diff --git a/research/fresh-helper-invoice-audit/README.md b/research/fresh-helper-invoice-audit/README.md
new file mode 100644
index 0000000000..668d81d4aa
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/README.md
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+# Independent reconstruction of PR4441's complete complex invoice
+
+**The declared finite invoice reproduces. No accounting discrepancy was found
+in the checked scope.** This package independently derives the paid transition
+and helper-width profiles of
+[PR #4441](https://github.com/CrocSwap/integer-mult-bounds/pull/4441) at
+`5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39`, then reconstructs the complete
+query-thinned controller invoice. It claims no new kappa or supplier admission.
+
+| Quantity | Before helper retiming | After helper retiming |
+| --- | ---: | ---: |
+| Paid calls per full native invocation | 3,554 | 3,363 |
+| Productive helper rank mass per invocation | 3,301 | 3,434 |
+| Paid rank mass per invocation | 5,157 | 5,290 |
+| Complete controller productive fields | 11,560 | 11,560 |
+| Complete controller paid calls | 72,902 | 69,273 |
+| Complete productive rank mass | 258,271 | 260,798 |
+| Complete paid rank mass | 257,471 | 259,998 |
+| Rank surplus | 800 | 800 |
+
+Each of 19 full invocations removes 191 paid calls, totaling **3,629**. The
+local paid-count changes by rank are `{1:-234, 2:-198, 3:+221, 5:+20}`.
+Both productive and paid mass increase by 133 per invocation. This changes
+the rank distribution without creating an unpaid rank-mass gain.
+
+## What is independently checked
+
+`audit.py` imports no predecessor implementation. It uses binary Gaussian
+elimination to check all 1,159 frame bases and nested transitions. From the
+literal native programs it collects a separate chronological contact path for
+each of 632 persistent roles, in both orientations. It binds every one of the
+117 entrance, 42 exit and 395 scalar-frame patches to its original location.
+The 17,253 persistent-only scalar gates have the stated inverse-transpose
+correspondence. Unmodified warp contacts are retained. The resulting per-role
+bills agree between orientations; 319 role bills change.
+
+The empty patch is a positive control: contact-derived costs equal the source's
+explicit climbs. All eight complete owned-center paths remain charged at rank
+eight, using the predecessor's unsplit-center convention; the stored native
+file expresses each as two adjacent rank-three/rank-five events.
+
+A second implementation replays the entire controller as sparse rational
+Laurent row expressions on all 34 formal input coordinates. It executes the
+actual right boundary, 164 physical events, and left boundary, separately
+checks the two boundary programs against their matrices, and derives the
+diagonal monomials. It counts **19 full calls, 16 copied query shears, 16 whole
+idle events, 96 additions and 17 signed swaps**. Each query is charged 112
+rank-one jobs; the idle events cost 3,584 jobs. Main output ranks come from the
+replayed monomials, not the stored diagonal or invoice. The expected receipts
+are compared only after reconstruction.
+
+These are separately written checks after reading the source formats and
+proof; they are not a blind replication or independent human review. The
+source author's existing native, phase and numerical checks are not relabelled
+as this package's independent evidence.
+
+## Why the surplus is conserved
+
+Let `d(f)` be the dimension of a frame. For one persistent role, sum the paid
+ascending transitions along its chronological path. Fixed warps can change
+frame dimensions without belonging to that sum. Telescoping therefore gives
+
+```
+paid rank mass = d(final) - d(start)
+                 - sum_over_fixed_warps(d(warp_out) - d(warp_in)).
+```
+
+The checker verifies this equality separately for every role in both
+orientations. Subtracting the old and new equations cancels all fixed warp
+jumps and main endpoints. The remaining change is exactly the change in helper
+boundary widths: 133. The eight center jobs, query shears, main diagonal and
+idle bill are unchanged. Multiplication by 19 gives 2,527 added rank mass on
+each side and leaves the complete surplus at 800. This identity is about
+accounting under the stated frame contract, not physical operator correctness.
+
+## Sources, replay and failure controls
+
+Base: canonical main `2a13eb1827784206202db90e5dc8327cf8a250db`, priority
+revision 7. [SOURCES.json](SOURCES.json) pins the two native input files already
+on main, plus historical catalogue/selected-record provenance.
+[snapshot/MANIFEST.json](snapshot/MANIFEST.json) binds the exact five exported
+PR4441 files to their public commit, original paths, Git blobs and SHA256s.
+The source README and attribution are retained unchanged. These snapshots are
+committed with this audit: replay needs neither an unmerged Git object nor a
+network fetch. The two main inputs were also checked byte-identical at the
+audited PR head. Snapshot hashes authenticate retained bytes; their association
+with the public commit was checked at acquisition, not by a network call during
+every replay.
+
+Python 3.12, standard library only, from the repository root:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/fresh-helper-invoice-audit --check-only
+python3.12 -B scripts/research_package.py --package research/fresh-helper-invoice-audit
+```
+
+Direct replay, also supported from a Git-free package export containing its two
+declared inputs:
+
+```sh
+python3.12 -B research/fresh-helper-invoice-audit/verify.py
+python3.12 -O -B research/fresh-helper-invoice-audit/verify.py
+```
+
+[RESULT.json](RESULT.json) contains all derived profiles and **13 rejection
+controls**: duplicate helper boundary, wrong original scalar frame, omitted
+scalar retiming, omitted helper exit, incompatible contact frame, equal-rank
+distinct spaces, dependent frame basis, missing query, missing idle, unsigned
+swap, wrong boundary coefficient, unearned productive stage, and altered source
+bytes. Acceptance uses explicit exceptions and remains active under `-O`.
+
+Validation on CPython **3.12.0**, Windows 11 x64 (`10.0.26300`): metadata/pins
+and both registered commands passed. The committed-byte preflight and a
+15-file export integrity check passed at `6ffff4e474b97e9fcc1e13164676e372a9d3af80`.
+Both direct modes also passed from that export in a fresh directory with no
+Git checkout or predecessor Python modules. That commit contains the complete
+scientific code and inputs; the subsequent change only records validation and
+concurrent-work context. The optional full-history ancestry preflight was not
+run in this shallow checkout. The prescribed selected baseline was attempted
+but its unrelated source inventory is incomplete in the sparse checkout;
+neither it nor the full selected cold replay is claimed as passed.
+
+## Limits
+
+The 632-role analysis checks frame paths and tariffs, not the full native
+operator on 632 arbitrary input columns. Native adapters are treated under
+their retained rank-zero contract. It does not rederive Clifford lowering or
+absolute phases, prove the owned-query copy/erase implementation, audit owned
+center erasure, validate arbitrary-column physical lifting, or recompute the
+moment, paid tails, compiler, BIT, precision, stock, tape or outer admission.
+In particular, the 112-port query tariff is the inherited contract, not newly
+proved physical implementation. Neither the proposed kappa nor the full
+multiplication theorem is independently accepted here. The selected record is
+unchanged.
+
+## Open next questions
+
+The next useful check is the **native arbitrary-input/owned-query boundary**
+of this exact proposal. Reconstruct the changed physical Clifford routes and
+both helper normalizers with a separate interpreter, then check the copied
+query's arbitrary dirty inputs and exact erase before composing them with the
+main word. This matters because matching tariffs and a formal controller
+identity do not discharge physical realization. Start with one changed edge
+and one query, with a wrong-phase or omitted-erase control; a complete all-column
+audit needs a separate budget and the retained native contracts. Further digits
+of the same moment are not the next missing coverage. See [TASK.json](TASK.json).
+
+## Credit and coordination
+
+Construction credit remains with @1337isnot1337 for #4441's helper retiming and
+combination; Cinna Davis for #4440's query thinning and owned queries; zxv for
+the native/controller and compiler lineage; Jacob Alan Sussman for the mixed
+integer flow; and the native, Clifford, BIT, precision and outer contributors
+credited in the retained source. This package contributes the independent
+contact-path accounting, symbolic controller replay, conservation check and
+failure controls only.
+
+Prepared for Mihir Srivastava (@mihir-s-05) with substantial OpenAI Codex
+assistance. No subagents were used. Apache-2.0.
+
+Canonical investigation: [Discussion #4443](https://github.com/CrocSwap/integer-mult-bounds/discussions/4443).
+The task-picker seed is `500420262fb1df156828aa2604637058`; the
+`independent-moment` card is refined to the newer #4441 invoice. Entry overlap
+covered 301 open PRs and 3,289 Discussion records with complete remote paging;
+the sparse local note corpus and remote closed PR bodies were incomplete.
+The focused terms found #4440 and #4441. This deliberately audits their claims
+and makes no claim that the mechanism is new.
+
+The closing snapshot (21:12–21:14 UTC) covered 302 open PRs and 3,294 Discussion
+records; canonical main and the audited #4441 head were unchanged. The recent
+PR check also found concurrent
+[#4446](https://github.com/CrocSwap/integer-mult-bounds/pull/4446), head
+`7d05d73f96c27a9d360011e04af69b23fa903757`, which certifies the same profile
+and a slightly different endpoint. Its `local_supplier.py` freshly calls
+#4441's retained `native.py`; this audit adds a separately implemented
+per-role contact-path reconstruction and dimension-conservation check without
+those imports. #4446's own geometry and interval work retains its credit and
+was not independently replayed here. The scope remains this finite accounting
+audit; its result is compatible corroboration, not a competing construction.
diff --git a/research/fresh-helper-invoice-audit/RESULT.json b/research/fresh-helper-invoice-audit/RESULT.json
new file mode 100644
index 0000000000..b2bf11ae1d
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/RESULT.json
@@ -0,0 +1,167 @@
+{
+  "changed_role_bills": 319,
+  "controller_events": {
+    "ADD": 96,
+    "IDLE": 16,
+    "LOCAL": 19,
+    "QUERY_SHEAR": 16,
+    "SIGNED_SWAP": 17
+  },
+  "helper_entrance_patches": 117,
+  "helper_exit_patches": 42,
+  "local_helper_delta": {
+    "4": 26,
+    "5": -26,
+    "6": -18,
+    "7": -27,
+    "8": -51,
+    "9": 96
+  },
+  "local_helpers": {
+    "4": 26,
+    "5": 2,
+    "7": 29,
+    "8": 42,
+    "9": 309
+  },
+  "local_paid": {
+    "1": 2253,
+    "2": 515,
+    "3": 445,
+    "4": 102,
+    "5": 40,
+    "8": 8
+  },
+  "local_paid_calls_saved": 191,
+  "local_paid_delta": {
+    "1": -234,
+    "2": -198,
+    "3": 221,
+    "5": 20
+  },
+  "local_target_and_paid_mass_increment": 133,
+  "main_targets": {
+    "153": 224,
+    "17": 448,
+    "25": 448,
+    "33": 448,
+    "41": 448,
+    "49": 448,
+    "57": 448,
+    "65": 448,
+    "73": 448
+  },
+  "native_orientations": [
+    "backward",
+    "forward"
+  ],
+  "paid": {
+    "1": 44599,
+    "16": 448,
+    "2": 9785,
+    "24": 448,
+    "3": 8455,
+    "32": 448,
+    "4": 1938,
+    "40": 448,
+    "48": 448,
+    "5": 760,
+    "56": 448,
+    "64": 448,
+    "72": 448,
+    "8": 152
+  },
+  "paid_calls": 69273,
+  "paid_calls_saved": 3629,
+  "paid_rank_mass": 259998,
+  "persistent_roles_per_orientation": 632,
+  "persistent_scalar_contacts": 17253,
+  "productive_fields": 11560,
+  "rank_surplus": 800,
+  "rejection_controls": [
+    {
+      "control": "duplicate-helper-boundary",
+      "rejected_by": "duplicate or nonhelper boundary patch"
+    },
+    {
+      "control": "wrong-old-scalar-frame",
+      "rejected_by": "scalar old-frame pin"
+    },
+    {
+      "control": "missing-scalar-retiming",
+      "rejected_by": "nonascending or nonnested contact path"
+    },
+    {
+      "control": "missing-helper-exit",
+      "rejected_by": "helper invoice differs from source receipt"
+    },
+    {
+      "control": "incompatible-contact-frame",
+      "rejected_by": "nonascending or nonnested contact path"
+    },
+    {
+      "control": "equal-dimension-distinct-spaces",
+      "rejected_by": "nonascending or nonnested contact path"
+    },
+    {
+      "control": "dependent-frame-basis",
+      "rejected_by": "dependent frame basis"
+    },
+    {
+      "control": "omitted-query_shear",
+      "rejected_by": "every controller stage must be present exactly once"
+    },
+    {
+      "control": "omitted-idle",
+      "rejected_by": "controller endpoint is not one monomial"
+    },
+    {
+      "control": "unsigned-controller-swap",
+      "rejected_by": "invalid diagonal endpoint"
+    },
+    {
+      "control": "changed-boundary-coefficient",
+      "rejected_by": "boundary program/matrix disagreement: left"
+    },
+    {
+      "control": "unearned-productive-stage",
+      "rejected_by": "declared diagonal differs from literal replay"
+    },
+    {
+      "control": "changed-source-bytes",
+      "rejected_by": "source SHA256 mismatch"
+    }
+  ],
+  "scalar_frame_patches": 395,
+  "scope": "Finite contact-path and full symbolic controller invoice only; no new kappa or supplier admission.",
+  "source_files_authenticated": 7,
+  "source_head": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39",
+  "status": "PASS_INDEPENDENT_FRESH_HELPER_INVOICE",
+  "target_rank_mass": 260798,
+  "targets": {
+    "153": 224,
+    "17": 448,
+    "25": 448,
+    "33": 448,
+    "4": 494,
+    "41": 448,
+    "49": 448,
+    "5": 38,
+    "57": 448,
+    "65": 448,
+    "7": 551,
+    "73": 448,
+    "8": 798,
+    "9": 5871
+  },
+  "whole_idle_paid": {
+    "16": 448,
+    "24": 448,
+    "32": 448,
+    "40": 448,
+    "48": 448,
+    "56": 448,
+    "64": 448,
+    "72": 448
+  }
+}
diff --git a/research/fresh-helper-invoice-audit/SOURCES.json b/research/fresh-helper-invoice-audit/SOURCES.json
new file mode 100644
index 0000000000..2ecb7cff6a
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/SOURCES.json
@@ -0,0 +1,30 @@
+{
+  "schema_version": 1,
+  "base_commit": "2a13eb1827784206202db90e5dc8327cf8a250db",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ed33caef5c5827693e9572d252a66f99cbb73d40",
+      "sha256": "5732707cc1e460b090b53f2463162749ad860de878a18f7408938671d295a9d9"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    },
+    {
+      "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz",
+      "usage": "input",
+      "git_blob": "4a8c4ed26e53a72362d571c972e65aff546be784",
+      "sha256": "6418ec3da24d548a57f5c3fe5b9062c26c9478e638504a61c387f5cfb5f4ed61"
+    },
+    {
+      "path": "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz",
+      "usage": "input",
+      "git_blob": "b46d44c6ee624968dd57be928b0c15d9d45f3b2c",
+      "sha256": "c54b0a3e129d28e6dbf74fa731fc3bb70fe3c6705f07256750fbecddcc842d39"
+    }
+  ]
+}
diff --git a/research/fresh-helper-invoice-audit/TASK.json b/research/fresh-helper-invoice-audit/TASK.json
new file mode 100644
index 0000000000..fc539da6f0
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/TASK.json
@@ -0,0 +1,126 @@
+{
+  "schema_version": 1,
+  "task_id": "independent-moment",
+  "priority_revision": 7,
+  "base_commit": "2a13eb1827784206202db90e5dc8327cf8a250db",
+  "original_card": {
+    "id": "independent-moment",
+    "question": "Does a new paid-profile or mixture-ceiling claim have independent source-bound coverage of its actual changed ledger?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/staged544-mixed-fourth-entry/README.md",
+      "research/staged-fourth-mixture-ceiling/README.md",
+      "research/r437-two-window-carrier/README.md"
+    ],
+    "methods": [
+      "Independently reconstruct one changed paid ledger or pooled dual with exact source and model binding.",
+      "Check a genuinely uncovered moment implication with a different enclosure method and semantic controls."
+    ],
+    "acceptance_gate": "Demonstrate independence, source binding, positive cases and semantic failure controls. Name the existing checks and the missing coverage. More digits or another equivalent evaluation of an unchanged root is not by itself new verification coverage.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Choose one uncovered implication in #4088 literal mixed fill, #4091 pooled dual/model binding or #4067 changed frame/host bill. #4091 pins an earlier #4088 head: validate word, capacity and stock equivalence before applying that ceiling to the later fill.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Independently reconstruct one changed ledger or pooled certificate with a positive case and a semantic failure control. Compare exact sources and name what existing checks miss. Keep this separate from supplier-boundary-audit (ordinary/outer dispatch) and uniform-transfer-audit (all-size proof). Stop after the chosen implication; more digits of an unchanged root are not additional mechanism coverage.",
+    "bottleneck_link": "Independent pricing prevents unsupported frontier claims and can reveal genuine accounting slack.",
+    "allowed_variations": [
+      "Reconstruct either a source ledger or a numeric enclosure with a different method."
+    ],
+    "scope_change_triggers": [
+      "Importing the primary function and calling its output independent verification.",
+      "Calling an aggregate histogram or source archive an independently accepted physical supplier."
+    ],
+    "overlap_terms": [
+      "independent moment",
+      "rank histogram",
+      "exact enclosure",
+      "2979",
+      "rank7 joint endframes",
+      "paired extraction",
+      "joint lowering",
+      "4088",
+      "4091",
+      "4067",
+      "staged544-mixed-fourth-entry",
+      "staged-fourth-mixture-ceiling",
+      "r437-two-window-carrier"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4088: mixed local/owner/phase ledger and moment reported.",
+        "evidence": "research/staged544-mixed-fourth-entry/README.md",
+        "remaining": "Independent binding of changed construction to paid histogram, distinct from full admission.",
+        "status": "author-checked",
+        "source_commit": "72d7efc181edb21806a878f174847c96dd410ab0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4091: sharp pooled ceiling proposed for fixed THREE/FOUR words and inventory.",
+        "evidence": "research/staged-fourth-mixture-ceiling/README.md",
+        "remaining": "Validate dual, exhaustive pattern scope and exact source equivalence before applying to newer fills.",
+        "status": "author-checked",
+        "source_commit": "a29bdd8f56cd18b805917775cdec09ff935eddc4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4067: paid (2,2) to (1,3) exchange and fixed OQ4 host reported.",
+        "evidence": "research/r437-two-window-carrier/README.md",
+        "remaining": "Independent full cost delta; remaining caller/precision/stock obligations are separate.",
+        "status": "author-checked",
+        "source_commit": "a95f11c52e3ca1e4c5171b3c20d8f4b0815aee2e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Independently reconstruct both native contact-path tariffs and the entire p17 complex invoice of PR4441 at 5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39, with a separate symbolic controller replay.",
+  "scope_change_reason": "The card asks for a changed ledger. Its older source examples predate the selected productive-helper interface; PR4441 supplies a current changed invoice without an independent per-role reconstruction in the inspected live overlap.",
+  "bottleneck_link": "Checks the construction-to-paid-profile implication behind the latest conditional claim; no new root digits or supplier admission.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after reconstructing this one invoice or identifying a counterexample; no full native, moment, Lean, Docker or selected cold replay.",
+  "outcome": "completed",
+  "evidence": "RESULT.json: both 632-role orientations, independent full controller replay, per-role telescoping, 13 semantic/source rejection controls; see README for the physical boundary.",
+  "author": "mihir-s-05",
+  "ai_assistance": "Substantial OpenAI Codex assistance; no subagents. Separate code implementation, not independent human review.",
+  "open_questions": [
+    {
+      "question": "Does a separate native interpreter validate the changed physical helper boundaries and arbitrary-input owned-query copy/erase at this exact head?",
+      "why_it_matters": "Frame tariffs and a symbolic controller identity do not prove physical lowering, absolute phase or restoration.",
+      "first_step": "Check one changed transport/helper normalizer and one owned query, retaining arbitrary dirty inputs; reject a wrong phase and omitted erase before expanding.",
+      "blocked_by": "Requires the retained native physical contracts and a separately bounded all-column replay; this invoice audit does not discharge those premises."
+    }
+  ],
+  "seed": "500420262fb1df156828aa2604637058",
+  "coordination_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/4443",
+  "orientation_limitations": [
+    "The prescribed research_baseline.py was attempted; its selected-source inventory check could not complete in this sparse checkout (missing research/kappa-0023-productive-jobs). No full selected replay was claimed.",
+    "Entry overlap: 301 open PRs and 3289 Discussion records fully paginated; 5730 of 5731 local HEAD note paths omitted; closed remote PR bodies not scanned."
+  ],
+  "submission_checkpoint": {
+    "canonical_main": "2a13eb1827784206202db90e5dc8327cf8a250db",
+    "priority_revision": 7,
+    "source_head_unchanged": true,
+    "open_prs": 302,
+    "discussion_records": 3294,
+    "complete_remote_pagination": true,
+    "checked_utc": "2026-10-21T21:14:30Z",
+    "concurrent_pr": 4446,
+    "concurrent_head": "7d05d73f96c27a9d360011e04af69b23fa903757",
+    "decision": "Continue bounded corroboration: the concurrent local supplier calls the retained native.py; this package independently derives per-role paths and conservation. No new construction or endpoint claimed."
+  },
+  "validation_environment": {
+    "python": "CPython 3.12.0 (MSC v.1935 64 bit AMD64)",
+    "platform": "Windows-11-10.0.26300-SP0",
+    "registered_normal_and_optimized": "passed",
+    "git_free_normal_and_optimized": "passed",
+    "committed_bytes_and_export_integrity": "passed at scientific commit 6ffff4e474b97e9fcc1e13164676e372a9d3af80",
+    "full_history_ancestry_preflight": "not run: shallow checkout"
+  }
+}
diff --git a/research/fresh-helper-invoice-audit/VERIFY.json b/research/fresh-helper-invoice-audit/VERIFY.json
new file mode 100644
index 0000000000..7f21e6f47d
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/VERIFY.json
@@ -0,0 +1,31 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-CANONICAL.json.gz",
+    "research/kappa-rebuild/complex/full-identity-certificates/THREE-base-FULL-IDENTITY-NATIVE.json.gz"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Reconstruct original and retimed per-role native tariffs in both orientations, replay all symbolic controller events and boundaries, telescope rank mass, and reject 13 source/semantic mutations."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Repeat all acceptance checks and mutations with Python assertions disabled; explicit rejection logic remains active."
+    }
+  ]
+}
diff --git a/research/fresh-helper-invoice-audit/audit.py b/research/fresh-helper-invoice-audit/audit.py
new file mode 100644
index 0000000000..6105912477
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/audit.py
@@ -0,0 +1,309 @@
+"""Independent contact-path accounting and sparse Laurent replay.
+
+Prepared for mihir-s-05 with substantial OpenAI Codex assistance. Apache-2.0.
+No predecessor Python module is imported. This checks a finite invoice, not
+physical Clifford lowering, arbitrary-column native action or admission.
+"""
+from collections import Counter
+from fractions import Fraction
+
+
+def require(condition, message):
+    if not condition:
+        raise ValueError(message)
+
+
+def binary_rank(vectors):
+    pivots = {}
+    for value in vectors:
+        while value:
+            bit = value.bit_length() - 1
+            if bit in pivots:
+                value ^= pivots[bit]
+            else:
+                pivots[bit] = value
+                break
+    return len(pivots)
+
+
+class Frames:
+    def __init__(self, frames):
+        self.frames = frames
+        self.dimensions = []
+        self.cache = {}
+        for basis in frames:
+            require(all(type(x) is int and 0 < x < 512 for x in basis),
+                    'invalid nine-axis frame vector')
+            rank = binary_rank(basis)
+            require(rank == len(basis), 'dependent frame basis')
+            self.dimensions.append(rank)
+
+    def width(self, before, after):
+        require(type(before) is int and type(after) is int and
+                0 <= before < len(self.frames) and 0 <= after < len(self.frames),
+                'invalid frame index')
+        if before == after:
+            return 0
+        key = before, after
+        if key not in self.cache:
+            delta = self.dimensions[after] - self.dimensions[before]
+            require(delta > 0 and binary_rank(self.frames[before] + self.frames[after])
+                    == self.dimensions[after], 'nonascending or nonnested contact path')
+            self.cache[key] = delta
+        return self.cache[key]
+
+
+def scalar_roles(gate):
+    require(gate[0] in ('add', 'copy', 'scale', 'clear'), 'unknown native scalar')
+    return gate[1:3] if gate[0] in ('add', 'copy') else gate[1:2]
+
+
+def patched_endpoints(canonical, changes, frames):
+    starts, ends = list(canonical['start']), list(canonical['final'])
+    require(len(starts) == len(ends) == 632, 'persistent field inventory')
+    for key, values in (('entrances', starts), ('exits', ends)):
+        seen = set()
+        for role, old, new in changes[key]:
+            require(type(role) is int and 224 <= role < 632 and role not in seen,
+                    'duplicate or nonhelper boundary patch')
+            require(values[role] == old, 'boundary old-frame pin')
+            require(type(new) is int and 0 <= new < len(frames.frames), 'invalid new boundary')
+            seen.add(role)
+            values[role] = new
+    helpers = Counter()
+    for role in range(224, 632):
+        width = frames.width(starts[role], ends[role])
+        require(width > 0, 'unproductive helper')
+        helpers[width] += 1
+    return starts, ends, helpers
+
+
+def audit_orientation(canonical, program, changes, frames):
+    starts, ends, helpers = patched_endpoints(canonical, changes, frames)
+    patch = {}
+    for phase, ordinal, old, new in changes['gates']:
+        key = phase, ordinal
+        require(key not in patch, 'duplicate scalar-frame patch')
+        patch[key] = old, new
+
+    # Extract each role's ordered demands, independently of the emitted climbs.
+    paths = [[] for _ in starts]
+    original_state = list(canonical['start'])
+    original_paid = Counter()
+    phase, ordinal = None, 0
+    used = set()
+    contacts = {}
+    centers = []
+    warp_dimension_changes = [0] * len(starts)
+    event_counts = Counter()
+    for position, event in enumerate(program):
+        kind = event[0]
+        event_counts[kind] += 1
+        if kind == 'phase':
+            phase, ordinal = event[1], 0
+        elif kind == 'climb':
+            _, _, role, old, new, declared = event
+            require(original_state[role] == old, 'source climb chronology')
+            width = frames.width(old, new)
+            require(width > 0 and width == declared, 'source climb tariff')
+            original_paid[width] += 1
+            original_state[role] = new
+        elif kind == 'scalar':
+            gate, old = event[1:]
+            roles = scalar_roles(gate)
+            new = old
+            if all(role[0] == 'L' for role in roles):
+                key = phase, ordinal
+                ordinal += 1
+                require(key not in contacts, 'repeated phase/ordinal')
+                contacts[key] = gate, old
+                if key in patch:
+                    expected, new = patch[key]
+                    require(old == expected, 'scalar old-frame pin')
+                    used.add(key)
+            for bank, role in roles:
+                require(bank in ('L', 'C'), 'unknown native bank')
+                if bank == 'L':
+                    require(original_state[role] == old, 'source scalar contact')
+                    paths[role].append(('contact', new, position))
+        elif kind == 'warp':
+            _, bank_role, _, old, new = event
+            bank, role = bank_role
+            require(bank == 'L' and original_state[role] == old, 'source warp contact')
+            paths[role].append(('contact', old, position))
+            paths[role].append(('warp', new, position))
+            warp_dimension_changes[role] += frames.dimensions[new] - frames.dimensions[old]
+            original_state[role] = new
+        elif kind == 'center':
+            centers.append((position, event))
+        elif kind not in ('adapter', 'residual_adapter'):
+            raise ValueError('unknown native event: ' + kind)
+    require(used == set(patch), 'unconsumed scalar-frame patch')
+    require(original_state == canonical['final'], 'source final frames')
+    require(len(centers) == 16, 'eight complete owned center jobs required')
+    # Each adjacent 3+5 pair is one rank-eight job in the source unsplit model.
+    for (pos, first), (next_pos, second) in zip(centers[::2], centers[1::2]):
+        require(next_pos == pos + 1 and first[1] == second[1] == 0 and
+                first[3] == second[2] and sorted((first[4], second[4])) == [3, 5],
+                'owned center pair must be contiguous and complete')
+        for item in (first, second):
+            require(abs(frames.dimensions[item[3]] - frames.dimensions[item[2]]) == item[4],
+                    'center dimension tariff')
+    original_paid[8] += len(centers) // 2
+    paid = Counter({8: len(centers) // 2})
+    role_paid = []
+    for role, demands in enumerate(paths):
+        current = starts[role]
+        bill = Counter()
+        for kind, target, _ in demands + [('contact', ends[role], len(program))]:
+            if kind == 'contact':
+                width = frames.width(current, target)
+                if width:
+                    bill[width] += 1
+            current = target
+        role_paid.append(bill)
+        paid.update(bill)
+        # A second, order-independent mass check. Warps are fixed contacts,
+        # not newly credited paid climbs; their dimension jumps must be removed.
+        telescope = (frames.dimensions[ends[role]] - frames.dimensions[starts[role]]
+                     - warp_dimension_changes[role])
+        require(sum(width * count for width, count in bill.items()) == telescope,
+                'per-role rank mass does not telescope')
+    return {'helpers': helpers, 'paid': paid, 'original_paid': original_paid,
+            'contacts': contacts, 'role_paid': role_paid, 'events': event_counts,
+            'contact_count': sum(len(path) for path in paths)}
+
+
+def local_invoice(canonical, native, changes):
+    frames = Frames(canonical['frames'])
+    require(set(native) == {'forward', 'backward'}, 'both native orientations required')
+    results = {direction: audit_orientation(canonical, program, changes, frames)
+               for direction, program in native.items()}
+    forward, backward = results['forward'], results['backward']
+    for key in ('helpers', 'paid', 'original_paid', 'role_paid'):
+        require(forward[key] == backward[key], 'orientation mismatch: ' + key)
+    require(forward['contacts'].keys() == backward['contacts'].keys(),
+            'orientation scalar inventories differ')
+    for key, (gate, frame) in forward['contacts'].items():
+        other, other_frame = backward['contacts'][key]
+        if gate[0] == 'add':
+            expected = ['add', gate[2], gate[1], -gate[3], gate[4]]
+        else:
+            require(gate[0] == 'scale', 'unexpected persistent scalar')
+            expected = ['scale', gate[1], gate[3], gate[2]]
+        require(other == expected and frame == other_frame, 'inverse-transpose scalar correspondence')
+    return forward, results
+
+
+def add_row(target, source, coefficient=1):
+    result = dict(target)
+    for term, value in source.items():
+        result[term] = result.get(term, 0) + coefficient * value
+        if not result[term]:
+            del result[term]
+    return result
+
+
+def shift_row(row, q=0, stages=(), coefficient=1):
+    result = {}
+    for term, value in row.items():
+        shifted = list(term)
+        shifted[1] += q
+        for stage in stages:
+            shifted[stage + 2] += 1
+        key = tuple(shifted)
+        result[key] = result.get(key, 0) + coefficient * value
+    return {key: value for key, value in result.items() if value}
+
+
+def identity_rows(size, stages):
+    return [{(role, 0) + (0,) * stages: Fraction(1)} for role in range(size)]
+
+
+def scalar_program(rows, program):
+    for event in program:
+        op = event[0]
+        if op == 'ADD':
+            _, dst, src, c = event
+            rows[dst] = add_row(rows[dst], rows[src], Fraction(c))
+        elif op == 'SCALE':
+            _, dst, c = event
+            rows[dst] = shift_row(rows[dst], coefficient=Fraction(c))
+        elif op == 'SWAP':
+            _, dst, src = event
+            rows[dst], rows[src] = rows[src], rows[dst]
+        else:
+            raise ValueError('unknown boundary gate: ' + op)
+    return rows
+
+
+def controller_invoice(controller, helpers, local_paid):
+    require(controller['kind'] == 'complex', 'complex controller required')
+    pairs = controller['pairs']
+    size, stages = 2 * pairs, 2 * pairs + 1
+    for side in ('left', 'right'):
+        rows = scalar_program(identity_rows(size, stages), controller['boundaries'][side + '_program'])
+        matrix = controller['boundaries'][side]
+        for i in range(size):
+            expected = {(j, 0) + (0,) * stages: Fraction(matrix[i][j])
+                        for j in range(size) if Fraction(matrix[i][j])}
+            require(rows[i] == expected, 'boundary program/matrix disagreement: ' + side)
+    rows = scalar_program(identity_rows(size, stages), controller['boundaries']['right_program'])
+    paid, targets, idles = Counter(), Counter(), Counter()
+    event_counts = Counter()
+    local_stages, query_stages = [], []
+    for event in controller['physical_events']:
+        op = event[0]
+        event_counts[op] += 1
+        if op in ('LOCAL', 'QUERY_SHEAR'):
+            _, stage, pair, backward = event
+            require(0 <= stage < stages and 0 <= pair < pairs and type(backward) is bool,
+                    'invalid local/query event')
+            x, y = 2 * pair, 2 * pair + 1
+            if backward:
+                x, y = y, x
+            rows[y] = add_row(rows[y], shift_row(rows[x], q=1 if backward else -1),
+                              -1 if backward else 1)
+            if op == 'LOCAL':
+                local_stages.append(stage)
+                targets.update(helpers)
+                paid.update(local_paid)
+                for role in (x, y):
+                    rows[role] = shift_row(rows[role], stages=(stage,))
+            else:
+                query_stages.append(stage)
+                paid[1] += 112
+        elif op == 'IDLE':
+            _, pair, active = event
+            require(0 <= pair < pairs and active and len(active) == len(set(active)) and
+                    all(0 <= s < stages for s in active), 'invalid whole idle event')
+            idles[8 * len(active)] += 224
+            paid[8 * len(active)] += 224
+            for role in (2 * pair, 2 * pair + 1):
+                rows[role] = shift_row(rows[role], stages=active)
+        elif op == 'ADD':
+            _, dst, src, c = event
+            rows[dst] = add_row(rows[dst], rows[src], Fraction(c))
+        elif op in ('SWAP', 'SIGNED_SWAP'):
+            _, x, y = event
+            rows[x], rows[y] = rows[y], shift_row(rows[x], coefficient=-1 if op == 'SIGNED_SWAP' else 1)
+        else:
+            raise ValueError('unknown controller event: ' + op)
+    require(sorted(local_stages + query_stages) == list(range(stages)),
+            'every controller stage must be present exactly once')
+    rows = scalar_program(rows, controller['boundaries']['left_program'])
+    diagonal, main = [], Counter()
+    for role, row in enumerate(rows):
+        require(len(row) == 1, 'controller endpoint is not one monomial')
+        (term, coefficient), = row.items()
+        require(term[0] == role and coefficient == 1 and term[1] in (-1, 1) and
+                all(power in (0, 1) for power in term[2:]), 'invalid diagonal endpoint')
+        require(all(not power or stage in local_stages for stage, power in enumerate(term[2:])),
+                'thin stage receives productive credit')
+        diagonal.append(list(term[1:]))
+        main[1 + 8 * sum(term[2:])] += 112
+    require(diagonal == controller['diagonal'], 'declared diagonal differs from literal replay')
+    targets.update(main)
+    return {'targets': targets, 'paid': paid, 'main': main, 'whole_idle': idles,
+            'event_counts': event_counts, 'local_stages': local_stages,
+            'query_stages': query_stages, 'diagonal': diagonal}
diff --git a/research/fresh-helper-invoice-audit/snapshot/MANIFEST.json b/research/fresh-helper-invoice-audit/snapshot/MANIFEST.json
new file mode 100644
index 0000000000..e21326fe1a
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/snapshot/MANIFEST.json
@@ -0,0 +1,42 @@
+[
+  {
+    "file": "changes.json",
+    "source_path": "research/fresh-helper-boundary/CHANGES.json",
+    "commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39",
+    "git_blob": "45744fedd0e28967aa72586048b8bc0c72f419a9",
+    "sha256": "cde73b8ff5b3c0d06e69e2293b991b24fd14a16dd4ccab7ff6b3439074a94624",
+    "url": "https://github.com/1337isnot1337/integer-mult-bounds/blob/5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39/research/fresh-helper-boundary/CHANGES.json"
+  },
+  {
+    "file": "native-receipt.json.gz",
+    "source_path": "research/fresh-helper-boundary/NATIVE-RESULT.json.gz",
+    "commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39",
+    "git_blob": "e6fdb31624e4eb8c7c770bb4422cd07ea99ab152",
+    "sha256": "37d0848458b289eb50271c47adef6e74014ae30be6363d09394b2337b566b839",
+    "url": "https://github.com/1337isnot1337/integer-mult-bounds/blob/5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39/research/fresh-helper-boundary/NATIVE-RESULT.json.gz"
+  },
+  {
+    "file": "controller.json",
+    "source_path": "research/query-thinned-controllers/COMPLEX-CONTROLLER.json",
+    "commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39",
+    "git_blob": "39318f6ad9baf0838a274ca1042b1e3ba0e74bf9",
+    "sha256": "bf1143325d8380fab40cd5a85449f9a5412f0340deba7f4693714c92ae320088",
+    "url": "https://github.com/1337isnot1337/integer-mult-bounds/blob/5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39/research/query-thinned-controllers/COMPLEX-CONTROLLER.json"
+  },
+  {
+    "file": "combined-receipt.json",
+    "source_path": "research/fresh-helper-thinned/RESULT.json",
+    "commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39",
+    "git_blob": "e223acd07a6b1f4f1c9f2778b8ea64d4b7a2be55",
+    "sha256": "8e7db2fed5f4be6a7f944bc59e7942ccbcc3e6c36130b5671331540c183ada21",
+    "url": "https://github.com/1337isnot1337/integer-mult-bounds/blob/5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39/research/fresh-helper-thinned/RESULT.json"
+  },
+  {
+    "file": "source-README.md",
+    "source_path": "research/fresh-helper-thinned/README.md",
+    "commit": "5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39",
+    "git_blob": "344616d6654a96085dd45cf2c3189ef283deeac1",
+    "sha256": "70c1c872c2327c3f71918e218d5f1ecb7a00037771a5dd1b8ae415b84cc90dc2",
+    "url": "https://github.com/1337isnot1337/integer-mult-bounds/blob/5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39/research/fresh-helper-thinned/README.md"
+  }
+]
diff --git a/research/fresh-helper-invoice-audit/snapshot/changes.json b/research/fresh-helper-invoice-audit/snapshot/changes.json
new file mode 100644
index 0000000000..45744fedd0
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/snapshot/changes.json
@@ -0,0 +1,562 @@
+{
+  "entrances": [
+    [448, 114, 0],
+    [449, 114, 0],
+    [450, 115, 0],
+    [451, 115, 0],
+    [452, 115, 0],
+    [453, 115, 0],
+    [454, 114, 0],
+    [455, 114, 0],
+    [457, 116, 0],
+    [458, 116, 0],
+    [460, 117, 0],
+    [462, 117, 0],
+    [473, 114, 0],
+    [474, 118, 0],
+    [475, 118, 0],
+    [476, 119, 0],
+    [477, 119, 0],
+    [478, 120, 0],
+    [480, 120, 0],
+    [482, 114, 0],
+    [483, 114, 0],
+    [484, 121, 0],
+    [485, 121, 0],
+    [486, 122, 0],
+    [487, 122, 0],
+    [492, 115, 0],
+    [493, 115, 0],
+    [502, 115, 0],
+    [503, 115, 0],
+    [504, 115, 0],
+    [513, 115, 0],
+    [514, 115, 0],
+    [515, 115, 0],
+    [516, 123, 0],
+    [517, 123, 0],
+    [518, 124, 0],
+    [519, 124, 0],
+    [520, 125, 0],
+    [521, 125, 0],
+    [522, 126, 0],
+    [523, 126, 0],
+    [524, 115, 0],
+    [525, 115, 0],
+    [526, 115, 0],
+    [527, 115, 0],
+    [528, 127, 0],
+    [529, 127, 0],
+    [530, 128, 0],
+    [531, 128, 0],
+    [532, 129, 0],
+    [533, 129, 0],
+    [534, 130, 0],
+    [535, 130, 0],
+    [536, 115, 0],
+    [537, 115, 0],
+    [538, 131, 114],
+    [539, 114, 0],
+    [544, 132, 0],
+    [545, 132, 0],
+    [546, 133, 0],
+    [547, 133, 0],
+    [548, 114, 0],
+    [549, 114, 0],
+    [550, 114, 0],
+    [551, 114, 0],
+    [553, 134, 0],
+    [555, 134, 0],
+    [556, 135, 0],
+    [557, 135, 0],
+    [558, 136, 0],
+    [559, 136, 0],
+    [563, 134, 0],
+    [565, 134, 0],
+    [570, 134, 0],
+    [571, 134, 0],
+    [572, 134, 0],
+    [573, 134, 0],
+    [578, 114, 0],
+    [579, 114, 0],
+    [580, 115, 0],
+    [581, 115, 0],
+    [582, 115, 0],
+    [583, 115, 0],
+    [585, 114, 0],
+    [586, 137, 0],
+    [587, 137, 0],
+    [588, 137, 0],
+    [589, 137, 0],
+    [590, 138, 0],
+    [591, 137, 0],
+    [592, 137, 0],
+    [593, 137, 0],
+    [596, 137, 0],
+    [597, 137, 0],
+    [598, 114, 0],
+    [599, 114, 0],
+    [600, 114, 0],
+    [601, 114, 0],
+    [606, 115, 0],
+    [607, 115, 0],
+    [608, 115, 0],
+    [609, 115, 0],
+    [610, 115, 0],
+    [611, 115, 0],
+    [612, 115, 0],
+    [614, 115, 0],
+    [615, 115, 0],
+    [616, 115, 0],
+    [617, 115, 0],
+    [618, 115, 0],
+    [619, 115, 0],
+    [620, 115, 0],
+    [621, 140, 0],
+    [622, 114, 0],
+    [623, 114, 0],
+    [624, 114, 0],
+    [625, 114, 0]
+  ],
+  "exits": [
+    [277, 256, 299],
+    [282, 257, 299],
+    [293, 258, 301],
+    [298, 258, 301],
+    [307, 261, 303],
+    [309, 261, 303],
+    [311, 262, 1],
+    [314, 263, 303],
+    [323, 265, 304],
+    [325, 266, 304],
+    [327, 267, 1],
+    [330, 268, 304],
+    [337, 270, 305],
+    [339, 270, 305],
+    [341, 271, 305],
+    [346, 271, 305],
+    [353, 272, 307],
+    [355, 272, 307],
+    [357, 273, 307],
+    [362, 273, 307],
+    [369, 275, 308],
+    [371, 275, 308],
+    [373, 275, 308],
+    [378, 276, 308],
+    [385, 277, 309],
+    [387, 277, 309],
+    [389, 278, 309],
+    [394, 278, 309],
+    [494, 262, 1],
+    [495, 262, 1],
+    [505, 267, 1],
+    [506, 267, 1],
+    [548, 285, 1],
+    [560, 285, 1],
+    [566, 286, 279],
+    [567, 286, 279],
+    [568, 287, 280],
+    [569, 287, 280],
+    [574, 288, 279],
+    [575, 288, 279],
+    [576, 289, 281],
+    [577, 289, 281]
+  ],
+  "gates": [
+    ["A", 626, 115, 0],
+    ["A", 627, 115, 0],
+    ["A", 628, 115, 0],
+    ["A", 629, 114, 0],
+    ["A", 630, 114, 0],
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diff --git a/research/fresh-helper-invoice-audit/snapshot/combined-receipt.json b/research/fresh-helper-invoice-audit/snapshot/combined-receipt.json
new file mode 100644
index 0000000000..e223acd07a
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/snapshot/combined-receipt.json
@@ -0,0 +1,237 @@
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diff --git a/research/fresh-helper-invoice-audit/snapshot/controller.json b/research/fresh-helper-invoice-audit/snapshot/controller.json
new file mode 100644
index 0000000000..39318f6ad9
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/snapshot/controller.json
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+      "ADD",
+      9,
+      7,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      8,
+      3,
+      false
+    ],
+    [
+      "ADD",
+      6,
+      8,
+      -1
+    ],
+    [
+      "ADD",
+      9,
+      7,
+      1
+    ],
+    [
+      "LOCAL",
+      9,
+      4,
+      true
+    ],
+    [
+      "IDLE",
+      5,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9
+      ]
+    ],
+    [
+      "ADD",
+      8,
+      10,
+      1
+    ],
+    [
+      "ADD",
+      11,
+      9,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      10,
+      4,
+      false
+    ],
+    [
+      "ADD",
+      8,
+      10,
+      -1
+    ],
+    [
+      "ADD",
+      11,
+      9,
+      1
+    ],
+    [
+      "LOCAL",
+      11,
+      5,
+      true
+    ],
+    [
+      "IDLE",
+      6,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9,
+        11
+      ]
+    ],
+    [
+      "ADD",
+      10,
+      12,
+      1
+    ],
+    [
+      "ADD",
+      13,
+      11,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      12,
+      5,
+      false
+    ],
+    [
+      "ADD",
+      10,
+      12,
+      -1
+    ],
+    [
+      "ADD",
+      13,
+      11,
+      1
+    ],
+    [
+      "LOCAL",
+      13,
+      6,
+      true
+    ],
+    [
+      "IDLE",
+      7,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9,
+        11,
+        13
+      ]
+    ],
+    [
+      "ADD",
+      12,
+      14,
+      1
+    ],
+    [
+      "ADD",
+      15,
+      13,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      14,
+      6,
+      false
+    ],
+    [
+      "ADD",
+      12,
+      14,
+      -1
+    ],
+    [
+      "ADD",
+      15,
+      13,
+      1
+    ],
+    [
+      "LOCAL",
+      15,
+      7,
+      true
+    ],
+    [
+      "IDLE",
+      8,
+      [
+        0,
+        1,
+        3,
+        5,
+        7,
+        9,
+        11,
+        13,
+        15
+      ]
+    ],
+    [
+      "ADD",
+      14,
+      16,
+      1
+    ],
+    [
+      "ADD",
+      17,
+      15,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      16,
+      7,
+      false
+    ],
+    [
+      "ADD",
+      14,
+      16,
+      -1
+    ],
+    [
+      "ADD",
+      17,
+      15,
+      1
+    ],
+    [
+      "LOCAL",
+      17,
+      8,
+      true
+    ],
+    [
+      "ADD",
+      16,
+      18,
+      1
+    ],
+    [
+      "ADD",
+      19,
+      17,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      18,
+      8,
+      false
+    ],
+    [
+      "ADD",
+      16,
+      18,
+      -1
+    ],
+    [
+      "ADD",
+      19,
+      17,
+      1
+    ],
+    [
+      "LOCAL",
+      19,
+      9,
+      true
+    ],
+    [
+      "ADD",
+      18,
+      20,
+      1
+    ],
+    [
+      "ADD",
+      21,
+      19,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      20,
+      9,
+      false
+    ],
+    [
+      "ADD",
+      18,
+      20,
+      -1
+    ],
+    [
+      "ADD",
+      21,
+      19,
+      1
+    ],
+    [
+      "LOCAL",
+      21,
+      10,
+      true
+    ],
+    [
+      "ADD",
+      20,
+      22,
+      1
+    ],
+    [
+      "ADD",
+      23,
+      21,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      22,
+      10,
+      false
+    ],
+    [
+      "ADD",
+      20,
+      22,
+      -1
+    ],
+    [
+      "ADD",
+      23,
+      21,
+      1
+    ],
+    [
+      "LOCAL",
+      23,
+      11,
+      true
+    ],
+    [
+      "ADD",
+      22,
+      24,
+      1
+    ],
+    [
+      "ADD",
+      25,
+      23,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      24,
+      11,
+      false
+    ],
+    [
+      "ADD",
+      22,
+      24,
+      -1
+    ],
+    [
+      "ADD",
+      25,
+      23,
+      1
+    ],
+    [
+      "LOCAL",
+      25,
+      12,
+      true
+    ],
+    [
+      "ADD",
+      24,
+      26,
+      1
+    ],
+    [
+      "ADD",
+      27,
+      25,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      26,
+      12,
+      false
+    ],
+    [
+      "ADD",
+      24,
+      26,
+      -1
+    ],
+    [
+      "ADD",
+      27,
+      25,
+      1
+    ],
+    [
+      "LOCAL",
+      27,
+      13,
+      true
+    ],
+    [
+      "ADD",
+      26,
+      28,
+      1
+    ],
+    [
+      "ADD",
+      29,
+      27,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      28,
+      13,
+      false
+    ],
+    [
+      "ADD",
+      26,
+      28,
+      -1
+    ],
+    [
+      "ADD",
+      29,
+      27,
+      1
+    ],
+    [
+      "LOCAL",
+      29,
+      14,
+      true
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      30,
+      14,
+      false
+    ],
+    [
+      "ADD",
+      28,
+      30,
+      -1
+    ],
+    [
+      "ADD",
+      31,
+      29,
+      1
+    ],
+    [
+      "LOCAL",
+      31,
+      15,
+      true
+    ],
+    [
+      "ADD",
+      30,
+      32,
+      1
+    ],
+    [
+      "ADD",
+      33,
+      31,
+      -1
+    ],
+    [
+      "QUERY_SHEAR",
+      32,
+      15,
+      false
+    ],
+    [
+      "ADD",
+      30,
+      32,
+      -1
+    ],
+    [
+      "ADD",
+      33,
+      31,
+      1
+    ],
+    [
+      "LOCAL",
+      33,
+      16,
+      true
+    ],
+    [
+      "LOCAL",
+      34,
+      16,
+      false
+    ],
+    [
+      "IDLE",
+      8,
+      [
+        19,
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      9,
+      [
+        21,
+        23,
+        25,
+        27,
+        29,
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      10,
+      [
+        23,
+        25,
+        27,
+        29,
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      11,
+      [
+        25,
+        27,
+        29,
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      12,
+      [
+        27,
+        29,
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      13,
+      [
+        29,
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      14,
+      [
+        31,
+        33,
+        34
+      ]
+    ],
+    [
+      "IDLE",
+      15,
+      [
+        33,
+        34
+      ]
+    ],
+    [
+      "ADD",
+      32,
+      30,
+      1
+    ],
+    [
+      "ADD",
+      31,
+      33,
+      -1
+    ],
+    [
+      "ADD",
+      30,
+      28,
+      1
+    ],
+    [
+      "ADD",
+      29,
+      31,
+      -1
+    ],
+    [
+      "ADD",
+      28,
+      26,
+      1
+    ],
+    [
+      "ADD",
+      27,
+      29,
+      -1
+    ],
+    [
+      "ADD",
+      26,
+      24,
+      1
+    ],
+    [
+      "ADD",
+      25,
+      27,
+      -1
+    ],
+    [
+      "ADD",
+      24,
+      22,
+      1
+    ],
+    [
+      "ADD",
+      23,
+      25,
+      -1
+    ],
+    [
+      "ADD",
+      22,
+      20,
+      1
+    ],
+    [
+      "ADD",
+      21,
+      23,
+      -1
+    ],
+    [
+      "ADD",
+      20,
+      18,
+      1
+    ],
+    [
+      "ADD",
+      19,
+      21,
+      -1
+    ],
+    [
+      "ADD",
+      18,
+      16,
+      1
+    ],
+    [
+      "ADD",
+      17,
+      19,
+      -1
+    ],
+    [
+      "ADD",
+      16,
+      14,
+      1
+    ],
+    [
+      "ADD",
+      15,
+      17,
+      -1
+    ],
+    [
+      "ADD",
+      14,
+      12,
+      1
+    ],
+    [
+      "ADD",
+      13,
+      15,
+      -1
+    ],
+    [
+      "ADD",
+      12,
+      10,
+      1
+    ],
+    [
+      "ADD",
+      11,
+      13,
+      -1
+    ],
+    [
+      "ADD",
+      10,
+      8,
+      1
+    ],
+    [
+      "ADD",
+      9,
+      11,
+      -1
+    ],
+    [
+      "ADD",
+      8,
+      6,
+      1
+    ],
+    [
+      "ADD",
+      7,
+      9,
+      -1
+    ],
+    [
+      "ADD",
+      6,
+      4,
+      1
+    ],
+    [
+      "ADD",
+      5,
+      7,
+      -1
+    ],
+    [
+      "ADD",
+      4,
+      2,
+      1
+    ],
+    [
+      "ADD",
+      3,
+      5,
+      -1
+    ],
+    [
+      "ADD",
+      2,
+      0,
+      1
+    ],
+    [
+      "ADD",
+      1,
+      3,
+      -1
+    ],
+    [
+      "SIGNED_SWAP",
+      0,
+      1
+    ],
+    [
+      "SIGNED_SWAP",
+      2,
+      3
+    ],
+    [
+      "SIGNED_SWAP",
+      4,
+      5
+    ],
+    [
+      "SIGNED_SWAP",
+      6,
+      7
+    ],
+    [
+      "SIGNED_SWAP",
+      8,
+      9
+    ],
+    [
+      "SIGNED_SWAP",
+      10,
+      11
+    ],
+    [
+      "SIGNED_SWAP",
+      12,
+      13
+    ],
+    [
+      "SIGNED_SWAP",
+      14,
+      15
+    ],
+    [
+      "SIGNED_SWAP",
+      16,
+      17
+    ],
+    [
+      "SIGNED_SWAP",
+      18,
+      19
+    ],
+    [
+      "SIGNED_SWAP",
+      20,
+      21
+    ],
+    [
+      "SIGNED_SWAP",
+      22,
+      23
+    ],
+    [
+      "SIGNED_SWAP",
+      24,
+      25
+    ],
+    [
+      "SIGNED_SWAP",
+      26,
+      27
+    ],
+    [
+      "SIGNED_SWAP",
+      28,
+      29
+    ],
+    [
+      "SIGNED_SWAP",
+      30,
+      31
+    ],
+    [
+      "SIGNED_SWAP",
+      32,
+      33
+    ]
+  ],
+  "prefix_pairs": 8
+}
diff --git a/research/fresh-helper-invoice-audit/snapshot/native-receipt.json.gz b/research/fresh-helper-invoice-audit/snapshot/native-receipt.json.gz
new file mode 100644
index 0000000000..e6fdb31624
Binary files /dev/null and b/research/fresh-helper-invoice-audit/snapshot/native-receipt.json.gz differ
diff --git a/research/fresh-helper-invoice-audit/snapshot/source-README.md b/research/fresh-helper-invoice-audit/snapshot/source-README.md
new file mode 100644
index 0000000000..344616d665
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/snapshot/source-README.md
@@ -0,0 +1,92 @@
+# Conditional κ = 0.00300105: fresh helper retiming on query-thinned controllers
+
+This builds on the stronger [PR4440](https://github.com/CrocSwap/integer-mult-bounds/pull/4440)
+found during the requested 20-minute frontier check. After auditing its exact
+head, replace all 19 full complex native calls by the verified fresh-helper
+unit of `research/fresh-helper-boundary`. The main controller, 16 paid query
+shears and stronger ordinary BIT supplier stay those of PR4440. The proposed
+conditional bound is
+
+```
+T(n) = O(n (log n)^(1 - 0.00300105)).
+```
+
+The gain is **0.00004105 (about 1.39%) over PR4440's 0.00296**,
+**about 11.71% over PR4416's 0.00268647**, and **30.48% over the pinned
+selected 0.0023**. The new result is author-checked and awaits review; it
+retains the conditional source implementation and transfer contracts.
+
+| Complete complex raw invoice | PR4440 | Combined construction |
+| --- | ---: | ---: |
+| Full native calls / paid query shears | 19 / 16 | 19 / 16 |
+| Independent productive fields | 11,560 | 11,560 |
+| Paid calls | 72,902 | **69,273** |
+| Productive / paid rank mass | 258,271 / 257,471 | 260,798 / 259,998 |
+| Rank-one surplus | 800 | 800 |
+| Proposed conditional κ | 0.00296 | **0.00300105** |
+
+The native retiming removes **3,629 paid calls**. It changes 117 helper
+entrances, 42 exits and 395 scalar frames in each full invocation, with exactly
+the same main operator and complete owned-center program. Thus substitution
+is a native operator equivalence, not merely replacement of a histogram.
+Every helper is still a distinct arbitrary original input; query copies and
+centers receive no productive credit. [PROOF.md](PROOF.md) gives the join.
+
+The exact changed-profile root is enclosed by
+
+```
+0.0030010541830 < root < 0.0030010541834.
+```
+
+An interval proof covers every real `0<C<1`, giving a fixed-profile ceiling.
+Only about `4.18e-9` headroom remains; further substantial progress needs another
+profile. At tested saving `0.003001052`, tensor power 1024, cutoff `20^1024`
+and target floor `21^1024` pay both tails. The changed profile needs the
+explicit gamma limit `97/100`; copying PR4440's `31/32` limit would fail.
+PR4433's general logarithmic compiler supplies an explicit sufficient rank
+recorded in RESULT.json. Its enormous word is specified algorithmically and
+has not been materialized. The unchanged stronger BIT supplier, atom power
+0.004, all nine outer rows, 54 predicates and four functional guards are retained.
+
+## Replay and source pins
+
+Python 3.12, standard library only:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/fresh-helper-thinned
+```
+
+Normal replay freshly runs **both complete source verifiers**, then independently
+counts every full/query/idle event and checks the combined moment, root ceiling,
+charged tails, finite rank, scalar/route bound and entire consumer. The `--write`
+authoring option assembles only the new receipt from previously audited source
+receipts; normal replay never uses that shortcut and does not write.
+
+The exact predecessor heads are `40e22a83ed660d3d6074c4f2dbf14bfb621eee51`
+(PR4440) and `ccdae89b2ab9ced24ee3e7adfdb670ef80d223d9` (the first version of
+this helper-retiming PR). SOURCES.json pins all transitive live inputs against
+those commits or canonical `3a23e9d9d`. Both predecessor commits are actual
+ancestors of the submission. Their source files are unchanged. See
+[AUDIT-4440.md](AUDIT-4440.md) and [VALIDATION.md](VALIDATION.md).
+
+## Scope and credit
+
+The native/all-column, permitted physical movement and whole-job matching,
+owned-erasure, precision, finite-template, analytic, fixed-tape, prime and
+exact-recovery premises remain conditional. No selected-record change, formal
+verification, independent human proof review, global optimum or practical
+runtime claim is made.
+
+Credit: PR4440's query thinning, stronger BIT and owned-query construction;
+zxv's native controllers and higher-moment/logarithmic compiler work;
+Jacob Alan Sussman's mixed integer flow; the PR4416 paid-completion construction;
+and the retained native, Clifford, BIT, precision and outer contributors.
+The helper boundary retiming and combined construction were prepared for
+1337isnot1337 with substantial OpenAI Codex assistance, Apache-2.0.
+All predecessor notices remain intact. No subagents were used.
+
+## Open next questions
+
+TASK.json specifies independent all-column/owned-query review and a changed
+multi-frame or controller topology as the next useful work. Neither the finite
+path screen nor the fixed-profile ceiling proves global optimality.
diff --git a/research/fresh-helper-invoice-audit/verify.py b/research/fresh-helper-invoice-audit/verify.py
new file mode 100644
index 0000000000..c02dd63eee
--- /dev/null
+++ b/research/fresh-helper-invoice-audit/verify.py
@@ -0,0 +1,211 @@
+#!/usr/bin/env python3
+"""Source-bound finite invoice audit; no source-verifier imports.
+
+Prepared for mihir-s-05 with substantial OpenAI Codex assistance. Apache-2.0.
+Predecessor construction and attribution are recorded in README.md.
+"""
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+import gzip
+from hashlib import sha1, sha256
+import json
+from pathlib import Path
+
+from audit import Frames, controller_invoice, local_invoice, require
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+SOURCE = 'research/kappa-rebuild/complex/full-identity-certificates/'
+
+
+def read(path):
+    raw = path.read_bytes()
+    return json.loads(gzip.decompress(raw) if path.suffix == '.gz' else raw)
+
+
+def authenticate_bytes(raw, row):
+    require(sha256(raw).hexdigest() == row['sha256'], 'source SHA256 mismatch')
+    blob = sha1(b'blob ' + str(len(raw)).encode() + b'\0' + raw).hexdigest()
+    require(blob == row['git_blob'], 'source Git blob mismatch')
+
+
+def authenticate():
+    live = [row for row in read(HERE / 'SOURCES.json')['files'] if row['usage'] == 'input']
+    require({row['path'] for row in live} == {
+        SOURCE + 'THREE-base-FULL-IDENTITY-CANONICAL.json.gz',
+        SOURCE + 'THREE-base-FULL-IDENTITY-NATIVE.json.gz'}, 'exact live input inventory')
+    for row in live:
+        path = ROOT
+        for part in Path(row['path']).parts:
+            path = path / part
+            require(not path.is_symlink(), 'source symlink')
+        authenticate_bytes(path.read_bytes(), row)
+    snapshot = read(HERE / 'snapshot/MANIFEST.json')
+    require({row['file'] for row in snapshot} == {
+        'changes.json', 'native-receipt.json.gz', 'controller.json',
+        'combined-receipt.json', 'source-README.md'}, 'snapshot input inventory')
+    require(len(snapshot) == 5, 'duplicate snapshot row')
+    for row in snapshot:
+        require(row['commit'] == '5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39',
+                'snapshot source head')
+        path = HERE / 'snapshot' / row['file']
+        require(not path.is_symlink(), 'snapshot symlink')
+        authenticate_bytes(path.read_bytes(), row)
+    return live, snapshot
+
+
+def histogram(value):
+    return Counter({int(rank): count for rank, count in value.items()})
+
+
+def compare_local(result, expected):
+    require(result['helpers'] == histogram(expected['helpers']), 'helper invoice differs from source receipt')
+    require(result['paid'] == histogram(expected['paid']), 'paid invoice differs from source receipt')
+
+
+def compare_controller(result, expected):
+    for key in ('targets', 'paid'):
+        require(result[key] == histogram(expected[key]), 'complete invoice differs: ' + key)
+
+
+def mass(profile):
+    return sum(rank * count for rank, count in profile.items())
+
+
+def signed_delta(new, old):
+    return {rank: new[rank] - old[rank] for rank in sorted(new.keys() | old.keys())
+            if new[rank] != old[rank]}
+
+
+def rejected(name, function):
+    try:
+        function()
+    except ValueError as exc:
+        return {'control': name, 'rejected_by': str(exc)}
+    raise ValueError('negative control accepted: ' + name)
+
+
+def run():
+    live, snapshots = authenticate()
+    canonical = read(ROOT / (SOURCE + 'THREE-base-FULL-IDENTITY-CANONICAL.json.gz'))
+    native = read(ROOT / (SOURCE + 'THREE-base-FULL-IDENTITY-NATIVE.json.gz'))
+    changes = read(HERE / 'snapshot/changes.json')
+    controller = read(HERE / 'snapshot/controller.json')
+    expected_local = read(HERE / 'snapshot/native-receipt.json.gz')
+    expected_combined = read(HERE / 'snapshot/combined-receipt.json')
+    require(canonical['v'] == 112 and canonical['h'] == 9 and
+            len(canonical['ports']) == len(set(canonical['ports'])) == 112 and
+            len(canonical['centers']) == 8, 'source port/axis/center contract')
+
+    # Without a patch, recover the explicit source climbs and eight unsplit centers.
+    empty = {key: [] for key in ('entrances', 'exits', 'gates')}
+    old, _ = local_invoice(canonical, native, empty)
+    require(old['paid'] == old['original_paid'], 'unpatched reconstruction differs from explicit source climbs')
+    baseline = controller_invoice(controller, old['helpers'], old['paid'])
+    compare_controller(baseline, controller['invoice'])
+
+    unit, both = local_invoice(canonical, native, changes)
+    compare_local(unit, expected_local)
+    combined = controller_invoice(controller, unit['helpers'], unit['paid'])
+    compare_controller(combined, expected_combined)
+    require(combined['event_counts'] == {'LOCAL': 19, 'QUERY_SHEAR': 16,
+            'IDLE': 16, 'ADD': 96, 'SIGNED_SWAP': 17}, 'complete event census')
+    require(sum(combined['targets'].values()) == 11560 and sum(combined['paid'].values()) == 69273,
+            'combined field/call totals')
+    require(mass(combined['targets']) == 260798 and mass(combined['paid']) == 259998,
+            'combined rank masses')
+    require(mass(unit['helpers']) - mass(old['helpers']) ==
+            mass(unit['paid']) - mass(old['paid']) == 133, 'local conserved mass increment')
+
+    # Fixed warp jumps and main endpoints cancel in old-versus-new subtraction.
+    # Only helper boundary widths change the telescoped persistent rank mass.
+    require(mass(combined['targets']) - mass(combined['paid']) ==
+            mass(baseline['targets']) - mass(baseline['paid']) == 800,
+            'rank surplus conservation')
+    require(sum(baseline['paid'].values()) - sum(combined['paid'].values()) ==
+            19 * (sum(old['paid'].values()) - sum(unit['paid'].values())) == 3629,
+            'complete call savings')
+
+    controls = []
+    bad = deepcopy(changes)
+    bad['entrances'].append(bad['entrances'][0])
+    controls.append(rejected('duplicate-helper-boundary', lambda: local_invoice(canonical, native, bad)))
+    bad = deepcopy(changes)
+    bad['gates'][0][2] = -1
+    controls.append(rejected('wrong-old-scalar-frame', lambda: local_invoice(canonical, native, bad)))
+    bad = deepcopy(changes)
+    bad['gates'].pop(0)
+    controls.append(rejected('missing-scalar-retiming', lambda: compare_local(
+        local_invoice(canonical, native, bad)[0], expected_local)))
+    bad = deepcopy(changes)
+    bad['exits'].pop(0)
+    controls.append(rejected('missing-helper-exit', lambda: compare_local(
+        local_invoice(canonical, native, bad)[0], expected_local)))
+    bad = deepcopy(changes)
+    bad['gates'][0][3] = next(i for i, frame in enumerate(canonical['frames']) if len(frame) == 1)
+    controls.append(rejected('incompatible-contact-frame', lambda: local_invoice(canonical, native, bad)))
+    controls.append(rejected('equal-dimension-distinct-spaces', lambda: Frames([[1], [2]]).width(0, 1)))
+    controls.append(rejected('dependent-frame-basis', lambda: Frames([[1, 2, 3]])))
+
+    for kind in ('QUERY_SHEAR', 'IDLE'):
+        bad_word = deepcopy(controller)
+        index = next(i for i, event in enumerate(bad_word['physical_events']) if event[0] == kind)
+        bad_word['physical_events'].pop(index)
+        controls.append(rejected('omitted-' + kind.lower(), lambda: controller_invoice(
+            bad_word, unit['helpers'], unit['paid'])))
+    bad_word = deepcopy(controller)
+    index = next(i for i, event in enumerate(bad_word['physical_events']) if event[0] == 'SIGNED_SWAP')
+    bad_word['physical_events'][index][0] = 'SWAP'
+    controls.append(rejected('unsigned-controller-swap', lambda: controller_invoice(
+        bad_word, unit['helpers'], unit['paid'])))
+    bad_word = deepcopy(controller)
+    gate = next(g for g in bad_word['boundaries']['left_program'] if g[0] == 'ADD')
+    gate[-1] = str(-Fraction(gate[-1]))
+    controls.append(rejected('changed-boundary-coefficient', lambda: controller_invoice(
+        bad_word, unit['helpers'], unit['paid'])))
+    bad_word = deepcopy(controller)
+    bad_word['diagonal'][0][1] ^= 1
+    controls.append(rejected('unearned-productive-stage', lambda: controller_invoice(
+        bad_word, unit['helpers'], unit['paid'])))
+    raw = (HERE / 'snapshot/changes.json').read_bytes()
+    row = next(row for row in snapshots if row['file'] == 'changes.json')
+    controls.append(rejected('changed-source-bytes', lambda: authenticate_bytes(raw + b'\n', row)))
+
+    report = {
+        'status': 'PASS_INDEPENDENT_FRESH_HELPER_INVOICE',
+        'source_head': '5f9d871c6bd1b9e34db5a7ea5ef08a908e94db39',
+        'source_files_authenticated': len(live) + len(snapshots),
+        'native_orientations': sorted(both),
+        'persistent_roles_per_orientation': 632,
+        'changed_role_bills': sum(a != b for a, b in zip(old['role_paid'], unit['role_paid'])),
+        'scalar_frame_patches': len(changes['gates']),
+        'helper_entrance_patches': len(changes['entrances']),
+        'helper_exit_patches': len(changes['exits']),
+        'persistent_scalar_contacts': len(unit['contacts']),
+        'local_helpers': unit['helpers'], 'local_paid': unit['paid'],
+        'local_paid_delta': signed_delta(unit['paid'], old['paid']),
+        'local_helper_delta': signed_delta(unit['helpers'], old['helpers']),
+        'local_paid_calls_saved': sum(old['paid'].values()) - sum(unit['paid'].values()),
+        'local_target_and_paid_mass_increment': 133,
+        'controller_events': combined['event_counts'],
+        'main_targets': combined['main'], 'whole_idle_paid': combined['whole_idle'],
+        'targets': combined['targets'], 'paid': combined['paid'],
+        'productive_fields': sum(combined['targets'].values()),
+        'paid_calls': sum(combined['paid'].values()),
+        'paid_calls_saved': 3629,
+        'target_rank_mass': mass(combined['targets']),
+        'paid_rank_mass': mass(combined['paid']),
+        'rank_surplus': 800,
+        'rejection_controls': controls,
+        'scope': 'Finite contact-path and full symbolic controller invoice only; no new kappa or supplier admission.',
+    }
+    return json.loads(json.dumps(report))
+
+
+if __name__ == '__main__':
+    report = run()
+    require(report == read(HERE / 'RESULT.json'), 'audit receipt differs')
+    print(json.dumps({'status': report['status'], 'paid_calls': report['paid_calls'],
+                      'calls_saved': report['paid_calls_saved'], 'surplus': report['rank_surplus'],
+                      'controls_rejected': len(report['rejection_controls'])}, sort_keys=True))