Add native centre capture and local fixed-reader services

research/native-centre-capture/COSTS.md

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+# Literal local costs and bounds
+
+The scalar unit is the source model's real primitive tariff. A unit
+complex ADD costs eight. A complex sign costs two; a double or half
+costs two more when present. A monomial map count is not a finite price.
+Native mass is sum r H_r. Recursive cost depends on the full histogram,
+not only its mass.
+
+Define the two shared profiles:
+
+```text
+P9 = 1392 H1 + 64 H2 + 48 H3 + 16 H9;
+P8 = 1392 H1 + 64 H2 + 48 H3 + 16 H8.
+```
+
+Both have 1520 children. Their masses are 1808 and 1792.
+
+| Complete local word | Real scalars | Profile | Input views | Output views | Native side-map upper bound |
+| --- | ---: | --- | ---: | ---: | ---: |
+| Row formation, direct FULL | 11640 | P9 | 112 | 96 | 3008 |
+| Same-reader line-entry reuse | 9880 | P8 | 128 | 96 | 3040 |
+| Clean exchange, I entry | 8600 | P9 | 112 | 96 | 3008 |
+| Clean exchange, Q entry | 8600 | P8 | 128 | 96 | 3040 |
+| Clean Q inverse-adjoint or selected conjugate | 8600 | P8 | 128 | 96 | 3040 |
+| A native forward or backward | 9416 | P9 | 112 | 96 | 3008 |
+| A^T native forward or backward | 8936 | P9 | 112 | 96 | 3008 |
+| Complete D25 fixed-reader forward or dual | 14896 | P8 | 128 | 96 | 3040 |
+| Route32 raw forward or backward | 4312 | 944 H1 + 48 H3 + 64 H5 + 64 H6 | 112 | 112 | 2240 |
+| Direct Fsimple or Bcustom | 2912 | 96 H1 + 128 H8 + 96 H9 | 0 | 0 | 448 |
+
+The route32 raw word has 1120 children and mass 1792. The direct clean
+word has 320 children and mass 1984. The direct word changes the old
+native paths; it is not a cheaper scalar suffix with the old profile.
+
+The D25 row also has 448 DATA maps and 672 query maps. Its complete
+map-call bound is 448+224+3040+672=4384. The local rows above contain no
+implicit DATA charge. The generic formation before the direct-FULL
+refinement has 3040 side maps; the refinement removes the 32 identity
+maps on its sixteen H9 children. H8 side maps remain charged.
+
+The main scalar splits are:
+
+```text
+formation:        6456 retained + 1760 precode + 3424 query = 11640;
+line entry:       6456 retained + 3424 query = 9880;
+clean exchange:   6456 retained + 1760 source code + 384 exchange = 8600;
+A native:         6456 retained + 2960 late query = 9416;
+A^T native:       6952 retained + 1984 late query = 8936;
+D25 reader:       6456 carrier + 8440 routed query = 14896;
+direct clean:     768 self ADDs + 1760 source code + 384 exchange = 2912.
+```
+
+The separate common-frame A and A^T words each cost 3276 scalars. They
+are used twice in the complete fixed-reader query. Route32's pivot code
+and inverse each cost 1870; its reflection capture code and inverse each
+cost 2486. These code costs are not included in its raw native bill.
+The literal route32 entry adds 112 explicit Q^2 translation maps.
+
+| Emitted word | Maximum content row one-norm | Additional binary denominator height |
+| --- | ---: | ---: |
+| Formation | 132 | 1 |
+| Line-entry reuse | 112 | 1 |
+| Clean exchange | 22 | 1 |
+| Clean dual or selected conjugate | 12 | 2 |
+| A native forward / backward | 70 / 22 | 1 |
+| A^T native forward / backward | 30 / 62 | 1 |
+| Complete D25 forward | 202 | 2 |
+| Complete D25 dual | 40 | 2 |
+| Route32 raw, either direction | 14 | Not reported in the native review |
+| Route32 pivot code / inverse | 8 / 4 | 0 / 3 |
+| Route32 reflection code / inverse | 8 / 4 | 1 / 2 |
+| Direct Fsimple / Bcustom | 22 / 4 | 1 |
+
+These are ideal content bounds at emitted operation boundaries. They do
+not bound scalar primitive interiors, recursive child interiors, or the
+full roundoff error. For the routed reader, the complete dual prefix has
+norm 12 and its isolated late query has norm 30; the complete word reaches
+40. The forward routed query reaches 202 on the stated regular cover.
+
+All native rows preserve 416 arbitrary outside values. A scalar code on
+X alone preserves the other 528 fields. Neither statement creates a
+recursive parking schedule or gives productive progress to those values.

research/native-centre-capture/EXTERNAL-NOTICES.json

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+  "scope": "Unchanged notices from verified historical GitHub file objects."
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research/native-centre-capture/HISTORICAL-BUDGETS.md

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+# Conditional historical budget appendix
+
+These are strict inequalities for specified histograms. They do not admit
+a routed composition, a changed output, a cleanup service, or a terminal
+decoder. They do not change the complete kappa calculation.
+
+The retained selected certificate and assembly at commit
+`bce54fb3f895cbe5cd4c0eb477c3afeed100190f` give
+
+```text
+b = 67018507072324140917 / 40000000000000000000000.
+```
+
+For D=25, productive width W=224, three calls, and no idle jobs, use
+
+```text
+M(H) = sum_r H[r] * r/5600 * (25/r)^b.
+```
+
+The current publication base is different. No threshold below is a
+recalculation at the current selected rate.
+
+## Literal invoice and exact interval checks
+
+The low-displacement review recounts all 24 raw and changed words. It
+checks sixteen unchanged scalar sequences and 176 complete profile
+intervals. These include raw rank30/rank16, W48/I64 and W112 changed exits,
+mixed exits, and a separate H9 comparator. The clean review recounts all
+eight I/Q/dual local words. The coalesced review takes its frozen histogram
+as a premise; it does not recount the twelve earlier native words.
+
+The independent numerical engine uses rational arithmetic only. It reduces
+logarithms to 1<=y<2 and uses 64 terms of the atanh series, with its positive
+tail bounded above. It uses the degree-20 exponential polynomial with an
+upper tail. Outward rounding keeps valid intervals. Every reported
+maximum has an upper endpoint below one, and its successor has a lower
+endpoint above one. No floating-point value decides a sign.
+
+## Useful strict thresholds
+
+The columns are alternative allowances for all added native work. They
+cannot both be spent.
+
+| Fixed three-call profile | Extra H1 limit | Extra H2 limit |
+| --- | ---: | ---: |
+| Raw rank30 | 199 | 99 |
+| Raw rank16 | 195 | 97 |
+| Clean Q + Q + Q | 196 | 98 |
+| Clean I + Q + Q | 180 | 90 |
+| Coalesced fixed profile | 198 | 99 |
+| Coalesced with stipulated 64 H1 cleanup | 134 | 67 |
+
+The coalesced profile is exactly
+
+```text
+{1:2913, 2:711, 3:138, 4:36, 5:15, 6:33, 7:30}.
+```
+
+For the clean Q+Q+Q profile, every H1/H2 mixture passes exactly when
+n1+2n2<=196. For I+Q+Q the condition is n1+2n2<=180. The cheapest mixture
+at the next rank fails. This classifies the specified numerical mixtures;
+it does not construct the physical children.
+
+For arbitrary legal extra ranks 1 through 17, strict concavity of
+r^(1-b) makes the cheapest profile at a fixed total rank consist of as
+many rank17 children as possible and at most one remainder. The maximum
+added rank is 197 for three Q calls and 181 for I+Q+Q. The passing profiles
+are 11 H17+H10 and 10 H17+H11. Increasing the remainder by one fails.
+This at most one-rank gain is a fact of these fixed base histograms.
+
+A full 224-H1 terminal fails for both clean profiles. In the Q case the
+total mass is 5600 and every child rank is less than 25, so M>1 for b>0.
+The I case has mass 5616 and fails already at b=0. At the pinned exponent,
+a terminal with all other work fixed must save at least 28 or 44 H1 calls.
+The number 224 is a comparator, not an admitted decoder.
+
+For the earlier W48/I64 changed exits, each changed call replaces
+48(H1+H3) by 48H2. Its saving in H1 moment units is strictly between
+95.846609456084463 and 95.846609456084464. With one, two, or three changed
+calls and the hypothetical 224-H1 terminal, the extra H1/H2 limits are:
+
+| Family | Changed calls | Extra H1 | Extra H2 |
+| --- | ---: | ---: | ---: |
+| Rank30 | 1 | 71 | 35 |
+| Rank30 | 2 | 167 | 83 |
+| Rank30 | 3 | 263 | 131 |
+| Rank16 | 1 | 66 | 33 |
+| Rank16 | 2 | 162 | 81 |
+| Rank16 | 3 | 258 | 129 |
+
+These bounds give necessary cost targets for later constructions. They
+supply no stage access, owner dispatcher, helper host, terminal, or
+precision proof. In particular, the direct clean comparator's mass 1984
+profile is not assigned any of these smaller-profile allowances.