diff --git a/research/staged544-a2-graph-rewrite/.gitattributes b/research/staged544-a2-graph-rewrite/.gitattributes
new file mode 100644
index 0000000000..712e2786b3
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/.gitattributes
@@ -0,0 +1,2 @@
+inputs/*.gz -text
+vendor/SOURCE-CREDITS.md -text whitespace=cr-at-eol
diff --git a/research/staged544-a2-graph-rewrite/.gitignore b/research/staged544-a2-graph-rewrite/.gitignore
new file mode 100644
index 0000000000..7a60b85e14
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/.gitignore
@@ -0,0 +1,2 @@
+__pycache__/
+*.pyc
diff --git a/research/staged544-a2-graph-rewrite/LEDGER.json b/research/staged544-a2-graph-rewrite/LEDGER.json
new file mode 100644
index 0000000000..76f58df35f
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/LEDGER.json
@@ -0,0 +1,260 @@
+{
+  "PR3945_base": {
+    "cleanup_ADD_delta": -1,
+    "coefficient_heights": {
+      "maximum_complete_words_denominator_bits": 4,
+      "maximum_complete_words_numerator_bits": 4,
+      "maximum_replacement_gates_denominator_bits": 1,
+      "maximum_replacement_gates_numerator_bits": 1
+    },
+    "fixed_all_other_top_level_fields": true,
+    "forward_ADD_delta": -1,
+    "fresh_native_phase_or_supplier_admission": false,
+    "rank_mass": 5160,
+    "recursive_children": 3549,
+    "source_head": "91f81d131252db704f945891da1ea54e29d46b8b",
+    "source_profile": {
+      "1": 2482,
+      "2": 712,
+      "3": 218,
+      "4": 109,
+      "5": 20,
+      "8": 8
+    }
+  },
+  "PR3945_extra": {
+    "cleanup_ADD_delta": -1,
+    "coefficient_heights": {
+      "maximum_complete_words_denominator_bits": 4,
+      "maximum_complete_words_numerator_bits": 4,
+      "maximum_replacement_gates_denominator_bits": 1,
+      "maximum_replacement_gates_numerator_bits": 1
+    },
+    "fixed_all_other_top_level_fields": true,
+    "forward_ADD_delta": -1,
+    "fresh_native_phase_or_supplier_admission": false,
+    "rank_mass": 5160,
+    "recursive_children": 3549,
+    "source_head": "91f81d131252db704f945891da1ea54e29d46b8b",
+    "source_profile": {
+      "1": 2482,
+      "2": 712,
+      "3": 218,
+      "4": 109,
+      "5": 20,
+      "8": 8
+    }
+  },
+  "base": {
+    "added_forward_ADDs_per_candidate": 1,
+    "additional_helpers_buffers_native_maps": 0,
+    "baseline_primitives": {
+      "A": {
+        "add": 3557,
+        "scale": 498,
+        "warp": 24
+      },
+      "B": {
+        "add": 1796,
+        "scale": 73
+      },
+      "cleanup": {
+        "add": 4633,
+        "scale": 519,
+        "warp": 72
+      },
+      "compensation": {
+        "add": 5736
+      },
+      "cut": {
+        "add": 176
+      },
+      "precondition": {
+        "add": 136,
+        "scale": 56
+      },
+      "restore": {
+        "add": 196,
+        "scale": 16
+      }
+    },
+    "baseline_profile": {
+      "1": 2440,
+      "2": 725,
+      "3": 224,
+      "4": 102,
+      "5": 20,
+      "8": 8
+    },
+    "boundary_end_sha256": "ebd6650741d3b91cd4c0c7f4c5d5aa680094654768f3c0a0342864ab79c4e5dc",
+    "boundary_start_sha256": "e82d4f3c4e35e6aaf384c90fc7cc3ed89ad939a7760ad5f06aff80a519c7353c",
+    "candidate_rank_masses": [
+      5134
+    ],
+    "candidate_recursive_children_range": [
+      3519,
+      3521
+    ],
+    "changed_B_warp_positions": "Only numerical indices shift after insertion; same ordered warp with same neighbouring scalar events.",
+    "cleanup_added_ADDs": [
+      0,
+      1
+    ],
+    "contraction_cleanup_ADD_deltas": [
+      -1
+    ],
+    "contraction_forward_ADD_delta": -1,
+    "contraction_profiles": [
+      {
+        "1": 2440,
+        "2": 725,
+        "3": 224,
+        "4": 102,
+        "5": 20,
+        "8": 8
+      }
+    ],
+    "dirty_buffers": 91,
+    "helper_roles": 408,
+    "helper_widths": {
+      "4": 26,
+      "5": 2,
+      "6": 18,
+      "7": 53,
+      "8": 96,
+      "9": 213
+    },
+    "initial_operator_corrections": 36,
+    "live_inputs": 632,
+    "maximum_complete_words_denominator_bits": 4,
+    "maximum_complete_words_numerator_bits": 4,
+    "maximum_replacement_gates_denominator_bits": 4,
+    "maximum_replacement_gates_numerator_bits": 3,
+    "native_warps": 72,
+    "new_supplier_or_kappa": false,
+    "proved": [
+      "Exact rational arbitrary-dirty three-register matrix equality for every orientation and coefficient motif",
+      "All compatible frame flags and complete chronological recursive invoice for every legal flag",
+      "Projected non-target matrix equality and literal inverse cleanup for every flag",
+      "All source free-operator symbols plus deterministic full-word sample replay",
+      "Finite primitive and scalar coefficient bounds; fixed roles, entrance/exit frames and native maps"
+    ],
+    "rank_mass": 5134,
+    "recursive_children": 3519,
+    "replaced_ADD_count": 2,
+    "replacement_ADD_count": 3,
+    "unknown": [
+      "Physical allocation/hosting and complete owner schedule after extra ADD",
+      "Fresh Gaussian/Clifford realization and phase admission",
+      "Uniform precision/stock/tape tariff and implementation cost of additional scalar primitives",
+      "All-size compiler, outer/supplier admission, analytic transfer and BIT H1-H5"
+    ],
+    "unknown_costs_are_zero": false
+  },
+  "extra": {
+    "added_forward_ADDs_per_candidate": 1,
+    "additional_helpers_buffers_native_maps": 0,
+    "baseline_primitives": {
+      "A": {
+        "add": 3557,
+        "scale": 498,
+        "warp": 24
+      },
+      "B": {
+        "add": 1796,
+        "scale": 73
+      },
+      "cleanup": {
+        "add": 4633,
+        "scale": 519,
+        "warp": 72
+      },
+      "compensation": {
+        "add": 5736
+      },
+      "cut": {
+        "add": 176
+      },
+      "precondition": {
+        "add": 136,
+        "scale": 56
+      },
+      "restore": {
+        "add": 196,
+        "scale": 16
+      }
+    },
+    "baseline_profile": {
+      "1": 2440,
+      "2": 725,
+      "3": 224,
+      "4": 102,
+      "5": 20,
+      "8": 8
+    },
+    "boundary_end_sha256": "ebd6650741d3b91cd4c0c7f4c5d5aa680094654768f3c0a0342864ab79c4e5dc",
+    "boundary_start_sha256": "e82d4f3c4e35e6aaf384c90fc7cc3ed89ad939a7760ad5f06aff80a519c7353c",
+    "candidate_rank_masses": [
+      5134
+    ],
+    "candidate_recursive_children_range": [
+      3519,
+      3521
+    ],
+    "changed_B_warp_positions": "Only numerical indices shift after insertion; same ordered warp with same neighbouring scalar events.",
+    "cleanup_added_ADDs": [
+      0,
+      1
+    ],
+    "contraction_cleanup_ADD_deltas": [
+      -1
+    ],
+    "contraction_forward_ADD_delta": -1,
+    "contraction_profiles": [
+      {
+        "1": 2440,
+        "2": 725,
+        "3": 224,
+        "4": 102,
+        "5": 20,
+        "8": 8
+      }
+    ],
+    "dirty_buffers": 91,
+    "helper_roles": 408,
+    "helper_widths": {
+      "4": 26,
+      "5": 2,
+      "6": 18,
+      "7": 53,
+      "8": 96,
+      "9": 213
+    },
+    "initial_operator_corrections": 36,
+    "live_inputs": 632,
+    "maximum_complete_words_denominator_bits": 4,
+    "maximum_complete_words_numerator_bits": 4,
+    "maximum_replacement_gates_denominator_bits": 4,
+    "maximum_replacement_gates_numerator_bits": 3,
+    "native_warps": 72,
+    "new_supplier_or_kappa": false,
+    "proved": [
+      "Exact rational arbitrary-dirty three-register matrix equality for every orientation and coefficient motif",
+      "All compatible frame flags and complete chronological recursive invoice for every legal flag",
+      "Projected non-target matrix equality and literal inverse cleanup for every flag",
+      "All source free-operator symbols plus deterministic full-word sample replay",
+      "Finite primitive and scalar coefficient bounds; fixed roles, entrance/exit frames and native maps"
+    ],
+    "rank_mass": 5134,
+    "recursive_children": 3519,
+    "replaced_ADD_count": 2,
+    "replacement_ADD_count": 3,
+    "unknown": [
+      "Physical allocation/hosting and complete owner schedule after extra ADD",
+      "Fresh Gaussian/Clifford realization and phase admission",
+      "Uniform precision/stock/tape tariff and implementation cost of additional scalar primitives",
+      "All-size compiler, outer/supplier admission, analytic transfer and BIT H1-H5"
+    ],
+    "unknown_costs_are_zero": false
+  }
+}
diff --git a/research/staged544-a2-graph-rewrite/PROOF.md b/research/staged544-a2-graph-rewrite/PROOF.md
new file mode 100644
index 0000000000..afa6241fda
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/PROOF.md
@@ -0,0 +1,206 @@
+# Consecutive A2 graph rewrites with fixed staged544 boundaries
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+
+## Scope and statement
+
+The inputs are the exact `43base` and `43extra` PR3734 BORROW-WORDs at
+`fa041037a3374eaa08feeca0b26a5d6893194147`. The domain consists of consecutive
+nonzero ADD pairs in A **after** `prelude_events`, B strictly inside the intervals
+cut by native warp positions, and restore. A prelude, native warp, or intervening
+scalar instruction is not crossed. The two ADDs involve three distinct registers
+and form a directed path. Every other event, scalar coefficient, entrance/exit
+frame, caller state, role and native map is fixed. This is a change of event graph,
+not a retiming of two retained ADDs.
+
+For every such pair, replace it by the reversed pair plus the exact central ADD
+below, at each of its three possible positions. Jointly choose **all** common
+binary subspaces for the three ADDs, subject to monotone register frames and fixed
+neighbouring frames. The output records every compatible flag and separately
+reports rejection by exact whole-word boundary checks. Every compatible flag
+already has a non-improving recursive invoice for every `0<a<1`; extra scalar
+implementation costs cannot turn these into gains. The finite literal inverse
+three-to-two motif census contains exactly one block per provider; its unique
+legal contracted frame assignment removes one forward and one cleanup ADD,
+with the entire paid profile unchanged. No further consecutive inverse motif
+remains after this one contraction. This does not rule out nonconsecutive A2
+identities, longer graph changes, changed boundaries, or other root systems.
+
+## Exact group identity and sign convention
+
+An ADD `(t,s,c)` updates `x_t <- x_t + c x_s`, so its matrix is
+`T_ts(c)=I+c E_ts`. A chronological list `[g,h]` acts as `H G`, not `G H`.
+For distinct `i,j,k`, let `g=(i,j,a)`, `h=(j,k,b)`. Then
+
+```
+[g,h] = [h,(i,k,-ab),g].
+```
+
+Indeed `H G=I+aE_ij+bE_jk`, whereas `G H` also contains `ab E_ik`; the negative
+central gate cancels that term. For the opposite chronological orientation,
+`g=(j,k,a)`, `h=(i,j,b)`, the central coefficient is `+ab`.
+`E_ik` commutes with both simple-root matrices, so the central ADD may occupy
+any of the three positions. These equalities are identities over the rational
+polynomial ring in `a,b`; they apply to arbitrary initial values in all three
+registers, including dirty helpers. The independent control computes all six
+register permutations, two orientations and three central positions in that
+polynomial ring. Wrong sign, omitted central gate and replacing `ab` by `a+b`
+are rejected. Actual source coefficients are separately checked with exact
+rational matrices in the production census.
+
+The new root joins two existing registers and allocates no helper or buffer.
+It adds one forward scalar ADD. Literal inverse cleanup adds one ADD when the
+new target is a non-target register, and zero when the new target is a target.
+The latter is legitimate only under the retained hygiene rule that a non-target
+never reads a target. All full-word hygiene checks remain enabled.
+
+## Exhaustive framed search
+
+For each of the three touched registers, extract its frame immediately before
+its first old event and its first fixed frame after its last old event. Call
+these `P_r,Q_r`. Include that successor climb in both local invoices. Thus no
+boundary charge is silently removed. Native entry and centre/target cut checks
+are fixed checks; allowing a positive successor climb at such a cut is only an
+optimistic relaxation, and the full word auditor identifies any such candidate
+as inadmissible.
+
+A replacement event touching registers `r,s` must use a common subspace `U`
+satisfying
+
+```
+current(r) + current(s) <= U <= Q_r intersect Q_s.
+```
+
+Enumerate every intermediate binary subspace in this interval, update both
+current frames, then recurse to the next event. Every legal flag follows a
+unique recursion branch. Conversely, every branch respects the stated local
+monotone constraints. The enumerator repeatedly adjoins an ambient vector and
+closes its span; every finite-dimensional intermediate subspace is reachable
+by adjoining a basis. Deduplication uses its complete point set. A resource
+check rejects quotient dimensions above four instead of silently pruning them;
+all inspected intervals obey the bound. Independent controls enumerate all
+subsets of the nonzero quotient vectors, close them by explicit XOR sets and
+compare the resulting subspace collections.
+
+The cost is one rank-`dim(U)-dim(current)` recursive child for every nonzero
+climb, plus the complete fixed-successor climbs. Zero climbs cost no child.
+All other register climbs cancel. The production verifier nevertheless rebuilds
+and prices the **entire** word for each legal flag and checks equality to the
+local delta. The independent checker computes the local rank invoice from the
+retained auditor's event chains and independently represented point sets.
+
+An initial dimension-only relaxation ignores subspace incidence while retaining
+event ordering and dimension bounds. It contains apparently favorable cells.
+They are nominations only: none survives exact geometry with a favorable price.
+This demonstrates why optimizing rank numbers alone would give a false gain.
+
+For the inverse census, each consecutive triple is considered at each possible
+central position. Removing that position leaves the reversed original pair;
+its endpoints and rational central coefficient must agree with the derived
+identity. Comparing rational values avoids assuming canonical numerator and
+denominator encodings. This census finds exactly the A1858 block in each provider, described below.
+No search over separated triples is claimed.
+
+## Constructive inverse rewrite
+
+The unique triple at zero-based A index 1858 is, in chronological order,
+
+```
+457 <- 457 - 475
+456 <- 456 + 457
+456 <- 456 + 475
+```
+
+All three operations use the common frame span(82,42). It equals
+
+```
+456 <- 456 + 457
+457 <- 457 - 475
+```
+
+at the same frame. The two-register endpoint is `(x456+x457, x457-x475)`;
+register475 is unchanged, so arbitrary dirty inputs are preserved exactly.
+The exhaustive two-event frame search has exactly this one legal assignment.
+Both source providers' complete 723-input ordinary/dual/reverse semantics and
+cleanup-boundary checks are replayed for this contracted word. The inverse
+cleanup has 5223 events instead of 5224. A has 4078 events instead of 4079.
+The paid profile remains `{1:2440,2:725,3:224,4:102,5:20,8:8}`. No helper,
+buffer or native map is added or deleted. The replacement occurs after the A
+prelude, so every existing native event and B warp index is unchanged.
+
+A second complete scan of the contracted word finds no consecutive literal
+inverse A2 motif. This is one fixed-point check, not a claim about every possible
+sequence involving expansions or other rewrites. The canonical edited-word and
+cleanup digests are retained, together with the exact replacement gates and
+source input pins, so the construction is reproducible without storing another
+copy of the frozen supplier. This is a concrete scalar simplification with no
+recursive-moment or kappa improvement; it is not the PR3863 rank exchange.
+
+The exact same single A1858 contraction is additionally checked on both
+PR3945 words at 91f81d131252db704f945891da1ea54e29d46b8b. Their actual source
+profiles, full ordinary/dual/reverse dirty semantics before and after, and all
+unchanged top-level fields are checked independently. In particular, native
+operators and their scalar normalization are byte-identical to their own
+PR3945 baselines. The complete expansion census above remains scoped to the
+older PR3734 words. No PR3945 graph-wide expansion result is inferred.
+
+## Exact all-exponent sign certificate
+
+Write `[r]` for one rank-`r` child and `p=1-a`, so `0<p<1`. The only signed
+profile differences are zero and
+
+```
+2[1]-[2],  4[1]-2[2],  [1]+[2]-[3],  3[1]-[3].
+```
+
+For positive `x,y`, strict subadditivity gives
+`(x+y)^p < x^p+y^p`. Therefore each nonzero difference has strictly positive
+moment; zero is an exact tie. Their rank masses are all zero, so a common width
+normalization multiplies these inequalities by the same positive factor. This
+argument covers the entire open exponent interval, not a floating-point sample.
+The source-specific histogram is retained in each RESULT. No unclassified sign
+is converted into a negative theorem: the verifier fails if one appears.
+
+## Composition, cleanup and validation boundary
+
+All root identities are exact on arbitrary dirty rational symbols. The graph
+change happens wholly inside a scalar segment and preserves its full boundary
+operator. Thus composing with the unchanged surrounding native/free-operator
+program preserves the full operator. For B, every subsequent native warp's
+numeric list position increases by one while its chronological placement after
+the same old events is preserved. The verifier regenerates literal cleanup
+from the entire edited forward word. It separately compares the non-target
+projection of every before/after block, which is the part inverted by cleanup;
+target outputs are omitted exactly as specified by the inherited contract.
+
+Every compatible candidate is checked by exact local matrices; every legal
+candidate receives full chronological invoice/hygiene checks and regenerated
+cleanup. Both baseline full 723-input free-operator programs and deterministic
+edited whole-word samples are replayed in ordinary and dual orientations, with
+reverse pullback and cleanup-boundary checks. **Edited whole-word interpreter
+coverage is sampled**, while universal coverage of the enumerated candidates
+uses the exact local matrix composition and inverse-cleanup argument. This is
+not a native Clifford phase proof or a full multiplication theorem.
+
+## Costs and limits
+
+The ledger lists both complete source profiles, all candidate profiles, helper
+widths, live and dirty inputs, primitive counts, native maps, correction counts,
+added scalar/cleanup operations and finite coefficient heights. No new register
+is created. All unchanged inherited charges remain inherited; unknown physical
+hosting, owner chronology, uniform precision/stock/tape, all-size compilation,
+outer admission and analytic/BIT obligations are explicitly unknown. Since the
+recursive change already does not improve, assigning any nonnegative cost to
+the added operations cannot rescue this particular proposal. This is a stop
+rule for this finite graph domain, not for changed interfaces in general.
+
+## Predecessor credit
+
+Dataisfire supplies the literal PR3734 words. The retained frame trace and
+subspace representation come from PR3886; the scalar/dirty semantic auditor
+credits Sagar Thakrar, roger-sato and Arham Tahir in its original notices.
+Jeremy Kothe's retained rank-profile rewrites and the PR3941/3942/3957/3964/3970
+fixed-graph investigations motivate changing the graph. Dugongue's PR3863
+provides the paid `2+2 -> 1+3` implementation target and overhead discipline;
+this package does not claim to realize that target or to originate its budget
+certificate. Full upstream notices are retained in vendor/SOURCE-CREDITS.md.
diff --git a/research/staged544-a2-graph-rewrite/README.md b/research/staged544-a2-graph-rewrite/README.md
new file mode 100644
index 0000000000..dcd14ef45b
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/README.md
@@ -0,0 +1,119 @@
+# A literal A2 graph contraction and its exact staged544 frame budget
+
+The A2 root-system identity yields a concrete simplification on both frozen
+PR3734 staged544 providers: replace the three ADDs at A1858 by two ADDs,
+removing **one forward and one inverse-cleanup ADD**. The full chronological
+recursive profile is unchanged. Every dirty-input and caller boundary is
+preserved. The same literal contraction is independently checked on both
+current PR3945 terminal-gap-filled words at 91f81d13, with their own complete
+profiles and full dirty-word replay. This supplies a reproducible scalar
+simplification, **no new κ**.
+
+The same package completes the complementary consecutive two-to-three A2
+rewrite search. Each provider has 168 directed two-ADD motifs. All three central
+commutator positions and every compatible binary-frame flag are included.
+All 460 legal flags have non-improving recursive moments for every `0<a<1`:
+396 exact ties and 64 strictly worse flags. The five signed profile types have
+an elementary exact subadditivity proof. An initial dimension-only relaxation
+has 2714 candidate triples, including 1014 uncertified potentially favorable
+cells; exact subspace incidence rejects all apparently favorable candidates.
+This is a concrete demonstration that rank-dimension optimization alone can
+misprice a changed dependency graph.
+
+The primary field is framed rational circuit optimization. The contrasting
+specialization is algebraic groups: the A2/Steinberg transvection relation
+changes the literal scalar event graph while an exact rational matrix check
+preserves arbitrary dirty state. This differs from the fixed-graph retiming
+and stationary-frame domains of PR3886/3941/3942/3957/3964/3970.
+
+## Literal construction
+
+At zero-based A index 1858, all frames are span(82,42):
+
+```
+Before                         After
+457 <- 457 - 475               456 <- 456 + 457
+456 <- 456 + 457               457 <- 457 - 475
+456 <- 456 + 475
+```
+
+Both sides map `(x456,x457,x475)` to `(x456+x457,x457-x475,x475)` for arbitrary
+inputs. The unique legal contracted frame assignment has the complete profile
+`{1:2440,2:725,3:224,4:102,5:20,8:8}`: 3519 recursive children, rank mass 5134.
+These are the older PR3734 counts; PR3945 applicability retains its separately
+recorded source profile. There are 408 helper roles and 91 dirty buffers. A has 4078 events after the rewrite
+and cleanup has 5223. No further consecutive inverse A2 motif remains in the
+contracted word. This is one bounded fixed-point check, not an arbitrary graph
+normal-form theorem.
+
+`RESULT-base.json` and `RESULT-extra.json` retain the exact source bindings,
+replacement gates, full invoices, canonical contracted-word/cleanup digests,
+all expansion records, complete frame intervals and full-word replay receipts.
+`PROOF.md` gives the exact scope and composition argument. `LEDGER.json` states
+proved, finite bounded and unknown costs; unknown costs are not zero.
+
+## Reproduce
+
+Python 3.12 or later, standard library only. Commands are read-only by default.
+
+```
+python3 -B research/staged544-a2-graph-rewrite/verify.py --provider base
+python3 -B research/staged544-a2-graph-rewrite/verify.py --provider extra
+python3 -O -B research/staged544-a2-graph-rewrite/check_controls.py
+python3 scripts/research_package.py --package research/staged544-a2-graph-rewrite
+```
+
+Each complete provider replay takes about four minutes on the author's host;
+see `VALIDATION.json` for exact measured runs and failures. A replay may export
+the literal contracted word only to an explicit path outside this package:
+
+```
+python3 -B research/staged544-a2-graph-rewrite/verify.py --provider base --emit-contracted-word /tmp/staged544-a2-base.json
+```
+
+The files under `inputs/` and `vendor/` are immutable predecessor snapshots.
+The verifier authenticates byte counts, SHA256 and Git blob IDs before loading
+source. These public source heads are attribution pins, not an assertion that
+they are ancestors of the package's base. Standalone replay is Git-free; the
+repository hook additionally checks pinned catalogue provenance in Git history.
+
+## Coverage and limits
+
+Only consecutive scalar motifs in A after `prelude_events`, B between fixed
+native warp cuts, and restore are included. Prelude events, crossed native
+maps, separated motifs, changed boundaries and additional registers are outside
+the certificate. Exact dirty block and complete frame/cleanup invoice checks
+cover every legal flag. All four PR3734/PR3945 baselines and **every contracted word** receive
+full 723-input ordinary, dual, reverse and cleanup-boundary replay. Expanded
+whole-word interpreter checks are six deterministic samples per provider;
+universal expansion coverage uses exact local matrix composition and projected
+inverse cleanup. No fresh Clifford-phase, physical owner-schedule, uniform
+precision/stock/tape, all-size supplier or multiplication theorem is claimed.
+
+## Open next questions
+
+- Can a nonconsecutive A2 relation or a coordinated graph cycle pay its complete
+  frame and restoration invoice? First exhibit one exact block and a favorable
+  full optimistic bill before enlarging the search. Intervening frames and the
+  physical scalar schedule remain obligations.
+- Can one specific rejected dimension-only candidate become useful under a
+  changed, fully paid entrance/exit or native consumer? Name that consumer and
+  its dirty restoration and phase costs first. Free boundary relaxation does
+  not supply an implementation.
+
+## Credit and status
+
+Dataisfire supplies PR3734's frozen literal providers. PR3886 supplies the
+retained trace and binary-subspace representation. The retained scalar auditor
+credits Sagar Thakrar, roger-sato and Arham Tahir; its original notices are kept.
+Jeremy Kothe's rank-profile rewrites and the subsequent fixed-graph obstruction
+stream motivate this changed-graph question. Dugongue's PR3945 supplies the changed terminal-gap-filled applicability
+words, frozen separately; its native lineage notice is retained. Dugongue's
+PR3863 supplies the
+`2+2 -> 1+3` implementation target and paid-overhead discipline; the present
+scalar contraction does not realize that rank exchange. See `SOURCES.json` and
+`vendor/SOURCE-CREDITS.md` for exact pins and full lineage.
+
+Chris R / Clear1nsight, with substantial OpenAI Codex assistance. Apache-2.0.
+Author-checked finite construction/certificate; no independent human review,
+formal-kernel proof, supplier admission or selected-frontier change claimed.
diff --git a/research/staged544-a2-graph-rewrite/RESULT-base.json b/research/staged544-a2-graph-rewrite/RESULT-base.json
new file mode 100644
index 0000000000..a7ba2d9a7c
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/RESULT-base.json
@@ -0,0 +1,32773 @@
+{
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+        "nonzero_endpoint_terms": 835,
+        "reverse_pullback_equals_forward": true
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+}
diff --git a/research/staged544-a2-graph-rewrite/RESULT-extra.json b/research/staged544-a2-graph-rewrite/RESULT-extra.json
new file mode 100644
index 0000000000..c8b81e77e0
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/RESULT-extra.json
@@ -0,0 +1,32773 @@
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+      "All compatible frame flags and complete chronological recursive invoice for every legal flag",
+      "Projected non-target matrix equality and literal inverse cleanup for every flag",
+      "All source free-operator symbols plus deterministic full-word sample replay",
+      "Finite primitive and scalar coefficient bounds; fixed roles, entrance/exit frames and native maps"
+    ],
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+      "All-size compiler, outer/supplier admission, analytic transfer and BIT H1-H5"
+    ],
+    "unknown_costs_are_zero": false
+  },
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+}
diff --git a/research/staged544-a2-graph-rewrite/SOURCES.json b/research/staged544-a2-graph-rewrite/SOURCES.json
new file mode 100644
index 0000000000..431f5b94cd
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/SOURCES.json
@@ -0,0 +1,123 @@
+{
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "external_snapshot_contract": "Package-local exact source snapshots are authenticated by byte count, SHA256, and Git blob. Their source heads are attribution pins, not runtime Git ancestry requirements. The standalone verifier is Git-free.",
+  "files": [
+    {
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "path": "docs/research/agent-task-catalog.json",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0",
+      "usage": "provenance"
+    }
+  ],
+  "method_predecessors": [
+    {
+      "author": "Chris R / Clear1nsight",
+      "pr": 3886,
+      "scope": "Single-move theorem, chronological trace, retiming applier, and all-power certificate are reused explicitly.",
+      "source_commit": "359fe0fe77d29544972fd22ee674085ed5a3b4d0"
+    },
+    {
+      "author": "Dugongue",
+      "head": "635fe84596c19016f3d0316a5cf7abbe48285490",
+      "pr": 3863,
+      "scope": "Uniform rational paid-profile credit and proposed 2+2 to 1+3 target; read, not reimplemented as new mathematics."
+    },
+    {
+      "author": "Jeremy Kothe",
+      "pr": 2957,
+      "retained_record": "research/rank7-joint-endframes/data/REWRITES-2957.json",
+      "retained_record_base": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+      "scope": "Already-retained commuting swap used as a counterfactual rollback/recovery positive control."
+    },
+    {
+      "author": "Dugongue",
+      "pr": 3945,
+      "source_commit": "91f81d131252db704f945891da1ea54e29d46b8b",
+      "scope": "Exact changed terminal-gap-filled provider words for only the A1858 contraction applicability; no expansion census transferred."
+    }
+  ],
+  "schema_version": 1,
+  "snapshots": [
+    {
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+      "source_path": "research/staged544-terminal-gap-fill/inputs/NEW-extra.json.gz"
+    },
+    {
+      "local": "vendor/PR3945-NATIVE-LINEAGE-NOTICE",
+      "bytes": 2456,
+      "sha256": "ee0c73ca35877aad0e0b6adc560a3881cb82276dba4cf2d4fc58cd19e57cc420",
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+      "source_repository": "CrocSwap/integer-mult-bounds",
+      "source_commit": "91f81d131252db704f945891da1ea54e29d46b8b",
+      "source_path": "research/staged544-terminal-gap-fill/native/NATIVE-LINEAGE-NOTICE"
+    }
+  ]
+}
diff --git a/research/staged544-a2-graph-rewrite/TASK.json b/research/staged544-a2-graph-rewrite/TASK.json
new file mode 100644
index 0000000000..e870e304f6
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/TASK.json
@@ -0,0 +1,95 @@
+{
+  "task_id": "scalar-to-moment",
+  "original_card": {
+    "id": "scalar-to-moment",
+    "question": "Can one known scalar simplification be converted into an actual paid-profile improvement?",
+    "starting_points": [
+      "research/r439-bsection-stars-seed01/README.md",
+      "certificates/selected-result.json"
+    ],
+    "methods": [
+      "Derive the changed legal frame itinerary and exact child histogram.",
+      "Prove a scoped obstruction showing why that scalar gain cannot change the paid contract."
+    ],
+    "acceptance_gate": "An unchanged histogram is not a kappa gain; record any separate runtime or proof benefit explicitly.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/r439-bsection-stars-seed01/verify.py"
+      ],
+      "expected": "PASS_R439_BSECTION_STARS",
+      "inspect": "Observe that the positive control improves scalar counts while retaining the paid histogram.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Choose one simplification and derive the complete changed frame itinerary, or prove why it cannot change the histogram.",
+    "bottleneck_link": "A legal change to the histogram, not addition count alone, is the bridge to an exponent gain.",
+    "allowed_variations": [
+      "One existing scalar simplification and one proposed frame-path change."
+    ],
+    "scope_change_triggers": [
+      "Submitting only another scalar count as completion of a paid-profile task."
+    ],
+    "overlap_terms": [
+      "scalar simplification",
+      "paid profile",
+      "R439"
+    ]
+  },
+  "author": "Chris R / Clear1nsight",
+  "ai_assistance": "Substantial OpenAI Codex assistance; no independent human or kernel review claimed.",
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "scope_status": "changed",
+  "scope_change_reason": "Change the scalar event graph through an A2 root-system relation, instead of retiming existing gates or increasing the first-move radius.",
+  "actual_scope": "Consecutive directed two-ADD chains in A after prelude_events, B between native warp cuts and restore, on both frozen PR3734 providers. Replace with reversed pair plus the exact commutator ADD at each of three positions; all common binary-frame assignments. Also census literal inverse contractions. Separately validate only the unique A1858 contraction on both frozen PR3945 terminal-gap-filled words; no PR3945 expansion census.",
+  "bottleneck_link": "A changed dependency graph can escape fixed-graph retiming obstructions, but its additional gate and complete frame/restoration invoice must pay.",
+  "budget_minutes": 60,
+  "outcome": "completed",
+  "evidence": "Both PR3734 providers:168 motifs,460 fully priced legal expansion flags,396 ties and64 strictly worse; unique literal A1858 contraction removes one forward and one inverse-cleanup ADD. The same one-block contraction preserves the actual full profile on both PR3945 words; all four baseline and contracted dirty programs pass. Registered replay and controls in VALIDATION.json.",
+  "entry_checkpoint": {
+    "canonical_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+    "priority_revision": 6,
+    "utc": "2026-10-19T07:42:02Z",
+    "open_pr_bodies": 677,
+    "discussions": "Partial root signed-in1166 snapshot, no exhaustive novelty claim."
+  },
+  "family_expansion_decision": {
+    "decision": "Retain the literal one-forward-and-one-cleanup ADD contraction with unchanged paid profile, plus complete consecutive A2 expansion obstruction; stop after one contraction fixed-point check.",
+    "optimistic_budget": "Dimension-only first screen admits apparently favorable rank mergers, so exact frame constraints can change the decision. Extra scalar implementation cost is unknown and nonnegative, never zero by assumption.",
+    "boundary": "All caller, entrance, exit, native maps and helper/buffer identities fixed; added scalar gate included and inverse cleanup regenerated.",
+    "success": "A legal complete paid gain or finite exact obstruction with meaningful independent controls.",
+    "stop": "No exact compatible improving flag; no further radius/native/interface expansion in this package."
+  },
+  "open_questions": [
+    {
+      "question": "Can a nonlocal A2 relation or coordinated graph cycle produce a favorable complete invoice?",
+      "why_it_matters": "The present theorem covers consecutive motifs only; dependencies between separated events may admit other graphs.",
+      "first_step": "Exhibit one exact before/after block with declared fixed cuts and fully charged optimistic rank profile before enlarging a census.",
+      "blocked_by": "A paid allowance for intervening frames, restored dirty state, extra scalar operations and physical schedule."
+    },
+    {
+      "question": "Can a changed entrance or exit frame make a specific A2 graph replacement useful?",
+      "why_it_matters": "Rejected dimension-only gains show exact boundary geometry is the binding constraint here.",
+      "first_step": "Select one rejected optimistic motif and specify an actual consumer/native interface that pays its changed boundary.",
+      "blocked_by": "Complete changed consumer/restoration and native phase costs; a free boundary relaxation is insufficient."
+    }
+  ],
+  "claim": "https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19035159",
+  "schema_version": 1,
+  "stop_rule": "No exact compatible improving flag; no further radius/native/interface expansion in this package.",
+  "final_checkpoint": {
+    "canonical_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+    "priority_revision": 6,
+    "root_overlap_utc": "2026-10-19T08:17:28Z",
+    "open_pr_bodies": 698,
+    "own_main_connector_fetch": "2026-10-19T08:07:33Z",
+    "discussions": "Partial root signed-in1166 coverage; no exhaustive novelty claim.",
+    "nearby_prs": {
+      "3975": "Selected-provider successive rank-one macro-fusion feasibility screen; no exact scalar A2 identity, different provider.",
+      "3982": "R437 parabolic COPY algebraic-group construction and conditional cost; different interface/native operation.",
+      "3987": "Parallel native cocycle audit; actual native maps remain frozen in the A2 task.",
+      "3989": "Selected-provider rank-two Pauli fusion/transfer; different provider and interface, not the literal A2 contraction."
+    },
+    "selected_frontier_changed": false
+  }
+}
diff --git a/research/staged544-a2-graph-rewrite/VALIDATION.json b/research/staged544-a2-graph-rewrite/VALIDATION.json
new file mode 100644
index 0000000000..d1fe17f69d
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/VALIDATION.json
@@ -0,0 +1,141 @@
+{
+  "controls": [
+    {
+      "exit_code": 0,
+      "log": "controls-normal.log",
+      "receipt": {
+        "independent_frame_intervals": 494,
+        "independent_legal_invoices": 922,
+        "seconds": 5.439,
+        "symbolic_identities": 36,
+        "wrong_sign_missing_gate_wrong_product_controls": 108
+      },
+      "sha256": "f012af2b243d09f910ca3f81a4389de814d74a448920c55f6c90088aad2f4d54"
+    },
+    {
+      "exit_code": 0,
+      "log": "controls-optimized.log",
+      "receipt": {
+        "independent_frame_intervals": 494,
+        "independent_legal_invoices": 922,
+        "seconds": 4.417,
+        "symbolic_identities": 36,
+        "wrong_sign_missing_gate_wrong_product_controls": 108
+      },
+      "sha256": "ecca3fe752842f4b23f2b7f9df9baac74ae123c63d1681f36f65b0c90d99cc1a"
+    },
+    {
+      "exit_code": 0,
+      "log": "git-free-controls.log",
+      "receipt": {
+        "independent_frame_intervals": 494,
+        "independent_legal_invoices": 922,
+        "seconds": 5.796,
+        "symbolic_identities": 36,
+        "wrong_sign_missing_gate_wrong_product_controls": 108
+      },
+      "sha256": "88bf178675bd0e257233f8e9b80f241bd530fd2dc5d4d985bbbb98eb8d33c839"
+    }
+  ],
+  "coverage": {
+    "PR3734_expansion_ties_per_provider": 396,
+    "PR3734_legal_expansion_flags_per_provider": 460,
+    "PR3734_motifs_per_provider": 168,
+    "PR3734_strictly_losing_expansion_flags_per_provider": 64,
+    "additional_controls": [
+      "Actual production sign mutation",
+      "Missing cleanup ADD rejected by full semantics",
+      "Altered immutable source",
+      "Out-of-range frame vector",
+      "Non-ADD and two-register-cycle shape",
+      "Package root, descendant and existing-output CLI rejection before calculation"
+    ],
+    "baseline_full_word_replays": 4,
+    "contracted_full_word_replays": 4,
+    "exact_expansion_flag_dirty_matrices": 920,
+    "expanded_full_word_samples": 12,
+    "expanded_whole_word_coverage": "Sampled; universal candidate coverage is exact block composition plus projected inverse cleanup.",
+    "independent_frame_intervals": 494,
+    "independent_local_invoices": 922,
+    "provider_families": [
+      "PR3734",
+      "PR3945"
+    ],
+    "single_contraction_per_provider_family": 1,
+    "symbolic_inputs_per_word": 723,
+    "symbolic_polynomial_identities": 36,
+    "symbolic_sign_product_omission_rejections": 108
+  },
+  "environment": {
+    "dependencies": "standard library only",
+    "platform": "Linux-7.0.0-38-generic-x86_64-with-glibc2.39",
+    "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]"
+  },
+  "failed_or_corrected_exploration": [
+    {
+      "attempt": "Initial middle-position-only inverse probe",
+      "correction": "All three central-gate positions expose the unique last-position A1858 contraction.",
+      "status": "Incomplete preliminary probe; corrected before publication"
+    },
+    {
+      "attempt": "First independent event-chain cost oracle",
+      "correction": "Native warp output was incorrectly treated as a paid successor; use its exact entry check. Filter temporary centre descents from persistent frame state.",
+      "status": "Failed before final controls"
+    },
+    {
+      "attempt": "Preliminary control runtime label",
+      "correction": "A register variable shadowed the timer. Final independent timer uses a distinct variable and all final checks were rerun.",
+      "status": "Invalid timer field; not used as runtime evidence"
+    },
+    {
+      "attempt": "Draft metadata and output guards",
+      "correction": "Metadata passes; guard controls require the expected failure reason, not only nonzero exit.",
+      "status": "Schema fields and one syntax error corrected before science freeze"
+    }
+  ],
+  "git_free_scope": "Full independent controls and source authentication only; a second complete standalone provider census was not run in the read-only export. Final publication archive bytes are checked separately.",
+  "publication_boundary": "This file records pre-publication checks. Exact GitHub-authored commit import, committed-byte/source-history gate, final archive and hosted CI are recorded separately in the publication handoff; this statement does not claim those later steps already passed.",
+  "registered_replay": {
+    "command": [
+      "python3",
+      "-B",
+      "scripts/research_package.py",
+      "--package",
+      "research/staged544-a2-graph-rewrite"
+    ],
+    "complete_outer_wall_time": "Not separately instrumented; per-command elapsed receipts are exact measured outputs.",
+    "coverage": "Both full PR3734 expansion/contraction certificates and both separate PR3945 single-contraction applicability checks regenerate and exactly match retained receipts.",
+    "exit_code": 0,
+    "full_provider_elapsed_seconds": {
+      "base": 180.154,
+      "extra": 156.274
+    },
+    "log_sha256": "97d6eab5db20373b69f885b861ae3fbb993a2db1348221e5bbb43bcc1cab827f",
+    "optimized_controls_receipt": {
+      "independent_frame_intervals": 494,
+      "independent_legal_invoices": 922,
+      "seconds": 4.351,
+      "symbolic_identities": 36,
+      "wrong_sign_missing_gate_wrong_product_controls": 108
+    }
+  },
+  "schema_version": 1,
+  "science_code_sha256": {
+    "check_controls.py": "d279167a2c834c218255cc9190d3cfe07d751b2c5b0a4aa62729d41a7992cf60",
+    "search.py": "37831f41b94eb8dd639e5029de83a42e206172516bfb6d2d2349e783c6f4b031",
+    "vendor/audit_core.py": "888679ca8502cdcb100420fe5382a052529a494bf76cb332928b86e62612b951",
+    "vendor/audit_verify.py": "99971d3cc143cc894600e08c8cfbad3e8f537a544212f21dfbe4271cfa97354d",
+    "vendor/retiming.py": "591d7278541ac4de9e9b6fc1e17aba23b205ac4b6c81824a28fc08294658ef0d",
+    "verify.py": "b36f397576e033a9a5571a25126d60db7cd22bcf09e624515f24a0b26dc4a8f4"
+  },
+  "selected_frontier_changed": false,
+  "status": "PASS: complete registered science replay, independent normal/optimized controls, and read-only Git-free optimized controls.",
+  "unrun_obligations": [
+    "Independent human or formal-kernel review",
+    "Fresh native Gaussian/Clifford phase admission",
+    "Physical allocation, hosting and complete owner scheduling",
+    "Uniform precision/stock/tape tariffs",
+    "All-size compiler and outer/supplier admission",
+    "Analytic transfer and BIT H1-H5"
+  ]
+}
diff --git a/research/staged544-a2-graph-rewrite/VERIFY.json b/research/staged544-a2-graph-rewrite/VERIFY.json
new file mode 100644
index 0000000000..a6328d89b2
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/VERIFY.json
@@ -0,0 +1,41 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py",
+        "--provider",
+        "base"
+      ],
+      "timeout_seconds": 540,
+      "checks": "Authenticated exact consecutive A2 graph census, all compatible frames, full chronological invoice and dirty block/cleanup checks, plus whole-word samples."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py",
+        "--provider",
+        "extra"
+      ],
+      "timeout_seconds": 540,
+      "checks": "Authenticated exact consecutive A2 graph census, all compatible frames, full chronological invoice and dirty block/cleanup checks, plus whole-word samples."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/check_controls.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Independent all-subspace flag enumeration and direct frame invoices; symbolic polynomial group identity, sign/coefficient mutation, omitted-gate, source/frame/cleanup/barrier rejection controls."
+    }
+  ]
+}
diff --git a/research/staged544-a2-graph-rewrite/check_controls.py b/research/staged544-a2-graph-rewrite/check_controls.py
new file mode 100644
index 0000000000..16b310ae84
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/check_controls.py
@@ -0,0 +1,153 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Independent finite-subspace and polynomial-identity checks; all failures explicit."""
+import json,itertools,time
+from collections import Counter
+from copy import deepcopy
+from functools import lru_cache
+from pathlib import Path
+import types
+P=Path(__file__).resolve().parent
+V=types.ModuleType('entry');V.__file__=str(P/'verify.py');exec(compile((P/'verify.py').read_bytes(),str(P/'verify.py'),'exec'),V.__dict__)
+need=V.need
+
+def pointset(vectors):
+    out={0}
+    for v in vectors:out|={x^v for x in tuple(out)}
+    return frozenset(out)
+
+def points(mask):return frozenset(x for x in range(512) if mask>>x&1)
+
+def dim(space):return len(space).bit_length()-1
+
+@lru_cache(None)
+def independent_frames(low,high):
+    if not low<=high:return ()
+    # Form quotient representatives without calling retained span/join/basis.
+    reps={min(v^u for u in low) for v in high};nonzero=sorted(reps-{0})
+    need(len(nonzero)<=15,'independent quotient cap')
+    out=set()
+    for bits in range(1<<len(nonzero)):
+        generators=[nonzero[i] for i in range(len(nonzero)) if bits>>i&1]
+        quotient=pointset(generators)
+        out.add(frozenset(x^y for x in quotient for y in low))
+    return tuple(sorted(out,key=lambda x:tuple(sorted(x))))
+
+def plus(a,b):
+    out=a.copy()
+    for k,v in b.items():out[k]=out.get(k,0)+v
+    return {k:v for k,v in out.items() if v}
+
+def times(a,b):
+    out={}
+    for (i,j),v in a.items():
+        for (k,l),w in b.items():out[i+k,j+l]=out.get((i+k,j+l),0)+v*w
+    return {k:v for k,v in out.items() if v}
+
+def poly_matrix(gates):
+    rows=[[{(0,0):int(i==j)} if i==j else {} for j in range(3)] for i in range(3)]
+    for t,s,c in gates:rows[t]=[plus(x,times(c,y)) for x,y in zip(rows[t],rows[s])]
+    return rows
+
+def group_controls():
+    a={(1,0):1};b={(0,1):1};ab={(1,1):1};n_ab={(1,1):-1};checks=0
+    for i,j,k in itertools.permutations(range(3)):
+        for orientation in (0,1):
+            g=(i,j,a) if not orientation else(j,k,a)
+            h=(j,k,b) if not orientation else(i,j,b)
+            central=(i,k,n_ab if not orientation else ab)
+            before=poly_matrix([g,h])
+            for pos in (0,1,2):
+                after=[h,g];after.insert(pos,central)
+                need(before==poly_matrix(after),'symbolic A2 identity')
+                bad=deepcopy(after);bad[pos]=(i,k,{power:-v for power,v in central[2].items()})
+                need(before!=poly_matrix(bad),'wrong sign not rejected')
+                need(before!=poly_matrix([h,g]),'missing central gate not rejected')
+                bad[pos]=(i,k,plus(a,b));need(before!=poly_matrix(bad),'wrong product not rejected');checks+=1
+    return checks
+
+def expect(fn):
+    try:fn()
+    except (ValueError,ZeroDivisionError):return
+    raise ValueError('expected rejection absent')
+
+def main():
+    started=time.monotonic();S,C,A=V.setup();identities=group_controls();intervals=0;flags=0
+    for tag in ('base','extra'):
+        w=V.load(tag);receipt=json.loads((P/f'RESULT-{tag}.json').read_text());data=receipt['census']
+        # Independent quotient-subset closure is exhaustive, not a random check.
+        for low,high in data['intervals']+data['contractions']['intervals']:
+            l,h=int(low),int(high);actual={points(x) for x in S.frames(l,h)}
+            need(actual==set(independent_frames(points(l),points(h))),'subspace enumeration mismatch');intervals+=1
+        # Recompute every retained local rank invoice from independent point sets.
+        _,_,chain,start,end=C.frame_bill(w)
+        expected=Counter()
+        for row in data['records']+data['contractions']['records']:
+            sec,i=row['section'],row['index'];old_length=3 if len(row['gates'])==2 else 2;block=w[sec][i:i+old_length];regs={r for g in block for r in g[1:3]};bounds={};old=Counter()
+            for r in regs:
+                seq=[event for event in chain[r] if event[0][0]!='centre'];inds=[j for j,(where,d,u) in enumerate(seq) if where in tuple((sec,j) for j in range(i,i+old_length))]
+                need(inds,'missing independent event');lo,hi=min(inds),max(inds)
+                before=seq[lo-1][2] if lo else start[r]
+                # Native entry is an exact check; the recorded warp row is its
+                # output map, not a paid successor climb. Centre descent is
+                # temporary service, filtered above, never persistent state.
+                after=seq[hi][2] if type(seq[hi+1][1]) is not int else seq[hi+1][2]
+                bounds[r]=(points(before),points(after))
+                for _,d,u in seq[lo:hi+1]:need(type(d)is int,'crossed native boundary');old[d]+=1
+                old[dim(points(after))-dim(points(seq[hi][2]))]+=1
+            cur={r:x for r,(x,y) in bounds.items()};new=Counter()
+            for gate in row['gates']:
+                fr=pointset(gate[-1])
+                for r in gate[1:3]:
+                    need(cur[r]<=fr<=bounds[r][1],'independent frame failure');new[dim(fr)-dim(cur[r])]+=1;cur[r]=fr
+            for r,(x,y) in bounds.items():new[dim(y)-dim(cur[r])]+=1
+            delta=[0]+[new[r]-old[r] for r in range(1,10)];need(delta==row['delta'],'independent invoice mismatch');flags+=1
+            if old_length==2:expected[tuple(delta)]+=1
+        need([{'delta':list(d),'count':n} for d,n in sorted(expected.items())]==data['profiles'],'histogram mismatch')
+        # Independently enumerate graph sites using the dependency matrix support.
+        sites=[]
+        for sec in ('A','B','restore'):
+            for lo,hi in S.R.segments(w,sec):
+                for i in range(lo,hi-1):
+                    g,h=w[sec][i:i+2]
+                    if g[0]!='add' or h[0]!='add':continue
+                    t,s=g[1:3];u,v=h[1:3]
+                    if len({t,s,u,v})==3 and ((s==u) != (v==t)):sites.append([sec,i])
+        need(sites==data['motifs'],'motif completeness')
+        # Separately assemble the complete Cartesian flag state sets with
+        # frozenset geometry; production DFS/deduplication is not reused.
+        nodes,where,_=S.R.tracing(w);all_flags=set()
+        for sec,i in sites:
+            bounds,_=S.boundary(nodes,where,w,sec,i)
+            bounds={r:(points(a),points(b)) for r,(a,b) in bounds.items()}
+            for pos in (0,1,2):
+                gates=S.expand(*w[sec][i:i+2],pos)
+                states=[({r:a for r,(a,b) in bounds.items()},())]
+                for gate in gates:
+                    next_states=[];a,b=gate[1:3]
+                    for cur,chosen in states:
+                        lower=pointset(cur[a]|cur[b]);upper=bounds[a][1]&bounds[b][1]
+                        for frame in independent_frames(lower,upper):
+                            new=cur.copy();new[a]=new[b]=frame
+                            next_states.append((new,chosen+(tuple(sorted(frame)),)))
+                    states=next_states
+                all_flags.update((sec,i,pos,chosen) for cur,chosen in states)
+        retained={(r['section'],r['index'],r['central_position'],tuple(tuple(sorted(pointset(g[-1]))) for g in r['gates'])) for r in data['records']}
+        retained.update((sec,i,pos,tuple(tuple(sorted(pointset(f))) for f in frames)) for sec,i,pos,frames,error in data['fixed_boundary_rejections'])
+        need(all_flags==retained,'complete independent flag set mismatch')
+        row=data['records'][0];m=S.apply(w,row['section'],row['index'],row['gates'],C)
+        bad=deepcopy(m);j=next(j for j,g in enumerate(bad['cleanup']) if g[0]=='add');bad['cleanup'].pop(j)
+        need(not C.same_cleanup(C.derive_cleanup(bad),bad['cleanup']),'cleanup deletion undetected')
+        expect(lambda:A.semantics(C,bad))
+        bad=deepcopy(row['gates']);bad[0][-1]=[512];expect(lambda:S.invoice({r:(1,(1<<512)-1) for r in {r for g in bad for r in g[1:3]}},bad))
+        expect(lambda:S.expand(['scale',1,1,1,[]],['add',2,1,1,1,[]],0))
+        expect(lambda:S.expand(['add',1,2,1,1,[]],['add',2,1,1,1,[]],0))
+    # The actual production sign mutation must break a source identity.
+    mutated=types.ModuleType('wrong_production_sign');mutated.__file__=str(P/'search.py')
+    source=(P/'search.py').read_text();need('h[2],-a*b' in source,'mutation anchor')
+    exec(compile(source.replace('h[2],-a*b','h[2],a*b'),str(P/'search.py'),'exec'),mutated.__dict__)
+    g=['add',0,1,2,1,[]];h=['add',1,2,3,1,[]]
+    need(mutated.matrix([g,h])!=mutated.matrix(mutated.expand(g,h,1)),'production sign mutation survived')
+    sources=json.loads((P/'SOURCES.json').read_text())['snapshots'];row=sources[0];raw=(P/row['local']).read_bytes();expect(lambda:V.authenticate(raw[:-1]+bytes([raw[-1]^1]),row))
+    print('PASS_A2_CONTROLS',json.dumps({'symbolic_identities':identities,'wrong_sign_missing_gate_wrong_product_controls':3*identities,'independent_frame_intervals':intervals,'independent_legal_invoices':flags,'seconds':round(time.monotonic()-started,3)},sort_keys=True))
+if __name__=='__main__':main()
diff --git a/research/staged544-a2-graph-rewrite/inputs/BORROW-WORD-43base.json.gz b/research/staged544-a2-graph-rewrite/inputs/BORROW-WORD-43base.json.gz
new file mode 100644
index 0000000000..674ea18ade
Binary files /dev/null and b/research/staged544-a2-graph-rewrite/inputs/BORROW-WORD-43base.json.gz differ
diff --git a/research/staged544-a2-graph-rewrite/inputs/BORROW-WORD-43extra.json.gz b/research/staged544-a2-graph-rewrite/inputs/BORROW-WORD-43extra.json.gz
new file mode 100644
index 0000000000..b17e2be67e
Binary files /dev/null and b/research/staged544-a2-graph-rewrite/inputs/BORROW-WORD-43extra.json.gz differ
diff --git a/research/staged544-a2-graph-rewrite/inputs/PR3945-WORD-base.json.gz b/research/staged544-a2-graph-rewrite/inputs/PR3945-WORD-base.json.gz
new file mode 100644
index 0000000000..806784bf99
Binary files /dev/null and b/research/staged544-a2-graph-rewrite/inputs/PR3945-WORD-base.json.gz differ
diff --git a/research/staged544-a2-graph-rewrite/inputs/PR3945-WORD-extra.json.gz b/research/staged544-a2-graph-rewrite/inputs/PR3945-WORD-extra.json.gz
new file mode 100644
index 0000000000..c531be7383
Binary files /dev/null and b/research/staged544-a2-graph-rewrite/inputs/PR3945-WORD-extra.json.gz differ
diff --git a/research/staged544-a2-graph-rewrite/search.py b/research/staged544-a2-graph-rewrite/search.py
new file mode 100644
index 0000000000..abd38e9d34
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/search.py
@@ -0,0 +1,192 @@
+# SPDX-License-Identifier: Apache-2.0
+"""A2 graph change, jointly framed, with exact chronological invoices.
+Chris R / Clear1nsight; substantial OpenAI Codex assistance.
+PR3886 tracing/subspace representation is credited reuse, not independent code.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction as Q
+from functools import lru_cache
+from pathlib import Path
+import hashlib,json,types,itertools
+P=Path(__file__).resolve().parent
+
+def require(ok,msg):
+    if not ok: raise ValueError(msg)
+
+def module(name,path):
+    m=types.ModuleType(name);m.__file__=str(path)
+    exec(compile(path.read_bytes(),str(path),'exec'),m.__dict__);return m
+R=module('retained_retiming',P/'vendor/retiming.py')
+
+def digest(x):return hashlib.sha256(json.dumps(x,sort_keys=True,separators=(',',':')).encode()).hexdigest()
+
+def chain(g,h):
+    return g[0]==h[0]=='add' and len(set(g[1:3]+h[1:3]))==3 and (g[1]==h[2] or g[2]==h[1])
+
+def expand(g,h,position):
+    require(chain(g,h),'not an A2 chain');require(position in (0,1,2),'central position')
+    a,b=Q(g[3],g[4]),Q(h[3],h[4])
+    # Chronological composition acts on column vectors on the left.
+    if g[2]==h[1]: t,s,c=g[1],h[2],-a*b
+    else: t,s,c=h[1],g[2],a*b
+    central=['add',t,s,c.numerator,c.denominator,[]]
+    out=[deepcopy(h),deepcopy(g)];out.insert(position,central);return out
+
+def matrix(gates):
+    regs=sorted({r for g in gates for r in g[1:3]});index={r:i for i,r in enumerate(regs)}
+    rows=[[Q(i==j) for j in range(len(regs))] for i in range(len(regs))]
+    for g in gates:
+        require(g[0]=='add','matrix ADD domain');t,s=index[g[1]],index[g[2]]
+        require(t!=s,'self ADD');a=Q(g[3],g[4]);rows[t]=[x+a*y for x,y in zip(rows[t],rows[s])]
+    return regs,rows
+
+@lru_cache(None)
+def frames(low,high):
+    if not R.contained(low,high):return ()
+    require(R.rank(high)-R.rank(low)<=4,'frame quotient resource cap')
+    seen={low};todo=[low]
+    while todo:
+        u=todo.pop()
+        for v in range(1,512):
+            if high>>v&1 and not u>>v&1:
+                z=R.join(u,R.span((v,)))
+                if z not in seen:seen.add(z);todo.append(z)
+    return tuple(sorted(seen))
+
+def boundary(nodes,where,word,section,index,length=2):
+    gates=word[section][index:index+length];bounds={};old=Counter()
+    for r in sorted({r for g in gates for r in R.touched(g)}):
+        indices=[i for i in range(index,index+length) if r in R.touched(word[section][i])]
+        seq=nodes[r];a=where[((section,indices[0]),r)];b=where[((section,indices[-1]),r)]
+        require(seq[b+1][1]!='map','missing fixed warp-entry check')
+        bounds[r]=(seq[a][2],seq[b+1][3])
+        for k in range(a,b+2):old[R.rank(seq[k][3])-R.rank(seq[k][2])]+=1
+    return bounds,old
+
+def apply(word,section,index,gates,C,old_length=2):
+    out=deepcopy(word);out[section][index:index+old_length]=deepcopy(gates)
+    if section=='B':
+        for rec in out['warps']:
+            if rec[0]>=index+old_length:rec[0]+=len(gates)-old_length
+    out['cleanup']=C.derive_cleanup(out)
+    return out
+
+def invoice(bounds,gates):
+    cur={r:p for r,(p,q) in bounds.items()};bill=Counter()
+    for g in gates:
+        u=R.span(tuple(g[-1]))
+        for r in R.touched(g):
+            require(R.contained(cur[r],u) and R.contained(u,bounds[r][1]),'illegal frame')
+            bill[R.rank(u)-R.rank(cur[r])]+=1;cur[r]=u
+    for r,(p,q) in bounds.items():bill[R.rank(q)-R.rank(cur[r])]+=1
+    return bill
+
+def enumerate_flags(bounds,gates,intervals):
+    def visit(t,cur,chosen):
+        if t==len(gates):yield chosen;return
+        a,b=gates[t][1:3];low=R.join(cur[a],cur[b]);high=bounds[a][1]&bounds[b][1]
+        intervals.add((low,high))
+        for u in frames(low,high):
+            nextcur=cur.copy();nextcur[a]=nextcur[b]=u
+            yield from visit(t+1,nextcur,chosen+[u])
+    yield from visit(0,{r:p for r,(p,q) in bounds.items()},[])
+
+def relaxed(bounds,gates,old):
+    count=optimistic=0
+    for dims in itertools.product(range(10),repeat=3):
+        cur={r:R.rank(p) for r,(p,q) in bounds.items()};bill=Counter();ok=True
+        for g,d in zip(gates,dims):
+            for r in R.touched(g):
+                if not cur[r]<=d<=R.rank(bounds[r][1]):ok=False;break
+                bill[d-cur[r]]+=1;cur[r]=d
+            if not ok:break
+        if ok:
+            for r,(p,q) in bounds.items():bill[R.rank(q)-cur[r]]+=1
+            delta=[0]+[bill[r]-old[r] for r in range(1,10)];count+=1
+            optimistic+=not R.all_power_nonnegative(delta)
+    return count,optimistic
+
+def inverse_sites(word):
+    found=[]
+    for section in ('A','B','restore'):
+        for lo,hi in R.segments(word,section):
+            for i in range(lo,hi-2):
+                block=word[section][i:i+3]
+                if not all(g[0]=='add' for g in block):continue
+                for pos in (0,1,2):
+                    remaining=[g for j,g in enumerate(block) if j!=pos]
+                    g,h=remaining[::-1]
+                    if chain(g,h):
+                        expected=expand(g,h,pos)
+                        if all(a[:3]==b[:3] and Q(a[3],a[4])==Q(b[3],b[4]) for a,b in zip(block,expected)):
+                            found.append([section,i,pos])
+    return found
+
+def compute(word,C):
+    nodes,where,baseline=R.tracing(word);hist=Counter();records=[];intervals=set();motifs=[];inverse=[]
+    rejected=[];optimistic=Counter();matrix_count=0;inverse=inverse_sites(word)
+    for section in ('A','B','restore'):
+        for lo,hi in R.segments(word,section):
+            for i in range(lo,hi-1):
+                g,h=word[section][i:i+2]
+                if not chain(g,h):continue
+                bounds,old=boundary(nodes,where,word,section,i);motifs.append([section,i])
+                for pos in (0,1,2):
+                    new=expand(g,h,pos);require(matrix([g,h])==matrix(new),'A2 matrix identity');matrix_count+=1
+                    rc,ro=relaxed(bounds,new,old);optimistic['dimension_triples']+=rc;optimistic['uncertified_triples']+=ro
+                    for flag in enumerate_flags(bounds,new,intervals):
+                        gates=deepcopy(new)
+                        for gate,u in zip(gates,flag):gate[-1]=list(R.basis(u))
+                        local=invoice(bounds,gates);delta=tuple([0]+[local[r]-old[r] for r in range(1,10)])
+                        require(R.all_power_nonnegative(delta),'uncertified exact signed profile')
+                        moved=apply(word,section,i,gates,C)
+                        try: bill,widths,*_=C.frame_bill(moved)
+                        except C.AuditFailure as e:
+                            rejected.append([section,i,pos,[list(R.basis(u)) for u in flag],str(e)]);continue
+                        C.hygiene(moved)
+                        require(all(bill.get(r,0)-baseline.get(r,0)==delta[r] for r in range(1,10)),'whole invoice mismatch')
+                        require(matrix([g,h])==matrix(gates),'dirty frame assignment')
+                        # The inverse cleanup projected to non-target registers is checked
+                        # separately: target reads cannot feed non-targets under hygiene.
+                        projected_before=[x for x in [g,h] if not C.is_target(x[1])]
+                        projected_after=[x for x in gates if not C.is_target(x[1])]
+                        regs=sorted({r for x in [g,h]+gates for r in x[1:3]})
+                        require(embedded_matrix(projected_before,regs)==embedded_matrix(projected_after,regs),'projected cleanup matrix')
+                        hist[delta]+=1
+                        records.append({'section':section,'index':i,'central_position':pos,'gates':gates,'delta':list(delta),'cleanup_length':len(moved['cleanup']),
+                                        'profile':bill,'central_scalar':[new[pos][3],new[pos][4]]})
+    return {'motifs':motifs,'matrix_identity_checks':matrix_count,'inverse_contractions':inverse,
+            'optimistic_dimension_relaxation':dict(optimistic),'compatible_flags':sum(hist.values())+len(rejected),'legal_flags':len(records),
+            'fixed_boundary_rejections':rejected,'profiles':[{'delta':list(d),'count':n} for d,n in sorted(hist.items())],
+            'intervals':[[str(l),str(h)] for l,h in sorted(intervals)],'records':records,
+            'contractions':contract(word,C,inverse,nodes,where,baseline)}
+
+def embedded_matrix(gates,regs):
+    rows={r:{s:Q(r==s) for s in regs} for r in regs}
+    for g in gates:
+        t,s=g[1:3];a=Q(g[3],g[4]);rows[t]={r:rows[t][r]+a*rows[s][r] for r in regs}
+    return rows
+
+
+def contract(word,C,inverse,nodes,where,baseline):
+    rows=[];intervals=set()
+    for section,i,pos in inverse:
+        block=word[section][i:i+3]
+        remainder=[g for j,g in enumerate(block) if j!=pos]
+        gates=[deepcopy(remainder[1]),deepcopy(remainder[0])]
+        require(matrix(block)==matrix(gates),'inverse A2 matrix')
+        bounds,old=boundary(nodes,where,word,section,i,3)
+        for flag in enumerate_flags(bounds,gates,intervals):
+            candidate=deepcopy(gates)
+            for g,u in zip(candidate,flag):g[-1]=list(R.basis(u))
+            bill=invoice(bounds,candidate);delta=tuple([0]+[bill[r]-old[r] for r in range(1,10)])
+            require(R.all_power_nonnegative(delta),'profitable inverse contraction: retain witness')
+            moved=apply(word,section,i,candidate,C,3)
+            profile,widths,*_=C.frame_bill(moved);C.hygiene(moved)
+            require(all(profile.get(r,0)-baseline.get(r,0)==delta[r] for r in range(1,10)),'inverse invoice')
+            regs=sorted({r for g in block for r in g[1:3]})
+            require(embedded_matrix([g for g in block if not C.is_target(g[1])],regs)==embedded_matrix([g for g in candidate if not C.is_target(g[1])],regs),'inverse projected cleanup')
+            rows.append({'section':section,'index':i,'central_position':pos,'gates':candidate,'delta':list(delta),'profile':profile,'cleanup_length':len(moved['cleanup']),'canonical_word_sha256':digest(moved),
+                         'cleanup_sha256':digest(moved['cleanup']),'post_contraction_inverse_sites':inverse_sites(moved)})
+    return {'records':rows,'intervals':[[str(l),str(h)] for l,h in sorted(intervals)]}
diff --git a/research/staged544-a2-graph-rewrite/vendor/PR3945-NATIVE-LINEAGE-NOTICE b/research/staged544-a2-graph-rewrite/vendor/PR3945-NATIVE-LINEAGE-NOTICE
new file mode 100644
index 0000000000..380e979f0e
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/vendor/PR3945-NATIVE-LINEAGE-NOTICE
@@ -0,0 +1,14 @@
+Anticipatory dirty borrowing: PR2226 (Cinna Davis / 1337isnot1337, with substantial OpenAI Codex assistance) is credited first. Its alias rule, changed-reference K_G handoffs, initial compensation and exact free-operator replay (vendored under new/code/borrow/vendor, see new/code/borrow/NOTICE-PR2226.md) are applied here to the T74 pivot-566+554 words; the native lowering, window-exact owner fill and independent audit of the borrow words are new in this package. Bootstrap carried-cutoff repair: PR1956 (Josie Elliston); Lemma G label/adapter checks and X/Y/Z mutants: PR1964 (thakrarsagar), extended here with borrow warp/zero-buffer controls.
+
+New research prepared by Rohan Arun with substantial OpenAI Codex assistance. Apache-2.0. Parent words and build recipe method derive from Jeremy Kothe PR1274 and Rohan Arun PR1218, with lineage credited in README.md. All inherited mathematical qualifications are retained.
+Additional pivot555 and567 composition by Rohan Arun with substantial OpenAI Codex assistance.
+
+T74 exact-fill owner construction by Rohan Arun with substantial OpenAI Codex assistance.
+
+PR1377 grid refinement credited to Jeremy Kothe. Outer witness refinement by Rohan Arun with OpenAI Codex assistance; construction unchanged.
+
+Pivot-566 kernel, words, edits, rebuild.py and rebind.py: PR1625 (mdumitrean). Endpoint/outer-witness stacking, fine_cache.py and oracle stage by jeremykothe2 with oh-my-pi assistance.
+
+The preceding paragraphs are inherited source notices, not attribution of this derivative.
+This joint twelve-source construction, generator, independent replay, hosting composition and package: Tekalign (@tekuuu), with substantial OpenAI Codex assistance. No independent human review claimed.
+Credits: Cinna Davis/PR2226 anticipatory dirty borrowing; Tekalign/PR2436 four lifted targets; Jeremy Kothe/PR2462,2588,2673 source pipeline, source-label swap and order/fill; zxv/PR2530 eight aliases; Mason Hale/PR2696 concentrated source-partner assignment and independent local interpreter; Philippe Van Velzen/PR2559,2679 evacuation, six pre-life hosts and refit/alias; themilkman216/PR2621 priority order; Marius-Paul Dumitrean/PR2733 independent concentrated/pre-life composition; Vlado Vojdanovski/PR2322 generator utilities. PR2720's fixed-old-path cut obstruction motivates the changed premise. The retained owner/native/bit/modern outer lineage and their notices remain in the pinned source. New work Apache-2.0.
diff --git a/research/staged544-a2-graph-rewrite/vendor/SOURCE-CREDITS.md b/research/staged544-a2-graph-rewrite/vendor/SOURCE-CREDITS.md
new file mode 100644
index 0000000000..c054fad87e
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/vendor/SOURCE-CREDITS.md
@@ -0,0 +1,14 @@
+# Source credit and independence
+
+New work: dataisfire with substantial OpenAI Codex assistance, Apache-2.0. No independent human review, fresh third-party AI review or proof-kernel verification is claimed.
+
+The construction extends [PR3682](https://github.com/CrocSwap/integer-mult-bounds/pull/3682), head431e6c6023ef352c41696469de7fb614cd4ded8c. Its retimed word, actual T360 source clock and immutable native/parent framework are retained. The complete new source/receipt snapshot is bound by REPLAY-INPUTS.json. The new ordinary source stage is an explicit pinned record applied after the unchanged predecessor reconstruction.
+
+- [PR3605](https://github.com/CrocSwap/integer-mult-bounds/pull/3605), Ross Richardson, supplies the staged-entrance mechanism, literal cleanup and exact Gaussian residual-check pattern. staged_pair.py is retained; the new544 shear and its proof are separate.
+- [PR3638](https://github.com/CrocSwap/integer-mult-bounds/pull/3638), head d62e1acd7518a231440383f0d0dddf54d6edf8c1, supplies the T360 source-window clock, chronological aggregate model and integral-network/literal construction, with its retained PR3605 and earlier credits. The new inventory, integer incumbent and literal fill are recomputed. No predecessor owner receipt is used as proof of the new fill.
+- [PR3687](https://github.com/CrocSwap/integer-mult-bounds/pull/3687) and [PR3693](https://github.com/CrocSwap/integer-mult-bounds/pull/3693), Sagar Thakrar and roger-sato with their credited AI assistance, supply audit_core.py and the whole-word semantics adapter audit_verify.py. These bytes are retained and reused. They are independent of the current constructor in the stated interpreter scope, not a newly written independent audit or new reviewer approval.
+- The coupled-word source lineage includes PR3133, PR2979, Marius-Paul Dumitrean, dcharb78, Jeremy Kothe and the retained native/owner/block-norm/outer authors. All notices and scientific engines inside the source snapshot remain intact.
+
+owner_audit.py is a standalone standard-library adaptation of the source-window/family/prefix/invoice predicates in PR3638's independent_literal.py. It imports no producer, optimizer or retained owner checker. Its source template, plan and actual native canonical words are authenticated inputs. Three controls mutate actual literal roles and must fail for the intended reason. It shares the credited contract interpretation; it is not evidence of independent human agreement.
+
+The rational finite-price enclosure is retained from the PR3682 sources. New script adapters bind it to the actual finite histogram. Native forward/backward scalar replay, wrapper/phase lowering and all-column warp recipes were freshly run for both new words; unchanged native and parent ancestry is explicitly reused. The separate new544 span(414,51) residual check includes global Gaussian phase.
diff --git a/research/staged544-a2-graph-rewrite/vendor/audit_core.py b/research/staged544-a2-graph-rewrite/vendor/audit_core.py
new file mode 100644
index 0000000000..8b5e1d5f2a
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/vendor/audit_core.py
@@ -0,0 +1,480 @@
+"""Independent exact semantics and binary-frame bill for the BORROW-WORD format.
+
+Standard library only. Nothing is imported from the audited authors' code
+(PR3133/PR3605 producers, cleanup generator, evaluator or frame solver); the word
+format and its semantic contract were read from those pinned sources and are
+credited there.  The frame-bill and free-word structure (point-set spans, warp
+frame and lifted-frame checks, target levels keyed by register, dual symbol
+naming) re-implements, without importing, Arham Tahir's
+research/coupled-carrier-independent-audit/verify.py (Apache-2.0) and shares its
+reading of the contract, so this module is not independent of that audit.
+
+Sagar Thakrar (thakrarsagar), with substantial AI assistance from Claude
+(Anthropic, Claude Opus 5.5). Apache-2.0.
+"""
+from collections import Counter
+from fractions import Fraction as Q
+
+V, N, H = 112, 704, 9          # sources 0..111, targets 112..223, helpers 224..703
+DUAL = 10 ** 6                  # offset naming the independent dual symbols D_k = K_k^(-T)
+
+
+class AuditFailure(Exception):
+    """Explicit failure; never disabled by python -O."""
+
+
+def need(ok, *why):
+    if not ok:
+        raise AuditFailure(' '.join(map(str, why)))
+
+
+def is_target(r):
+    return V <= r < 2 * V
+
+
+def touched(g):
+    return g[1:3] if g[0] == 'add' else g[1:2]
+
+
+# ----------------------------------------------------------------------------
+# Binary frames: a subspace of F_2^9 is stored as a 512-bit point-set mask
+# (bit x set iff x lies in the subspace).  Containment is mask inclusion.
+# ----------------------------------------------------------------------------
+_SPAN = {}
+
+
+def span(vectors):
+    key = tuple(vectors)
+    mask = _SPAN.get(key)
+    if mask is None:
+        points = {0}
+        for u in key:
+            need(type(u) is int and 0 <= u < 512, 'frame vector out of range', u)
+            if u not in points:
+                points |= {p ^ u for p in points}
+        mask = sum(1 << p for p in points)
+        _SPAN[key] = mask
+    return mask
+
+
+def points(mask):
+    return [x for x in range(512) if mask >> x & 1]
+
+
+def dim(mask):
+    size = bin(mask).count('1')
+    need(size and size & (size - 1) == 0, 'not a subspace point set')
+    return size.bit_length() - 1
+
+
+FULL = (1 << 512) - 1
+ZERO = 1
+
+
+def hyperplane(port):
+    return sum(1 << x for x in range(512) if bin(x & port).count('1') % 2 == 0)
+
+
+def warp_images(columns):
+    """Images of all 512 vectors under the F_2-linear map with columns G e_i."""
+    need(len(columns) == H and all(type(c) is int and 0 <= c < 512 for c in columns), 'warp columns')
+    images = [0] * 512
+    for x in range(1, 512):
+        low = x & -x
+        images[x] = images[x ^ low] ^ columns[low.bit_length() - 1]
+    need(len(set(images)) == 512, 'singular warp')
+    return images
+
+
+def image_mask(images, mask):
+    return sum(1 << images[x] for x in points(mask))
+
+
+def lagrangian_action_ok(images, U, E):
+    """K_G(x,z)=(Gx, Gx+G^{-T}(x+z)) is symplectic and maps L_U to L_E, L_0 and L_FULL to themselves.
+
+    L_U={(x,x+p): x in U, p in U^perp}.  This is the binary frame action only; it
+    is not a Clifford phase or Gaussian-product certificate.  For invertible G with
+    G(U)=E it is implied by the frame-map check (<G^-T p, Gu> = <p, u>), so it is a
+    consistency check of the implementation, not extra evidence.
+    """
+    inverse = [0] * 512
+    for x, y in enumerate(images):
+        inverse[y] = x
+    # G^{-T} z: bit j of the result is <G^{-1} e_j, z>.
+    git = lambda z: sum((bin(inverse[1 << j] & z).count('1') & 1) << j for j in range(H))
+    lift = lambda x, z: (images[x], images[x] ^ git(x ^ z))
+    pair = lambda a, b: (bin(a[0] & b[1]).count('1') + bin(a[1] & b[0]).count('1')) & 1
+    basis = [(1 << i, 0) for i in range(H)] + [(0, 1 << i) for i in range(H)]
+    lifted = [lift(*b) for b in basis]
+    if any(pair(lifted[i], lifted[j]) != pair(basis[i], basis[j]) for i in range(18) for j in range(i + 1, 18)):
+        return False
+
+    def frame(mask):
+        us = points(mask)
+        perp = [p for p in range(512) if all(bin(p & u).count('1') % 2 == 0 for u in us)]
+        return {(u, u ^ p) for u in us for p in perp}
+    return all({lift(*pt) for pt in frame(a)} == frame(b) for a, b in ((ZERO, ZERO), (FULL, FULL), (U, E)))
+
+
+# ----------------------------------------------------------------------------
+# Chronological binary-frame bill (BORROW-WORD contract)
+# ----------------------------------------------------------------------------
+def frame_bill(w, lagrangian=False):
+    rep = w['report']
+    need((rep['v'], 2 * rep['v'] + rep['R'], rep['h']) == (V, N, H), 'word geometry')
+    removed = set(w['removed'])
+    need(len(removed) == len(w['removed']) and all(2 * V <= r < N for r in removed), 'removed helpers')
+    live = [r for r in range(N) if r not in removed]
+    liveset = set(live)
+    B, warps = w['B'], w['warps']
+    for k, (pos, lender, cols, U, E) in enumerate(warps, 1):
+        need(0 <= pos <= len(B), 'warp position', k)
+        need(lender in liveset and not is_target(lender), 'warp lender', k)
+        images = warp_images(cols)
+        su, se = span(U), span(E)
+        need(dim(su) == len(U) == len(E) == dim(se), 'warp frame bases', k)
+        need(image_mask(images, su) == se, 'warp does not map its frame', k)
+        if lagrangian:
+            need(lagrangian_action_ok(images, su, se), 'lifted frame action', k)
+    for name in ('A', 'B', 'restore'):
+        for g in w[name]:
+            if g[0] != 'warp':
+                need(all(r in liveset for r in touched(g)), 'removed/out-of-range register', name, g)
+                if g[0] == 'add' and not is_target(g[1]):
+                    need(not is_target(g[2]), 'non-target reads a target', name, g)
+    need(all(g[-1] is None and is_target(g[1]) and g[0] == 'add' for g in w['cut']), 'cut gates')
+    need(all(g[-1] == [] and is_target(g[1]) for g in w['precondition'] + w['compensation']), 'zero-frame wrapper writes')
+    need(all(not is_target(g[1]) for g in w['restore']), 'restore writes a target')
+
+    ports = w['ports']
+    start, end = {}, {}
+    for r in live:
+        if r < V:
+            start[r], end[r] = span((ports[r],)), FULL
+        elif r < 2 * V:
+            start[r], end[r] = ZERO, hyperplane(ports[r - V])
+        else:
+            start[r], end[r] = ZERO, FULL
+    for q, U in w['start_extra'].items():
+        need(int(q) in liveset and int(q) >= 2 * V, 'entrance names a live helper', q)
+        start[int(q)] = span(U)
+    for q, U in w['helper_final'].items():
+        need(int(q) in liveset and int(q) >= 2 * V, 'terminal names a live helper', q)
+        end[int(q)] = span(U)
+
+    current, bill, chain = dict(start), Counter(), {}
+
+    def climb(r, mask, where):
+        need(current[r] & ~mask == 0, 'frame containment fails', where, r)
+        d = dim(mask) - dim(current[r])
+        if d:
+            bill[d] += 1
+        chain.setdefault(r, []).append((where, d, mask))
+        current[r] = mask
+
+    npre = w['prelude_events']
+    for i, g in enumerate(w['A']):
+        if g[0] == 'warp':
+            need(i < npre and len(g) == 5, 'warp outside the prelude', i)
+            _, r, op, fr, to = g
+            need(op != 0 and abs(op) <= len(warps) and warps[abs(op) - 1][1] == r, 'prelude warp lender', i)
+            images = warp_images(warps[abs(op) - 1][2])
+            if op < 0:
+                inverse = [0] * 512
+                for x, y in enumerate(images):
+                    inverse[y] = x
+                images = inverse
+            need(image_mask(images, span(fr)) == span(to), 'prelude warp frame action', i)
+            need(current[r] == span(fr), 'prelude warp entry frame', i, r)
+            current[r] = span(to)
+            chain.setdefault(r, []).append((('A', i), 'warp', span(to)))
+        else:
+            if i < npre:
+                need(is_target(g[1]), 'prelude scalar writes a non-target', i)
+            for r in touched(g):
+                climb(r, span(g[-1]), ('A', i))
+    levels = {V + int(t): span(U) for t, U in w['target_levels'].items()}
+    need(all(current[t] == levels.get(t, ZERO) for t in range(V, 2 * V)), 'target cut levels')
+    for q, U in zip(w['centers'], w['center_frames']):
+        U = span(U)
+        need(current[q] == U, 'centre entry frame', q)
+        served = {levels.get(g[1], ZERO) for g in w['cut'] if g[2] == q}
+        for T in sorted(served, key=lambda m: -dim(m)):
+            need(T & ~U == 0, 'centre descent not nested', q)
+            d = dim(U) - dim(T)
+            if d:
+                bill[d] += 1
+                chain.setdefault(q, []).append((('centre',), d, T))
+            U = T
+    at = {}
+    for k, rec in enumerate(warps, 1):
+        at.setdefault(rec[0], []).append(k)
+    for p in range(len(B) + 1):
+        for k in at.get(p, ()):
+            _, lender, _, U, E = warps[k - 1]
+            need(current[lender] == span(U), 'native warp entry frame', k, lender)
+            current[lender] = span(E)
+            chain.setdefault(lender, []).append((('warp', k), 'warp', span(E)))
+        if p < len(B):
+            for r in touched(B[p]):
+                climb(r, span(B[p][-1]), ('B', p))
+    for i, g in enumerate(w['restore']):
+        for r in touched(g):
+            climb(r, span(g[-1]), ('restore', i))
+    for r in live:
+        climb(r, end[r], ('end',))
+    restored = set(map(int, w['helper_final']))
+    need(all(end[r] == FULL for r in live if r not in restored and not is_target(r)), 'a FULL-cleanup register ends low')
+    widths = Counter(dim(end[r]) - dim(start[r]) for r in live if r >= 2 * V)
+    return dict(sorted(bill.items())), dict(sorted(widths.items())), chain, start, end
+
+
+def hygiene(w):
+    """Inherited structural contract: dyadic scalars, power-of-two scales, wrapper and correction access."""
+    entering = set(map(int, w['start_extra']))
+    restored = set(map(int, w['helper_final']))
+    live = set(range(N)) - set(w['removed'])
+    for name in ('precondition', 'compensation', 'A', 'cut', 'B', 'restore', 'cleanup'):
+        for g in w[name]:
+            if g[0] == 'warp':
+                continue
+            q = Q(g[3], g[4]) if g[0] == 'add' else Q(g[2], g[3])
+            need(q != 0 and q.denominator & (q.denominator - 1) == 0, 'non-dyadic scalar', name, g)
+            if g[0] == 'scale':
+                need(abs(q.numerator) & (abs(q.numerator) - 1) == 0, 'non power-of-two scale', name, g)
+    for g in w['precondition'] + w['compensation']:
+        need(not any(r in entering | restored for r in touched(g)), 'wrapper touches an entering or restored helper', g)
+    for c in w['initial_corrections']:
+        word = c['operator_word']
+        need(is_target(c['target']) and c['source'] in live and c['source'] >= 2 * V
+             and c['source'] not in entering, 'correction access', c)
+        need(word and all(w['warps'][abs(o) - 1][1] == c['source'] for o in word), 'correction operator lender', c)
+        q = Q(c['coefficient'])
+        need(q != 0 and q.denominator & (q.denominator - 1) == 0, 'correction coefficient', c)
+    return True
+
+
+# ----------------------------------------------------------------------------
+# Literal inverse cleanup, derived from the contract
+# ----------------------------------------------------------------------------
+def ordinary_forward(w):
+    """Chronological non-wrapper actions whose inverse forms cleanup."""
+    out = [g for g in w['A'][w['prelude_events']:]]
+    at = {}
+    for k, rec in enumerate(w['warps'], 1):
+        at.setdefault(rec[0], []).append(['warp', rec[1], k])
+    for p in range(len(w['B']) + 1):
+        out += at.get(p, [])
+        if p < len(w['B']):
+            out.append(w['B'][p])
+    return out + list(w['restore'])
+
+
+def derive_cleanup(w):
+    restored = set(map(int, w['helper_final']))
+    buf = lambda r: r + N if r in restored else r
+    full = [256, 128, 64, 32, 16, 8, 4, 2, 1]
+    out = []
+    for g in reversed(ordinary_forward(w)):
+        if g[0] == 'warp':
+            out.append(['warp', buf(g[1]), -g[2], full])
+        elif is_target(g[1]):
+            continue
+        elif g[0] == 'add':
+            out.append(['add', buf(g[1]), buf(g[2]), -g[3], g[4], full])
+        else:
+            need(g[0] == 'scale', 'unknown primitive', g)
+            out.append(['scale', buf(g[1]), g[3], g[2], full])
+    return out
+
+
+def same_cleanup(a, b):
+    norm = lambda c: [(g[:-1], span(g[-1])) for g in c]
+    return len(a) == len(b) and norm(a) == norm(b)
+
+
+# ----------------------------------------------------------------------------
+# Exact free-operator semantics.  A value is a dict {(input, word): Fraction};
+# word is a reduced tuple of signed operator ids (leftmost = applied last).
+# ----------------------------------------------------------------------------
+def program(w, cleanup=None):
+    """Literal executed sequence: corrections, wrapper, A, cut, B+warps, restore | cleanup."""
+    items = [('corr', c['target'], c['source'], tuple(c['operator_word']), Q(c['coefficient']))
+             for c in w['initial_corrections']]
+    items += w['precondition'] + w['compensation'] + w['A'] + w['cut']
+    at = {}
+    for k, rec in enumerate(w['warps'], 1):
+        at.setdefault(rec[0], []).append(['warp', rec[1], k])
+    for p in range(len(w['B']) + 1):
+        items += at.get(p, [])
+        if p < len(w['B']):
+            items.append(w['B'][p])
+    items += w['restore']
+    return items, list(w['cleanup'] if cleanup is None else cleanup)
+
+
+def dual_op(op):
+    return (1 if op > 0 else -1) * (abs(op) + DUAL)
+
+
+def _left(op, word):
+    return word[1:] if word and word[0] == -op else (op,) + word
+
+
+def _right(word, op):
+    return word[:-1] if word and word[-1] == -op else word + (op,)
+
+
+def _axpy(dst, src, q):
+    for key, x in src.items():
+        y = dst.get(key, 0) + q * x
+        if y:
+            dst[key] = y
+        else:
+            dst.pop(key, None)
+
+
+def forward_rows(w, cleanup=None, dual=False, symbolic_buffers=True, snapshot=None):
+    """Schrodinger pass: every register's value as a combination of initial inputs.
+
+    Live inputs are independent symbols.  Private buffers are independent symbols
+    when symbolic_buffers is set (dirty), otherwise zero.  The optional snapshot
+    callback sees the rows at the cleanup boundary.
+    """
+    removed = set(w['removed'])
+    live = [r for r in range(N) if r not in removed]
+    restored = sorted(map(int, w['helper_final']))
+    rows = {r: {(r, ()): Q(1)} for r in live}
+    for c in restored:
+        rows[c + N] = {(c + N, ()): Q(1)} if symbolic_buffers else {}
+    prefix, tail = program(w, cleanup)
+
+    def apply(g):
+        kind = g[0]
+        if kind == 'add':
+            t, s, q = g[1], g[2], Q(g[3], g[4])
+            need(t != s and q, 'add gate', g)
+            if dual:
+                t, s, q = s, t, -q
+            _axpy(rows[t], rows[s], q)
+        elif kind == 'scale':
+            q = Q(g[2], g[3])
+            need(q != 0, 'zero scale', g)
+            if dual:
+                q = 1 / q
+            rows[g[1]] = {k: q * x for k, x in rows[g[1]].items()}
+        elif kind == 'warp':
+            op = dual_op(g[2]) if dual else g[2]
+            rows[g[1]] = {(var, _left(op, word)): x for (var, word), x in rows[g[1]].items()}
+        elif kind == 'corr':
+            _, t, s, word, c = g
+            if dual:
+                src, ops, dst, c = rows[t], [-dual_op(o) for o in word], s, -c
+            else:
+                src, ops, dst = rows[s], list(reversed(word)), t
+            moved = {}
+            for (var, wd), x in src.items():
+                for o in ops:
+                    wd = _left(o, wd)
+                moved[var, wd] = x
+            _axpy(rows[dst], moved, c)
+        else:
+            raise AuditFailure('unknown primitive ' + repr(g))
+
+    for g in prefix:
+        apply(g)
+    if snapshot is not None:
+        snapshot(rows)
+    for g in tail:
+        apply(g)
+    return rows
+
+
+def reverse_columns(w, cleanup=None, upto_cleanup=False):
+    """Heisenberg pull-back: process the forward program backwards.
+
+    cols[s] = {(output, word): coefficient}: the final output register 'output'
+    contains coefficient*word*x_s.  Words grow on the right.  Every live input and
+    every private buffer is an independent symbol.
+    """
+    removed = set(w['removed'])
+    live = [r for r in range(N) if r not in removed]
+    restored = sorted(map(int, w['helper_final']))
+    regs = live + [c + N for c in restored]
+    cols = {r: {(r, ()): Q(1)} for r in regs}
+    prefix, tail = program(w, cleanup)
+    seq = prefix if upto_cleanup else prefix + tail
+    for g in reversed(seq):
+        kind = g[0]
+        if kind == 'add':
+            t, s, q = g[1], g[2], Q(g[3], g[4])
+            need(t != s and q, 'add gate', g)
+            _axpy(cols[s], cols[t], q)
+        elif kind == 'scale':
+            q = Q(g[2], g[3])
+            need(q != 0, 'zero scale', g)
+            cols[g[1]] = {k: q * x for k, x in cols[g[1]].items()}
+        elif kind == 'warp':
+            op = g[2]
+            cols[g[1]] = {(out, _right(word, op)): x for (out, word), x in cols[g[1]].items()}
+        elif kind == 'corr':
+            _, t, s, word, c = g
+            moved = {}
+            for (out, wd), x in cols[t].items():
+                for o in word:
+                    wd = _right(wd, o)
+                moved[out, wd] = x
+            _axpy(cols[s], moved, c)
+        else:
+            raise AuditFailure('unknown primitive ' + repr(g))
+    return cols
+
+
+def transpose(cols):
+    rows = {}
+    for s, col in cols.items():
+        for (r, word), x in col.items():
+            rows.setdefault(r, {})[s, word] = x
+    return rows
+
+
+def endpoint_defects(w, rows, dual=False):
+    """Compare final rows with the contract on the zero-buffer (live-input) domain.
+
+    Returns (bad live registers, dirty buffers, buffer->live leaks, buffer self-map identity).
+    """
+    removed = set(w['removed'])
+    live = [r for r in range(N) if r not in removed]
+    restored = sorted(map(int, w['helper_final']))
+    bad = []
+    for r in live:
+        expect = {(r, ()): Q(1)}
+        if dual and r < V:
+            expect[r + V, ()] = Q(-1)
+        if not dual and is_target(r):
+            expect[r - V, ()] = Q(1)
+        got = {k: x for k, x in rows.get(r, {}).items() if k[0] < N}
+        if got != expect:
+            bad.append(r)
+    dirty = [c for c in restored if any(k[0] < N for k in rows.get(c + N, {}))]
+    leaks = sorted({r for r in live for k in rows.get(r, {}) if k[0] >= N})
+    buffer_identity = all({k: x for k, x in rows.get(c + N, {}).items() if k[0] >= N} == {(c + N, ()): Q(1)}
+                          for c in restored)
+    return bad, dirty, leaks, buffer_identity
+
+
+def boundary_defects(w, rows):
+    """Contract at the cleanup boundary (forward): targets sheared, restored helpers clean and isolated."""
+    restored = set(map(int, w['helper_final']))
+    out = []
+    for t in range(V, 2 * V):
+        if {k: x for k, x in rows[t].items() if k[0] < N} != {(t, ()): Q(1), (t - V, ()): Q(1)}:
+            out.append(('target', t))
+    for c in restored:
+        if rows[c] != {(c, ()): Q(1)}:
+            out.append(('restored', c))
+    for r, row in rows.items():
+        if r < N and r not in restored and any(k[0] in restored for k in row):
+            out.append(('restored input read', r))
+    return out
diff --git a/research/staged544-a2-graph-rewrite/vendor/audit_verify.py b/research/staged544-a2-graph-rewrite/vendor/audit_verify.py
new file mode 100644
index 0000000000..7f9fc1df42
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/vendor/audit_verify.py
@@ -0,0 +1,254 @@
+#!/usr/bin/env python3
+"""Whole-word cross-check of published RETIMED and DELAYED supplier words.
+
+Reuses Sagar Thakrar's exact PR3687 audit_core, unchanged and authenticated
+before execution. This is not a new interpreter. No construction/native checker
+is imported. roger-sato with substantial OpenAI Codex assistance; Apache-2.0.
+"""
+from collections import Counter
+from copy import deepcopy
+import gzip
+import hashlib
+import json
+from pathlib import Path
+import sys
+import types
+
+HERE = Path(__file__).resolve().parent
+STAGED = {1: 2439, 2: 726, 3: 224, 4: 102, 5: 20, 8: 8}
+RETIMED = {1: 2437, 2: 724, 3: 226, 4: 102, 5: 20, 8: 8}
+WIDTHS = {4: 26, 5: 2, 6: 18, 7: 52, 8: 97, 9: 213}
+MOVES = ((591, 1045, 640, 644, 2, [423, 65, 20, 10]),
+         (641, 1085, 656, 660, -1, [427, 96, 24, 6]))
+SOURCE_COMMITS = {
+    3605: '3efbb5de06a49ffeea6684482f2d3fe48cdca3fb',
+    3642: '044d24f12e74f228dd462c07ae2d7f3ea35e2be9',
+    3653: '607a09ff441c79b215a8127a81f4cc70021d0d9b',
+    3682: '431e6c6023ef352c41696469de7fb614cd4ded8c',
+    3687: 'f798838eb8ede4178e94f240e7b7e54b3f80c82d',
+}
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+def authenticate():
+    rows = json.loads((HERE / 'SOURCES.json').read_text())['snapshots']
+    expected = {(3687, 'vendor/audit_core.py')}
+    for provider in ('base', 'extra'):
+        expected.update((number, f'inputs/{kind}-{provider}.json.gz') for number, kind in
+                        ((3605, 'STAGED'), (3642, 'RETIMED'), (3653, 'RETIMED'), (3682, 'DELAYED')))
+    keys = [(row['source_pr'], row['local']) for row in rows]
+    need(len(keys) == len(expected) and set(keys) == expected, 'source mapping inventory differs')
+    for row in rows:
+        need(row['source_commit'] == SOURCE_COMMITS[row['source_pr']], 'source commit differs')
+        raw = (HERE / row['local']).read_bytes()
+        need(len(raw) == row['bytes'], 'source byte length: ' + row['local'])
+        need(hashlib.sha256(raw).hexdigest() == row['sha256'], 'source SHA256: ' + row['local'])
+        blob = hashlib.sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest()
+        need(blob == row['git_blob'], 'source Git blob: ' + row['local'])
+    core = types.ModuleType('retained_audit_core')
+    path = HERE / 'vendor/audit_core.py'
+    # Execute the authenticated source bytes, without accepting a .pyc cache.
+    exec(compile(path.read_bytes(), str(path), 'exec'), core.__dict__)
+    return core
+
+
+def load(kind, provider):
+    return json.loads(gzip.decompress((HERE / 'inputs' / f'{kind}-{provider}.json.gz').read_bytes()))
+
+
+def events(w):
+    result = []
+    for pos in range(len(w['B']) + 1):
+        result += [('warp', k, deepcopy(rec)) for k, rec in enumerate(w['warps']) if rec[0] == pos]
+        if pos < len(w['B']):
+            result.append(('gate', pos, deepcopy(w['B'][pos])))
+    return result
+
+
+def replace_events(w, seq):
+    result = deepcopy(w)
+    body, warps = [], [None] * len(w['warps'])
+    for kind, label, gate in seq:
+        gate = deepcopy(gate)
+        if kind == 'gate':
+            body.append(gate)
+        else:
+            gate[0] = len(body)
+            warps[label] = gate
+    need(all(rec is not None for rec in warps), 'lost warp in reconstruction')
+    result['B'], result['warps'] = body, warps
+    return result
+
+
+def reconstruct(C, staged, kind):
+    """Literal prose recipes: adjacent shear swap, or move before first producer.
+
+    This repeats the credited local structural arguments as an input control;
+    the new evidence is the full word calculation below.
+    """
+    seq = events(staged)
+    for start, stop, donor, pivot, coefficient, frame in MOVES:
+        source = next(x for x in seq if x[:2] == ('gate', start))
+        need(source[2] == ['add', donor, pivot, coefficient, 1, [429, 30]], 'source release')
+        if kind == 'RETIMED':
+            target = next(x for x in seq if x[:2] == ('gate', start + 1))
+            need(target[2][0] == 'add' and target[2][2] == pivot, 'adjacent same-pivot shear')
+            need(not any(rec[0] == start + 1 for rec in staged['warps']), 'unexpected crossed warp')
+            where = seq.index(target) + 1
+        else:
+            target = next(x for x in seq if x[:2] == ('gate', stop))
+            writes = [i for i, g in enumerate(staged['B']) if i > start and g[1] == pivot]
+            need(writes[0] == stop, 'first producer cut')
+            where = seq.index(target)
+        changed = deepcopy(source[2])
+        changed[-1] = frame
+        seq.insert(where, ('gate', -pivot, changed))
+        seq.remove(source)
+    result = replace_events(staged, seq)
+    result['cleanup'] = C.derive_cleanup(result)
+    result['report']['local_profile'] = {str(k): v for k, v in RETIMED.items()}
+    return result
+
+
+def semantics(C, w):
+    """All live and buffer inputs are symbols, with no zero-buffer assumption."""
+    def endpoint(name, result):
+        bad_live, dirty_buffers, leaks, buffer_identity = result
+        need(not bad_live and not dirty_buffers and not leaks and buffer_identity,
+             name + ' endpoint: ' + repr(result))
+    boundary = {}
+    rows = C.forward_rows(w, symbolic_buffers=True,
+                          snapshot=lambda values: boundary.setdefault('defects', C.boundary_defects(w, values)))
+    endpoint('forward', C.endpoint_defects(w, rows))
+    dual_rows = C.forward_rows(w, dual=True, symbolic_buffers=True)
+    endpoint('dual', C.endpoint_defects(w, dual_rows, dual=True))
+    need(not boundary['defects'], 'cleanup boundary: ' + repr(boundary['defects']))
+    pulled = C.transpose(C.reverse_columns(w))
+    need(pulled == {r: row for r, row in rows.items() if row}, 'reverse pull-back differs from forward')
+    pre = C.transpose(C.reverse_columns(w, upto_cleanup=True))
+    pre = {r: pre.get(r, {}) for r in set(pre) | set(range(C.N))}
+    need(not C.boundary_defects(w, pre), 'reverse cleanup-boundary contract')
+    live = C.N - len(w['removed'])
+    buffers = len(w['helper_final'])
+    need((live, buffers, len(rows)) == (632, 91, 723), 'complete symbolic domain')
+    # Endpoint expectations are derived by the retained checker: live x,y,h
+    # map to x,y+x,h; all private buffer symbols return unchanged.
+    return {'live_inputs': live, 'dirty_buffers': buffers, 'matrix_dimension': len(rows),
+            'forward': 'PASS', 'dual': 'PASS', 'reverse_pullback_equals_forward': True,
+            'cleanup_boundary_forward_and_reverse': 'PASS',
+            'buffer_to_live_leaks': 0, 'buffer_self_map': 'identity',
+            'nonzero_endpoint_terms': sum(len(row) for row in rows.values())}
+
+
+def inspect(C, w, profile):
+    C.hygiene(w)
+    bill, widths, chain, _, _ = C.frame_bill(w)
+    need(bill == profile, 'computed profile differs')
+    need(w['report']['local_profile'] == {str(k): v for k, v in bill.items()}, 'declared profile differs')
+    need(widths == WIDTHS, 'helper widths differ')
+    need(w['cleanup'] == C.derive_cleanup(w), 'literal cleanup differs')
+    return {'semantics': semantics(C, w), 'profile': bill, 'widths': widths,
+            'rank_mass': sum(r * n for r, n in bill.items())}, chain
+
+
+def expect_rejection(C, fn, phrase):
+    try:
+        fn()
+    except (ValueError, C.AuditFailure) as exc:
+        need(phrase in str(exc), 'wrong rejection: ' + str(exc))
+        return phrase
+    raise ValueError('mutant unexpectedly passed: ' + phrase)
+
+
+def negative_controls(C, staged, w, kind):
+    controls = []
+    for _, _, donor, pivot, _, _ in MOVES:
+        seq = events(w)
+        release = next(x for x in seq if x[0] == 'gate' and x[2][0] == 'add' and x[2][1:3] == [donor, pivot])
+        for defect in ('omit', 'flip', 'cross_first_producer'):
+            changed = deepcopy(seq)
+            index = seq.index(release)
+            if defect == 'omit':
+                changed.pop(index)
+            elif defect == 'flip':
+                changed[index][2][3] *= -1
+            else:
+                producer = next(x for x in changed[index + 1:] if x[0] == 'gate' and x[2][1] == pivot)
+                moved = changed.pop(index)
+                changed.insert(changed.index(producer) + 1, moved)
+            bad = replace_events(w, changed)
+            bad['cleanup'] = C.derive_cleanup(bad)
+            # Repair the literal inverse so stale cleanup is not the rejection.
+            reason = expect_rejection(C, lambda: semantics(C, bad), 'forward endpoint')
+            controls.append({'defect': defect, 'pivot': pivot, 'rejected_by': reason})
+    old_cleanup = deepcopy(w)
+    old_cleanup['cleanup'] = staged['cleanup']
+    # The inverse shears commute: this is a format failure, not a wrong operator.
+    semantic_control = semantics(C, old_cleanup)
+    need(old_cleanup['cleanup'] != C.derive_cleanup(old_cleanup), 'old cleanup unexpectedly literal')
+    controls.append({'defect': 'old_cleanup_order', 'semantics': semantic_control,
+                     'rejected_by': expect_rejection(C, lambda: inspect(C, old_cleanup, RETIMED), 'literal cleanup differs')})
+    old_frames = deepcopy(w)
+    for gate in old_frames['B']:
+        if gate[0] == 'add' and gate[1:3] in ([640, 644], [656, 660]):
+            gate[-1] = [429, 30]
+    need(semantics(C, old_frames) == semantic_control, 'frame-only mutation changed operator')
+    if kind == 'RETIMED':
+        need(C.frame_bill(old_frames)[0] == STAGED, 'old frame control does not restore staged bill')
+        controls.append({'defect': 'old_release_frames', 'semantic_operator': 'PASS',
+                         'profile': STAGED, 'rejected_by': expect_rejection(C, lambda: inspect(C, old_frames, RETIMED), 'computed profile differs')})
+    else:
+        # The later release encounters a donor that has already climbed, so
+        # the original rank-2 frame is now illegal, despite the same operator.
+        controls.append({'defect': 'old_release_frames', 'semantic_operator': 'PASS',
+                         'rejected_by': expect_rejection(C, lambda: inspect(C, old_frames, RETIMED), 'frame containment fails')})
+    fake_report = deepcopy(w)
+    fake_report['report']['local_profile']['1'] += 1
+    controls.append({'defect': 'wrong_declared_profile', 'rejected_by':
+                     expect_rejection(C, lambda: inspect(C, fake_report, RETIMED), 'declared profile differs')})
+    return controls
+
+
+def run(C):
+    results = {}
+    for provider in ('base', 'extra'):
+        staged = load('STAGED', provider)
+        control, old_chain = inspect(C, staged, STAGED)
+        records = {'STAGED': control}
+        for kind in ('RETIMED', 'DELAYED'):
+            w = load(kind, provider)
+            need(reconstruct(C, staged, kind) == w, 'prose reconstruction differs: ' + kind)
+            record, chain = inspect(C, w, RETIMED)
+            deltas = {}
+            for register in set(chain) | set(old_chain):
+                before = Counter(d for _, d, _ in old_chain.get(register, []) if type(d) is int and d > 0)
+                after = Counter(d for _, d, _ in chain.get(register, []) if type(d) is int and d > 0)
+                delta = {r: after[r] - before[r] for r in set(after) | set(before) if after[r] != before[r]}
+                if delta:
+                    deltas[register] = delta
+            need(deltas == {640: {1: -1, 2: -1, 3: 1}, 656: {1: -1, 2: -1, 3: 1}}, 'per-register invoice differs')
+            record['prose_reconstruction'] = 'exact complete JSON equality'
+            record['changed_register_bills'] = deltas
+            record['controls'] = negative_controls(C, staged, w, kind)
+            records[kind] = record
+            print('CHECKED', provider, kind, '723-register forward/dual/pull-back and 9 controls', flush=True)
+        results[provider] = records
+    return {'status': 'PASS_RETIMED_AND_DELAYED_WHOLE_WORD_AUDIT',
+            'scope': 'Reused PR3687 interpreter; finite exact operator/frame audit only. No native Gaussian, owner, root, or complete supplier claim.',
+            'providers': results}
+
+
+if __name__ == '__main__':
+    need(sys.argv[1:] in ([], ['--write']), 'usage: verify.py [--write]')
+    C = authenticate()
+    result = run(C)
+    output = json.dumps(result, sort_keys=True, indent=2) + '\n'
+    if sys.argv[1:] == ['--write']:
+        (HERE / 'RESULT.json').write_text(output)
+    else:
+        need((HERE / 'RESULT.json').read_text() == output, 'committed result differs')
+    print(result['status'])
diff --git a/research/staged544-a2-graph-rewrite/vendor/retiming.py b/research/staged544-a2-graph-rewrite/vendor/retiming.py
new file mode 100644
index 0000000000..c33d7bbcdf
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/vendor/retiming.py
@@ -0,0 +1,269 @@
+# SPDX-License-Identifier: Apache-2.0
+"""Exact, fixed-neighbour single-ADD retiming relaxation.
+
+Chris R / Clear1nsight, with substantial OpenAI assistance. The BORROW-WORD
+frame contract and scalar-retiming mechanism are credited in README.md.
+This module does not import the retained auditor or a numerical optimiser.
+"""
+from bisect import bisect_left
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+from functools import lru_cache
+
+
+def need(ok, message):
+    if not ok:
+        raise ValueError(message)
+
+
+@lru_cache(maxsize=None)
+def span(vectors):
+    points = {0}
+    for v in vectors:
+        need(type(v) is int and 0 <= v < 512, 'invalid frame vector')
+        points |= {x ^ v for x in tuple(points)}
+    return sum(1 << x for x in points)
+
+
+@lru_cache(maxsize=None)
+def basis(mask):
+    answer = []
+    have = 1
+    for v in range(1, 512):
+        if (mask >> v) & 1 and not (have >> v) & 1:
+            answer.append(v)
+            have = span(tuple(answer))
+    need(have == mask, 'not a binary subspace')
+    return tuple(answer)
+
+
+@lru_cache(maxsize=None)
+def join(a, b):
+    return span(basis(a) + basis(b))
+
+
+@lru_cache(maxsize=None)
+def rank(mask):
+    n = mask.bit_count()
+    need(n > 0 and n & (n - 1) == 0, 'invalid subspace cardinality')
+    return n.bit_length() - 1
+
+
+def contained(a, b):
+    return not a & ~b
+
+
+def touched(gate):
+    return gate[1:3] if gate[0] == 'add' else gate[1:2]
+
+
+def tracing(word):
+    """Own chronological trace; centre descent is NOT persistent state.
+
+    A check node is a fixed boundary, not a charged instruction. The census
+    relaxes it to a virtual climb. Every legal witness has zero such charge.
+    """
+    full = (1 << 512) - 1
+    live = set(range(704)) - set(word['removed'])
+    start, end = {}, {}
+    for r in live:
+        if r < 112:
+            start[r], end[r] = span((word['ports'][r],)), full
+        elif r < 224:
+            p = word['ports'][r - 112]
+            start[r] = 1
+            end[r] = sum(1 << x for x in range(512) if (x & p).bit_count() % 2 == 0)
+        else:
+            start[r], end[r] = 1, full
+    for r, fr in word['start_extra'].items():
+        start[int(r)] = span(tuple(fr))
+    for r, fr in word['helper_final'].items():
+        end[int(r)] = span(tuple(fr))
+    current = dict(start)
+    nodes = {r: [] for r in live}
+    where = {}
+    bill = Counter()
+
+    def event(r, frame, address, kind='climb'):
+        before = current[r]
+        if kind != 'map':
+            need(contained(before, frame), 'source frame containment')
+            d = rank(frame) - rank(before)
+            if kind == 'check':
+                need(d == 0, 'source fixed boundary')
+            elif d:
+                bill[d] += 1
+        if kind == 'climb':
+            where[(address, r)] = len(nodes[r])
+        nodes[r].append((address, kind, before, frame))
+        current[r] = frame
+
+    for i, gate in enumerate(word['A']):
+        if gate[0] == 'warp':
+            event(gate[1], span(tuple(gate[3])), ('check-A', i), 'check')
+            event(gate[1], span(tuple(gate[4])), ('map-A', i), 'map')
+        else:
+            for r in touched(gate):
+                event(r, span(tuple(gate[-1])), ('A', i))
+    levels = {112 + int(r): span(tuple(fr)) for r, fr in word['target_levels'].items()}
+    for r in range(112, 224):
+        event(r, levels.get(r, 1), ('target-cut', r), 'check')
+    for r, fr in zip(word['centers'], word['center_frames']):
+        u = span(tuple(fr))
+        event(r, u, ('centre-cut', r), 'check')
+        served = {levels.get(g[1], 1) for g in word['cut'] if g[2] == r}
+        for v in sorted(served, key=lambda x: -rank(x)):
+            need(contained(v, u), 'centre nesting')
+            if rank(u) > rank(v):
+                bill[rank(u) - rank(v)] += 1
+            u = v
+        # The main forward register remains at its declared centre entry.
+    warps = {}
+    for j, rec in enumerate(word['warps']):
+        warps.setdefault(rec[0], []).append((j, rec))
+    for i in range(len(word['B']) + 1):
+        for j, rec in warps.get(i, []):
+            event(rec[1], span(tuple(rec[3])), ('check-B', j), 'check')
+            event(rec[1], span(tuple(rec[4])), ('map-B', j), 'map')
+        if i < len(word['B']):
+            gate = word['B'][i]
+            for r in touched(gate):
+                event(r, span(tuple(gate[-1])), ('B', i))
+    for i, gate in enumerate(word['restore']):
+        for r in touched(gate):
+            event(r, span(tuple(gate[-1])), ('restore', i))
+    for r in live:
+        event(r, end[r], ('end',))
+    return nodes, where, dict(sorted(bill.items()))
+
+
+def crosses(g, h):
+    """Sufficient exact scalar normal form, not all algebraic commutations."""
+    if h[0] == 'add':
+        return g[1] != h[2] and h[1] != g[2]
+    return h[0] == 'scale' and h[2] != 0
+
+
+def segments(word, section):
+    if section == 'A':
+        cuts = [word['prelude_events'], len(word['A'])]
+    elif section == 'B':
+        cuts = sorted({0, len(word['B'])} | {rec[0] for rec in word['warps']})
+    else:
+        cuts = [0, len(word[section])]
+    return list(zip(cuts, cuts[1:]))
+
+
+def caps(delta):
+    return [sum(n * min(r, k) for r, n in enumerate(delta)) for k in range(1, 10)]
+
+
+def all_power_nonnegative(delta):
+    """Sufficient exact certificate using decreasing positive curvatures."""
+    values = caps(delta)
+    prefix = 0
+    for value in values[:-1]:
+        prefix += value
+        if prefix < 0:
+            return False
+    return values[-1] == 0
+
+
+def census(word):
+    nodes, where, bill = tracing(word)
+    deltas = Counter()
+    counts = {}
+    for section in ('A', 'B', 'restore'):
+        gates = word[section]
+        count = 0
+        for lo, hi in segments(word, section):
+            occurrences = {}
+            for i in range(lo, hi):
+                need(gates[i][0] in ('add', 'scale'), 'unexpected scalar segment')
+                for r in touched(gates[i]):
+                    occurrences.setdefault(r, []).append(i)
+            for i in range(lo, hi):
+                g = gates[i]
+                if g[0] != 'add':
+                    continue
+                lower = i
+                while lower > lo and crosses(g, gates[lower - 1]):
+                    lower -= 1
+                upper = i + 1
+                while upper < hi and crosses(g, gates[upper]):
+                    upper += 1
+                removal = [0] * 10
+                reduced, entries, exits = {}, {}, {}
+                for r in touched(g):
+                    seq = nodes[r]
+                    pos = where[((section, i), r)]
+                    _, _, p, u = seq[pos]
+                    need(pos + 1 < len(seq) and seq[pos + 1][1] != 'map', 'missing successor')
+                    q = seq[pos + 1][3]
+                    removal[rank(u) - rank(p)] -= 1
+                    removal[rank(q) - rank(u)] -= 1
+                    removal[rank(q) - rank(p)] += 1
+                    indices = occurrences[r]
+                    reduced[r] = [x for x in indices if x != i]
+                    entries[r] = seq[where[((section, indices[0]), r)]][2]
+                    last = where[((section, indices[-1]), r)]
+                    need(seq[last + 1][1] != 'map', 'missing exit check')
+                    exits[r] = seq[last + 1][3]
+                for cut in range(lower, upper + 1):
+                    if cut == i + 1:  # Same placement as cut i, counted once.
+                        continue
+                    boundaries = []
+                    for r in touched(g):
+                        indices = reduced[r]
+                        j = bisect_left(indices, cut)
+                        p = span(tuple(gates[indices[j - 1]][-1])) if j else entries[r]
+                        q = span(tuple(gates[indices[j]][-1])) if j < len(indices) else exits[r]
+                        boundaries.append((p, q))
+                    lower_frame = join(boundaries[0][0], boundaries[1][0])
+                    upper_frame = boundaries[0][1] & boundaries[1][1]
+                    if not contained(lower_frame, upper_frame):
+                        continue
+                    dims = [(rank(p), rank(q)) for p, q in boundaries]
+                    for d in range(rank(lower_frame), rank(upper_frame) + 1):
+                        delta = removal.copy()
+                        for p, q in dims:
+                            delta[q - p] -= 1
+                            delta[d - p] += 1
+                            delta[q - d] += 1
+                        delta[0] = 0
+                        need(sum(r * n for r, n in enumerate(delta)) == 0, 'rank mass drift')
+                        deltas[tuple(delta)] += 1
+                        count += 1
+        counts[section] = count
+    return {'per_section': counts, 'candidates': sum(counts.values()),
+            'source_profile': bill,
+            'deltas': [{'delta': {r: n for r, n in enumerate(d) if n}, 'count': n,
+                        'caps': caps(d), 'certificate': all_power_nonnegative(d)}
+                       for d, n in sorted(deltas.items())]}
+
+
+def apply_move(word, section, index, cut, frame):
+    """Apply one exact scalar retiming. Caller must rederive cleanup and audit."""
+    need(section in ('A', 'B', 'restore'), 'unknown section')
+    gates = word[section]
+    need(type(index) is int and 0 <= index < len(gates), 'bad source index')
+    need(type(cut) is int and 0 <= cut <= len(gates), 'bad insertion cut')
+    need(any(lo <= index < hi and lo <= cut <= hi for lo, hi in segments(word, section)),
+         'crosses prelude or native warp boundary')
+    g = deepcopy(gates[index])
+    need(g[0] == 'add', 'only ADD moves are covered')
+    crossed = gates[index + 1:cut] if cut > index else gates[cut:index]
+    need(all(crosses(g, h) for h in crossed), 'noncommuting scalar barrier')
+    coefficient = Fraction(g[3], g[4])
+    for h in crossed:
+        if h[0] == 'scale' and h[1] in touched(g):
+            power = (1 if h[1] == g[1] else -1) * (1 if cut > index else -1)
+            coefficient *= Fraction(h[2], h[3]) ** power
+    g[3:5] = [coefficient.numerator, coefficient.denominator]
+    g[-1] = list(basis(span(tuple(frame))))
+    result = deepcopy(word)
+    result[section].pop(index)
+    result[section].insert(cut - (cut > index), g)
+    # Segment length and all warp cuts are unchanged. No warp is crossed.
+    return result
diff --git a/research/staged544-a2-graph-rewrite/verify.py b/research/staged544-a2-graph-rewrite/verify.py
new file mode 100644
index 0000000000..142c8785b0
--- /dev/null
+++ b/research/staged544-a2-graph-rewrite/verify.py
@@ -0,0 +1,129 @@
+#!/usr/bin/env python3
+# SPDX-License-Identifier: Apache-2.0
+"""Read-only source-authenticated A2 rewrite certificate replay."""
+import argparse,gzip,hashlib,json,time,types
+from pathlib import Path
+from collections import Counter
+P=Path(__file__).resolve().parent
+
+def need(ok,msg):
+    if not ok:raise ValueError(msg)
+
+def module(name,path):
+    m=types.ModuleType(name);m.__file__=str(path);exec(compile(path.read_bytes(),str(path),'exec'),m.__dict__);return m
+
+def authenticate(raw,row):
+    need(len(raw)==row['bytes'],'source length '+row['local'])
+    need(hashlib.sha256(raw).hexdigest()==row['sha256'],'source SHA256 '+row['local'])
+    need(hashlib.sha1(b'blob '+str(len(raw)).encode()+b'\0'+raw).hexdigest()==row['git_blob'],'source Git blob '+row['local'])
+
+def setup():
+    for row in json.loads((P/'SOURCES.json').read_text())['snapshots']:authenticate((P/row['local']).read_bytes(),row)
+    return module('graph_search',P/'search.py'),module('retained_core',P/'vendor/audit_core.py'),module('retained_semantics',P/'vendor/audit_verify.py')
+
+def load(tag):return json.loads(gzip.decompress((P/f'inputs/BORROW-WORD-43{tag}.json.gz').read_bytes()))
+
+def normal(x):return json.loads(json.dumps(x,sort_keys=True))
+
+def coefficient_heights(word,records):
+    from fractions import Fraction
+    replacement=[Fraction(g[3],g[4]) for row in records for g in row['gates']]
+    complete=list(replacement)
+    for section in ('precondition','compensation','A','cut','B','restore','cleanup'):
+        for g in word[section]:
+            if g[0]=='add':complete.append(Fraction(g[3],g[4]))
+            elif g[0]=='scale':complete.append(Fraction(g[2],g[3]))
+    complete.extend(Fraction(c['coefficient']) for c in word['initial_corrections'])
+    result={}
+    for name,values in [('replacement_gates',replacement),('complete_words',complete)]:
+        result['maximum_'+name+'_numerator_bits']=max(abs(x.numerator).bit_length() for x in values)
+        result['maximum_'+name+'_denominator_bits']=max(x.denominator.bit_length() for x in values)
+    return result
+
+def current_producer(tag,S,C,A):
+    word=json.loads(gzip.decompress((P/f'inputs/PR3945-WORD-{tag}.json.gz').read_bytes()))
+    C.hygiene(word);profile,widths,*_=C.frame_bill(word)
+    need(profile=={int(r):n for r,n in word['report']['local_profile'].items()},'PR3945 source invoice')
+    need(C.derive_cleanup(word)==word['cleanup'],'PR3945 source cleanup')
+    block=word['A'][1858:1861]
+    expected=[['add',457,475,-1,1,[82,42]],['add',456,457,1,1,[82,42]],['add',456,475,1,1,[82,42]]]
+    need(block==expected,'PR3945 literal motif changed')
+    nodes,where,bill=S.R.tracing(word);need(bill==profile,'PR3945 trace invoice')
+    contracted=S.contract(word,C,[['A',1858,2]],nodes,where,bill)
+    need(len(contracted['records'])==1,'PR3945 contraction frame count')
+    row=contracted['records'][0];need(not any(row['delta']),'PR3945 moment changed')
+    after=S.apply(word,'A',1858,row['gates'],C,3)
+    need(all(word[k]==after[k] for k in word if k not in ('A','cleanup')),'PR3945 frozen boundary/native fields')
+    return {'source_canonical_sha256':S.digest(word),'source_head':'91f81d131252db704f945891da1ea54e29d46b8b',
+            'scope':'Only the literal A1858 inverse contraction; no PR3945 expansion census.',
+            'source_profile':profile,'recursive_children':sum(profile.values()),'rank_mass':sum(k*v for k,v in profile.items()),
+            'coefficient_heights':coefficient_heights(word,[row]),'width_inventory':widths,'before_gates':block,'contraction':row,
+            'source_semantics':A.semantics(C,word),'contracted_semantics':A.semantics(C,after),
+            'forward_ADD_delta':-1,'cleanup_ADD_delta':len(after['cleanup'])-len(word['cleanup']),
+            'fixed_all_other_top_level_fields':True,'fresh_native_phase_or_supplier_admission':False}
+
+def calculate(tag):
+    S,C,A=setup();w=load(tag);C.hygiene(w);baseline,widths,_,start,end=C.frame_bill(w)
+    need(C.derive_cleanup(w)==w['cleanup'],'source cleanup');need(baseline=={int(k):v for k,v in w['report']['local_profile'].items()},'source invoice')
+    need(S.R.tracing(w)[2]==baseline,'trace invoice')
+    result=S.compute(w,C);records=result['records'];samples=set()
+    for section in ('A','B','restore'):
+        group=[i for i,r in enumerate(records) if r['section']==section]
+        if group:samples.update((group[0],group[-1]))
+    replay=[]
+    contraction_replay=[]
+    for row in result['contractions']['records']:
+        m=S.apply(w,row['section'],row['index'],row['gates'],C,3)
+        contraction_replay.append({'record':row,'semantics':A.semantics(C,m)})
+    for i in sorted(samples):
+        row=records[i];m=S.apply(w,row['section'],row['index'],row['gates'],C)
+        replay.append({'record':i,'semantics':A.semantics(C,m)})
+    coeffs=[(abs(g[3]).bit_length(),abs(g[4]).bit_length()) for r in records for g in r['gates']]
+    ledger={'baseline_profile':baseline,'recursive_children':sum(baseline.values()),'rank_mass':sum(k*v for k,v in baseline.items()),
+       'helper_widths':widths,'helper_roles':sum(widths.values()),'live_inputs':C.N-len(w['removed']),'dirty_buffers':len(w['helper_final']),
+       'native_warps':len(w['warps']),'initial_operator_corrections':len(w['initial_corrections']),
+       'baseline_primitives':{s:dict(Counter(g[0] for g in w[s])) for s in ('precondition','compensation','A','cut','B','restore','cleanup')},
+       'replacement_ADD_count':3,'replaced_ADD_count':2,'added_forward_ADDs_per_candidate':1,
+       'cleanup_added_ADDs':sorted({r['cleanup_length']-len(w['cleanup']) for r in records}),
+       'candidate_recursive_children_range':[min(sum(r['profile'].values()) for r in records),max(sum(r['profile'].values()) for r in records)],
+       'candidate_rank_masses':sorted({sum(k*v for k,v in r['profile'].items()) for r in records}),
+       **coefficient_heights(w,records),
+       'contraction_forward_ADD_delta':-1,'contraction_cleanup_ADD_deltas':sorted({r['cleanup_length']-len(w['cleanup']) for r in result['contractions']['records']}),
+       'contraction_profiles':[r['profile'] for r in result['contractions']['records']],
+       'additional_helpers_buffers_native_maps':0,'changed_B_warp_positions':'Only numerical indices shift after insertion; same ordered warp with same neighbouring scalar events.',
+       'boundary_start_sha256':S.digest({str(k):str(v) for k,v in start.items()}),'boundary_end_sha256':S.digest({str(k):str(v) for k,v in end.items()}),
+       'proved':['Exact rational arbitrary-dirty three-register matrix equality for every orientation and coefficient motif',
+                 'All compatible frame flags and complete chronological recursive invoice for every legal flag',
+                 'Projected non-target matrix equality and literal inverse cleanup for every flag',
+                 'All source free-operator symbols plus deterministic full-word sample replay',
+                 'Finite primitive and scalar coefficient bounds; fixed roles, entrance/exit frames and native maps'],
+       'unknown':['Physical allocation/hosting and complete owner schedule after extra ADD',
+                  'Fresh Gaussian/Clifford realization and phase admission',
+                  'Uniform precision/stock/tape tariff and implementation cost of additional scalar primitives',
+                  'All-size compiler, outer/supplier admission, analytic transfer and BIT H1-H5'],
+       'unknown_costs_are_zero':False,'new_supplier_or_kappa':False}
+    return normal({'schema_version':1,'provider':tag,'source_canonical_sha256':S.digest(w),'source_semantics':A.semantics(C,w),
+                   'current_producer_applicability':current_producer(tag,S,C,A),
+                   'census':result,'whole_word_samples':replay,'contraction_whole_word_replays':contraction_replay,'ledger':ledger})
+
+def main():
+    ap=argparse.ArgumentParser();ap.add_argument('--provider',choices=('base','extra'),required=True);ap.add_argument('--emit',type=Path);ap.add_argument('--emit-contracted-word',type=Path);args=ap.parse_args()
+    outputs=[]
+    for path in (args.emit,args.emit_contracted_word):
+        if path is None:continue
+        target=path.resolve();need(target!=P and P not in target.parents,'output must be outside package')
+        need(not target.exists(),'output already exists');need(target.parent.is_dir(),'output parent missing')
+        need(target not in outputs,'output paths must differ');outputs.append(target)
+    start=time.monotonic();result=calculate(args.provider)
+    if args.emit:
+        path=args.emit.resolve()
+        with path.open('x') as stream:stream.write(json.dumps(result,sort_keys=True,indent=2)+'\n')
+    else:need(result==json.loads((P/f'RESULT-{args.provider}.json').read_text()),'retained result mismatch')
+    if args.emit_contracted_word:
+        target=args.emit_contracted_word.resolve();need(P not in target.parents,'word export must be outside package')
+        S,C,A=setup();rows=result['census']['contractions']['records'];need(len(rows)==1,'expected unique contraction')
+        row=rows[0];word=S.apply(load(args.provider),row['section'],row['index'],row['gates'],C,3)
+        need(S.digest(word)==row['canonical_word_sha256'],'exported word digest')
+        with target.open('x') as stream:stream.write(json.dumps(word,sort_keys=True,separators=(',',':'))+'\n')
+    print('PASS_A2_GRAPH',args.provider,len(result['census']['motifs']),result['census']['legal_flags'],f'{time.monotonic()-start:.3f}s')
+if __name__=='__main__':main()