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+# Independent audit of the P104 monotone-relay floor
+
+Under the explicit correction-network model below, the P104 side correction
+requires **at least 208 new monotone helper lifetimes**: at least two first
+entries into each of the 104 distinct target endpoint frames. This counts
+lifetimes, not simultaneous physical registers, and does not construct a
+208-helper network or establish a recursive price.
+
+The number 208 belongs to **Philippe Van Velzen's
+[correction screen](https://github.com/philippeVV/integer-mult-bounds/tree/7dfc7a176d7de4e7eabaf553a0b187c1bd647546/research/p104-correction-screen)**,
+reported in [Discussion #2245](https://github.com/CrocSwap/integer-mult-bounds/discussions/2245#discussioncomment-18939575).
+This independent audit supplies the missing explicit implication from its
+finite support-cover calculation to arbitrary monotone linear relay networks.
+It gives small rank-eight witnesses, a proof that permits cancellation and
+helper-to-helper relays, and a concrete boundary example from the frozen word.
+The predecessor's numerical floor and geometric cover are not claimed new.
+
+Evidence status: exact finite checks plus a written scoped proof, with separate
+AI-assisted mathematical review and premise reconstruction. No independent
+human review or proof assistant. No supplier, new κ, or selected-frontier change.
+[Canonical claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/2245#discussioncomment-18941961).
+
+## Precise model
+
+Keep the ordered source and target **frame paths** from PR #1972's 4,058-event
+word, retained by PR #1991. The sources are `X0..X103`, with initial binary
+labels `q_s`; target `Y_t` ends in an eight-dimensional subspace `H_t` of
+`F2^9`. Frames are subspaces, not a particular choice of basis. The added
+network must contribute `(I-G/2)x` to the targets for arbitrary source values
+and independent dirty inputs. Here `G` is the ordinary rational root Gram
+matrix in the pinned port order, reconstructed independently from the fixture.
+
+The added network may:
+
+- read the unchanged source `X_s` when it is in its retained frame;
+- make arbitrary rational linear combinations, copies and clears of helpers
+  **within an equal frame**, with coefficients independent of all input values;
+- use arbitrarily many fresh helpers with source-independent initial values,
+  including arbitrary dirty inputs, and mix those helpers freely;
+- transport a helper without changing its logical coefficients along any
+  nested path of subspaces, with jumps permitted;
+- add corrections to `Y_t` in its current frame, and freely retime operations
+  while preserving the ordered source/target paths.
+
+Targets receive additive writes only: they are not cleared or rescaled.
+The added network cannot read targets or the retained channel's `G/Q/D/C`
+helpers, modify source values, preload source-dependent helper inputs, or use
+any other operation to transfer source dependence. In particular, descending
+transports and cross-chart operations are excluded whether free **or paid**.
+No source reads may be hidden in coefficients, descriptors, or initialization.
+The retained channel itself may continue its unchanged work; these restrictions
+apply to the added correction network. The frozen word never writes an X value
+and never reads a Y value, so added target corrections do not feed back through
+that word.
+
+A **helper lifetime** starts with source-independent contents and follows one
+nested path. Discarding/reinitializing a physical register begins another
+lifetime. A single physical register may therefore count more than once.
+Restoration is relaxed for this lower bound: imposing valid dirty restoration
+cannot reduce it. This is a linear logical/common-frame model, not native
+operator or hosting admission.
+
+## Exact finite premises
+
+Write `supp_t = {s : (I-G/2)[t,s] != 0}`. Define
+
+```
+E_t = {s in supp_t : q_s occurs in an earlier frame of Y_t},
+D_t = {s in supp_t : some retained X_s frame equals H_t},
+N_t = supp_t minus (E_t union D_t).
+```
+
+The audit grants all earlier target contacts and all possible direct source
+reads, without enforcing their chronological availability. This is a favorable
+relaxation, so no source/target time-separation premise is needed.
+
+The independent checker establishes:
+
+| Finite premise | Result |
+|---|---:|
+| Distinct target endpoint subspaces `H_t` | 104, all dimension 8 |
+| Nonzero correction entries per target | 48 |
+| `supp_t = {s : q_s in H_t}` | all 104 targets |
+| Direct source reads at an endpoint (`D_t`) | none |
+| Binary span of `{q_s : s in N_t}` | exactly `H_t`, all 104 targets |
+| Cover by two proper hyperplanes of `H_t` | all 104 targets |
+
+The sizes of `N_t` are `{36:12, 44:24, 45:8, 46:24, 47:24, 48:12}`.
+[RESULT.json](RESULT.json) supplies eight independent source labels and two
+cover normals for each target. The rank-eight witness rules out any single
+proper-subspace cover, without an exhaustive lower-bound search. The two
+normals certify only the local geometric covering minimum of two; they do not
+certify a chronological circuit, compatible coefficients, or dirty restoration.
+
+The compressed labels need not use ordinary Euclidean binary pairing.
+The checker binds membership directly to the recorded endpoint subspaces and
+to the support of the root-derived correction matrix.
+
+## Relay-safe proof
+
+Project each helper's logical row onto the independent source inputs. At any
+frame `V`, every source with a nonzero coefficient has its label in `V`.
+Initially the projection is zero. A source read respects this invariant since
+all frames on `X_s`'s path contain `q_s`. A same-frame linear operation can only
+combine existing support; cancellation removes coefficients but creates no new
+source dependence. A nested transport preserves coefficients and enlarges the
+allowed subspace. This proves the invariant by induction, for arbitrary dirty
+state and arbitrary relay depth.
+
+Fix target `t`. For any `s in N_t`, the correction coefficient of `x_s` is
+nonzero. It cannot be written to the target in an earlier frame, by the
+invariant and the definition of `E_t`. Nor can it be supplied directly at `H_t`,
+by the definition of `D_t`. It must arrive through a new helper's first entry
+into `H_t` from a proper subspace. Helpers born at `H_t` have zero initial source
+dependence; mixing them there adds no other source of information.
+
+Suppose there were at most one such entering lifetime. Just before its entry,
+its support lies in one proper subspace `V < H_t`, of dimension at most seven.
+Subsequent mixing at `H_t`, including feedback among its helpers and arbitrary
+cancellation, cannot create an `N_t` variable absent from that entrance.
+Therefore every label in `N_t` would lie in `V`. The checked rank-eight witness
+contradicts this. At least two lifetimes must enter each `H_t`.
+
+Two different eight-dimensional subspaces are incomparable. One nested helper
+lifetime cannot enter both. Summing the 104 target requirements proves the
+**208-lifetime lower bound**. Any admitted proper-to-`H_t` transport has positive
+dimension increment; a paid-rank floor of 208 follows only if that increment is
+indeed the chosen billing rule. It is not a complete excess-cost invoice:
+productive coverage, other operations, residual children and owners still need
+an explicit accounting argument.
+
+## Boundaries and controls
+
+Counting target writers would give a false proof. As a local relay illustration,
+in `H = F2^2`, two helpers
+can enter from `<e1>` and `<e2>` with `x1+d` and `x2-d`. After adding the second
+into the first at `H`, only the first writes `x1+x2` to the target. The checker
+includes this positive relay/cancellation example: there are two entrances
+but only one target writer. A helper's support can grow after its first entry.
+
+Reusing the existing channel is a substantive change of premise. At zero-based
+event **2463** (cut 2464), the original private register `C` descends to
+`span(243)`. Its coefficient of `X8` is **−2**, while `q_8 = 408` is outside
+`{0,243}`. The checker propagates this exact scalar derivative through the
+frozen events. This is a concrete failure of the support invariant when those
+existing descents/values are admitted, not an error in the native channel.
+
+Five rejecting controls cover a wrong transport rank, removed puncture,
+dependent rank witness, one-hyperplane claim, and wrong correction support.
+The positive relay example and excluded-descent example complete seven control
+groups. Acceptance uses integers, rational arithmetic and explicit binary
+subspaces, with no Python assertions that disappear under optimization.
+
+## Reproduce and coverage
+
+Python standard library only. From the repository root:
+
+```sh
+python3 -I -O -B research/p104-monotone-relay-floor-audit/verify.py
+python3 scripts/research_package.py --package research/p104-monotone-relay-floor-audit --check-only
+python3.12 scripts/research_package.py --package research/p104-monotone-relay-floor-audit
+```
+
+Default replay authenticates the two source inputs, recomputes the complete
+receipt and compares it with `RESULT.json`; it writes nothing. `--out NEW.json`
+additionally writes the verified receipt exclusively to a fresh path. A source
+export preserving these relative paths works without Git or network; the
+registered metadata check separately requires Git provenance.
+
+This replay checks every recorded frame transition, common-frame ADD/COPY,
+source/target path, source/target read/write direction, all 104 support/rank
+certificates, and one scalar derivative. It does **not** recertify all 280
+channel columns, native phases, the original `G/2` identity, or the selected
+cold replay. The mathematical lower-bound proof is written above; the finite
+checker does not enumerate all possible networks. No simultaneous-stock bound,
+208-helper construction, pricing interval, complete moment, global hosting,
+precision/tape or all-size theorem is claimed.
+
+## Open next questions
+
+Can an explicitly scheduled relay network attain these geometric covers with
+useful cost? Start with one target's two recorded hyperplanes, assign source
+reads and helper lifetimes, then check arbitrary dirty restoration and price
+all transports. The covers alone do not ensure compatible timing or values.
+
+Can retained descending/private values beat this restricted floor? The cut-2464
+example identifies a concrete excluded information source. First state which
+retained lifetimes may be read and check their actual dirty coefficients;
+then derive a replacement invariant or a full correction identity. Existing
+P104 constructions and cut bounds must be checked for overlap before proceeding.
+
+## Credit and provenance
+
+Philippe Van Velzen / `philippeVV` supplied the 208 floor, the two-hyperplane
+cover calculation and the broader correction/pricing screen at exact fork head
+`7dfc7a176d7de4e7eabaf553a0b187c1bd647546`. This audit neither imports its code
+nor rechecks its Smith form, no-relay floor, or pricing claims.
+
+Rohan Arun / #1972 supplies the frozen scalar/frame word, Chafik Boukhalfa /
+#1991 its native realization, Adam Gall / #1940 the schedule, and Josie Elliston
+/ #1071 the fixture, with Ali Romman / #1125 and retained geometry/compiler
+lineage. The adjacent 96-dimensional pooled-space result belongs to Gonzalo
+Mier / #2173 and Gareth Davidson / #2251; it is not this lifetime count.
+
+Base: canonical main `0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2`, priority revision
+4. Exact input hashes and Git blobs are in [SOURCES.json](SOURCES.json).
+[TASK.json](TASK.json) preserves the single chooser draw, changed audit scope,
+live overlap coverage and remaining questions. Frozen inputs remain unchanged.
+
+Prepared by kumagi with substantial OpenAI Codex assistance in derivation,
+implementation, independent AI-assisted checking and writing. Apache-2.0.
diff --git a/research/p104-monotone-relay-floor-audit/RESULT.json b/research/p104-monotone-relay-floor-audit/RESULT.json
new file mode 100644
index 0000000000..8ac15d2943
--- /dev/null
+++ b/research/p104-monotone-relay-floor-audit/RESULT.json
@@ -0,0 +1,144 @@
+{
+  "controls": [
+    "wrong_transport_rank",
+    "missing_puncture",
+    "dependent_basis",
+    "one_hyperplane_claim",
+    "wrong_correction_support",
+    "two_arrivals_one_writer_with_dirty_cancellation",
+    "retained_private_descent_escapes_support_locality"
+  ],
+  "distinct_terminal_frames": 104,
+  "excluded_descent": {
+    "coefficient": "-2",
+    "completed_cut": 2464,
+    "event_index": 2463,
+    "frame_generators": [
+      243
+    ],
+    "register": "C",
+    "source": "X8",
+    "source_label": 408
+  },
+  "minimum_arrivals_per_target": 2,
+  "minimum_helper_lifetimes": 208,
+  "residual_label_rank": 8,
+  "residual_support_sizes": {
+    "36": 12,
+    "44": 24,
+    "45": 8,
+    "46": 24,
+    "47": 24,
+    "48": 12
+  },
+  "schema_version": 1,
+  "scope": "Finite premises for the README's restricted monotone correction-network theorem; no supplier or kappa claim.",
+  "status": "PASS_P104_MONOTONE_RELAY_FLOOR_AUDIT",
+  "target_count": 104,
+  "targets": [
+    {"basis_sources": [2, 4, 5, 7, 9, 15, 24, 37], "cover_normals": [1, 4], "direct_support_count": 0, "early_support_count": 3, "needed_sources": [2, 4, 5, 7, 9, 10, 12, 15, 17, 18, 20, 24, 26, 27, 29, 37, 39, 41, 43, 44, 46, 48, 50, 51, 53, 55, 57, 60, 62, 64, 66, 67, 69, 71, 73, 76, 78, 79, 81, 83, 85, 87, 89, 98, 100], "target": 0},
+    {"basis_sources": [2, 4, 5, 7, 9, 15, 24, 33], "cover_normals": [1, 7], "direct_support_count": 0, "early_support_count": 0, "needed_sources": [2, 4, 5, 7, 9, 10, 12, 15, 17, 18, 20, 24, 26, 27, 29, 33, 35, 36, 38, 40, 42, 45, 47, 49, 52, 54, 56, 58, 59, 61, 63, 65, 68, 70, 72, 74, 75, 77, 80, 82, 84, 86, 88, 90, 92, 96, 98, 100], "target": 1},
+    {"basis_sources": [0, 1, 3, 7, 8, 15, 24, 35], "cover_normals": [1, 11], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [0, 1, 3, 6, 7, 8, 11, 12, 15, 16, 19, 20, 24, 25, 28, 29, 35, 36, 39, 40, 43, 44, 47, 50, 51, 54, 55, 58, 59, 62, 63, 66, 67, 70, 71, 74, 75, 78, 79, 82, 85, 86, 89, 92, 97, 99, 100], "target": 2},
+    {"basis_sources": [2, 4, 5, 8, 13, 14, 23, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 0, "needed_sources": [2, 4, 5, 8, 11, 13, 14, 16, 19, 21, 23, 25, 28, 30, 33, 35, 36, 38, 41, 43, 44, 46, 48, 50, 51, 53, 56, 58, 59, 61, 64, 66, 67, 69, 72, 74, 75, 77, 80, 82, 84, 87, 89, 91, 95, 97, 99, 101], "target": 3},
+    {"basis_sources": [0, 1, 3, 9, 13, 14, 23, 35], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [0, 1, 3, 6, 9, 10, 13, 14, 17, 18, 21, 23, 26, 27, 30, 35, 36, 39, 41, 42, 45, 46, 48, 49, 52, 53, 55, 58, 59, 62, 64, 65, 68, 69, 71, 74, 75, 78, 79, 82, 85, 87, 88, 90, 95, 98, 101], "target": 4},
+    {"basis_sources": [0, 1, 3, 9, 13, 14, 23, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [0, 1, 3, 6, 9, 10, 13, 14, 17, 18, 21, 23, 26, 27, 30, 33, 37, 38, 40, 43, 44, 47, 50, 51, 54, 56, 57, 60, 61, 63, 66, 67, 70, 72, 73, 76, 77, 80, 81, 83, 84, 86, 89, 92, 95, 98, 101], "target": 5},
+    {"basis_sources": [2, 4, 5, 8, 13, 14, 23, 34], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 0, "needed_sources": [2, 4, 5, 8, 11, 13, 14, 16, 19, 21, 23, 25, 28, 30, 34, 37, 39, 40, 42, 45, 47, 49, 52, 54, 55, 57, 60, 62, 63, 65, 68, 70, 71, 73, 76, 78, 79, 81, 83, 85, 86, 88, 90, 92, 95, 97, 99, 101], "target": 6},
+    {"basis_sources": [0, 1, 2, 8, 13, 15, 22, 34], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 0, "needed_sources": [0, 1, 2, 8, 9, 10, 11, 13, 15, 20, 22, 24, 29, 31, 34, 35, 38, 39, 40, 41, 44, 45, 49, 50, 53, 54, 55, 56, 59, 60, 65, 66, 69, 70, 71, 72, 75, 76, 81, 84, 85, 86, 87, 90, 94, 96, 100, 102], "target": 7},
+    {"basis_sources": [2, 3, 6, 7, 9, 16, 22, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [2, 3, 6, 7, 9, 10, 12, 13, 16, 19, 22, 25, 28, 31, 33, 35, 37, 39, 40, 42, 44, 46, 48, 50, 52, 54, 55, 57, 59, 61, 64, 66, 70, 71, 73, 75, 77, 80, 83, 85, 86, 88, 91, 94, 97, 99, 102], "target": 8},
+    {"basis_sources": [0, 1, 4, 7, 8, 17, 22, 35], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 2, "needed_sources": [0, 1, 4, 5, 7, 8, 11, 12, 13, 17, 18, 22, 26, 27, 31, 35, 37, 38, 40, 43, 45, 46, 48, 49, 51, 54, 57, 59, 62, 64, 65, 67, 70, 72, 73, 75, 78, 79, 83, 84, 86, 89, 90, 94, 98, 102], "target": 9},
+    {"basis_sources": [0, 1, 4, 7, 8, 17, 22, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 2, "needed_sources": [0, 1, 4, 5, 7, 8, 11, 12, 13, 17, 18, 22, 26, 27, 31, 33, 36, 39, 41, 42, 44, 47, 50, 52, 53, 55, 58, 60, 61, 63, 66, 69, 71, 74, 76, 77, 80, 81, 82, 85, 87, 88, 92, 94, 98, 102], "target": 10},
+    {"basis_sources": [2, 3, 6, 7, 9, 16, 22, 34], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [2, 3, 6, 7, 9, 10, 12, 13, 16, 19, 22, 25, 28, 31, 34, 36, 38, 41, 43, 45, 47, 49, 51, 53, 58, 60, 62, 63, 65, 67, 69, 72, 74, 76, 78, 79, 81, 82, 84, 87, 89, 90, 92, 94, 97, 99, 102], "target": 11},
+    {"basis_sources": [0, 1, 2, 8, 13, 15, 22, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 0, "needed_sources": [0, 1, 2, 8, 9, 10, 11, 13, 15, 20, 22, 24, 29, 31, 33, 36, 37, 42, 43, 46, 47, 48, 51, 52, 57, 58, 61, 62, 63, 64, 67, 68, 73, 74, 77, 78, 79, 80, 82, 83, 88, 89, 91, 92, 94, 96, 100, 102], "target": 12},
+    {"basis_sources": [3, 4, 5, 7, 8, 14, 22, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 21, 22, 23, 31, 33, 34, 35, 44, 45, 46, 47, 48, 49, 50, 59, 60, 61, 62, 63, 64, 65, 66, 75, 76, 77, 78, 79, 80, 81, 90, 91, 92, 94, 95, 101, 102], "target": 13},
+    {"basis_sources": [3, 4, 5, 13, 15, 16, 23, 36], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 0, "needed_sources": [3, 4, 5, 6, 13, 15, 16, 17, 18, 19, 20, 23, 30, 32, 36, 37, 38, 39, 44, 45, 46, 47, 48, 49, 50, 55, 56, 57, 58, 67, 68, 69, 70, 75, 76, 77, 78, 79, 80, 81, 86, 87, 88, 89, 93, 95, 101, 103], "target": 14},
+    {"basis_sources": [0, 1, 2, 7, 14, 16, 24, 34], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [0, 1, 2, 7, 12, 14, 16, 17, 18, 19, 21, 24, 29, 32, 34, 35, 38, 39, 42, 43, 46, 47, 48, 52, 55, 56, 59, 60, 65, 66, 69, 70, 73, 74, 77, 78, 79, 80, 82, 83, 86, 87, 90, 93, 96, 100, 103], "target": 15},
+    {"basis_sources": [2, 3, 6, 8, 14, 17, 25, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 2, "needed_sources": [2, 3, 6, 8, 11, 14, 15, 17, 18, 20, 21, 25, 28, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 53, 55, 57, 59, 61, 64, 66, 70, 72, 74, 76, 78, 79, 81, 82, 84, 86, 88, 91, 93, 97, 99, 103], "target": 16},
+    {"basis_sources": [0, 1, 4, 9, 14, 16, 26, 35], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 4, "needed_sources": [0, 1, 4, 5, 9, 10, 14, 15, 16, 19, 20, 21, 26, 27, 32, 35, 37, 38, 41, 42, 44, 47, 50, 52, 57, 59, 62, 64, 65, 67, 70, 74, 76, 77, 80, 81, 82, 85, 86, 89, 90, 93, 98, 103], "target": 17},
+    {"basis_sources": [0, 1, 4, 9, 14, 16, 26, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 4, "needed_sources": [0, 1, 4, 5, 9, 10, 14, 15, 16, 19, 20, 21, 26, 27, 32, 33, 36, 39, 40, 43, 45, 46, 48, 49, 54, 55, 58, 60, 61, 63, 66, 69, 72, 75, 78, 79, 83, 84, 87, 88, 92, 93, 98, 103], "target": 18},
+    {"basis_sources": [2, 3, 6, 8, 14, 17, 25, 34], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 2, "needed_sources": [2, 3, 6, 8, 11, 14, 15, 17, 18, 20, 21, 25, 28, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 58, 60, 62, 63, 65, 67, 69, 73, 75, 77, 80, 83, 85, 87, 89, 90, 92, 93, 97, 99, 103], "target": 19},
+    {"basis_sources": [0, 1, 2, 7, 14, 16, 24, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [0, 1, 2, 7, 12, 14, 16, 17, 18, 19, 21, 24, 29, 32, 33, 36, 37, 40, 41, 44, 45, 49, 50, 53, 54, 57, 58, 61, 62, 63, 64, 67, 68, 72, 75, 76, 81, 84, 85, 88, 89, 91, 92, 93, 96, 100, 103], "target": 20},
+    {"basis_sources": [3, 4, 5, 13, 15, 16, 23, 33], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 3, "needed_sources": [3, 4, 5, 6, 13, 15, 16, 17, 18, 19, 20, 23, 32, 33, 34, 35, 40, 41, 42, 43, 52, 53, 54, 59, 60, 61, 62, 63, 64, 65, 66, 72, 73, 74, 82, 83, 84, 85, 90, 91, 92, 93, 95, 101, 103], "target": 21},
+    {"basis_sources": [7, 8, 9, 10, 13, 23, 40, 55], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 3, "needed_sources": [7, 8, 9, 10, 11, 12, 13, 23, 24, 25, 26, 27, 28, 29, 30, 40, 41, 42, 43, 44, 45, 46, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 79, 80, 81, 82, 83, 84, 85], "target": 22},
+    {"basis_sources": [3, 4, 5, 13, 14, 22, 24, 36], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [3, 4, 5, 6, 13, 14, 21, 22, 24, 25, 26, 27, 28, 29, 31, 36, 37, 38, 39, 44, 45, 46, 51, 52, 53, 54, 59, 60, 61, 62, 63, 64, 65, 66, 71, 72, 73, 74, 79, 80, 81, 86, 87, 88, 89, 95, 101], "target": 23},
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+    {"basis_sources": [3, 6, 8, 16, 36, 38, 44, 67], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 12, "needed_sources": [3, 6, 8, 11, 16, 19, 36, 38, 40, 42, 44, 46, 47, 49, 51, 53, 55, 57, 67, 69, 71, 73, 75, 77, 79, 81, 82, 84, 86, 88, 93, 94, 95, 101, 102, 103], "target": 97},
+    {"basis_sources": [0, 1, 4, 9, 17, 26, 35, 38], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 4, "needed_sources": [0, 1, 4, 5, 9, 10, 17, 18, 26, 27, 35, 37, 38, 41, 42, 44, 48, 49, 51, 54, 55, 58, 60, 64, 67, 70, 71, 74, 76, 77, 79, 83, 84, 87, 88, 92, 93, 94, 95, 97, 99, 101, 102, 103], "target": 98},
+    {"basis_sources": [2, 3, 6, 8, 16, 33, 35, 64], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 3, "needed_sources": [2, 3, 6, 8, 11, 16, 19, 33, 35, 37, 39, 41, 43, 45, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 83, 85, 87, 89, 90, 92, 93, 94, 95, 96, 100, 101, 102, 103], "target": 99},
+    {"basis_sources": [0, 1, 2, 7, 15, 24, 34, 38], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 1, "needed_sources": [0, 1, 2, 7, 12, 15, 20, 24, 29, 34, 35, 38, 39, 42, 43, 46, 49, 50, 53, 54, 57, 58, 61, 62, 65, 66, 69, 70, 73, 74, 77, 78, 81, 84, 85, 88, 89, 91, 92, 93, 94, 95, 97, 99, 101, 102, 103], "target": 100},
+    {"basis_sources": [3, 4, 5, 13, 14, 23, 36, 38], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 2, "needed_sources": [3, 4, 5, 6, 13, 14, 21, 23, 30, 36, 37, 38, 39, 44, 45, 46, 51, 52, 53, 54, 60, 61, 62, 67, 68, 69, 70, 75, 76, 77, 78, 82, 83, 84, 85, 90, 91, 92, 93, 94, 96, 97, 99, 100, 102, 103], "target": 101},
+    {"basis_sources": [7, 8, 9, 10, 13, 22, 40, 55], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 4, "needed_sources": [7, 8, 9, 10, 11, 12, 13, 22, 31, 40, 41, 42, 43, 44, 45, 46, 55, 56, 57, 60, 61, 62, 71, 72, 73, 74, 75, 76, 77, 78, 86, 87, 88, 90, 91, 92, 93, 95, 96, 97, 99, 100, 101, 103], "target": 102},
+    {"basis_sources": [14, 15, 16, 19, 47, 48, 55, 79], "cover_normals": [1, 12], "direct_support_count": 0, "early_support_count": 12, "needed_sources": [14, 15, 16, 19, 20, 21, 47, 48, 49, 52, 53, 54, 55, 56, 57, 60, 61, 62, 79, 80, 81, 83, 84, 85, 86, 87, 88, 90, 91, 92, 95, 96, 97, 99, 100, 101], "target": 103}
+  ]
+}
diff --git a/research/p104-monotone-relay-floor-audit/SOURCES.json b/research/p104-monotone-relay-floor-audit/SOURCES.json
new file mode 100644
index 0000000000..12554d7a6a
--- /dev/null
+++ b/research/p104-monotone-relay-floor-audit/SOURCES.json
@@ -0,0 +1,42 @@
+{
+  "schema_version": 1,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "e8870e5917057d59b730eb14721a778639eca050",
+      "sha256": "d46eb6d5b3e279428753d770653663fbdf1063e55c255ea073d768f344927ef7"
+    },
+    {
+      "path": "research/p104-native-channel/inputs/LOWRANK-WITNESS.json",
+      "usage": "input",
+      "git_blob": "86beaf424e9f0f800ae3a62797d94ec9386b7706",
+      "sha256": "0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e"
+    },
+    {
+      "path": "research/p104-native-channel/inputs/P104-FIXTURE.json",
+      "usage": "input",
+      "git_blob": "2e16f99b295bb386fd13bd8fbd57b42ef54143a9",
+      "sha256": "516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4"
+    }
+  ],
+  "context_sources": [
+    {
+      "author": "Philippe Van Velzen / philippeVV",
+      "commit": "7dfc7a176d7de4e7eabaf553a0b187c1bd647546",
+      "url": "https://github.com/philippeVV/integer-mult-bounds/tree/7dfc7a176d7de4e7eabaf553a0b187c1bd647546/research/p104-correction-screen",
+      "usage": "Attribution and audited claim only; no executable dependency or copied source.",
+      "inspected_sha256": {
+        "README.md": "0ece89eea65a1ba39367d1e59b756ef98d7f32abc367e02bdff6a63b582737e1",
+        "verify.py": "a6719987753f02ad068de7ca290d7f5b281a481849e5767c18a5a5761be563e5"
+      }
+    }
+  ]
+}
diff --git a/research/p104-monotone-relay-floor-audit/TASK.json b/research/p104-monotone-relay-floor-audit/TASK.json
new file mode 100644
index 0000000000..84f4c9be28
--- /dev/null
+++ b/research/p104-monotone-relay-floor-audit/TASK.json
@@ -0,0 +1,120 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 4,
+  "base_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can the native P104 low-rank channel be completed with a legal, fully charged I-G/2 side correction?",
+    "starting_points": [
+      "research/p104-native-channel/README.md",
+      "research/p104-native-channel/PROOF.md",
+      "docs/research/community-efficient1000-review.md"
+    ],
+    "methods": [
+      "Construct one side-correction word at an explicit chronological cut with the needed frames still available.",
+      "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget."
+    ],
+    "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the P104 open next questions and its fixed local histogram; inspect why appending I-G/2 after source completion is not justified. #1991 supplies the checked native channel, not the missing correction.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "Choose one exact side-correction cut and bound its allowed cost from a favorable completed moment at a declared target. Stop or hand off if the necessary source/target access cannot be justified or even the optimistic total misses the target.",
+    "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.",
+    "allowed_variations": [
+      "One correction factorization, one chronological cut, or one explicit hosting obstruction.",
+      "A changed correction schedule with an updated full bill and native frame contract."
+    ],
+    "scope_change_triggers": [
+      "Recompiling the already certified low-rank channel without closing a new obligation.",
+      "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier."
+    ],
+    "overlap_terms": [
+      "P104",
+      "I-G/2",
+      "side correction",
+      "native channel",
+      "1972",
+      "1991"
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Independently audit the 208 monotone new-helper floor in Discussion2245 comment18939575: exact finite target deficits and the support-propagation implication with relays.",
+  "scope_change_reason": "The live P104 completion space already contains several constructions and cut obstructions. This session targets a separate unreviewed relay-floor implication and its precise operation model, rather than claiming a completed supplier.",
+  "bottleneck_link": "The proposed 208\u2013482 helper window is a concrete side-correction lead; a sound scoped lower bound or a counterexample prevents an unsupported construction budget.",
+  "budget_minutes": 60,
+  "stop_rule": "One approximately 60-minute session. Stop with a source-bound proof and controls or a precise counterexample/model gap; do not synthesize a full supplier.",
+  "outcome": "completed",
+  "evidence": "RESULT.json: 104 distinct dimension-eight endpoint frames; all 104 residual supports rank eight; exact two-hyperplane covers; 208-lifetime scoped proof; seven control groups including a retained private descent outside the model.",
+  "author": "kumagi",
+  "ai_assistance": "Substantial OpenAI Codex assistance in research, implementation, proof review and writing, including parallel AI-assisted checking; no independent human review.",
+  "open_questions": [
+    {
+      "question": "Can a scheduled relay network attain the geometric covers at useful cost?",
+      "why_it_matters": "Two hyperplanes per target do not yet supply a correction word or favorable invoice.",
+      "first_step": "Use one target certificate to assign actual source reads and helper lifetimes, then check dirty restoration and all paid transports.",
+      "blocked_by": "Timing, coefficients, restoration, global sharing and complete pricing are unproved."
+    },
+    {
+      "question": "Can explicitly allowed retained descending/private values escape this restricted floor?",
+      "why_it_matters": "The cut-2464 example shows that the old channel contains source information outside the new-helper support invariant.",
+      "first_step": "Name allowed retained lifetimes, bind their dirty coefficients and derive a replacement invariant or exact correction identity after checking live overlap.",
+      "blocked_by": "This audit excludes those reads and provides no admitted realization or budget."
+    }
+  ],
+  "chooser_seed": "a71071a87492501cab47b3076ccee844",
+  "chooser_track": "complex-mechanisms",
+  "predecessor": {
+    "author": "Philippe Van Velzen / philippeVV",
+    "commit": "7dfc7a176d7de4e7eabaf553a0b187c1bd647546",
+    "url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2245#discussioncomment-18939575"
+  },
+  "freshness": {
+    "main_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+    "priority_revision": 4,
+    "checked_at": "2026-10-15T05:53:23Z",
+    "open_prs": 546,
+    "discussion_records": 1056,
+    "complete_pagination": true,
+    "limits": "No code-diff or arbitrary nested-file coverage."
+  },
+  "claim_url": "https://github.com/CrocSwap/integer-mult-bounds/discussions/2245#discussioncomment-18941961",
+  "verification": {
+    "environment": "macOS arm64; CPython 3.12.14 bundled runtime and CPython 3.14.7 Homebrew; standard library only",
+    "commands": [
+      "python3.12 scripts/research_package.py --package research/p104-monotone-relay-floor-audit",
+      "python3.14 -I -O -B research/p104-monotone-relay-floor-audit/verify.py",
+      "git diff --check"
+    ],
+    "additional_checks": [
+      "Git-free source export with only this package and two declared inputs: optimized CPython 3.12 replay passes; all file hashes unchanged.",
+      "Exported source drift and receipt drift reject; occupied --out path rejects without changing its bytes.",
+      "Separate AI-assisted proof/model review passed; independent scratch rank calculation agrees on all target residual sets."
+    ],
+    "not_run": [
+      "Full native-channel or selected cold replay",
+      "Supplier moment/pricing/hosting/precision/all-size admission",
+      "Proof assistant",
+      "Hosted CI"
+    ]
+  },
+  "submission_checkpoint": {
+    "main_commit": "0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2",
+    "priority_revision": 4,
+    "upstream_refetch": "Canonical origin/main refetched before submission; unchanged from scientific base.",
+    "searched_at": "2026-10-15T06:09:59.859303+00:00",
+    "open_prs": 561,
+    "discussion_records": 1073,
+    "complete_pagination": true,
+    "warnings": [],
+    "overlap_scope": "Open PR titles/bodies, Discussion bodies/comments/replies, local package notes and ledger; no arbitrary code-diff search. Targeted monotone+relay screen and live #2245 also inspected.",
+    "decision": "Continue the independently identified relay-floor audit; adjacent early-prefix and 41-contact chronological-lift work concern separate obligations."
+  }
+}
diff --git a/research/p104-monotone-relay-floor-audit/VERIFY.json b/research/p104-monotone-relay-floor-audit/VERIFY.json
new file mode 100644
index 0000000000..6d0abc07d9
--- /dev/null
+++ b/research/p104-monotone-relay-floor-audit/VERIFY.json
@@ -0,0 +1,23 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-native-channel/inputs/LOWRANK-WITNESS.json",
+    "research/p104-native-channel/inputs/P104-FIXTURE.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 60,
+      "checks": "Exact source-bound frame/support/rank premises, complete receipt comparison, five rejecting controls and two scope/relay controls."
+    }
+  ]
+}
diff --git a/research/p104-monotone-relay-floor-audit/verify.py b/research/p104-monotone-relay-floor-audit/verify.py
new file mode 100644
index 0000000000..d1123c33a4
--- /dev/null
+++ b/research/p104-monotone-relay-floor-audit/verify.py
@@ -0,0 +1,266 @@
+#!/usr/bin/env python3
+"""Independent finite premises for the P104 monotone-relay floor.
+
+kumagi, with substantial OpenAI Codex assistance. Apache-2.0.
+No predecessor executable is imported. Default replay is read-only.
+"""
+import argparse
+from collections import Counter
+from copy import deepcopy
+from fractions import Fraction
+from hashlib import sha256
+from itertools import combinations, product
+import json
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parent.parent
+WITNESS = "research/p104-native-channel/inputs/LOWRANK-WITNESS.json"
+FIXTURE = "research/p104-native-channel/inputs/P104-FIXTURE.json"
+
+
+class Invalid(ValueError):
+    pass
+
+
+def require(condition, message):
+    if not condition:
+        raise Invalid(message)
+
+
+def span(generators):
+    out = {0}
+    for v in generators:
+        require(type(v) is int and 0 <= v < 512, "invalid binary label")
+        out |= {w ^ v for w in tuple(out)}
+    return frozenset(out)
+
+
+def independent_indices(labels, indices):
+    """An explicit basis witness; no numerical rank or tolerance."""
+    generated, chosen = {0}, []
+    for s in indices:
+        if labels[s] not in generated:
+            chosen.append(s)
+            generated |= {v ^ labels[s] for v in tuple(generated)}
+    return chosen, frozenset(generated)
+
+
+def read_inputs(root):
+    pins = json.loads((HERE / "SOURCES.json").read_text())
+    result = {}
+    for pin in pins["files"]:
+        if pin["usage"] == "input":
+            raw = (root / pin["path"]).read_bytes()
+            require(sha256(raw).hexdigest() == pin["sha256"], "source drift: " + pin["path"])
+            result[pin["path"]] = json.loads(raw)
+    require(set(result) == {WITNESS, FIXTURE}, "unexpected input inventory")
+    return result[WITNESS], result[FIXTURE]
+
+
+def correction_support(fixture):
+    roots = set()
+    for i, j in combinations(range(8), 2):
+        for sign in (-1, 1):
+            r = [0] * 8
+            r[i], r[j] = 2, 2 * sign
+            roots.add(tuple(r))
+    for signs in product((-1, 1), repeat=7):
+        if signs.count(-1) % 2 == 0:
+            roots.add((1, *signs))
+    data = fixture["section4_explicit_P104"]
+    removed = {tuple(r) for r in data["F0"] + data["C"]}
+    require(len(roots) == 120 and len(removed) == 16 and removed <= roots,
+            "invalid P104 puncture")
+    ports = sorted(roots - removed)
+    gram = []
+    for r in ports:
+        row = []
+        for s in ports:
+            dot = sum(a * b for a, b in zip(r, s))
+            require(dot % 4 == 0, "nonintegral root pairing")
+            row.append(dot // 4)
+        gram.append(row)
+    supports = [{s for s in range(104) if 2 * (t == s) - gram[t][s] != 0}
+                for t in range(104)]
+    require(all(len(s) == 48 for s in supports), "correction support size")
+    return supports
+
+
+def frame_trace(word):
+    """Check common frames and X/Y paths; track only the X8 derivative.
+
+    This is not a replay of the full G/2 endpoint or native phases. The one
+    scalar derivative supplies an explicit excluded-descent control.
+    """
+    current = {r: span(f) for r, f in word["initial_frames"].items()}
+    histories = {r: [current[r]] for r in current if r.startswith(("X", "Y"))}
+    derivative = {r: Fraction(r == "X8") for r in current}
+    descending_example = None
+    for index, event in enumerate(word["program"]):
+        op = event[0]
+        if op == "add":
+            _, dst, src, coefficient, frame = event
+            require(not dst.startswith("X"), "original X is overwritten")
+            require(not src.startswith("Y"), "original Y is read")
+            require(current[dst] == current[src] == span(frame), "ADD frame mismatch")
+            derivative[dst] += Fraction(coefficient) * derivative[src]
+        elif op == "transport":
+            _, reg, before, after, rank = event
+            a, b = span(before), span(after)
+            require(current[reg] == a and (a < b or b < a), "transport frame mismatch")
+            require(abs(len(a).bit_length() - len(b).bit_length()) == rank,
+                    "transport rank mismatch")
+            if reg in histories:
+                require(a < b, "nonmonotone data path")
+                histories[reg].append(b)
+            current[reg] = b
+            if index == 2463:
+                require(reg == "C" and b == span([243]) and derivative[reg] == -2,
+                        "excluded-descent witness changed")
+                descending_example = {"event_index": index, "completed_cut": index + 1,
+                                      "register": reg, "source": "X8", "coefficient": "-2",
+                                      "source_label": 408, "frame_generators": [243]}
+        elif op == "zero":
+            _, reg, frame = event
+            require(reg == "C" and reg not in current, "private allocation mismatch")
+            current[reg], derivative[reg] = span(frame), Fraction(0)
+        elif op == "copy":
+            _, dst, src, frame = event
+            require(dst == "C" and not src.startswith("Y") and derivative[dst] == 0,
+                    "private copy mismatch")
+            require(current[dst] == current[src] == span(frame), "COPY frame mismatch")
+            derivative[dst] = derivative[src]
+        elif op == "erase":
+            _, reg, frame = event
+            require(reg == "C" and current[reg] == span(frame), "private erase mismatch")
+            del current[reg], derivative[reg]
+        else:
+            raise Invalid("unknown event")
+    require(current == {r: span(f) for r, f in word["final_frames"].items()}, "endpoint frames")
+    require(descending_example is not None, "missing descent example")
+    labels = []
+    for s in range(104):
+        path = histories[f"X{s}"]
+        require(len(path[0]) == 2 and len(path[-1]) == 512, "source boundary")
+        q = next(v for v in path[0] if v)
+        require(all(q in f for f in path), "source label escapes frame")
+        labels.append(q)
+    require(labels[8] == 408 and 408 not in span([243]), "descent no longer escapes locality")
+    return histories, labels, descending_example
+
+
+def target_certificate(t, support, histories, labels):
+    path = histories[f"Y{t}"]
+    terminal = path[-1]
+    require(path[0] == {0} and len(terminal) == 256, "target boundary")
+    require({s for s, q in enumerate(labels) if q in terminal} == support,
+            "root correction / binary frame binding")
+    early = {s for s in support if any(labels[s] in f for f in path[:-1])}
+    direct = {s for s in support if terminal in histories[f"X{s}"]}
+    needed = sorted(support - early - direct)
+    basis, generated = independent_indices(labels, needed)
+    require(len(basis) == 8 and generated == terminal, "residual labels do not span target")
+    # A geometric upper certificate, not a scheduled relay construction.
+    hyperplanes = {}
+    for normal in range(1, 512):
+        kernel = frozenset(v for v in terminal if (v & normal).bit_count() % 2 == 0)
+        if len(kernel) == 128:
+            hyperplanes.setdefault(kernel, normal)
+    require(len(hyperplanes) == 255, "target hyperplane count")
+    pair = next(((a, b) for (ka, a), (kb, b) in combinations(hyperplanes.items(), 2)
+                 if all(labels[s] in ka or labels[s] in kb for s in needed)), None)
+    require(pair is not None, "no two-hyperplane cover")
+    return {"target": t, "needed_sources": needed, "basis_sources": basis,
+            "early_support_count": len(early), "direct_support_count": len(direct),
+            "cover_normals": list(pair)}
+
+
+def check_certificate(row, terminal, labels):
+    needed, basis = row["needed_sources"], row["basis_sources"]
+    require(len(basis) == 8 and set(basis) <= set(needed), "invalid basis source list")
+    require(len(span(labels[s] for s in basis)) == 256, "basis does not have rank eight")
+    kernels = [frozenset(v for v in terminal if (v & n).bit_count() % 2 == 0)
+               for n in row["cover_normals"]]
+    require(len(kernels) == 2 and all(len(k) == 128 for k in kernels), "not two hyperplanes")
+    require(all(any(labels[s] in k for k in kernels) for s in needed), "incomplete cover")
+
+
+def expect_rejection(operation, message):
+    try:
+        operation()
+    except Invalid as exc:
+        require(str(exc) == message, "control rejected for an unexpected reason: " + str(exc))
+        return
+    raise Invalid("control accepted: " + message)
+
+
+def controls(word, fixture, histories, labels, rows):
+    bad = deepcopy(word)
+    e = next(e for e in bad["program"] if e[0] == "transport" and e[1].startswith("X"))
+    e[4] += 1
+    expect_rejection(lambda: frame_trace(bad), "transport rank mismatch")
+    bad = deepcopy(fixture)
+    bad["section4_explicit_P104"]["C"].pop()
+    expect_rejection(lambda: correction_support(bad), "invalid P104 puncture")
+    terminal = histories["Y0"][-1]
+    bad = deepcopy(rows[0])
+    bad["basis_sources"][-1] = bad["basis_sources"][0]
+    expect_rejection(lambda: check_certificate(bad, terminal, labels), "basis does not have rank eight")
+    bad = deepcopy(rows[0])
+    bad["cover_normals"][1] = bad["cover_normals"][0]
+    expect_rejection(lambda: check_certificate(bad, terminal, labels), "incomplete cover")
+    support = {s for s, q in enumerate(labels) if q in terminal}
+    support.remove(rows[0]["needed_sources"][0])
+    expect_rejection(lambda: target_certificate(0, support, histories, labels),
+                     "root correction / binary frame binding")
+    # Positive relay/cancellation example: two arrivals, one target writer.
+    # Helpers arrive from <1> and <2> in F2^2 with x1+d and x2-d.
+    h1, h2 = [1, 0, 1], [0, 1, -1]
+    merged = [a + b for a, b in zip(h1, h2)]
+    require(merged == [1, 1, 0], "dirty relay cancellation")
+    require(len(span([1, 2])) == 4, "merged support is not full rank")
+    require(2 not in span([1]) and merged[1] != 0, "relay boundary control")
+    return ["wrong_transport_rank", "missing_puncture", "dependent_basis",
+            "one_hyperplane_claim", "wrong_correction_support",
+            "two_arrivals_one_writer_with_dirty_cancellation",
+            "retained_private_descent_escapes_support_locality"]
+
+
+def calculate(root):
+    word, fixture = read_inputs(root)
+    supports = correction_support(fixture)
+    histories, labels, descent = frame_trace(word)
+    require(len({histories[f"Y{t}"][-1] for t in range(104)}) == 104,
+            "terminal frames are not distinct")
+    rows = [target_certificate(t, supports[t], histories, labels) for t in range(104)]
+    for row in rows:
+        check_certificate(row, histories[f"Y{row['target']}"][-1], labels)
+    require(all(row["direct_support_count"] == 0 for row in rows), "unexpected direct source access")
+    return {"schema_version": 1, "status": "PASS_P104_MONOTONE_RELAY_FLOOR_AUDIT",
+            "scope": "Finite premises for the README's restricted monotone correction-network theorem; no supplier or kappa claim.",
+            "target_count": 104, "distinct_terminal_frames": 104, "residual_label_rank": 8,
+            "minimum_arrivals_per_target": 2, "minimum_helper_lifetimes": 208,
+            "residual_support_sizes": dict(sorted(Counter(len(r["needed_sources"]) for r in rows).items())),
+            "excluded_descent": descent, "controls": controls(word, fixture, histories, labels, rows),
+            "targets": rows}
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--out", type=Path, help="also write the verified receipt exclusively to a new path")
+    args = parser.parse_args()
+    result = calculate(ROOT)
+    payload = json.dumps(result, indent=2, sort_keys=True) + "\n"
+    require(json.loads(payload) == json.loads((HERE / "RESULT.json").read_text()), "receipt drift")
+    if args.out:
+        with args.out.open("x", encoding="utf-8") as output:
+            output.write(payload)
+    print("PASS_P104_MONOTONE_RELAY_FLOOR_AUDIT targets=104 rank=8 arrivals=208 controls=7 no_new_kappa")
+
+
+if __name__ == "__main__":
+    try:
+        main()
+    except (Invalid, OSError, KeyError, TypeError, ValueError) as exc:
+        raise SystemExit("FAIL: " + str(exc)) from exc