
+  "inputs/blocks.json": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/inputs/blocks.json",
+   "git_blob": "c683574b3861678081fd5c5944dbd7a47309f6fd",
+   "sha256": "ddfac1dae1fe7cc0a91e7c7205c6d9d0c07c682880aa34eed83bf4ad7384da9f"
+  },
+  "inputs/gauge44.canonical.json.gz": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/inputs/gauge44.canonical.json.gz",
+   "git_blob": "4abb6e28f02c95b41ed345d4e4401d16d58ae791",
+   "sha256": "65c6d17ffee2eacf27bff438f37fc549c9ed0c909cbc7a52976cc75cf2d15b91"
+  },
+  "inputs/extra.canonical.json.gz": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/inputs/extra.canonical.json.gz",
+   "git_blob": "e0d670d4351229ce6921ecfbecf180070b17616b",
+   "sha256": "d7e48dcbafa236a2e1e41f7958244211506f7c7630fe6a2d43d2bdf17b7ae015"
+  },
+  "inputs/witness_43_base.json": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/inputs/witness_43_base.json",
+   "git_blob": "9f4b93f3bc52d4f4ffaa128cfd7ae574fd36c462",
+   "sha256": "67ffb66d94067f6e53aee9118fe90e14a57f497fc8b3f708b6dac3de2e58ff28"
+  },
+  "inputs/witness_43_extra.json": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/inputs/witness_43_extra.json",
+   "git_blob": "864ba533f50c2f1f639a6a3559b185bd321b923a",
+   "sha256": "d46449c6dbf4477f260cf5baea9bbb570a66ee0b6db81f4a220b9e3086ae9e46"
+  },
+  "inputs/PR2226-WITNESS.json": {
+   "pr": "PR2226",
+   "path": "research/anticipatory-dirty-borrowing/WITNESS.json",
+   "git_blob": "62edbcce166f7cf388231078c2cd7f75939b97e2",
+   "sha256": "86392adde6992a08ae90f7a69c58cace1b52d942f4d2c96e82ca79e5d1e15235"
+  },
+  "vendor/pr2269/emit_word.py": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/emit_word.py",
+   "git_blob": "a97e3d7506b63aacb8c845a4702be9ecded710b8",
+   "sha256": "c38cd936c5dfc5988c6d50294f94ff003dd1fcd2bab5c4161d7de2cc445ba8ab"
+  },
+  "vendor/pr2269/build_word.py": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/build_word.py",
+   "git_blob": "8684d54b319c3d3a3cbaeaf1bb3af8d45bde92cd",
+   "sha256": "a174c4ca05ef3c2dda789a042e16b20164fbc7d6ed7781c6b63964d30b498f36"
+  },
+  "vendor/pr2269/audit_local.py": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/audit_local.py",
+   "git_blob": "a90b00e0232bc9d7bc85138bad8d95553db673d4",
+   "sha256": "36c82ecbface61a5b824c59ea90d1f31a31ff4b87bfef24e16742f06e18fa3c5"
+  },
+  "vendor/pr2269/borrow_controls.py": {
+   "pr": "PR2269",
+   "path": "research/gmx-t74-borrow43/new/borrow/borrow_controls.py",
+   "git_blob": "99789e011d0d3dd699560e002a1c0b9ef7fbb3ac",
+   "sha256": "07fbbf8e2f06df063dc9d88e5e4f721222a9fcf30b983bf9127cd5aa4b611627"
+  },
+  "vendor/pr2226/operators.py": {
+   "pr": "PR2226",
+   "path": "research/anticipatory-dirty-borrowing/operators.py",
+   "git_blob": "5c4fbe8cceedd769a1c367a31cd0beeae2175dc1",
+   "sha256": "b37b67a04681c776dafcdc6c9af0e8a2dbfa9893b02e0fa2d77ccc9182a87988"
+  },
+  "vendor/pr2226/NOTICE.md": {
+   "pr": "PR2226",
+   "path": "research/anticipatory-dirty-borrowing/NOTICE.md",
+   "git_blob": "5ea70357a04d083dba066fbc5c809a5736d8edd6",
+   "sha256": "f1d45d886926915531e3a59968abf0a4c974d7038f869848e71bd3a21b834422"
+  }
+ },
+ "adapted": {
+  "replay_core.py": "function form of PR2226 research/anticipatory-dirty-borrowing/replay.py (blob see PR2226 head) ; only the 80/32 pair-count assertion parameterised, diagnostic residual mode and probe hook added"
+ },
+ "outputs": {
+  "witness/witness_80_base.json": "9380f74c032b0616d5b13e8ef94b6d9f80cac36239e329357e7d5fcab5283ad0",
+  "witness/witness_80_extra.json": "6737072dcca47c6e6526bd62a41585dd09026549550c9e62eb53e64b265a6709",
+  "words/BORROW-WORD-80base.json.gz": "61290abffd8c8225e0abb3958c1506674e256de688fc4cdf358bbe7c981df493",
+  "words/BORROW-WORD-80extra.json.gz": "1dd2d6f2ae5b5a27b5f89fb830203f0cca7a78d0323a7845e85e1e80f8f6d1a5"
+ },
+ "tools": {
+  "check_ext.py": "independent word check (stdlib only; reads PR2269/PR2226 blobs via git at the heads above)",
+  "price_ext.py": "model pricing harness; `sources` re-reads PR2269/PR2260/PR2226 constants via git; PR2312 kappa is a reference value only",
+  "run_all.py": "runs check_ext.py + price_ext.py and cross-checks"
+ }
+}

research/t74-low-alias-borrowing/SOURCES.json

@@ -0,0 +1,24 @@
+{
+  "schema_version": 1,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "e8870e5917057d59b730eb14721a778639eca050",
+      "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7"
+    },
+    {
+      "path": "research/complex-local-word-ceiling/ceiling.py",
+      "usage": "input",
+      "git_blob": "6c0f54527d879396f689523bfde19928a9b6157c",
+      "sha256": "86a1432870b3b21d8454106ec9162fddc0471472d9214c590a1420f2426cedfc"
+    }
+  ]
+}