diff --git a/research/encoded-child-spectators/CERTIFICATE.json b/research/encoded-child-spectators/CERTIFICATE.json
new file mode 100644
index 0000000000..4879b20afb
--- /dev/null
+++ b/research/encoded-child-spectators/CERTIFICATE.json
@@ -0,0 +1,2664 @@
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+          -40,
+          -26,
+          -50
+        ],
+        "residue": [
+          22489,
+          4085,
+          23908
+        ]
+      },
+      "shared": {
+        "actions": {
+          "index": [
+            7389,
+            1537,
+            7272
+          ],
+          "record": [
+            8174,
+            2536,
+            6586
+          ],
+          "residue": [
+            523,
+            95,
+            556
+          ]
+        },
+        "borrowed_state_restored": true,
+        "case": {
+          "first": 0,
+          "n": 64,
+          "name": "no-remainder-rank42",
+          "q": 3,
+          "second": 86,
+          "spectators": [
+            1,
+            1,
+            1
+          ],
+          "w": 1,
+          "width": 42
+        },
+        "created_record_backing": 396,
+        "created_record_roles": 13,
+        "exponents": [
+          0,
+          44,
+          0
+        ],
+        "extra_numerical_peak": {
+          "index": 21,
+          "residue": 6
+        },
+        "index_width": 10,
+        "new_numerical_slots": {
+          "index": 21,
+          "residue": 0
+        },
+        "output_hex": [
+          "02010003",
+          "02010000000101010000010000010101000000000101000000010100000000000001010101010101010100010100000000010000000101010000010000000101000100010001010003",
+          "02010003"
+        ],
+        "output_values": [
+          "1",
+          "984770902183611232881",
+          "1"
+        ],
+        "owned_backing_erased": true,
+        "radix_invoice": [
+          523,
+          95,
+          556
+        ],
+        "residue_width": 3,
+        "shared": true,
+        "total_actions": 34668
+      },
+      "total_action_saving": 50309
+    }
+  ],
+  "physical_dispatch_stock_caller": "Not admitted by this geometry/action certificate.",
+  "status": "PASS_ENCODED_CHILD_SPECTATORS"
+}
diff --git a/research/encoded-child-spectators/CONTEXT.json b/research/encoded-child-spectators/CONTEXT.json
new file mode 100644
index 0000000000..1862e89a14
--- /dev/null
+++ b/research/encoded-child-spectators/CONTEXT.json
@@ -0,0 +1,43 @@
+{
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "track": "bit-supplier",
+  "seed": 4,
+  "claim": "https://github.com/CrocSwap/integer-mult-bounds/pull/4062#issuecomment-6268379494",
+  "predecessors": [
+    {
+      "pr": 4025,
+      "head": "84bd28ef6da3a3473d14a48088f30ba82d414450",
+      "author": "ToikY",
+      "role": "Shared traversal for a fixed d\u00b2 high_power; credited mechanism precedent. Not imported."
+    },
+    {
+      "pr": 4062,
+      "head": "d7df855fc64525b43bfda7e7a24b17356d6c1d0e",
+      "author": "Chris R / Clear1nsight",
+      "role": "Complete Context/directory/admission preparation interval and released geometry/extents handoff. Not imported."
+    },
+    {
+      "pr": 2753,
+      "head": "7dba5452a4071a856a0b11cebdcd2d3b6bcd7659",
+      "author": "David Arias",
+      "role": "Actual ordered child geometry and Layout.child_extents, retained canonically in PR2809."
+    },
+    {
+      "pr": 2809,
+      "head": "e7d93dd0de0bb81308bc3356f65eddeeb22fd712",
+      "author": "Jose Manuel / jmbarrancoml",
+      "role": "Fixed-role physical caller and frozen Word/Count/Counter/Geometry closure."
+    }
+  ],
+  "overlap": {
+    "open_pr_bodies": 772,
+    "scope": "Complete open body pagination including drafts; current1166 and12 recently updated discussion threads; exact4025/4062/4011/4059/4067 sources/comments. Broader closed/private/code coverage is partial."
+  },
+  "scope": "Only the new isolated package. Eight canonical runtime inputs are authenticated before execution; pending PRs supply handoff/provenance, not executable dependencies.",
+  "publication_refresh": {
+    "canonical_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+    "recent_updated_pr_bodies": 100,
+    "parent_head": "d7df855fc64525b43bfda7e7a24b17356d6c1d0e",
+    "parent_comments": "The current comments contain our narrow claim; no competing claim or objection observed."
+  }
+}
diff --git a/research/encoded-child-spectators/PROOF.md b/research/encoded-child-spectators/PROOF.md
new file mode 100644
index 0000000000..0e4bbcf04f
--- /dev/null
+++ b/research/encoded-child-spectators/PROOF.md
@@ -0,0 +1,218 @@
+# Encoded shared atom powers at the child-spectator boundary
+
+## 1. Statement and exact source boundary
+
+Let q be the fixed source radix, let the admitted Ring modulus be A=q^w,
+w>=1, and let each e_i be a borrowed canonical unsigned Word of width I.
+For one to three distinct owned Count outputs v_i, the operation computes
+
+`v_i <- v_i * A^(e_i)`.
+
+The e_i and Ring/arena inputs return byte-for-byte unchanged at canonical
+head 1. The caller supplies, or the setup creates, one distinct owned blank
+counter role. It is returned blank at head 1, including its erased visited
+backing. This is not an arbitrary-dirty loan. Output and workspace aliases
+are rejected. Fixed output-role selection and fixed q are compile-time data;
+e_i and w are never decoded into host integers or loop bounds.
+
+The actual source is the eight-file closure in SOURCES.json, at canonical
+base 20ecf2891d80b5acf18d980b2164fb44ea7faa90. Authentication checks its sealed
+inventory, complete SHA256 and Git blob pins before executing any source.
+The private Counter class contains the exact frozen class AST, with only
+its Tape constructor bound to the single reusable blank role. The full Word,
+Count, Natural, Counter, radix, Layout and Geometry methods are retained.
+Only Geometry is extracted from numeric.py; native forms, source admission
+and Callback are deliberately not imported or certified here.
+
+The claim is successful valid-input source-method equivalence and an exact
+source-action delta. It is not complete physical machine refinement, a full
+caller/supplier admission or a multiplication exponent improvement.
+
+## 2. Algorithm and encoded-loop proof
+
+The old multiply_atom_power does the following for each output separately:
+
+1. Create a Counter from e_i.
+2. For each of its e_i decrements, run the complete radix_power validator.
+3. On each of that validator's w yields, multiply v_i by fixed q.
+4. Close the Counter and every validator temporary.
+
+The new multi-power method first constructs and immediately closes a Counter
+for each e_i, using only its finished Boolean to select zero versus positive.
+If all are zero it returns, matching the old absence of a radix traversal.
+Otherwise it runs one complete radix_power. At each yield it independently
+counts down every positive e_i and multiplies its v_i by q once per decrement.
+The new iteration order is radix digit, output role, atom. The former order
+was output role, atom, radix digit.
+
+Each v_i is multiplied by q exactly w*e_i times in either word. These
+multiplications commute, touch no other v_j, and leave each Count head
+canonical. Therefore the exact result is v_i*q^(w*e_i)=v_i*A^(e_i).
+For each individual output, its sequence of Count values and Count primitive
+operations is identical, even though operations on different outputs are
+interleaved differently. Thus all Count multiplication work is unchanged.
+The source radix validator is exhausted exactly once if any exponent is
+positive; its prime-power checks and final cleanup remain active.
+
+Counter construction copies the complete encoded Word, including padding;
+decrement uses a finite borrow flag; multiplication by q uses a carry bounded
+in terms of fixed q. The active-role list has at most three entries. There
+is no numerical-width-dependent control table or cached host value of w/e_i.
+
+After each Counter.close, the canonical body and every previously visited
+body cell of its role are blank. Initially the role is blank. By induction
+the next exact Counter constructor sees the same empty entrance as the
+original Tape constructor supplied. Old erased suffix cells remain charged
+backing. The one-role reuse is therefore an explicit sequential lifecycle,
+not a sum-of-live-sizes claim that forgets retained cells.
+
+## 3. Exact counter tariff
+
+Vectors below are `(reads,writes,unit moves)` in one source-action lane.
+Let b=bitlength(e), z=I-b. Counter construction reads the I-bit input once
+through its full source loops and trims high zero digits. Its record invoice is
+
+```
+J(0,I) = (2I+5, 3I+3, 4I+8),
+J(e,I) = (2I+3, I+1+2z, 2I+4+2z),  e>0.
+```
+
+The input Word copy has the separate **index** invoice
+
+`C(I) = (3I+3, 0, 2I+4)`.
+
+For example, the initial rewind reads LEFT and moves twice. The I digit
+iterations read the Word twice per digit and move once, the terminating
+RIGHT test reads once, and the final rewind reads I+1 cells and moves I+2.
+No numerical Word writes are omitted.
+
+Closing a positive, not-yet-consumed Counter with B=bitlength(e) costs
+`(2B+5,B+1,2B+6)` record actions. For zero use B=1. Define
+
+`P(e,I) = J(e,I) + (2 max(1,b)+5, max(1,b)+1, 2 max(1,b)+6)`
+
+as the complete probe constructor/close invoice. A fully consumed Counter
+ends as ZERO,RIGHT; its close costs `(7,2,8)`.
+
+For a decrement from k>0, let t be the number of trailing zero bits.
+
+| k class | Record decrement invoice |
+| --- | --- |
+| k=1 | (6,4,8) |
+| k=2^j, j>=1, B=j+1 | (2B+3,B+2,2B+4) |
+| otherwise | (2t+5,t+1,2t+4) |
+
+Since `sum_(k=1)^e v2(k)=e-popcount(e)`, summing these classes gives
+
+`D(e)=(7e-2popcount(e)+1, 2e-popcount(e)+2b+1, 6e-2popcount(e)+2b+2)`.
+
+The complete rundown tariff is `R(0,I)=P(0,I)` and, for e>0,
+`R(e,I)=J(e,I)+D(e)+(7,2,8)`. The independent checker instead sums the
+individual decrement cases, importing neither this closed-form implementation
+nor the primary/runtime code. The control suite additionally compares both
+formulas with the real source Counter at 26 zero/power-of-two/neighbor cases.
+
+## 4. Complete source-action difference
+
+Let E=sum e_i, k be the number of positive exponents, and rho the complete
+residue-Word invoice of one source radix_power validator at the actual
+modulus and Word width. Put u=1 if k>0, otherwise 0. Old-minus-new differences are
+
+```
+residue:  (E-u) rho,
+index:    -w*k*C(I),
+record:   sum_i R(e_i,I) - sum_i P(e_i,I) - w*sum_(e_i>0) R(e_i,I).
+```
+
+The old implementation has one Counter per exponent and E radix traversals.
+The new method has all probes plus w rundowns per positive exponent, sharing
+one radix traversal. All output Count operations cancel from the difference.
+These equations include every additional probe, index copy, countdown and
+clear; negative lanes are retained. The verifier meters rho independently
+outside the compared interval, with every validator allocation and cleanup.
+Its value is not supplied by a presumed O(1) arithmetic primitive.
+
+This is not a universal cost improvement. With one exponent e=1,w=1, both
+methods have one radix traversal and one rundown, while the new one adds a
+probe and index copy. The complete same-output losing control executes both.
+Use the exact formula to establish affordability at a proposed source site;
+any runtime selector or new parameter guard has its own implementation cost.
+
+## 5. Actual Layout.child_extents integration
+
+For parent width n, f=floor(n/64), delta=n-64f, define the unchanged physical
+embedding phi(x)=x for x<64f and phi(x)=x+2delta otherwise. For child starts
+a=phi(first), b=phi(second), width c, the method validates c>0, disjointness,
+body bounds, physical contiguity of both complete chunks, and that no chunk
+crosses the original external gap. It then forms powers with exponents
+
+`e=(a, b-a-c, 2n-b-c)`.
+
+Before the gap factor is installed, the three Counts are
+`(B*A^e0, A^e1, S*A^e2)`. Exactly one receives G: the first if a>=n, the
+last if b+c<=n, otherwise the middle. Consequently
+
+`B' G' S' A^(2c) = B G S A^(2n)`.
+
+More strongly, the unchanged phi and complete source guards preserve the
+ordered three spectator regions, not merely their volume. Returned Counts
+retain the source's one-high-zero marginal format and canonical heads.
+
+The adapter authenticates the complete Layout source and rewrites only its
+three power-call expressions. The first two become deferred no-ops; the third
+invokes the shared method on all three output/exponent pairs. All exponents
+and output Counts are live at that point, before any gap multiplication or
+release. Their intervening arithmetic depends only on geometry, not on the
+Count values. It is therefore legal to defer the first two updates. Every
+other statement, rejection guard, marginal conversion and finally cleanup
+remains from the exact frozen method. The rewrite fails unless it finds the
+expected three complete argument lists in source order.
+
+## 6. Measured interval and completed coverage
+
+Each comparison starts with the same canonical borrowed size/depth/child
+Words, modulus/Ring, before/gap/suffix Counts, templates and unused spectator
+Word. It includes the encoded size/64 division, real Geometry and Layout
+construction, fields=depth+1, complete child_extents, marginal output disposal,
+and geometry/field/column cleanup. Both variants preserve every borrowed byte,
+head and live numerical owner; all newly created record and numerical backing
+is erased. The observer checks full serialization without influencing runtime
+control, and Word.inspect raises during the measured computation.
+
+Fifteen pairs cover good, across-bank unit, head/tail pair and head/tail half
+geometry at w=1 and3; a width 70 internal-child geometry; q=5 and an even-column
+case; and the no-remainder/rank 42 boundary. OS seed 4 selects the nonunit
+spectators. These are admissible geometry instances, not claims of literal
+top-level reachability of every chosen current native source or of a complete
+selected GL64 payload. q=3/5 fixtures do not instantiate the asymptotic large-q
+supplier hypothesis. The identity/cost equations are uniform on their stated
+valid-input domain; finite timings are additional observations only.
+
+The named pairs save between about 28.49% and59.20% of complete source actions.
+The width 70 pair is7,046,111→5,038,964 (28.49%). Each tested pair has the same
+additional per-bank numerical peaks (index 21,residue 6). This does not prove
+a complete joint physical reserve. Counter-role backing and all other newly
+created source record backing are retained in the receipts, including erased
+cells. No arbitrary dirty array is silently cleared or acquired.
+
+## 7. Remaining boundaries and failure scope
+
+The action units are retained source Tape/Word reads, writes and unit moves.
+Python execution times in TIMINGS.json are single same-input observations;
+there is no claimed physical-step tariff, stable wall-clock speedup or optimality.
+The loop/control compiler, finite-q source setup, actual allocator and original
+root-width stock retain their own costs. A supplied blank record role is not
+a free dirty register. Malformed modulus contexts still reject, but the source
+validator can retain its failing quotient/remainder, and loop interchange can
+change partial outputs before rejection. Full malformed-input/interrupt rollback
+is outside the successful admitted-input equivalence.
+
+This fills the encoded atom-power/child-geometry component left separate by
+PR4025/4062. Context/directory/admission composition, source-bound whole payload
+handoff, coefficients, native routing, copied state, physical lifetime maxima,
+precision and full supplier admission remain separate. No κ is inferred.
+
+Credit: Jose Manuel/jmbarrancoml, David Arias/PR2753, ywz65/PR2590,
+ToikY/PR4025, Chris R/Clear1nsight/PR4062 and the retained source/record/caller
+lineage. Tekalign (`tekuuu`) with substantial OpenAI Codex assistance;
+Apache-2.0. Frozen inputs are unchanged.
diff --git a/research/encoded-child-spectators/README.md b/research/encoded-child-spectators/README.md
new file mode 100644
index 0000000000..c4373db5f3
--- /dev/null
+++ b/research/encoded-child-spectators/README.md
@@ -0,0 +1,114 @@
+# Encoded shared atom powers for recursive child spectators
+
+The actual BIT caller builds three spectator cardinalities through repeated
+`radix_power` traversals. This package moves that traversal outside the runtime
+atom loop and shares it across all three powers. The exponents stay encoded;
+one reusable blank counter role replaces repeated validator work.
+
+This fills the **child-geometry component** explicitly left open by
+[PR4025](https://github.com/CrocSwap/integer-mult-bounds/pull/4025) and
+[PR4062](https://github.com/CrocSwap/integer-mult-bounds/pull/4062).
+It supplies an opt-in kernel, an adapter to the **actual frozen
+`Layout.child_extents` method**, and a complete source-action comparison.
+It does not supply the complete recursive caller or a new κ.
+
+| Same complete geometry/cleanup input | Original actions | Shared actions | Reduction |
+| --- | ---: | ---: | ---: |
+| Internal-child width 70, n=321, q=3, w=2 | 7,046,111 | 5,038,964 | 28.49% |
+| q=5, even columns, w=2 | 2,334,453 | 1,042,650 | 55.34% |
+| No remainder, rank 42, w=1 | 84,977 | 34,668 | 59.20% |
+
+Across the fifteen declared pairs the reduction is about 28.49%–59.20%.
+These totals sum retained **record, residue-Word and index-Word** reads,
+writes and unit moves. Added probes, counters, copies, marginal conversions
+and disposal are charged. They are not physical-machine step counts or a
+measured production-runtime speedup. The tested additional per-bank numerical
+peaks remain index 21/residue 6. No complete physical reserve follows.
+
+## Component API and exact budget
+
+`Powers(env, workspace=None).multiply(items, ring, q)` accepts one to three
+fixed pairs `(owned_count, borrowed_exponent_word)`. It maps each Count v to
+`v*(q^w)^e`, preserves the Ring/exponent inputs at their canonical heads,
+and returns its distinct **owned blank** counter role erased at head 1.
+A caller can provide an existing blank role; arbitrary dirty acquisition is
+not implemented. `runtime.adapt(env,powers)` returns the source-method adapter
+without changing the original method or frozen files. The reference loader
+uses a private interpreter/module context; this is a research component,
+not shared-caller installation.
+
+For E=sum(e), k positive exponents and complete radix invoice rho, the exact
+old-minus-new residue invoice is `(E-1)*rho` when k>0. The extra index bill
+is `w*k*(3I+3,0,2I+4)`; the complete counter delta has a closed form in
+[PROOF.md](PROOF.md). It is checked against individual trailing-zero cases
+and actual source Counters. Counter costs are not treated as free.
+
+A **same-output exponent-one losing control** demonstrates why this is not
+a universally faster primitive. Future callers must prove the complete
+budget at their site, including any dispatch rule, instead of replacing
+all powers indiscriminately.
+
+## Reproduce
+
+From the repository root, Python 3.12, standard library only:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/encoded-child-spectators
+```
+
+Expected markers: `PASS_ENCODED_CHILD_SPECTATORS`,
+`PASS_INDEPENDENT_CHILD_SPECTATORS`, `PASS_CHILD_SPECTATOR_CONTROLS`, then
+`PASS_REGISTERED_RESEARCH_PACKAGE`. Normal replay is read-only; receipt
+creation with `verify.py --write` refuses an existing destination.
+
+[CERTIFICATE.json](CERTIFICATE.json) records all paired bytes, complete
+lane invoices, ownership/head restoration, erased backing and geometry.
+[TIMINGS.json](TIMINGS.json) records single same-input Python observations;
+timing values are not mathematical acceptance fields.
+
+Coverage includes all six source child-geometry branches at w=1/w3, remainder
+and gap placements, width 70 (above the recursive cutoff), q=5 and rank 42.
+These are valid geometry instances, not complete production packets or a
+proof of every chosen source's top-level reachability. The independent
+checker imports no runtime/primary code. It rederives geometry and counter
+accounting, taking rho as the measured validator invoice rather than
+reimplementing the source's full Ring arithmetic. Controls include real source
+geometry guards, 26 Counter tariff calibrations, omitted output work,
+alias/reentrancy, invalid radix detection, source/inventory corruption,
+typed receipts and overwrite refusal. Word.inspect is disabled during the
+measured interval. Error detection is retained; full malformed-input or
+interruption rollback is not claimed.
+
+Exact base: `20ecf2891d80b5acf18d980b2164fb44ea7faa90`.
+[SOURCES.json](SOURCES.json) seals eight canonical live files; all are checked
+before source execution. [CONTEXT.json](CONTEXT.json) pins predecessor heads
+and the claim. OS seed 4 selects the BIT track and nonunit spectator cases.
+Frozen predecessors and the selected frontier remain unchanged.
+
+## Open next questions
+
+Compose this adapter with #4062's actual Context/directory/admission interval,
+using one existing blank counter role, then pay fixed capsule and payload
+copies and all lifetime backing. That is the next concrete join; a tiny
+controlled payload does not establish the full production caller.
+
+Prove a useful source-coupled parameter region from the exact action formula,
+including any encoded original/shared dispatch. The existing finite savings
+do not establish a global speedup. Physical control/allocator tariffs,
+original-width stock, whole payload/source admission and supplier transfer
+remain separate. Structured first steps and blockers are in [TASK.json](TASK.json).
+
+## Credit
+
+David Arias/PR2753 supplied ordered child geometry and the logical caller;
+Jose Manuel/jmbarrancoml supplied the fixed-role caller and retained runtime.
+ToikY/PR4025 supplied the fixed-d² shared-radix precedent, following ywz65/PR2590;
+Chris R/Clear1nsight/PR4062 supplied the preparation composition and released
+geometry handoff. All retained source/record/codec/caller attribution remains
+with the unchanged originals. This extends the mechanism to **runtime encoded
+atom exponents and the actual three-spectator method**; it does not re-claim
+the fixed-d² result.
+
+Tekalign (`tekuuu`), substantial OpenAI Codex assistance in design, tariff
+proof, implementation, controls and packaging. Apache-2.0. Exact finite
+checks are not independent human review or formal multiplication verification.
diff --git a/research/encoded-child-spectators/SOURCES.json b/research/encoded-child-spectators/SOURCES.json
new file mode 100644
index 0000000000..32e976d4de
--- /dev/null
+++ b/research/encoded-child-spectators/SOURCES.json
@@ -0,0 +1,66 @@
+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/layout.py",
+      "usage": "input",
+      "git_blob": "aa554b14fe0f6b308d9fba0a2afc92e5a28e20cb",
+      "sha256": "3beef6534b02c3b011b741f957a7d9fb05a9ac0bba1fed53b2c71834e4ea6bc1"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/cardinal_counts.py",
+      "usage": "input",
+      "git_blob": "6a14feac45094ae9156e8c2c982d6727544f180e",
+      "sha256": "59ddeac102a0cc51fa49b15aae6aeb68cd68ed217fa974ce916372a177d2ec8f"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/cardinality.py",
+      "usage": "input",
+      "git_blob": "b8ba857e32c5903408e1e61ff916300848b4a208",
+      "sha256": "505d5e560c5a507e6184edcc19a87cf1fed243eb34a5cb21fbe1e4fe017e7f22"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/counts.py",
+      "usage": "input",
+      "git_blob": "81b48940ce222290a40d4fb349ce827f4788469d",
+      "sha256": "00b476dbda0e8cc99886bf794439e1cb9e775f435f599a3557e99321fe084069"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/numeric.py",
+      "usage": "input",
+      "git_blob": "6d4ebca8398008375b8f4762d1a9f1514e8c2611",
+      "sha256": "7327b05c4ec3e0f6d9c352cc7de85bfd4ebe940482553e77c59a773a8c09c514"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/records.py",
+      "usage": "input",
+      "git_blob": "4f00467a0ff580954ad2fd0c7380240c753ddef3",
+      "sha256": "0c9c4b23e998597fb877bb1a29da69ac869b68262abe635b162b4dba9c69b372"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/stream.py",
+      "usage": "input",
+      "git_blob": "5e5a4bb0f98971447043e25d4dd6991bfc070389",
+      "sha256": "c7dc7da5b00f27016982ada4c0416f8328568b00df16d97012f33d4b372d79b5"
+    },
+    {
+      "path": "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/words.py",
+      "usage": "input",
+      "git_blob": "8d4ba37e2778acb35b34e0719df2caf138fbeb50",
+      "sha256": "5c37f57708ba3131bdcb03139f9dbc29886bee44569c09cbba51b68f75acd7f9"
+    }
+  ]
+}
diff --git a/research/encoded-child-spectators/TASK.json b/research/encoded-child-spectators/TASK.json
new file mode 100644
index 0000000000..3dba6e551d
--- /dev/null
+++ b/research/encoded-child-spectators/TASK.json
@@ -0,0 +1,70 @@
+{
+  "schema_version": 1,
+  "task_id": "bit-helper-contract",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "bit-helper-contract",
+    "question": "Can one precisely specified helper-mixing word satisfy a replacement for the inherited H2/K interface?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/r439-bsection-stars-seed01/README.md",
+      "research/r439-copy-path-sharing-barrier/README.md"
+    ],
+    "methods": [
+      "Derive a replacement interface lemma and price its implementation.",
+      "Seek an exact dirty-input or chronological-cut counterexample to the proposed replacement."
+    ],
+    "acceptance_gate": "A full boundary contract and paid profile; unchanged scalar counts alone are insufficient. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/r439-bsection-stars-seed01/verify.py"
+      ],
+      "expected": "PASS_R439_BSECTION_STARS",
+      "inspect": "Compare the two false H2/K flags with the unchanged paid profile in its README.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Write one replacement H2/K implication for a single helper-star operation, then try to falsify it on dirty inputs.",
+    "bottleneck_link": "A legitimate replacement could admit a cheaper bit circuit; scalar savings alone do not alter the selected moment.",
+    "allowed_variations": [
+      "Choose one helper-star or quartet instance; narrow to one boundary implication."
+    ],
+    "scope_change_triggers": [
+      "Changing only source count or scalar addition count without an interface argument."
+    ],
+    "overlap_terms": [
+      "H2_D_frame0_targets_from_helpers",
+      "K_equals_D",
+      "helper-star"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Share the complete encoded radix traversal across runtime atom exponents and all three recursive child spectator powers, preserving the actual Layout.child_extents contract and exact source-action/lifetime invoices.",
+  "scope_change_reason": "OS seed4 assigns BIT supply. The card concerns helper interfaces; the current released #4025/#4062 handoff identifies the adjacent concrete metadata preparation gap. The selected result is an opt-in encoded arithmetic/geometry implementation, not a changed helper word or general compiler admission.",
+  "bottleneck_link": "The actual recursive caller constructs three large spectator cardinalities through repeated radix validators. A reusable multi-power operation removes those repeated numerical traversals while pricing added counters, so the preparation and CALL/RETURN contributors can use a concrete source-bound component.",
+  "budget_minutes": 60,
+  "stop_rule": "Finish the uniform successful-input identity and complete operation delta; fifteen before/after geometry pairs covering all six source shapes, precision1/3, a width70 recursive boundary and q5; separate integer/counter oracle; correctness and cost-negative controls. Do not expand to complete payload transport, physical dispatch, original-width stock or kappa.",
+  "outcome": "completed",
+  "evidence": "CERTIFICATE.json contains the complete paired action and restoration receipts. PROOF.md gives the loop and counter-tariff proof; independent.py imports no runtime or primary implementation; controls.py includes source failures and same-output cost loss.",
+  "author": "Tekalign (tekuuu), with substantial OpenAI Codex assistance",
+  "ai_assistance": "Substantial OpenAI Codex assistance in kernel/adapter design, exact counter tariff derivation, code, proof, controls and packaging. No human peer review or formal-kernel acceptance is claimed.",
+  "open_questions": [
+    {
+      "question": "Can the preparation composition consume this geometry adapter at one whole actual recursive handoff?",
+      "why_it_matters": "The source-method interval is ready to use, but current #4062 excludes extents and handoff copies.",
+      "first_step": "Supply an existing owned blank counter role, compose the returned marginal extents with #4062 context/directory/admission, and include fixed capsule copies, payload lengths and all teardown.",
+      "blocked_by": "Literal full production reachability, complete physical control/allocator tariffs and original-width stock remain separate; a tiny controlled payload is not that proof."
+    },
+    {
+      "question": "Which source-coupled parameter region guarantees a positive whole-method saving?",
+      "why_it_matters": "The added counters make exponent-one kernel calls slower even though the same-output identity holds.",
+      "first_step": "Use the exact action-delta theorem with the actual source root/history/index-width coupling; include any encoded dispatch that chooses original versus shared powers.",
+      "blocked_by": "The present15 cases are finite completed coverage, not a universal speedup or free runtime parameter-selection rule."
+    }
+  ],
+  "assignment_seed": 4,
+  "assignment_seed_source": "Operating-system randomness,2026-10-19T13:18:35.810663+00:00. It selects the BIT track and seeds the nonunit spectator witnesses.",
+  "orientation_baseline": "Attempted python3 -B scripts/research_baseline.py; sparse checkout lacks research/complex-sw4-frame8. This source-inventory orientation failed; no selected cold replay is claimed. All8 actual replay inputs are present and pinned."
+}
diff --git a/research/encoded-child-spectators/TIMINGS.json b/research/encoded-child-spectators/TIMINGS.json
new file mode 100644
index 0000000000..9d97cda48d
--- /dev/null
+++ b/research/encoded-child-spectators/TIMINGS.json
@@ -0,0 +1,95 @@
+{
+  "environment": "CPython3.12.14/Linux; single same-input observations, not a stable runtime speedup claim.",
+  "seconds": [
+    {
+      "case": "good",
+      "precision": 1,
+      "original": 0.1922826640002313,
+      "shared": 0.1141907219971472
+    },
+    {
+      "case": "unit-across",
+      "precision": 1,
+      "original": 0.17906486799984123,
+      "shared": 0.08954453699698206
+    },
+    {
+      "case": "pair-head",
+      "precision": 1,
+      "original": 0.24648311700002523,
+      "shared": 0.15203634799763677
+    },
+    {
+      "case": "pair-tail",
+      "precision": 1,
+      "original": 0.18684801700146636,
+      "shared": 0.08634001899918076
+    },
+    {
+      "case": "half-head",
+      "precision": 1,
+      "original": 0.2493441669976164,
+      "shared": 0.1651440760033438
+    },
+    {
+      "case": "half-tail",
+      "precision": 1,
+      "original": 0.19629453599918634,
+      "shared": 0.08865573000002769
+    },
+    {
+      "case": "good",
+      "precision": 3,
+      "original": 1.3255489249968377,
+      "shared": 0.8883866899996065
+    },
+    {
+      "case": "unit-across",
+      "precision": 3,
+      "original": 1.259572336999554,
+      "shared": 0.6892865789995994
+    },
+    {
+      "case": "pair-head",
+      "precision": 3,
+      "original": 1.89642437600196,
+      "shared": 1.28900153900031
+    },
+    {
+      "case": "pair-tail",
+      "precision": 3,
+      "original": 1.2186933670018334,
+      "shared": 0.6592229599991697
+    },
+    {
+      "case": "half-head",
+      "precision": 3,
+      "original": 1.9868932479985233,
+      "shared": 1.3572804920004273
+    },
+    {
+      "case": "half-tail",
+      "precision": 3,
+      "original": 1.279704201999266,
+      "shared": 0.7272620199983066
+    },
+    {
+      "case": "recursive-good-width70",
+      "precision": 2,
+      "original": 1.4927622859977419,
+      "shared": 1.0793072640008177
+    },
+    {
+      "case": "q5-even-columns",
+      "precision": 2,
+      "original": 0.4703553899998951,
+      "shared": 0.21433322099983343
+    },
+    {
+      "case": "no-remainder-rank42",
+      "precision": 1,
+      "original": 0.017502282000350533,
+      "shared": 0.00721335399794043
+    }
+  ]
+}
diff --git a/research/encoded-child-spectators/VERIFICATION.md b/research/encoded-child-spectators/VERIFICATION.md
new file mode 100644
index 0000000000..15de5fadd2
--- /dev/null
+++ b/research/encoded-child-spectators/VERIFICATION.md
@@ -0,0 +1,67 @@
+# Reproduction and integration handoff
+
+Kernel/adapter/primary-receipt freeze:
+`69a07699bc39e6f2ea40db446c7f1e165500dcc5`.
+Canonical base: `20ecf2891d80b5acf18d980b2164fb44ea7faa90`.
+Later packaging strengthens independent receipt-type/semantic controls and
+documents the handoff; kernel, adapter, primary receipt and source pins are
+unchanged from that freeze.
+
+On Linux with CPython3.12.14, all three registered commands pass:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/encoded-child-spectators
+```
+
+* 15 full before/after geometry intervals; equal complete marginal bytes,
+  exact integer geometry, borrowed heads/ownership and erased work backing.
+* Separate no-runtime/no-primary-import geometry and trailing-zero Counter
+  oracle; complete read/write/move differences, including negative lanes.
+* 30 control groups, including 26 actual source Counter calibrations, all six
+  source geometry guards in both variants, an omitted-output adapter, same-output
+  cost loss, alias/reentrancy, corrupted or weakened source pins before execution,
+  semantic/typed receipts and CLI overwrite refusal.
+
+The initial scientific 24-file official export/check passed. All three commands
+also passed with `-I -O -B` in a read-only Git-free extraction, PATH pointing to
+a nonexistent directory, and a failing json.py shadow trap in the working
+directory. All26 files (24 payload files, export receipt and shadow trap) were
+unchanged. The stricter final checker/controls are replayed from their final
+committed export before publication. Timing observations are not regenerated
+or used as acceptance fields.
+
+The cheap selected-baseline inventory command was attempted but failed because
+this sparse checkout omits research/complex-sw4-frame8. No complete selected
+cold replay is claimed. All eight inputs used by this package are present and
+matched to exact canonical Git blobs and SHA256 pins before execution.
+
+## Next concrete integration
+
+Use the same authenticated runtime namespace for the layout and its inputs,
+supply one owned blank record role, and bind the returned adapter explicitly:
+
+```python
+powers = Powers(env, workspace=owned_blank_counter_role)
+child_extents = runtime.adapt(env, powers)
+extents = child_extents(layout, first, second, width, before=before)
+```
+
+`env` must refer to the same frozen classes/modules that created the borrowed
+inputs. The reference loader is intended for a private interpreter context;
+do not overlay a second namespace on a running caller. Source authentication
+and Counter-class compilation are fixed-source setup, not an unpriced runtime
+oracle. Returned extents are owned marginal Counts, and the counter role is
+blank at return. The caller still owns their later consumption/disposal costs.
+
+The exact delta formula decides whether a proposed site saves source actions.
+The exponent-one losing control rules out indiscriminate replacement. Compose
+this component with #4062's Context/directory/admission work, then include the
+actual fixed handoff/payload copies and all backing at original widths.
+Do not equate a legal geometry fixture with a completed production packet.
+
+Physical dispatch/allocator tariffs, dirty acquisition, whole source/native
+admission, full reserve/stock, approximate numerical precision and supplier
+transfer remain separate. A malformed modulus still rejects, but no stronger
+source rollback guarantee is introduced. No κ or production speedup is claimed.
+
+Tekalign with substantial OpenAI Codex assistance; Apache-2.0.
diff --git a/research/encoded-child-spectators/VERIFY.json b/research/encoded-child-spectators/VERIFY.json
new file mode 100644
index 0000000000..9b1f60364d
--- /dev/null
+++ b/research/encoded-child-spectators/VERIFY.json
@@ -0,0 +1,48 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/selected-bit-physical-caller/inputs/pr2753/layout.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/cardinal_counts.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/cardinality.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/counts.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/numeric.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/records.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/stream.py",
+    "research/selected-bit-physical-caller/inputs/pr2753/predecessor/vendor/words.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "All15 identical-input original/shared geometry intervals, exact output bytes, all source actions including counter overhead, independent delta, borrowed heads/ownership and erased backing."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/independent.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "No primary/runtime imports: direct integer geometry and marginal decoding plus individual trailing-zero-class counter accounting; all15 complete invoice differences."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/controls.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Actual source Counter tariff calibrations; six source geometry guards in both variants; incomplete-adapter, non-prime-power, alias/reentrancy, typed/source/inventory/overwrite rejections; same-output exponent-one losing control."
+    }
+  ]
+}
diff --git a/research/encoded-child-spectators/bench.py b/research/encoded-child-spectators/bench.py
new file mode 100644
index 0000000000..cbb9366545
--- /dev/null
+++ b/research/encoded-child-spectators/bench.py
@@ -0,0 +1,95 @@
+"""Meter the whole named geometry/child-extents interval, including teardown."""
+from types import SimpleNamespace as NS
+import time
+from runtime import need,load,adapt
+from powers import Powers
+from tariff import predicted
+LANES=('record','residue','index')
+
+
+def actions(m):return [m.reads,m.writes,m.moves]
+def sub(a,b):return [x-y for x,y in zip(a,b)]
+def decode(tape):
+    cells=tape.cells[1:];end=cells.index(3)
+    need(all(x in (0,1) for x in cells[:end]),'observer binary Count')
+    return sum(v<<i for i,v in enumerate(cells[:end]))
+
+
+def run(case,shared):
+    env=load();w=env.words;r=env.records;registry=[]
+    old_init=r.Tape.__init__
+    def observed(t):old_init(t);registry.append(t)
+    r.Tape.__init__=observed
+    q,precision,n=case['q'],case['w'],case['n'];I=case.get('I',max(9,(2*n+128).bit_length()+1))
+    L=(q**precision).bit_length()+1
+    ia=w.Arena(I,128);ra=w.Arena(L,64)
+    modulus=ra.literal(q**precision);ring=w.Ring(modulus)
+    size,depth,first,second,width=[ia.literal(x) for x in (n,case.get('h',2),case['first'],case['second'],case['width'])]
+    before,gap,suffix=[env.cardinal_counts.Count.literal(x) for x in case.get('spectators',(3,5,7))]
+    spectators=(before,gap,suffix)
+    extra=ra.literal(1);extra.head=2
+    protected=[(obj,bytes(obj.cells),obj.head) for obj in [ia.template,ra.template]+list(ia.words)+list(ra.words)+[x.tape for x in spectators]]
+    live=(set(ia.live),set(ra.live));slot_start=(len(ia.words),len(ra.words))
+    prior_tapes=set(map(id,registry))
+    def snapshot():
+        return {'record':[sum(actions(t.meter)[k] for t in registry) for k in range(3)],
+                'residue':actions(ra.meter),'index':actions(ia.meter)}
+    # Measure one complete validator walk outside the compared interval.
+    b=actions(ra.meter);steps=sum(1 for _ in env.cardinality.radix_power(ring,q));rho=sub(actions(ra.meter),b)
+    need(steps==precision,'complete valid q-power radix witness')
+    slot_start=(len(ia.words),len(ra.words))
+    powers=Powers(env) if shared else None
+    method=adapt(env,powers) if shared else env.layout.Layout.child_extents
+    ia.meter.peak_live=len(ia.live);ra.meter.peak_live=len(ra.live)
+    old_inspect=w.Word.inspect;w.Word.inspect=lambda _self:(_ for _ in ()).throw(ValueError('runtime numerical decoding forbidden'))
+    baseline=snapshot();started=time.perf_counter();outputs=[];page=None;layout=None;columns=None;fields=None
+    try:
+        raw=w.Unsigned(ia);divisor=ia.literal(64)
+        columns,remainder=raw.divmod(size,divisor);ia.free_many(divisor,remainder)
+        page=env.Geometry(NS(dimension=64),ia,columns,depth,0,object())
+        layout=env.layout.Layout(page,size,ring,q,*spectators)
+        fields=page.plus(depth,page.one)
+        outputs=method(layout,first,second,width,before=before)
+        result=[decode(x.tape) for x in outputs]  # Checker observation, never runtime control.
+        serialized=[bytes(x.tape.cells).hex() for x in outputs]
+        need(all(x.tape.head==1 for x in outputs),'returned marginal heads')
+        for x in outputs:x.close()
+        outputs=[];layout.close();layout=None;page.close();page=None
+        ia.free_many(columns,fields);columns=fields=None
+    finally:
+        w.Word.inspect=old_inspect;r.Tape.__init__=old_init
+    elapsed=time.perf_counter()-started;final=snapshot()
+    delta={k:sub(final[k],baseline[k]) for k in LANES}
+    need(live==(set(ia.live),set(ra.live)),'all geometry numerical ownership returned')
+    need(all(bytes(obj.cells)==data and obj.head==head for obj,data,head in protected),'all borrowed bytes and heads restored')
+    new_tapes=[t for t in registry if id(t) not in prior_tapes]
+    need(all(t.head==1 and all(v==w.BLANK for v in t.cells[1:]) for t in new_tapes),'all created record backing erased')
+    need(all(word.head==1 and all(v==w.BLANK for v in word.cells[1:]) for bank in (ia,ra) for j,word in enumerate(bank.words) if j not in bank.live),'all released numerical backing erased')
+    if powers:need(not powers.busy,'counter workspace released')
+    f=n//64;delta_n=n-64*f
+    phi=lambda x:x if x<64*f else x+2*delta_n
+    a,b=phi(case['first']),phi(case['second']);c=case['width']
+    exponents=[a,b-a-c,2*n-b-c]
+    need(all(e>=0 for e in exponents),'valid nonnegative complete child spectators')
+    B,G,S=case.get('spectators',(3,5,7));A=q**precision
+    expected=[B*A**exponents[0],A**exponents[1],S*A**exponents[2]]
+    region=0 if a>=n else 2 if b+c<=n else 1;expected[region]*=G
+    need(result==expected,'independent actual ordered geometry values')
+    need(result[0]*result[1]*result[2]*A**(2*c)==B*G*S*A**(2*n),'complete spectator/body volume with external gap exactly once')
+    return {'case':case,'shared':shared,'index_width':I,'residue_width':L,'exponents':exponents,
+            'radix_invoice':rho,'actions':delta,'total_actions':sum(sum(v) for v in delta.values()),
+            'output_hex':serialized,'output_values':[str(v) for v in result],
+            'extra_numerical_peak':{'index':ia.meter.peak_live-len(live[0]),'residue':ra.meter.peak_live-len(live[1])},
+            'new_numerical_slots':{'index':len(ia.words)-slot_start[0],'residue':len(ra.words)-slot_start[1]},
+            'created_record_roles':len(new_tapes),'created_record_backing':sum(len(t.cells) for t in new_tapes),
+            'seconds_observation':elapsed,'borrowed_state_restored':True,'owned_backing_erased':True}
+
+
+def pair(case):
+    old,new=run(case,False),run(case,True)
+    need(old['output_hex']==new['output_hex'],'identical complete returned serialization')
+    expected=predicted(old['exponents'],old['index_width'],case['w'],old['radix_invoice'])
+    actual={k:sub(old['actions'][k],new['actions'][k]) for k in LANES}
+    need(all(actual[k]==list(expected[k+'_saving']) for k in LANES),'exact whole-interval independent delta')
+    return {'original':old,'shared':new,'saving':actual,'predicted_delta':expected,
+            'total_action_saving':old['total_actions']-new['total_actions']}
diff --git a/research/encoded-child-spectators/cases.py b/research/encoded-child-spectators/cases.py
new file mode 100644
index 0000000000..9b3f3e8caa
--- /dev/null
+++ b/research/encoded-child-spectators/cases.py
@@ -0,0 +1,20 @@
+"""Declared finite coverage; seed4 chooses nonunit spectator witnesses."""
+from random import Random
+def cases():
+    out=[];rng=Random(4)
+    for precision in (1,3):
+        n=193;f=3
+        for name,a,b,c in (
+            ('good',0,(128-14)*f,14*f),
+            ('unit-across',2*f,70*f,f),
+            ('pair-head',2*f,6*f,f),
+            ('pair-tail',66*f,70*f,f),
+            ('half-head',4*f,5*f-1,1),
+            ('half-tail',68*f,69*f-1,1)):
+            out.append(dict(name=name,q=3,w=precision,n=n,first=a,second=b,width=c,spectators=rng.sample([3,5,7,11,13,17],3)))
+    out.extend([
+        dict(name='recursive-good-width70',q=3,w=2,n=321,first=0,second=570,width=70,spectators=[1,3,5]),
+        dict(name='q5-even-columns',q=5,w=2,n=129,first=4,second=140,width=2,spectators=[7,11,13]),
+        dict(name='no-remainder-rank42',q=3,w=1,n=64,first=0,second=86,width=42,spectators=[1,1,1]),
+    ])
+    return out
diff --git a/research/encoded-child-spectators/controls.py b/research/encoded-child-spectators/controls.py
new file mode 100644
index 0000000000..bd5d499af8
--- /dev/null
+++ b/research/encoded-child-spectators/controls.py
@@ -0,0 +1,126 @@
+#!/usr/bin/env python3
+"""Actual source failures, all-counter tariffs, losing controls and integrity."""
+import json,sys,subprocess,tempfile,shutil
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE))
+import runtime,bench
+from runtime import need,load,adapt
+from powers import Powers
+from tariff import probe,rundown,index_copy
+from verify import read,canonical
+from independent import check as independent_check
+
+
+def main():
+    passed=[]
+    def rejects(name,fn,text):
+        try:fn()
+        except ValueError as error:
+            need(text in str(error),'wrong rejection '+name+': '+str(error));passed.append(name)
+        else:raise ValueError('accepted '+name)
+    env=load();w=env.words;I=12;arena=w.Arena(I,128)
+    for e in (0,1,2,3,7,8,9,15,16,31,32,63,64):
+        word=arena.literal(e)
+        for probing in (False,True):
+            before=bench.actions(arena.meter);c=env.stream.Counter(word)
+            if not probing:
+                while not c.finished:c.decrement()
+            c.close()
+            expected=probe(e,I) if probing else rundown(e,I)
+            need(bench.actions(c.tape.meter)==list(expected),'complete actual source Counter tariff')
+            need(bench.sub(bench.actions(arena.meter),before)==list(index_copy(I)),'actual Counter encoded-index copy tariff')
+        arena.free(word)
+    passed.append('26-source-counter-tariff-calibrations')
+    # Correctness is not a universal cost claim: an exponent-one kernel has
+    # no removable radix traversal, so the extra probe is an actual loss.
+    def kernel(shared):
+        env=load();w=env.words;ia=w.Arena(9,64);ra=w.Arena(3,64)
+        m=ra.literal(3);ring=w.Ring(m);e=ia.literal(1);v=env.cardinal_counts.Count.literal(7)
+        tapes=[];old=env.records.Tape.__init__
+        def track(t):old(t);tapes.append(t)
+        env.records.Tape.__init__=track
+        start=[bench.actions(ia.meter),bench.actions(ra.meter)]
+        value_start=bench.actions(v.tape.meter)
+        if shared:p=Powers(env);p.multiply([(v,e)],ring,3)
+        else:env.cardinality.multiply_atom_power(v,e,ring,3)
+        total=sum(sum(bench.actions(t.meter)) for t in tapes)+sum(sum(bench.sub(bench.actions(bank.meter),b)) for bank,b in zip((ia,ra),start))+sum(bench.sub(bench.actions(v.tape.meter),value_start))
+        env.records.Tape.__init__=old
+        return bench.decode(v.tape),total
+    a,b=kernel(False),kernel(True)
+    need(a[0]==b[0]==21 and b[1]>a[1],'same-output exponent-one losing control')
+    passed.append('same-output-exponent-one-cost-loss')
+    for name,change,message in (
+        ('zero-width',{'width':0},'positive recursive child width'),
+        ('reversed-chunks',{'first':90,'second':0},'ordered disjoint recursive child chunks'),
+        ('overlapping-chunks',{'first':0,'second':4,'width':14},'ordered disjoint recursive child chunks'),
+        ('outside-complete-body',{'second':128,'width':14},'recursive child lies in the complete body'),
+        ('embedding-discontinuity',{'first':63,'second':90,'width':2},'physically contiguous'),
+        ('original-gap-crossing',{'n':64,'first':63,'second':90,'width':2},'does not cross the original gap'),
+    ):
+        c={'q':3,'w':1,'n':65,'first':0,'second':114,'width':14};c.update(change)
+        for shared in (False,True):rejects(name+str(shared),lambda:bench.run(c,shared),message)
+    class OmitTail(Powers):
+        def multiply(self,items,ring,q):return super().multiply(items[:2],ring,q)
+    saved=bench.Powers;bench.Powers=OmitTail
+    try:rejects('actual-incomplete-three-power-adapter',lambda:bench.run({'q':3,'w':2,'n':193,'first':6,'second':210,'width':3},True),'independent actual ordered geometry values')
+    finally:bench.Powers=saved
+    env=load();ia=env.words.Arena(9,64);ra=env.words.Arena(5,64)
+    modulus=ra.literal(9);ring=env.words.Ring(modulus);e=ia.literal(2);v=env.cardinal_counts.Count.literal(1);p=Powers(env)
+    rejects('aliased-output-role',lambda:p.multiply([(v,e),(v,e)],ring,3),'disjoint power outputs')
+    alias=Powers(env,v.tape)
+    rejects('counter-output-alias',lambda:alias.multiply([(v,e)],ring,3),'counter workspace separate from outputs')
+    zero=ia.literal(0);original_radix=env.cardinality.radix_power
+    env.cardinality.radix_power=lambda *_args:(_ for _ in ()).throw(ValueError('zero exponent must not validate modulus'))
+    try:
+        original=bytes(v.tape.cells);p.multiply([(v,zero)],ring,3)
+        need(bytes(v.tape.cells)==original,'zero exponent preserves full Count serialization')
+    finally:env.cardinality.radix_power=original_radix
+    passed.append('zero-exponent-preserves-source-no-validation-path')
+    p.busy=True;rejects('reentrant-counter-workspace',lambda:p.multiply([(v,e)],ring,3),'non-reentrant');p.busy=False
+    bad=ra.literal(12);bad_ring=env.words.Ring(bad);initial=(set(ia.live),set(ra.live))
+    rejects('non-prime-power-validator',lambda:p.multiply([(v,e)],bad_ring,3),'cardinality prime-power context')
+    need(not p.busy and p.workspace.head==1 and all(x==env.words.BLANK for x in p.workspace.cells[1:]),'failed validator returns private record role')
+    # The inherited validator can retain its failing quotient/remainder. Its
+    # rejection is preserved; full malformed-input rollback is not claimed.
+    ra.rollback(initial[1])
+    rejects('legacy-non-prime-power-validator',lambda:env.cardinality.multiply_atom_power(v,e,bad_ring,3),'cardinality prime-power context')
+    passed.append('failed-validator-private-record-return-only')
+    receipt=read(HERE/'CERTIFICATE.json')
+    for name,path,value,message in (
+        ('free-counter-invoice',('pairs',0,'saving','record'),[0,0,0],'independent complete exact action delta'),
+        ('missing-gap-value',('pairs',0,'shared','output_values'),['1','1','1'],'independent full marginal bytes/values'),
+        ('boolean-counter-width',('pairs',0,'shared','index_width'),True,'typed source widths'),
+        ('floating-action-count',('pairs',0,'total_action_saving'),float(receipt['pairs'][0]['total_action_saving']),'typed complete action gain'),
+    ):
+        bad=json.loads(json.dumps(receipt));cursor=bad
+        for key in path[:-1]:cursor=cursor[key]
+        cursor[path[-1]]=value
+        need(canonical(receipt)!=canonical(bad),'typed full-receipt projection differs')
+        rejects(name,lambda:independent_check(bad),message)
+    with tempfile.TemporaryDirectory(prefix='child-power-controls-') as td:
+        root=Path(td);package=root/'research/encoded-child-spectators';package.mkdir(parents=True)
+        manifest=(HERE/'SOURCES.json').read_bytes();(package/'SOURCES.json').write_bytes(manifest)
+        for row in json.loads(manifest)['files']:
+            if row['usage']!='input':continue
+            target=root/row['path'];target.parent.mkdir(parents=True,exist_ok=True)
+            shutil.copyfile(runtime.ROOT/row['path'],target)
+        saved_here,saved_root=runtime.HERE,runtime.ROOT
+        try:
+            runtime.HERE,runtime.ROOT=package,root;runtime.authenticate()
+            target=root/runtime.PREFIX/'predecessor/vendor/words.py';target.write_text("raise RuntimeError('UNAUTHENTICATED_EXECUTION')\n")
+            rejects('source-corruption-before-execution',runtime.load,'source SHA256')
+            broken=json.loads(manifest);broken['files']=[r for r in broken['files'] if r['path']!=str(target.relative_to(root))]
+            (package/'SOURCES.json').write_text(json.dumps(broken))
+            rejects('source-inventory-removal-before-execution',runtime.load,'sealed source inventory')
+        finally:runtime.HERE,runtime.ROOT=saved_here,saved_root
+        duplicate=root/'duplicate.json';duplicate.write_text('{"x":1,"x":2}')
+        rejects('duplicate-receipt-key',lambda:read(duplicate),'duplicate receipt key')
+    before=(HERE/'CERTIFICATE.json').read_bytes()
+    proc=subprocess.run([sys.executable,'-I','-B',str(HERE/'verify.py'),'--write'],capture_output=True,text=True,timeout=10)
+    need(proc.returncode!=0 and 'refuse certificate overwrite' in proc.stderr and (HERE/'CERTIFICATE.json').read_bytes()==before,'CLI overwrite refusal before recomputation')
+    passed.append('CLI-overwrite-refusal')
+    print('PASS_CHILD_SPECTATOR_CONTROLS '+json.dumps({'groups':len(passed),'checks':passed},sort_keys=True))
+
+
+if __name__=='__main__':main()
diff --git a/research/encoded-child-spectators/independent.py b/research/encoded-child-spectators/independent.py
new file mode 100644
index 0000000000..7ae21806d1
--- /dev/null
+++ b/research/encoded-child-spectators/independent.py
@@ -0,0 +1,76 @@
+#!/usr/bin/env python3
+"""Separate integer geometry and per-binary-decrement accounting oracle."""
+import json
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+
+
+def need(ok,msg):
+    if not ok:raise ValueError(msg)
+def add(*rows):return [sum(v) for v in zip(*rows)]
+def mul(n,row):return [n*v for v in row]
+def sub(a,b):return [x-y for x,y in zip(a,b)]
+
+
+def counter(e,I,probe=False):
+    # Count input construction, high-zero trimming, clearing and each actual
+    # binary decrement by its trailing-zero class. No primary/runtime import.
+    b=e.bit_length();z=I-b
+    initial=[2*I+5,3*I+3,4*I+8] if e==0 else [2*I+3,I+1+2*z,2*I+4+2*z]
+    if probe or not e:
+        B=max(1,b);return add(initial,[2*B+5,B+1,2*B+6])
+    steps=[]
+    for k in range(e,0,-1):
+        t=(k&-k).bit_length()-1
+        if k==1:steps.append([6,4,8])
+        elif k&(k-1)==0:
+            B=k.bit_length();steps.append([2*B+3,B+2,2*B+4])
+        else:steps.append([2*t+5,t+1,2*t+4])
+    return add(initial,*steps,[7,2,8])
+
+
+def check(receipt):
+    need(len(receipt['pairs'])==15,'declared fifteen complete pairs')
+    shapes=set();ranges=[]
+    for row in receipt['pairs']:
+        old,new=row['original'],row['shared'];c=old['case'];shapes.add(c['name'])
+        need(type(row['total_action_saving']) is int,'typed complete action gain')
+        need(all(type(r[k]) is int and r[k]>0 for r in (old,new) for k in ('index_width','residue_width')),'typed source widths')
+        need(old['index_width']==new['index_width'] and old['residue_width']==new['residue_width'] and old['case']==new['case'],'same compared input contexts')
+        q,w,n=c['q'],c['w'],c['n'];A=q**w;f=n//64;delta=n%64
+        phi=lambda x:x if x<64*f else x+2*delta
+        a,b=phi(c['first']),phi(c['second']);width=c['width']
+        e=[a,b-a-width,2*n-b-width]
+        need(width>0 and a+width<=b and b+width<=2*n,'actual complete disjoint child chunks')
+        need(phi(c['first']+width-1)==a+width-1 and phi(c['second']+width-1)==b+width-1,'full physical contiguity')
+        B,G,S=c['spectators'];want=[B*A**e[0],A**e[1],S*A**e[2]]
+        region=0 if a>=n else 2 if b+width<=n else 1;want[region]*=G
+        need(e==old['exponents']==new['exponents'],'independent complete spectator exponents')
+        for result in (old,new):
+            need(type(result['total_actions']) is int and all(len(v)==3 and all(type(x) is int and x>=0 for x in v) for v in result['actions'].values()),'typed complete source action lanes')
+            values=[]
+            for encoded in result['output_hex']:
+                raw=list(bytes.fromhex(encoded));need(raw[0]==2,'retained LEFT marker')
+                end=raw.index(3);digits=raw[1:end]
+                need(len(digits)>=2 and digits[-2:]==[1,0] and all(v in (0,1) for v in digits) and all(v==4 for v in raw[end+1:]),'one high zero margin and erased suffix')
+                values.append(sum(v<<i for i,v in enumerate(digits)))
+            need(values==want and list(map(int,result['output_values']))==want,'independent full marginal bytes/values')
+            need(result['borrowed_state_restored'] is True and result['owned_backing_erased'] is True,'complete interval state controls')
+            need(result['total_actions']==sum(sum(v) for v in result['actions'].values()),'three disjoint source-action lanes')
+        I=old['index_width'];active=[v for v in e if v]
+        old_counter=add(*(counter(v,I) for v in e))
+        new_counter=add(*(counter(v,I,True) for v in e),*(mul(w,counter(v,I)) for v in active))
+        expected={'record':sub(old_counter,new_counter),'index':mul(-w*len(active),[3*I+3,0,2*I+4]),
+                  'residue':mul(sum(e)-int(bool(active)),old['radix_invoice'])}
+        need(old['radix_invoice']==new['radix_invoice'],'same complete measured source radix invoice')
+        actual={k:sub(old['actions'][k],new['actions'][k]) for k in expected}
+        need(actual==expected==row['saving'],'independent complete exact action delta')
+        gain=old['total_actions']-new['total_actions']
+        need(gain==row['total_action_saving']>0,'positive complete declared-case saving')
+        ranges.append((gain,old['total_actions']))
+    need({'good','unit-across','pair-head','pair-tail','half-head','half-tail'}<=shapes,'all six source branch geometries')
+    return {'pairs':len(ranges),'branch_shapes':6,'runtime_imports':0,'counter_oracle':'individual trailing-zero cases, not primary closed form'}
+
+
+if __name__=='__main__':
+    print('PASS_INDEPENDENT_CHILD_SPECTATORS '+json.dumps(check(json.loads((HERE/'CERTIFICATE.json').read_text())),sort_keys=True))
diff --git a/research/encoded-child-spectators/powers.py b/research/encoded-child-spectators/powers.py
new file mode 100644
index 0000000000..b22a76cffb
--- /dev/null
+++ b/research/encoded-child-spectators/powers.py
@@ -0,0 +1,38 @@
+"""Encoded atom powers sharing one validated radix walk; no numerical decoding."""
+from runtime import need
+
+
+class Powers:
+    def __init__(self,env,workspace=None):
+        self.env=env
+        # Caller may supply its existing owned blank counter role. This is
+        # not an arbitrary-dirty loan; its clean backing remains charged.
+        self.workspace=env.records.Tape() if workspace is None else workspace
+        self.Counter=env.counter_type(self.workspace)
+        self.busy=False
+
+    def multiply(self,items,ring,q):
+        need(not self.busy,'non-reentrant fixed counter role')
+        need(1<=len(items)<=3,'one to three compiled output roles')
+        need(len({id(value.tape) for value,exponent in items})==len(items),'disjoint power outputs')
+        need(all(value.tape is not self.workspace for value,exponent in items),'counter workspace separate from outputs')
+        self.busy=True;counter=None;walk=None
+        try:
+            active=[]
+            for value,exponent in items:
+                counter=self.Counter(exponent)
+                if not counter.finished:active.append((value,exponent))
+                counter.close();counter=None
+            if not active:return
+            walk=self.env.cardinality.radix_power(ring,q)
+            for _ in walk:
+                for value,exponent in active:
+                    counter=self.Counter(exponent)
+                    while not counter.finished:
+                        value.multiply_small(q)
+                        counter.decrement()
+                    counter.close();counter=None
+        finally:
+            if counter is not None:counter.close()
+            if walk is not None:walk.close()
+            self.busy=False
diff --git a/research/encoded-child-spectators/runtime.py b/research/encoded-child-spectators/runtime.py
new file mode 100644
index 0000000000..56deefc868
--- /dev/null
+++ b/research/encoded-child-spectators/runtime.py
@@ -0,0 +1,86 @@
+"""Authenticate eight canonical inputs before isolated source execution."""
+import ast
+from hashlib import sha1,sha256
+import importlib.util
+import json
+from pathlib import Path
+import sys
+from types import SimpleNamespace
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+SEAL='826d4dcdc29c66b7395bad8de9201dafee12aa5aa0eaf2772b14e621439daf44'
+PREFIX='research/selected-bit-physical-caller/inputs/pr2753/'
+
+
+def need(ok,message):
+    if not ok:raise ValueError(message)
+
+
+def authenticate():
+    raw=(HERE/'SOURCES.json').read_bytes()
+    need(sha256(raw).hexdigest()==SEAL,'sealed source inventory')
+    result={}
+    for row in json.loads(raw)['files']:
+        if row['usage']!='input':continue
+        data=(ROOT/row['path']).read_bytes()
+        need(sha256(data).hexdigest()==row['sha256'],'source SHA256: '+row['path'])
+        need(sha1(b'blob '+str(len(data)).encode()+b'\0'+data).hexdigest()==row['git_blob'],'source Git blob')
+        result[row['path']]=data
+    need(len(result)==8,'complete eight-source closure')
+    return result
+
+
+def source_module(name,path,raw):
+    spec=importlib.util.spec_from_file_location(name,path)
+    module=importlib.util.module_from_spec(spec);sys.modules[name]=module
+    exec(compile(raw,str(path),'exec',optimize=0),module.__dict__)
+    return module
+
+
+def load():
+    data=authenticate();modules={}
+    for name in ('words','records','stream','cardinality','counts'):
+        path=PREFIX+'predecessor/vendor/'+name+'.py'
+        modules[name]=source_module(name,ROOT/path,data[path])
+    path=PREFIX+'predecessor/cardinal_counts.py'
+    modules['cardinal_counts']=source_module('cardinal_counts',ROOT/path,data[path])
+    path=PREFIX+'layout.py'
+    modules['layout']=source_module('layout',ROOT/path,data[path])
+    # Only Geometry is needed. Native forms/Callback/field admission are not
+    # executed, imported, or certified by this child-geometry interval.
+    path=PREFIX+'predecessor/vendor/numeric.py'
+    tree=ast.parse(data[path]);node=next(n for n in tree.body if isinstance(n,ast.ClassDef) and n.name=='Geometry')
+    ns={'Unsigned':modules['words'].Unsigned,'need':need}
+    exec(compile(ast.Module(body=[node],type_ignores=[]),str(ROOT/path),'exec',optimize=0),ns)
+    modules['Geometry']=ns['Geometry']
+    # A private exact Counter class borrows one permanent blank record role.
+    tree=ast.parse(data[PREFIX+'predecessor/vendor/stream.py'])
+    node=next(n for n in tree.body if isinstance(n,ast.ClassDef) and n.name=='Counter')
+    def counter_type(workspace):
+        ns=dict(modules['stream'].__dict__);ns['Tape']=lambda:workspace
+        exec(compile(ast.Module(body=[node],type_ignores=[]),'<pinned-counter>','exec',optimize=0),ns)
+        return ns['Counter']
+    modules['counter_type']=counter_type
+    return SimpleNamespace(**modules)
+
+
+def adapt(env,powers):
+    """Preserve the entire frozen method except its three power invocations."""
+    raw=authenticate()[PREFIX+'layout.py'];tree=ast.parse(raw)
+    cls=next(n for n in tree.body if isinstance(n,ast.ClassDef) and n.name=='Layout')
+    fn=next(n for n in cls.body if isinstance(n,ast.FunctionDef) and n.name=='child_extents')
+    found=[]
+    class Rewrite(ast.NodeTransformer):
+        def visit_Expr(self,node):
+            value=node.value
+            if isinstance(value,ast.Call) and isinstance(value.func,ast.Name) and value.func.id=='multiply_atom_power':
+                found.append(tuple(ast.unparse(a) for a in value.args))
+                if len(found)<3:return ast.copy_location(ast.Pass(),node)
+                return ast.copy_location(ast.parse('_shared([(pre,a),(middle,between),(tail,after)], self.ring, self.q)').body[0],node)
+            return self.generic_visit(node)
+    fn=Rewrite().visit(fn);ast.fix_missing_locations(fn)
+    need(found==[('pre','a','self.ring','self.q'),('middle','between','self.ring','self.q'),
+                 ('tail','after','self.ring','self.q')],'exact three-power source method shape')
+    ns=dict(env.layout.__dict__);ns['_shared']=powers.multiply
+    exec(compile(ast.Module(body=[fn],type_ignores=[]),'<adapted-child-extents>','exec',optimize=0),ns)
+    return ns['child_extents']
diff --git a/research/encoded-child-spectators/tariff.py b/research/encoded-child-spectators/tariff.py
new file mode 100644
index 0000000000..df1efb5aeb
--- /dev/null
+++ b/research/encoded-child-spectators/tariff.py
@@ -0,0 +1,34 @@
+"""Closed-form Counter invoice, independent of the source's loop evaluator."""
+def add(*rows):return tuple(sum(v) for v in zip(*rows))
+def scale(n,row):return tuple(n*v for v in row)
+def minus(a,b):return tuple(x-y for x,y in zip(a,b))
+
+
+def index_copy(width):return (3*width+3,0,2*width+4)
+
+
+def init(exponent,width):
+    if not exponent:return (2*width+5,3*width+3,4*width+8)
+    b=exponent.bit_length();zeros=width-b
+    return (2*width+3,width+1+2*zeros,2*width+4+2*zeros)
+
+
+def probe(exponent,width):
+    b=max(1,exponent.bit_length())
+    return add(init(exponent,width),(2*b+5,b+1,2*b+6))
+
+
+def rundown(exponent,width):
+    if not exponent:return probe(0,width)
+    b=exponent.bit_length();p=exponent.bit_count()
+    decrements=(7*exponent-2*p+1,2*exponent-p+2*b+1,6*exponent-2*p+2*b+2)
+    return add(init(exponent,width),decrements,(7,2,8))
+
+
+def predicted(exponents,width,precision,rho):
+    active=[e for e in exponents if e]
+    old=add(*(rundown(e,width) for e in exponents))
+    new=add(*(probe(e,width) for e in exponents),*(scale(precision,rundown(e,width)) for e in active))
+    return {'record_saving':minus(old,new),'index_saving':scale(-precision*len(active),index_copy(width)),
+            'residue_saving':scale(sum(exponents)-int(bool(active)),rho),
+            'old_radix_traversals':sum(exponents),'new_radix_traversals':int(bool(active))}
diff --git a/research/encoded-child-spectators/verify.py b/research/encoded-child-spectators/verify.py
new file mode 100644
index 0000000000..c8b5ac7575
--- /dev/null
+++ b/research/encoded-child-spectators/verify.py
@@ -0,0 +1,50 @@
+#!/usr/bin/env python3
+"""Exact same-input before/after child spectator construction and invoices."""
+import argparse,json,sys
+from pathlib import Path
+HERE=Path(__file__).resolve().parent
+sys.path.insert(0,str(HERE))
+from runtime import authenticate,need
+from bench import pair
+from cases import cases
+
+
+def read(path):
+    def unique(pairs):
+        out={}
+        for key,value in pairs:
+            need(key not in out,'duplicate receipt key');out[key]=value
+        return out
+    return json.loads(path.read_text(),object_pairs_hook=unique)
+
+
+def canonical(data):return json.dumps(data,sort_keys=True,separators=(',',':'),allow_nan=False)
+
+
+def result():
+    authenticate();rows=[];timings=[]
+    for case in cases():
+        row=pair(case)
+        timings.append({'case':case['name'],'precision':case['w'],
+                        'original':row['original'].pop('seconds_observation'),
+                        'shared':row['shared'].pop('seconds_observation')})
+        need(row['total_action_saving']>0,'complete named-case source-action improvement')
+        rows.append(row)
+    return {'status':'PASS_ENCODED_CHILD_SPECTATORS','base':'20ecf2891d80b5acf18d980b2164fb44ea7faa90',
+            'assignment_seed':4,'domain':'15 stated complete geometry pairs; all6 branch shapes at w1/w3 plus recursive-width/q5/remainder boundary cases.',
+            'pairs':rows,'physical_dispatch_stock_caller':'Not admitted by this geometry/action certificate.'},timings
+
+
+def main():
+    p=argparse.ArgumentParser();p.add_argument('--write',action='store_true');args=p.parse_args()
+    dest=HERE/'CERTIFICATE.json'
+    if args.write:need(not dest.exists(),'refuse certificate overwrite')
+    data,timing=result()
+    if args.write:
+        with dest.open('x') as stream:stream.write(json.dumps(data,indent=2,sort_keys=True)+'\n')
+        with (HERE/'TIMINGS.json').open('x') as stream:stream.write(json.dumps({'environment':'CPython3.12.14/Linux; single same-input observations, not a stable runtime speedup claim.','seconds':timing},indent=2)+'\n')
+    else:need(canonical(data)==canonical(read(dest)),'complete typed spectator receipt')
+    print('PASS_ENCODED_CHILD_SPECTATORS pairs='+str(len(data['pairs'])))
+
+
+if __name__=='__main__':main()