Stream norm-six features with 320 live integer slots (no κ)

research/norm6-streaming-features/README.md

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+# Stream norm-six features without a transform table
+
+**Scoped streaming construction; no new kappa.** Emit all 19,600 norm-six
+feature pairs with at most **320 live integer slots**, including both input
+vectors, plus **2,304 Gram entries**. There is no per-feature transform table
+or target accumulator array. A consumer must release each output before the
+next; retaining outputs requires additional storage.
+
+| Quantity | Bound |
+|---|---:|
+| Emitted factor pairs | 19,600 |
+| Owned vector slots | 192 |
+| Borrowed x/y input slots | 96 |
+| Scalar/counter/current-record allowance | 32 |
+| Per-feature descriptor / target accumulator slots | 0 / 0 |
+| Immutable Gram slots | 2,304 |
+| Common target denominator, not asserted minimal | 256 |
+| Uniform target numerator magnitude | 146,804 |
+| Uniform source feature magnitude | 32,768 |
+
+The term count and algebraic support upper bill `49*19600=960400` are inherited
+from Nick Petalas's [#5084](https://github.com/CrocSwap/integer-mult-bounds/pull/5084).
+Concurrent JoyboyBrian [#5132](https://github.com/CrocSwap/integer-mult-bounds/pull/5132)
+publicly supplied an explicit construction during this investigation and
+receives credit for closing that gap. Its stated allocations are 19,712 target
+slots, 64 source slots and 245,884 immutable descriptor slots including G.
+The new delta is a one-pass stream with O(d) live workspace and only the O(d^2)
+Gram as fixed data. This compares explicit upper allocations, not an optimal
+space lower bound. The feature bases differ and must not be interchanged.
+
+## Construction and exact boundary
+
+The kernel is `K(x,y)=((x^T G y)^3-4*x^T G y)/192` on `x^T G x=y^T G y=6`.
+A two-coordinate Gram block `[[6,-1],[-1,6]]` gives a dyadic-unit pivot of
+determinant -8 for the 48 shell relations. It removes two square-linear
+features and 46 distinct-index cubics. Parity gives integral coefficients
+over the common scale 256.
+
+[streaming.py](streaming.py) contains the table-free iterator. It owns exactly
+four length-d vectors, generates feature keys by nested loops, and forms each
+coefficient from at most three local relation entries. [PROOF.md](PROOF.md)
+proves the identity, ownership/lifetime contract, operation counts and bounds
+on all intermediate integers. Borrowed G,x,y must remain immutable throughout
+iteration; the implementation preserves them but does not snapshot or police
+concurrent mutation. Outputs retained by the caller are outside the 320 slots.
+
+The combined stream uses at most 159,389 integer multiplications and 61,150
+additions/subtractions, with 96 exact divisions by three, two pivot halvings
+and at most 144 public Gram-diagonal halvings. All preprocessing intermediates
+fit 19 signed bits on the actual norm-six shell. The counts include the Gram
+dot-product prefixes, rather than pricing them by their smaller final values.
+Divisions define precomputed integer-valued label features, as in #2222; they
+are not dyadic scalar gates on arbitrary runtime data. This is an indexed
+integer model, not a Python heap measurement or a physical tape tariff.
+
+The optional exact pair-kernel consumer needs one additional 48-bit accumulator.
+It checks the feature identity; a variable-data physical decoder is not supplied.
+The expansion decision is to stop at the specified stream contract. The changed
+scope does not claim the historical card's whole-supplier/five-percent gate.
+
+## Evidence and reproduction
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/norm6-streaming-features
+python3.12 -I -B -W error research/norm6-streaming-features/verify.py
+python3.12 -I -O -B -W error research/norm6-streaming-features/verify.py
+python3.12 -B scripts/check_research_commit.py --package research/norm6-streaming-features --check-source-history
+```
+
+Expected direct marker: `PASS_NORM6_STREAMING_FEATURES`; the registered runner
+also prints `PASS_REGISTERED_RESEARCH_PACKAGE`. `verify.py --emit-result`
+generates the deterministic source-bound receipt on stdout; normal verification
+writes nothing and compares it to [RESULT.json](RESULT.json), including JSON types.
+
+New-result evidence:
+
+- An independently implemented literal polynomial-convolution oracle checks
+  all 48 relations, with 43,056 coefficient comparisons. It multiplies
+  polynomials and expands ordered Gram pairs rather than copying the
+  constructor's coefficient formulas.
+- The exact -8 minor and all 2,304 entries of `R_P^T Q=8I` check the full pivot
+  solve for arbitrary target values. Full polynomial comparisons cover 3,275
+  small-dimensional targets and five actual 48-dimensional targets.
+- All **3,449,600 emitted coordinates** in **176 complete streams** agree with
+  the materialized reference already checked by the independent oracle.
+  Borrowed-input preservation, order, completion, early close and the four
+  owned vectors are checked. Static inspection supplies the algorithmic
+  storage proof; sampled Python frame inventories are only corroboration.
+- The 44 actual-Gram norm-six vectors are a diagnostic set, not a full-shell
+  enumeration. A nonzero off-shell defect is tested. Exact multiplication of
+  G by its computed inverse establishes maximum inverse diagonal 172 and the
+  source-coordinate bound 32 under the cited positive-definiteness premise.
+- Thirteen mathematical/input/stream corruptions reject. Normal and optimized
+  execution retain all checks. The reference implementation and its full
+  feature/relation arrays occur only in verification, never in the stream.
+
+The proof supplies universal coverage; finite tests alone do not. The official
+export includes the sole live input, the Gram JSON, and direct replay needs
+neither Git nor any predecessor executable. Local publication/export evidence
+and hosted CI are reported separately in the PR.
+
+## Sources, coordination and credit
+
+Scientific base: `20a1e31bc6009b9b3f4d084bbaadc6350e34fcba`, priority revision 7.
+[SOURCES.json](SOURCES.json) pins exact base blobs and SHA256 hashes. The
+catalogue, selected record and predecessor proofs are provenance; only the
+Gram JSON is a live external input. No frozen source is edited or copied.
+
+- Cinna Davis / 1337isnot1337, [#2222](https://github.com/CrocSwap/integer-mult-bounds/pull/2222),
+  `82cf756186c0fc2c542fcd06e486c575d97ffc5c`: kernel, integral-valued features,
+  P48p Gram and 49-bit chart.
+- Nick Petalas, [#5084](https://github.com/CrocSwap/integer-mult-bounds/pull/5084),
+  `9d7f7805d147028fe5f0174e267ee05b73703f0b`: dyadic existence bound and handoff.
+- JoyboyBrian, [#5132](https://github.com/CrocSwap/integer-mult-bounds/pull/5132),
+  `08572fdb060e73ecc4cb09a024611039881185f4`: concurrent explicit construction
+  and its transform/target-array resource bounds. Its proof supplies comparison
+  context; its code is neither imported nor replayed.
+- DreamingOfClouds, [#2244](https://github.com/CrocSwap/integer-mult-bounds/pull/2244),
+  `8ef6fa81403973d3cacaf865bdabe9797a6c34a0`: rational shell-rank perspective.
+- David Ganz / Dugongue, [#4494](https://github.com/CrocSwap/integer-mult-bounds/pull/4494),
+  `ad31d9fdf000d4ca98dd911afe489a45d2ea4f74`: the dyadic factorization lemma
+  used by #5084; the explicit pivot does not need that general lemma.
+
+Nebe/Sloane and the retained Leech/Niemeier geometry and kernel lineage retain
+credit. Classical elimination and Cauchy-Schwarz are not new techniques.
+
+The [canonical investigation #5127](https://github.com/CrocSwap/integer-mult-bounds/discussions/5127)
+retains the initial claim and the [scope change](https://github.com/CrocSwap/integer-mult-bounds/discussions/5127#discussioncomment-19143848).
+The first snapshot covered 310 open PRs, 4,266 Discussion records and 6,884
+tracked notes. The later 10:23–10:24 UTC refresh covered 315 PRs and 4,284
+Discussion records and found #5132. Its claim had appeared between the
+preceding live read and ours. Before publication we narrowed the contribution
+to the different memory contract; we do not claim another first resolution of
+the original constructibility question. Final freshness is recorded in TASK.json.
+Arbitrary diffs, unpublished work and subsequent activity are outside snapshot
+coverage. The original account's reflection, Schur, Pauli, association, fanout,
+frame and A5 work is excluded.
+
+Prepared by Krzysztof Wojt with substantial OpenAI Codex assistance. Bounded
+Luna support covered overlap inventory, the independently written polynomial
+oracle, and arithmetic/storage review; the primary agent reviewed and
+integrated it. Apache-2.0. Independent human and proof-kernel acceptance are
+unclaimed.
+
+## Limitations
+
+Positive definiteness, lattice geometry and the binary chart remain cited
+premises. No full-shell table, exact rank, term/space optimality, minimum
+denominator or superior total arithmetic cost is claimed. Source acquisition,
+physical variable-data side programs, frames, owners, dirty restoration,
+precision, tape movement, compiler/recursive and outer admission remain
+unknown. Unknown costs are not zero. No selected frontier is changed.
+
+## Open next questions
+
+Can one chronological physical source/target contract consume the stream
+without retaining a cubic-size output array and with a favorable full invoice?
+Start with one actual kernel invocation, check its data lifetime/order and
+charge acquisition, preparation, frames, owners, dirty restoration, precision
+and tape placement. The explicit generator removes the transform-table and
+target-array requirement of this abstract interface; a physical caller and
+its complete cost are still missing. See [TASK.json](TASK.json).

research/norm6-streaming-features/RESULT.json

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+{
+  "actual_shell_fixture_count": 44,
+  "actual_shell_pairs": 176,
+  "dimension": 48,
+  "evaluation_budget": {
+    "retained_features": 19600,
+    "source_exact_divisions_by_3": 48,
+    "source_multiplications": 36850,
+    "source_subtractions": 48,
+    "target_additions_upper": 100446,
+    "target_common_denominator": 512,
+    "target_exact_divisions_by_3": 48,
+    "target_multiplications_upper": 159436
+  },
+  "global_target_numerator_bound": 293608,
+  "gram_sha256": "e25d51a0a9cdbc897d5db39fb698aa9bbc2f4ce29e8d7add2a44bae8f086add2",
+  "max_fixture_numerator": 3114,
+  "max_inverse_diagonal": "172",
+  "observed_owned_stream_vector_slots": 192,
+  "offshell_defect_times_3": 4320,
+  "original_features": 19648,
+  "package_sha256": {
+    "PROOF.md": "4d7c62c92bd636261ae4d64e83c1d274729f6bb46d323d4a70592e471db35673",
+    "README.md": "01cbce4bc286c5edd0a93440cc4634b9d10ebad8ae605941dfa6df10093d462b",
+    "SOURCES.json": "5aeaaf10528a59fc4022377875d59973b182845b34cebd68285de5e1cf9d9b85",
+    "TASK.json": "3cf1e8cdc52794b470349eaf9ee40bd553f3caaa4073987c2b3e055546e184ae",
+    "VERIFY.json": "b5add8380735ceb1fa827412e1154d186215d73fa7d838aec20cf7c1b367c36e",
+    "compression.py": "94974ecf6c0ff4b17e4057f8f6f5895f7dae37f2f37099ff438354bebeade096",
+    "oracle.py": "a7ddab8365229da02cbce8341f0ae8eacf8722ac1a0ea16a774546c76d5a734a",
+    "streaming.py": "4f888ec22eebcf702c6a3b4e9718ed5e9496782872e0c2f7b24b5b79e4f43c53",
+    "verify.py": "087dd7beb3216478d5635f493d8db2b9ffa7b6cfed7049678c748b8ad9cb7b8b"
+  },
+  "pivot_determinant": -8,
+  "pivot_inverse_entries_checked": 2304,
+  "polynomial_oracle": [
+    9176,
+    19312,
+    18573,
+    9176,
+    19453
+  ],
+  "rejected_controls": [
+    "wrong f coefficient",
+    "wrong shell constant",
+    "corrupted retained feature",
+    "wrong elimination multiplier",
+    "omitted final factor eight",
+    "wrong pivot sign",
+    "asymmetric Gram",
+    "odd Gram diagonal",
+    "short target",
+    "boolean coordinate",
+    "repeated pivot",
+    "omitted first stream record",
+    "corrupted stream target"
+  ],
+  "relation_column_l1_max": 15,
+  "relation_oracle": [
+    48,
+    43056
+  ],
+  "removed_features": 48,
+  "retained_features": 19600,
+  "schema": "norm6-streaming-features/v1",
+  "scope": "Written shell identity plus exact finite corroboration; no physical tariff or new kappa.",
+  "small_all_polynomial_targets": 3275,
+  "source_coordinate_bound": 32,
+  "source_feature_bound": 32768,
+  "status": "PASS_NORM6_STREAMING_FEATURES",
+  "stream_budget": {
+    "additions_subtractions_upper": 61150,
+    "borrowed_source_target_slots": 96,
+    "combined_live_plus_gram_slots_upper": 2624,
+    "combined_live_slots_upper": 320,
+    "common_target_denominator": 256,
+    "emitted_pairs": 19600,
+    "feature_exact_divisions_by_3": 96,
+    "immutable_gram_slots": 2304,
+    "indexed_reads_writes_upper": 2582528,
+    "multiplications_upper": 159389,
+    "multiplier_exact_divisions_by_2": 2,
+    "owned_vector_slots": 192,
+    "per_feature_descriptor_slots": 0,
+    "public_diagonal_halvings_upper": 144,
+    "scalar_counter_record_slots_upper": 32,
+    "target_accumulator_array_slots": 0
+  },
+  "stream_pair_accumulator_absolute_bound": 94285280051200,
+  "stream_pair_accumulator_signed_bits": 48,
+  "stream_preprocessing_signed_bits": 19,
+  "stream_target_denominator": 256,
+  "stream_target_numerator_bound": 146804,
+  "streamed_coordinates_checked": 3449600,
+  "target_denominator": 512
+}

research/norm6-streaming-features/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20a1e31bc6009b9b3f4d084bbaadc6350e34fcba",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "c35482cd9035843b15a634cc8276a7e1e40e8395",
+      "sha256": "6fe0a099b89aa2aed796a13c3a21dafc63f3388ebf397464e44e0451893b9375"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "f126dd2e2dad2b669e75d1d0d0bd05c600725602",
+      "sha256": "f7a48bfa2659b88378282a8eee7d9fe52cdf505594124c4d1686b58510fffd72"
+    },
+    {
+      "path": "research/norm6-dyadic-compression/README.md",
+      "usage": "provenance",
+      "git_blob": "69cd696606105c1e660b2379f148361b77d4899f",
+      "sha256": "00d6143d9f54c51b7f0a628d108900612c3631f22cf5289c33bd81842e09031c"
+    },
+    {
+      "path": "research/norm6-dyadic-decoder/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "25fc7d52b5c28b7575cb0878a36955c542c2af13",
+      "sha256": "10400041efc16ec3aa34cbe945aed13c353377981ffadc746136c9c928d50951"
+    },
+    {
+      "path": "research/norm6-dyadic-decoder/sources/P48p-GRAM.json",
+      "usage": "input",
+      "git_blob": "872dff9406881d567882d70882408eaa1e1f8f6c",
+      "sha256": "e25d51a0a9cdbc897d5db39fb698aa9bbc2f4ce29e8d7add2a44bae8f086add2"
+    }
+  ]
+}