# Existing runs: what was retained and what can be reconstructed

<!-- ledger
id: Q-data-reuse-audit
status: ANSWERED
todo: C
parity: This is an input-retention and finite reconstruction audit. Complete prime-power factors recover the actual Mobius and beta coefficients; aggregate survivor, Liouville and gap moments do not directly provide that weighted sum. No distribution estimate is inferred from the stored data.
question: Do existing runs or their embedded inputs retain what the current determinant-2 sum needs, and can useful data be recovered without repeating the old campaigns?
verdict: The fold CSV supplies a verified base-prime list and archived interval boundaries; three old rows are reproduced and their bounded prefixes reconstructed with full factorizations retained. Other inspected outputs are aggregate statistics or twin-gap records. These finite inputs support coefficient and grouping tests, not an asymptotic twin bound.
-->

Internal audit, 2026-09-05, following Chris's suggestion to inspect old runs
and their inputs. **No new asymptotic estimate follows from this data.**
There is reusable input, but most earlier producers saved their summaries
rather than the per-integer arithmetic needed by the current sum.

The research result using these inputs is in
[singleton-fiber-audit.md](singleton-fiber-audit.md). All new measurements
and the retained artifact are generated by
[singleton-fiber-validation.js](singleton-fiber-validation.js); its output
is embedded by the repository tool, with code and input hashes.

## 1. Required information

For the residual on dk−ev=2 we need μ(d), μ(e), β_V(k), β_Z(v), the strict
cutoffs, and the full interval defining each fiber. Complete prime-power
factorizations of n and n−2 allow all these weights to be reconstructed
for any subsequent cutoffs within the stored range. Primality flags alone
do not retain the individual squarefree-divisor signs and β weights.

There is also an exact support restriction: grouping by n gives
R=Σ C_{U,V}(n)C_{Y,Z}(n−2), with C_{A,B}(p)=0 at every prime p for
A,B≥1. Thus either member being prime makes that grouped coefficient
zero. Twin-only records are useful controls on the distinct detector S;
they do not directly measure R. This does not say the old inputs are
information-theoretically insufficient: integer coordinates can be
factored again. It says the required weights were not stored in those
aggregate output fields.

## 2. Inventory inspected

| Existing artifact or producer | Retained information | Use for this question |
|---|---|---|
| [fold-ledger-01.csv](fold-ledger-01.csv) | 1,226 prime-square interval rows; q, q_next, boundaries, removal channels and cumulative counts | Actually reused: consecutive prime columns recover the base-prime list and interval coordinates. No individual factors in the CSV. |
| [attack-lambda-ledger-01.js](attack-lambda-ledger-01.js), [its note](history/staging/attack-lambda-ledger.md) | Runtime segmented factor/remainder/multiplicity workspaces; saved marginals, covariance and band summaries | Reuse the factorization approach. The old workspace is overwritten between windows; per-integer factors were not saved by this producer. Its already closed covariance experiment is not rerun. |
| `t37-partials/t37-shard-37-{0,…,4}-of-5.json` and [shard producer](scanstat-t37-03-shard.js) | Five shard files: tile coordinates and window-length rows containing min, max, sum, sumsq | Window moments can be merged for their original purpose; they do not retain the slot stream or the arithmetic coefficients of R. |
| [zonegap-01.js](zonegap-01.js), [zonegap-04-sweep-1e12.js](zonegap-04-sweep-1e12.js), [record input](a113274-gap-records.js) | Embedded trusted gap records and aggregate output; the engine streams twins and keeps bounded runtime summaries | Gap/prime-count controls, not factorizations of composite pairs. The long sweep is not rerun and its bound output is not overwritten. |
| [tos-twin-gaps-1e16.txt](tos-twin-gaps-1e16.txt) | Gap g, first occurrence F(g), frequency T(g), record markers; attributed to Tomás Oliveira e Silva in the file | This is a gap-frequency/first-occurrence table, not the complete list of twin pairs or a raw integer sieve. |
| [foldL-window5-01-extinction.raw.txt](foldL-window5-01-extinction.raw.txt), [natal5-17tile-scour.txt](natal5-17tile-scour.txt), [natal5-variance.txt](natal5-variance.txt) | Text stdout: kill/run counts, counts and moments | “raw” in a filename does not mean per-integer raw factors. The inspected fields are aggregate results. |
| Six local `attestation/*.tar` archives | Member-name inventories inspected without extraction | No additional raw-factor artifact was identified by the inspected member names. The matching data-like members in v5/v6 were the two natal summaries above. These archives predate the fold CSV and Liouville run. |

The inventory covered the working tree's candidate data files, the relevant
producer code and the member names of those six local archives. It is not
a claim about unavailable machines, unlisted backups or the contents of
nested archives. No external account or off-machine dataset was searched.

## 3. Recovery from an existing input

The CSV's q values run from 7 through 9,973 and the last q_next is 10,007.
Appending 2,3,5 yields **1,230 consecutive base primes through 10,007**.
The validator checks this list against a separately constructed small
sieve and verifies interval widths, neighboring boundaries and row count
identities throughout the CSV. The last upper boundary is 100,140,049;
the old producer's smaller stale header limit is not used to truncate it.

Its SHA-256 input binding is
`ed5364404c9b84d16709a800e3eb5d7077788879dc1f2f5df4433fb55823461d`.

The old ledger counts channel openers a≡11,17,29 mod 30 in
[q²,q_next²), with a+2<q_next². We independently reproduce all the saved
counts used by the validator for the **entire** rows q=97,997,9973, using
all-prime marking and the original channel convention.

We then reconstruct bounded prefixes for the new question. These use
partner n=a+2, every residue class, and x equal to the smallest dyadic
endpoint above q_next². We store factors from lo−2 through hi, so both
n and n−2 are present. The fiber classification always uses the full J_x,
not just the prefix. These are newly computed weights on recovered old
coordinates, not weights claimed to have been saved in the original run.

| Archived row q | Dyadic x used for cutoffs | Measured partner n range | Partners | U=V | Y=Z |
|---:|---:|---|---:|---:|---:|
| 97 | 16,384 | 9,411–10,200 | 790 | 10 | 1 |
| 997 | 1,048,576 | 994,011–998,106 | 4,096 | 27 | 2 |
| 9,973 | 134,217,728 | 99,460,731–99,464,826 | 4,096 | 89 | 2 |

Each factorization is checked by multiplying its prime powers back to its
integer. The prime basis extends beyond the square root of every selected
endpoint. An independent all-prime marking checks the old channel counts,
while the new divisor enumeration uses the retained factors.

## 4. Measurements and reusable artifact

The measurements below are **per measured partner**, not divided by x.
They are partial-window sums and must not be substituted for R(x) in the
full-interval asymptotic identity.

| q | Signed singleton mass/partner | Signed longer-fiber mass/partner | Positive singleton mass/partner | Negative singleton mass/partner |
|---:|---:|---:|---:|---:|
| 97 | 3.968943 | −0.657148 | 85.739145 | 81.770202 |
| 997 | 6.190935 | −0.015693 | 358.112965 | 351.922029 |
| 9,973 | 2.732651 | 0.078707 | 1101.234101 | 1098.501451 |

All values are finite compensated floating-point measurements from the
bound output. No trend, power saving, asymptotic balance or typical-window
claim is fitted to these three prefixes. Even the largest prefix has inner
cutoff Y=Z=2. The companion proof of eventual mass growth uses classical
theorems, not extrapolation from this table.

The generated [data-reuse/factor-windows.json](data-reuse/factor-windows.json)
contains schema version, producer path, source path and hash, recovered
base primes, the three original CSV rows, exact prefix coordinates,
complete prime-power factors indexed from each `factorStart`, and result
objects for the prefixes and four full dyadic checks. It is 235,554 bytes
in this run. Its SHA-256 is
`fa30e65431c2f9fa7b66a4e3cf7eb44cdcc912c4de19b97d56dfbf279030b98b`.
The full dyadic checks' summaries are stored; their per-integer factors
are generated in memory, whereas the archived prefixes' factors are retained.

Regenerate this artifact and its bound output together with:

```sh
node research/qc/embed.js research/singleton-fiber-validation.js
```

If a subsequent code/input change intentionally changes the output, use
the embed tool's explicit update workflow; do not edit the numbers or hashes
by hand. No timestamp is written to the JSON, so unchanged inputs and code
produce the same data bytes.

## 5. Decision for subsequent work

Use the retained factorizations for a specified signed grouping or divisor
weight experiment. Keep the full dyadic geometry and the distinction
between whole intervals and prefixes. If a proposed mechanism needs a
larger range, record its required fields and falsifier before running it;
save those fields rather than only its final total.

The first signed grouping test has now consumed these saved factors:
[signed-divisor-grouping.md](signed-divisor-grouping.md) derives a controlled
product range, and [signed-divisor-validation.js](signed-divisor-validation.js)
retains its measurements in [signed-grouping.json](data-reuse/signed-grouping.json).
The archived factor artifact was read unchanged.

The present data question is answered: old inputs are useful and have
actually been reused, while the inspected aggregate outputs do not directly
contain the new weighted residual. The next arithmetic question is the
signed cancellation across fibers identified in the companion note.