diff --git a/audits/dropbox_import/2026-09-27/MATH_RETRO_BINDING_HANDOFF.md b/audits/dropbox_import/2026-09-27/MATH_RETRO_BINDING_HANDOFF.md
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+# Historical mathematical carriers in the public Dropbox import — provenance crosswalk
+
+**Engineering archive index only; NOT A RESULT.** Prepared 2026-10-23. Scientific effect: **NONE**. No new graph nodes, v2 bindings, mathematical proof review, accepted theorem, source promotion, or external-custody certification.
+
+## Scope and immutable inputs
+
+This is a narrow appendix to the **already-public and privacy-screened** [Dropbox import of 2026-09-27](README.md), not a new import from private Dropbox. The canonical source inventory is [MANIFEST.csv](MANIFEST.csv), Git blob `aea93c0498e370c8333faad88eed0de832c77e46`, at `d6g8k5htny-coder/main@a487cfd41bfe095842d9d9f5cec26fc23877b028`. Its `Math-imports-candidate` label appears in **11** rows. All row files are tracked public Git blobs in this frozen tree. **Seven** are byte-exact published text originals (as described by the historical import); **four** are *extracted-text surrogates* for PDF/Word originals, not the original document bytes.
+
+For this appendix, the eleven public GitHub file bodies were fetched at the pinned commit and their UTF-8 byte streams independently SHA-256 checked against the prior manifest: **11/11 MATCH**, **149,524 published bytes**, zero mismatches. The checksum implementation was checked against the standard SHA-256 `""` and `"abc"` vectors. Every file's native Git blob is given below. This check authenticates the **already-published Git content** against the **existing manifest**, not a fresh download or SHA-256 of the private Dropbox original. In particular, a manifest `dropbox_content_hash` is not an ordinary raw-file SHA-256 and an extracted PDF text hash is not the PDF hash.
+
+The broader original import recorded 5,105 Dropbox objects, 107 publications (93 exact originals and 14 extracted texts), and 26 project-related files not imported. The full import has **110** Git blobs including `README.md`, `MANIFEST.csv` and `NOT_IMPORTED.csv`. Those figures are historical as-of September 27, not a claim about current private cloud completeness. Never publish newly discovered private-source paths, names or access links on the basis of this appendix.
+
+## Eleven previously published mathematical carriers
+
+Archive paths below are relative to this directory and were **already public** in the original manifest. The `archive_sha256` column is SHA-256 of the published Git body; for extracted text it is not the original source file.
+
+| Row | Existing public `archive_path` | Publication form | Pinned Git blob (SHA-1) | Published `archive_sha256` | Provenance role / boundary |
+|---:|---|---|---|---|---|
+| 1 | `files/Github/02_PRE_REVIEW_DOSSIER.pdf.txt` | Extracted text | `6ab9bd8e8cc73391302b421a11a3d4a0a093f743` | `f70684ba563e9e008e9590f943a03fb07b4c9ff3e59cc8fff15e45d88eafdf8a` | Reviewer-facing SIDE24 dossier; PDF extraction only; no original PDF bytes or code implied |
+| 2 | `files/Github/03_SIDE24_MANUSCRIPT.pdf.txt` | Extracted text | `4fe100fee09c2a3e744b4caf67922f2667aebe6d` | `d0dbc29e77529fe217f76c30efecc531647420f60759570775af4b9afaaef773` | SIDE24 manuscript draft; PDF extraction only; do not equate to a reviewed Math proof |
+| 3 | `files/Github/070326claufe.pdf.txt` | Extracted text | `eab23bf56e2e0a97d25687aeee315cec86fb1385` | `0d7515b6dec5b7ee02297510f7df79e323ff755be01abcb3be815518e721fee6` | Topological-fingerprint overview; PDF extraction only; no tested implementation here |
+| 4 | `files/Github/LPW_Return_05_Archive_Audit_2026-09-12 (1)/02_CONSTANT_FINDINGS_AND_REPAIR.md` | Original text | `0f2fbad209857d807a3ac31acab3a3ff917ef9ae` | `feb8aa30795cfe44d5c9e49b1793e6cd5f62729b922af0b0aff5fe076868146a` | LPW Return-05 audit, AMEND REQUIRED for strongest displayed constant |
+| 5 | `files/Github/LPW_Return_05_Archive_Audit_2026-09-12 (1)/05_MATCHING_2D_UPPER_WORK_ORDER.md` | Original text | `7437eab6b92d8d851564a20365891c2c305be5a5` | `521870da3c56e1c0b01d1ddd95ed159b89925bc31957b6efecd8aa307e76c479` | 2D matching upper-bound work order; an open target, not an established theorem |
+| 6 | `files/Github/LPW_Return_05_Archive_Audit_2026-09-12 (1)/receipts/W8_RECOVERED_PREFLIGHT.out` | Original text | `9f94ba06ed6f13b05b8bb2de81551761e2b42ec5` | `85b1c5c424c931e1e01c99c2adbc38dafe2b50a3dcb7cf8c1e159f6272c5e953` | W8 lambda-grid preflight output; execution source is not among the archived public members |
+| 7 | `files/Github/LPW_Return_05_Archive_Audit_2026-09-12 (1)/source_excerpts/LPW_CONSTANT_REPORT.numbered.txt` | Original text | `dcc840cb5d7fd56e4440bdfb8ffd368f10af2e4d` | `b82f1031c64cd1872c7bdfa2f621c8fecc7b2c88d8626a4938119c996d3cddc0` | Line-numbered historical LPW constant report; received report, not a current verdict |
+| 8 | `files/Github/LPW_Return_05_Archive_Audit_2026-09-12 (1)/source_excerpts/lpw_constant.py.numbered.txt` | Original text | `a74c0e86dcb4a157c69cdb9b6cc3955833d64a4c` | `2f66f49286e6d90df34f933314b84ad8dc0bf5c6c47b552678ca89bae38143be` | Line-numbered Python certifier excerpt; not identical to an executable raw .py file |
+| 9 | `files/Github/LPW_Return_05_Archive_Audit_2026-09-12 (1)/tools/check_findings.py` | Original text | `54123700fb2b79e32fbd574536bda0eb8e4cd03f` | `55d6a213a42e729d5ff6687d1552a1b512e00638d73f9d4e5be6b867e86aa67e` | Return-05 regression checker; requires absent raw/constant package and sympy |
+| 10 | `files/Github/Three Bridges from Persistence Thermodynamics to Geometry, Entropy, and Field Theory13M+.pdf.txt` | Extracted text | `aac40e32c6b5de8ddb8966ecf94ff4748d3752b9` | `702eb70d1786216310b86ff92fe52f9cfdf67876cd8cb7d51d660c93c4c8bc52` | Cross-disciplinary literature synthesis; extracted PDF text, not proof implementation |
+| 11 | `files/Github/synthetic results.json` | Original text | `7124945b135c70b05e67049033a846edfe4644e6` | `151fd881d01ad01c273e5442ebb48a67e6f8faba188f62d289ca6dbd9b06307d` | Synthetic numerical results; no authenticated generator identified in this import |
+
+## Explicit, limited historical source → checker → output relationships
+
+The **LPW Return-05** group (rows 4–9) contains multiple, *different* evidence types, connected by their own already-public text:
+
+- The archived **`02_CONSTANT_FINDINGS_AND_REPAIR.md`** identifies its received `raw/constant/LPW_CONSTANT/` source and directly discusses the `lpw_constant.py` computation and `LPW_CONSTANT_REPORT.md`. Its declared disposition is **AMEND REQUIRED** for the *strongest displayed quantitative constant*. It documents a denominator/rounding mismatch and an invalid half-normal fourth-moment identity. Neither this appendix nor a successful checksum removes those defects. It expressly does **not** refute the qualitative pairing probability or endorse a replacement numerical theorem.
+- **`source_excerpts/LPW_CONSTANT_REPORT.numbered.txt`** is the line-numbered historical report; **`source_excerpts/lpw_constant.py.numbered.txt`** is the line-numbered Python source excerpt. The numbered text is **not** byte-equivalent to an executable `lpw_constant.py`; its original unnumbered raw program is **not present in this limited public archive subtree**. Do not invent a source blob or claim the original checker executed in the current checkout.
+- **`tools/check_findings.py`** is the archived *regression checker*, not a theorem verifier. Its source reads `ROOT/raw/constant/LPW_CONSTANT/lpw_constant.py` and pins that historical source's SHA-256; its imports also require `sympy`. That raw directory and program are absent from this public import, so **no self-contained reproduction of the checker is established from these public files alone**. It can be associated as an authored implementation artifact, not recorded as a current passing calculation.
+- **`receipts/W8_RECOVERED_PREFLIGHT.out`** is a historical *output*. Its header attributes itself to `verify_lambda_grid_v3.py` with an earlier v2 fail-closed quotient guard; the source program and complete original W8 inputs are **not present in these 110 imported public Git blobs**. Neither the received output nor the separate Return-05 replay receipt is a new execution performed for this appendix.
+- **`05_MATCHING_2D_UPPER_WORK_ORDER.md`** defines a separate target, the matching two-dimensional upper bound; it is not evidence that the all-small-r upper theorem was proved. **`synthetic results.json`** is a separate synthetic data carrier with no authenticated generating program identified in this import.
+
+The remaining documents are a pre-review dossier, a manuscript draft, a topology overview and a literature synthesis. The four extracted-document texts may be valuable historical *reading sources*, but do not carry the original PDF layout, formulas or figures by byte identity. None is silently joined to an independently reviewed present-day Math- theorem or implementation on the basis of a shared title.
+
+## Retroactive graph/accounting implications and next permitted joins
+
+The existing [RETRO-MATH-BIND-01 inventory and allocation](https://github.com/d6g8k5htny-coder/main/pull/527) counts 313 units on its frozen Math- and selected main source cuts; it does **not** by itself certify this older `audits/dropbox_import` collection as direct current Math- source. This appendix accounts for the *11 previously published, privacy-approved candidate carriers* without creating a competing ownership register or adding node IDs.
+
+To add a future **graph-to-artifact** edge, a separate source owner must first identify an *existing genuine graph node*, a reviewed target `owner/repo:path@40hexcommit#40hexblob`, the exact repository-qualified checked ref, and valid public bytes. Then distinguish `historical`, `external_unverified`, `absent` and current `file`/verified `tree` exactly as [the reviewed GB-5 v2 proposal](https://github.com/d6g8k5htny-coder/main/pull/522) requires; only actually supported current pins may be BOUND. Do **not** create an Artifact Index row or mathematical status from these archive excerpts. The ongoing GB-8a–x Math frontier assignment, future private-cloud DRV lanes and the original import's publication/hold decisions retain their own custody.
+
+## Reproduce the published archive identity checks
+
+From a checkout containing this pinned Git history, the following **standard-library-only read** checks the exact manifest-selected already-public math rows; it does not access Dropbox, execute mathematical programs or create files.
+
+```bash
+git switch --detach a487cfd41bfe095842d9d9f5cec26fc23877b028
+python -B -S - <<'PY'
+import csv, hashlib
+from pathlib import Path
+root = Path("audits/dropbox_import/2026-09-27")
+with (root / "MANIFEST.csv").open(newline="", encoding="utf-8") as f:
+    rows = [r for r in csv.DictReader(f)
+            if r["suggested_home"] == "Math-imports-candidate"]
+assert len(rows) == 11, len(rows)
+assert sum(r["disposition"] == "PUBLISHED_EXACT_ORIGINAL" for r in rows) == 7
+assert sum(r["disposition"] == "PUBLISHED_EXTRACTED_TEXT" for r in rows) == 4
+count = 0
+for r in rows:
+    raw = (root / r["archive_path"]).read_bytes()
+    assert hashlib.sha256(raw).hexdigest() == r["archive_sha256"], r["archive_path"]
+    count += len(raw)
+assert count == 149524, count
+print("PASS: 11 published math candidate archive carriers, 149524 bytes")
+PY
+```
+
+**Limit:** this checksum recipe was independently evaluated against the GitHub-provided content bytes in the authoring session; the Bash checkout command and this exact Python snippet were not executed here. GitHub checkout reproductions must preserve the original bytes. Consult [NOT_IMPORTED.csv](NOT_IMPORTED.csv) and the privacy/approval rules before any new copy or restoration. Scientific and reviewer statuses remain unchanged.
+
+[Complete owner mandate](https://github.com/d6g8k5htny-coder/main/blob/b665307520948308a53d190d7341bf301df3b3a2/governance/OWNER_MANDATE_20261015.md) · [Standing delegation](https://github.com/d6g8k5htny-coder/main/blob/main/governance/OP-AUTONOMY-20260923-v2.1.md).