Construct complete P104 forward word and conditional hosting invoice

research/p104-interleaved-search/NATIVE-CHAIN.json

@@ -0,0 +1,102 @@
+{
+  "schema": "natural-query-delivery-v1",
+  "source_sha256": {
+    "research/complex-block-rank-optimum/inputs/selected.json.gz": "16bc0ebb04b4be6c0ade74badc6a0c0cdba4215eda86e4ff9f13abf8ecebd219",
+    "research/frame-sa504/inputs/hamming/PROTOTYPE.json": "327d2a868043e846381aa58a33053c24425e8cad522ff401b10ec8af1d649a3f",
+    "research/p104-native-channel/inputs/P104-FIXTURE.json": "516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4"
+  },
+  "pair_hamming_root_indices": [
+    3,
+    113
+  ],
+  "query_register": 146,
+  "query_copy_coefficient": "-1/2",
+  "query_hoist_root_order": [
+    113,
+    47,
+    28,
+    57
+  ],
+  "contacts": [
+    {
+      "before_B_event": 548,
+      "register": 139,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 884,
+      "register": 582,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 653,
+      "register": 119,
+      "coefficient": "-2"
+    },
+    {
+      "before_B_event": 874,
+      "register": 572,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 553,
+      "register": 125,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 551,
+      "register": 127,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 658,
+      "register": 128,
+      "coefficient": "-2"
+    },
+    {
+      "before_B_event": 524,
+      "register": 134,
+      "coefficient": "-2"
+    },
+    {
+      "before_B_event": 523,
+      "register": 220,
+      "coefficient": "-2"
+    },
+    {
+      "before_B_event": 697,
+      "register": 450,
+      "coefficient": "4"
+    },
+    {
+      "before_B_event": 875,
+      "register": 573,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 785,
+      "register": 451,
+      "coefficient": "-4"
+    },
+    {
+      "before_B_event": 1192,
+      "register": 497,
+      "coefficient": "-4"
+    },
+    {
+      "before_B_event": 656,
+      "register": 154,
+      "coefficient": "-2"
+    },
+    {
+      "before_B_event": 1608,
+      "register": 162,
+      "coefficient": "2"
+    },
+    {
+      "before_B_event": 885,
+      "register": 583,
+      "coefficient": "2"
+    }
+  ]
+}

research/p104-interleaved-search/README.md

@@ -0,0 +1,199 @@
+# Exact P104 query construction and complete forward fanout word
+
+**All eight delivery terms now have an exact finite forward construction, but
+no κ improvement is certified.** Frame coalescing reduces its local cost;
+the concrete owner-window packing still misses the selected result. No global
+supplier or improved multiplication bound is claimed.
+
+The starting point is canonical main
+`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`. The selected result remains
+κ = `836330098538459/500000000000000000`. The requested significant, fully
+verified gain (working threshold: 1% relative improvement) is **not achieved**.
+
+## Constructive result
+
+`query_construction.py` derives all sixteen admissible query banks from the
+pinned selected word: eight coordinate centres and eight punctured Y roles.
+For this decoder, four coordinate banks are ready before B. A dependency
+permutation produces the other four after 94, 209, 337 and 507 of 1846 B events.
+It preserves every register's incident-event order, all frame inclusions, the
+704-column B transformation and its transport profile. Query construction uses
+actual public registers; it requires no external pure-query oracle.
+
+`fanout.py`, with the exact rational contacts in `FANOUT-PLANS.json`, realizes
+all eight decoder terms in one chronological word:
+
+1. At B prefix 507, copy each actual query at its hyperplane Hb, normalize it,
+   and descend through one rank-seven native child to its target line La.
+   The eight private copies are sequential; peak occupancy is one.
+2. Seed ordinary dirty helpers at La and ascend through their public contacts.
+   The joint schedule needs 31 helpers: 28 from the separate contact plans and
+   three more to avoid incompatible shared-reader frame promotions.
+3. Cancel the helper responses on non-output roles, restore every new helper
+   from its actual query bank, perform the old cleanup, and restore the eight
+   punctured Y roles. Initial frame-zero compensation removes the remaining
+   dirty contribution to live outputs.
+
+The checker replays all **735 independent public input columns**. Every live Y
+ends as its initial Y plus its corresponding initial X; all other public roles
+return to their initial values. It verifies actual query frames, arbitrary
+helper dirt, common charts for scalar additions, monotone public paths, owned
+private-copy lifetimes and fixed final boundaries. The word uses 832 initial
+compensation additions, 276 helper-response cleanup additions and 911 punctured
+Y restoration additions. Four controls change the source coefficient or omit
+private initialization, response cleanup or compensation while keeping the
+repair word fixed; each is rejected.
+
+`native_checks.py` lowers every literal transport from that verified word using
+the pinned predecessor compiler. An independent interpreter checks signed Pauli
+actions and exact global phases, 208 rank-zero intrinsic endpoint adapters, and
+all 4096 Gaussian basis columns across the eight private paths. A deliberately
+wrong global phase is rejected. `verify.py` binds the occurrence lists and paid
+profiles to the scalar/frame replay and cost calculation. Counts and recipe
+hashes are in `RESULT.json`.
+
+`coalesced.py` improves the same word by changing 339 common scalar frames,
+recorded sparsely in `COALESCED-FRAMES.json`. Scalar coefficients and order,
+every public boundary frame, and all private Hb/La copy and seed interfaces
+stay fixed. Transports are rebuilt and all 735 columns are checked afresh.
+The cheaper public histogram is
+`2429 H1 + 558 H2 + 389 H3 + 112 H4 + 108 H5 + 16 H6 + 6 H7`,
+plus the same `8 H7` private descents. Its native lowering is checked separately;
+two additional controls corrupt a contact coefficient or a private seed chart.
+The search heuristic is not part of the replay or an optimality claim.
+
+## Complete local cost and remaining admission
+
+Before coalescing, the public histogram is
+`2611 H1 + 514 H2 + 378 H3 + 132 H4 + 81 H5 + 15 H6 + 6 H7`;
+the eight private descents add `8 H7`. The total local rank mass is 5894.
+All eight delivery terms, helper entrances and dirty restoration paths are
+included. The 31 new helpers contribute 279 lifetime ranks; existing public
+roles add a further 21 ranks compared with the retained punctured baseline.
+
+`fanout_budget.py` checks exact rational interval brackets under the retained
+`m=73, W=832, N=9, COPY=56` coverage and balanced-transfer model. It grants all
+818 remaining paid ranks the favorable fractional rank-51 idle packing, without
+requiring that this packing exist. Even this relaxation gives:
+
+| Scenario | κ upper bound (approx.) | Relative to selected κ |
+| --- | ---: | ---: |
+| Actual complete forward profile | 0.00165721126536 | −0.92361448% |
+| Also grant four unused old gathers' cost credit | 0.00166251958654 | −0.60625646% |
+
+The extra gather credit is deliberately favorable: its joint compatibility with
+fanout cleanup is unproved. Both exact moments at the selected κ are strictly
+above one. These are **upper bounds**, not achieved exponents. They rule out
+this concrete profile within the stated model, not P104 schedules in general.
+
+The coalesced profile has a slightly positive **optimistic** ceiling: at most
++0.05455960% relative to selected κ, or +0.37824205% with the conditional gather
+credit. Both exact target moments rule out a 1% gain for these fixed profiles.
+A positive upper bound is not an achieved improvement.
+
+`hosting.py` constructs and checks a concrete owner-window packing for all
+527 ordinary roles in each of the selected schedule's 144 calls: **75,888
+placements**. It uses the actual complete lifetime widths, including the 21
+extra ranks on 17 old helpers, 16 reclassified roles and 31 new helpers. It
+checks window membership, distinct physical owner families within each call,
+exclusion of active data, nonoverlapping offsets and complete role coverage.
+The exact residual histogram has mass 117792, or 818 per call. It is reproduced
+from pinned schedule and owner inputs; its assignment digest is recorded.
+
+`coalesced_budget.py` also prices that actual residual histogram. The resulting
+fixed-invoice κ upper bound is **1.21466947% below selected κ**, or **0.89916793%
+below** after additionally granting the conditional gather credit. Thus this
+available packing does not turn the cheaper finite word into a gain. A better
+packing is not excluded by that calculation.
+
+The owner certificate is conditional on the retained schedule windows. It does
+not generate or admit a changed 104-port global emitter, backward supplier,
+route/wrapper proof or recursive precision/reserve account. Those remaining
+obligations cannot establish a gain for the rejected invoice. A cheaper local
+word or packing must first pass the full cost screen. The selected frontier is
+not modified.
+
+## Earlier checkpoints and scope
+
+The package retains its useful predecessor checkpoints separately.
+`actual_queries.py` checks an eight-query 704-column scalar identity whose 302
+scatter additions are explicitly unframed. `natural_delivery.py` and
+`NATIVE-CHAIN.json` check one actual-source rank-one increment through 16
+contacts; `natural_budget.py` prices it with the seven other deliveries mostly
+free. `scalar_surgery.py` is the older pure-query-cut identity; `delivery.py`
+and `CHAINS.json` check two externally supplied query fragments; `budget.py`
+prices those fragments. None of their optimistic ceilings is promoted to a
+supplier or substituted for the complete fanout invoice.
+
+The native fixture removes selected port positions
+`3, 14, 21, 34, 39, 61, 76, 93`. This differs from the puncture in the selected
+port adapter package. The aggregate checker binds the exact port set, decoder,
+query rows and normalizations rather than conflating the fixtures.
+
+## Reproduce
+
+From the repository root, with Python 3.12 and the standard library:
+
+```sh
+python3 -I -O -B research/p104-interleaved-search/verify.py
+python3 scripts/research_package.py --package research/p104-interleaved-search
+```
+
+The registered replay is read-only: it checks pinned source hashes, recomputes
+the receipt, compares it with `RESULT.json`, and runs the rejecting controls.
+`--write-result` explicitly regenerates the receipt. The registered replay
+passed on CPython 3.12.14 with assertions disabled. A separate CPython 3.14.7
+replay passed from a source-only export of the 23 package files and 13 declared
+inputs, without changing the export. Both ran on macOS 27.0.1, arm64. Exact
+commands and the receipt hash are recorded in `TASK.json`. Search optimizers are not
+needed for replay. The exact contacts are checked evidence; unsuccessful route,
+decoder, helper-reuse and frame-coalescing searches are not impossibility proofs.
+
+## Open next questions
+
+- **Can existing helper lifetimes replace new fanout helpers?** The full local
+  identity now exists, but its helper and small-rank transport costs exceed the
+  useful budget. Replace one complete lifetime, replay every input column and
+  the joint frame chronology, then reprice. Existing helpers acquire old scalar
+  payloads after B prefix 507, so they cannot simply be treated as persistent
+  query-plus-dirt storage.
+- **Can a different contact schedule reduce small-rank children?** The separate
+  flow plans minimize helper count without optimizing the joint native invoice.
+  Optimize the actual moment while preserving query-bank access and all dirty
+  restoration. Total rank mass alone does not measure the expense.
+- **Can a favorable local word satisfy full admission?** Only after a complete
+  local profile passes the necessary cost screen, construct its backward dual,
+  actual owner windows, residual children, precision/reserves and both exact
+  moment checks. Physical register capacity alone is not a hosting proof.
+
+## Provenance
+
+This follows the native P104 channel in PR1991 (Chafik Boukhalfa), the scalar
+channel in PR1972 (Rohan Arun), and the chronological gather schedule in PR1940
+(Adam Gall). The P104 geometry and decoder work originate in PR1071 (Josie
+Elliston), PR1125 (Ali Romman), PR717 and PR968. The selected scalar architecture
+and Hamming packet construction retain their predecessor attribution, including
+icekylinx's frame-sa504 work and the selected PR1042/PR1094 lineage. The packing
+ceiling engine is Douglas Colkitt's existing work, not a new theorem here.
+The native compiler and independent interpreter retain the notices pinned in
+`SOURCES.json`. The inherited T16 owner schedule is Rohan Arun's
+`complex-t16-rare-pattern-exchanges` package, following PR1087 and earlier
+packing work by jeremykothe2, FanPUYen's PR858 and the retained
+PR1018/PR1005 lineage. The archive and its notices remain unchanged.
+
+PR2082's earlier temporal-cut result concerns a frozen native schedule; this
+construction changes that hypothesis. PR2090 and PR2083/PR2089 cover distinct
+cut and terminal-correction questions. PR2139 (Jose Manuel, Discussion2121) independently publishes a distinct
+836-register delayed-query word based on full120/PR697. This construction
+instead rebuilds the selected P112 word on P104 and checks 735 public registers. Discussion2131 (Hope7Happiness) explores
+dirty carriers starting from the native 72-helper G/2 channel; this package
+uses the selected 480-helper word plus 16 reclassified roles. Discussion2123
+and PR2127 constrain retained transports; the changed paths here do not satisfy
+that premise. PR2148 extends the retained-obligation obstruction to subdivided
+intervals; this word replaces and coalesces original obligations. Discussion
+proposals remain provisional evidence. Source blobs,
+hashes and overlap snapshots are recorded in `SOURCES.json` and `TASK.json`.
+
+Prepared for David Arias with substantial OpenAI Codex assistance, including
+parallel construction and checking. Apache-2.0. No formal proof assistant or
+human independent review is claimed.