docs(research): map selected bootstrap proof obligations

docs/research/bottleneck-brief.md

@@ -42,7 +42,10 @@ The [review through #2027](community-efficient1000-review.md) leaves the selecte
   against that witness before designing a full schedule.
 - **Selected proof obligation:** [#1990's stock audit](../../research/selected-bootstrap-stock-audit/README.md)
   leaves the actual selected reserve coefficient unknown. Derive one source-bound
-  stage envelope rather than recomputing the already checked headrooms.
+  stage envelope rather than recomputing the already checked headrooms. The
+  [bootstrap obligation map](selected-bootstrap-scope-map.md) separates newer
+  conditional BIT coefficient proposals, time and fresh-field implications,
+  and the remaining implementation premises. These are not supplier admission.
 
 The new fixed-word frame bounds (#1995/#2013), Eisenstein additive pairing
 bound (#2017), and bounded register census (#1974) narrow particular search

docs/research/selected-bootstrap-scope-map.md

@@ -0,0 +1,173 @@
+# Which selected bootstrap obligation does this result address?
+
+Use this map before repeating stock-headroom arithmetic or treating a local
+row route as bootstrap admission. It covers the selected #1094 ordinary
+bootstrap, not every proposed outer algorithm. The
+[selected record](../../certificates/selected-result.json) remains authoritative;
+its [review](community-batch1099-review.md) retains the all-size, realization,
+hosting, precision/tape and analytic obligations. No new bound or proof
+adoption follows from this map.
+
+Snapshot: **2026-10-14, priority revision 4**, canonical main
+`0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`. The first three entries below are
+retained research with the scopes recorded in the
+[review through #2027](community-efficient1000-review.md). The four later
+entries are **open proposals**, pinned below and locally replayed for this
+map. Passing their finite checks does not promote their conditional proofs
+into the selected theorem.
+
+## Follow the obligation, not the largest coefficient cap
+
+| Result and author | What it establishes | What it does not establish |
+| --- | --- | --- |
+| [#1956, Josie Elliston](../../research/bootstrap-cutoff-carry/README.md) | All fourteen selected cutoffs reproduce; twelve fail the lemma's carried-time-constant rule as written. A corrected finite chain passes under its stated fresh-constant allowance. | A refutation of the asymptotic saving, or acceptance of a different proof wording. The numerical κ calculation does not read the cutoffs. |
+| [#1965, Josie Elliston](../../research/bootstrap-cutoff-time-space-split/README.md) | Under H1–H3, time constants can enter the new induction constant rather than the fit cutoff. The fourteen cutoffs have explicit sufficient stock headrooms. | H2's uniform implementation estimate or H3's actual selected stock coefficient. Its "valid exactly when" is a statement about its sufficient guard, not necessity for actual fit. |
+| [#1990, ToikY](../../research/selected-bootstrap-stock-audit/README.md) | An independent headroom audit and factor-16 extension of the sufficient stock-fit cap under the same envelope hypothesis. | A selected reserve implementation. The historical `m=120` increment 57,604 and external allowance 252 cannot simply be used as selected internal reserve coefficients. |
+| [#2084, Adam Gall](https://github.com/CrocSwap/integer-mult-bounds/blob/8001a23b003bec5dff5e61edec907b652c475932/research/selected-bit-parent-reserve/README.md) | Under explicit full-cover, fixed-width, fresh-field, restoration and internally completed-leaf interfaces, the selected **BIT** parent has `log_q S(e,w) <= 8194*w*(1+log2 e)`. The native first-stage fit guard passes. | A physical GL64 packet implementation, H2, or fourteen independently admitted stages. The coefficient implication is conditional on the named interfaces. |
+| [#2120, Nick Petalas](https://github.com/CrocSwap/integer-mult-bounds/blob/378593574261e0b0915e7e8a83147aa640274fc8/research/selected-bit-ceiling-free-stock/README.md) | With the same interfaces, terminal slack yields `D(n) <= (28/17)*log2(max(1,n))`, hence coefficient 6748 and a passing native first-stage fit guard. | Changed production pricing or a smaller implemented reserve. The row coefficient remains 18,355, and other stages need their preceding completed ordinary contract. |
+| [#2087, Adam Gall](https://github.com/CrocSwap/integer-mult-bounds/blob/b5ffc48e3dd5c92f591bdb4fabafa2c8e8b33970/research/selected-bootstrap-uniform-time/README.md) | An all-width **implication** for H2 from a uniform stopped recurrence and a complete wrapper bill, with first-stage `K = C*max(401501,2*sigma)` when its primitive coefficients are at most C. | A bound on C, a stock coefficient, or proof that actual primitives meet those uniform contracts. Complete-fiber descriptor amortization is another explicit premise. |
+| [#2097, Adam Gall](https://github.com/CrocSwap/integer-mult-bounds/blob/1d3ee0926656d5260c6cb1c0b81964ffe9fe1377/research/selected-cover-fresh-fibers/README.md) | Complete invocation fibers and the retained per-edge bad-class average follow from ancestor-only invocation decisions, fresh-role permutations, restoration and execution of the entire once-padded range. | An emitted selected all-size dependency certificate. A large reserve and restored final row alone do not imply those read/write restrictions or intermediate fiber completeness. |
+
+These are different implications. #1990 enlarges a **permitted coefficient
+cap**; #2084/#2120 derive **sufficient coefficients** under implementation
+premises; #2087 bounds time in terms of still-unknown primitive constants;
+#2097 explains the address conditions needed for the averaging contract.
+None makes the other premises automatic.
+
+H1 is the completed previous ordinary algorithm at every required width.
+H2 is the cutoff-independent time estimate whenever stock fits. H3 is the
+uniform stock envelope. With those premises established, #1965's restated
+lemma separates fit from time absorption. Maintainer adoption of that wording
+is separate from checking these implications; the frozen original proof and
+its carried-constant audit remain unchanged.
+
+## Bind the ordinary producer correctly
+
+The selected complex supplier has `m=73` and binds the shared saving, but the
+ordinary stopped producer in these four proposals is **PR589 BIT `m=64`**.
+Its maximum child rank is 42, with 28,416 live roles and **28,425 physical
+roles**, including nine work roles. Complex rank-48 depth work is a different
+producer. The fourteen selected arithmetic headrooms do not identify fourteen
+implemented reserve envelopes.
+
+For a fixed eligible odd prime `q>2^80` and integer `w>=1`, the BIT stock
+proof charges a complete level divisor
+
+```text
+W_q(w) = 28425 * |GL_64(F_q)| * q^(4096*(w-1)),
+log_q W_q(w) < 4097*w,
+S(n,w) = W_q(w)^D(n).
+```
+
+Here `W_q(w)` is an actual row divisor, not the time moment's live-role
+denominator. High-matrix fibers may cancel in normalized time but not in
+stock. Siblings and the two ordinary-wrapper calls reuse a restored quotient;
+they do not multiply it. The zero external leaf factor requires an internally
+completed ordinary leaf, not a claim that the leaf has no internal workspace.
+For borrowing, #2120 chooses stock from original width e **before** choosing
+borrowed width k and the resulting body width.
+
+The numerical connections are cheap to check without a supplier replay:
+
+```sh
+python3 -I -B - <<'PY'
+from fractions import Fraction
+
+assert 2**17 * 42**28 < 64**28
+assert 4097 * Fraction(28, 17) == 6748
+assert Fraction(6748, 8194) == Fraction(14, 17)
+for sigma, ell in ((8194, 17), (6748, 16)):
+    assert 2**(ell-1) < 8*sigma <= 2**ell
+assert max(401501, 2*6748) == 401501
+print("PASS_SELECTED_BOOTSTRAP_MAP_ARITHMETIC")
+PY
+```
+
+Thus substituting the conditional `sigma=6748` into #2087's displayed
+first-stage formula leaves `K=401501*C`. This is arithmetic, **not** a
+measurement of C or a composed implementation certificate. At the recorded
+native first-stage cutoff `L=4785575287428`, both stock proposals check the
+sufficient guard. Neither result lowers that cutoff or prices the selected
+supplier again.
+
+## Replay the right evidence
+
+The retained packages are present on the snapshot main. From the repository
+root, using standard-library Python 3.12:
+
+```sh
+python3.12 scripts/research_package.py --package research/bootstrap-cutoff-carry
+python3.12 scripts/research_package.py --package research/bootstrap-cutoff-time-space-split
+python3.12 scripts/research_package.py --package research/selected-bootstrap-stock-audit
+```
+
+The open packages are **not present on that main**. Run the same launcher in
+an isolated checkout of the corresponding pinned head, with the package path
+below. Do not overlay them onto frozen predecessors or substitute a moving
+PR head for the cited one.
+
+| PR | Exact replay head | Package under `research/` |
+| --- | --- | --- |
+| [2084](https://github.com/CrocSwap/integer-mult-bounds/pull/2084) | `8001a23b003bec5dff5e61edec907b652c475932` | `selected-bit-parent-reserve` |
+| [2120](https://github.com/CrocSwap/integer-mult-bounds/pull/2120) | `378593574261e0b0915e7e8a83147aa640274fc8` | `selected-bit-ceiling-free-stock` |
+| [2087](https://github.com/CrocSwap/integer-mult-bounds/pull/2087) | `b5ffc48e3dd5c92f591bdb4fabafa2c8e8b33970` | `selected-bootstrap-uniform-time` |
+| [2097](https://github.com/CrocSwap/integer-mult-bounds/pull/2097) | `1d3ee0926656d5260c6cb1c0b81964ffe9fe1377` | `selected-cover-fresh-fibers` |
+
+For example, at the cited #2120 head:
+
+```sh
+python3.12 -Werror -B scripts/research_package.py --package research/selected-bit-ceiling-free-stock
+```
+
+All seven registered replays passed locally on Linux x86_64 / CPython
+3.12.15 for this map, including their declared rejection controls. The four
+open-head replays used separate source-bound sparse worktrees, which remained
+clean afterwards. The arithmetic above and local link checks also passed.
+These are replays of the authors' finite evidence, not an independently
+implemented mathematical checker or human proof review. No selected cold
+replay, physical compiler, formal-kernel or hosted CI result is claimed here.
+
+## Open next questions
+
+- **Bind the implementation premises, rather than recomputing headroom.**
+  A feasible first step is a selected invocation whose guard, edge list and
+  weights read only ancestor fields, and whose routes fix unused descendant
+  stock. Check complete high fibers, restoration and paid routing together.
+  This matters because #2097's adaptive-current-field and pruned-dummy-row
+  counterexamples preserve final rows while breaking the averaging argument.
+  A scalar endpoint check alone is not the missing certificate.
+- **Bind an ordinary leaf and the uniform tolls.** Trace its internal borrowing,
+  completed spectators, conversion/preparation sites and row return at all
+  admitted widths. This determines whether H1, the external-factor-one stock
+  induction and #2087's width-independent primitive constants actually apply.
+  Component work is coordinated in
+  [Discussion #2114](https://github.com/CrocSwap/integer-mult-bounds/discussions/2114)
+  and the [whole-invocation claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/2179).
+  Those provisional follow-ups are not composed or audited by this map.
+- **Extend only after completion of the previous stage.** Each later native
+  or conservative stage needs its own preceding completed ordinary contract
+  and any remaining fit conditions. The fourteen headrooms are an arithmetic
+  starting point, not a substitute for that induction or maintainer adoption.
+
+## Scope and credit
+
+Task `scope-navigation`, consolidation; nonce
+`9540ac7c50e97c48ffce51501dabc841`, scope key `fff26335d457e528d9c4`.
+Scope refined to this dependency map and one onboarding link. The initial
+P104 alternative was not pursued because Aaron Wang's
+[scope-map PR #2133](https://github.com/CrocSwap/integer-mult-bounds/pull/2133)
+already covers it. Entry overlap covered 428 open PRs and 862 Discussion
+records at 22:30/22:31 UTC. The pre-submission refresh covered 428 open PRs
+and 864 Discussion records at 22:35/22:36 UTC, with complete pagination.
+Canonical main and all four cited open heads were unchanged. Metadata searches
+do not cover every code diff or unpublished result. The
+[canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/2114#discussioncomment-18935479)
+records coordination and final freshness.
+
+All mathematical results remain credited to the authors above. The selected
+PR589 word and its nine-stage lineage are DreamingOfClouds' work on eumemic's
+base; PR185/PR387 completed-row contracts and selected PR1094 are Rohan Arun's
+work, with Jeremy Kothe's PR1087 and the source527 cover/borrowing lineage
+retained. Sricharan Vagvala's separate complex-depth audit informed #2120's
+inverse-threshold cross-check, not a change of producer here. This document
+adds navigation and checked replay routes only. Apache-2.0.