# Prime digit-sum threshold witness pin

## Primary source

Jens Lehmann, *An Explicit Surjectivity Threshold for Digit Sums of
Primes*, arXiv:2606.04677v1.

```text
source/lehmann-2606.04677v1-source.tar
  ec4ef162ab852eb77fdeb42188a916c46f4e663f9b78362668783bebbe27b3b6
source/lehmann-2606.04677v1.pdf
  2a0d5b3f886658a66f004049b65e55fa6fa5e17ede3ef6156d8bef3908e2e2ae
source/lehmann-2606.04677v1/main.tex
  00d29add9944bf97233f1b160c1a2a33091ece08fbca92472eefc50c1fe783ae
```

Accompanying code:

```text
repository:
  https://github.com/JensLehmann/Prime-Digit-Sums.git
tag:
  v1.0-mcom-submission
commit:
  9f9903a862b83ad3b1c2fbb961af1ecf7857d214
source/Prime-Digit-Sums-v1.0-mcom-submission.tar
  fffbe0218b0eaed7c0d8e92f78f71609178c22b474dbcf6a3d24a039c57cb5d1
```

The primary verifier pins the load-bearing extracted code and theorem
certificate individually.

## Local witness

```text
verify.py
  08cdd18f2878fb9136fa5f31a277c378caa9c1435454f75cf9eae30c037b9dbb
verify_all.py
  9c13c1d475be1d2c5e4d8131dae71c1daa56bbb5760796eeaa7095c986f9d795
independent_check.jl
  a0a694bc0cae2c03f624cd055276ed50069cdaef8ffc56719797301bd7eacdac
author_replay.py
  0a64f5d5e742f268f9d89455349fe4c3a50194d3d54ef0b941a64777b55aa4b4
PROOF.md
  1a21694cb0311817c4ffc69e57e5b06241dd9399900a3316381c0e295efe6807
README.md
  34015afb03a24741b8b76db870e124cd3383e27f75ff9eb541a9dfccb3b5e5eb
SOURCES.md
  f6314ba3c5ca819d457f6dedb682d317a785933a58ec8338161235639b57cc6f
SOURCE-METADATA.md
  129d36e61e124b7636a44c5dcabef6f3dc0f0d1f3c260c408ac9217cc29744f1
```

Retained transcripts:

```text
primary-256-output.txt
  018207cc2aa3b0ae9e1b4c7530b92a5fed69bb47271a107286f33fcbf72d515f
primary-384-output.txt
  5b76b1d9c1baf221c69f162e2c0e6c3d7159962383235732e471581c229dd7ac
primary-512-output.txt
  267be1a735b11c22fbcdd31d8b566a81bd52298037efdb69bdf2de1fb56f43e0
independent-output.txt
  8956a138e4621765e7eb01fccdb50da8c6c35abfd3a366981c0bc7fec70b4063
author-replay-output.txt
  6088b3891992877a1598d25b622ef0dbb0e4010da2edba0090ece64d0ec1c8fa
```

Environment:

```text
julia/Project.toml
  ce419571c143090609ba6b89c3b1689fd5a9ed185feff3161a7969c9d79f8ba0
julia/Manifest.toml
  b362a726eb82506802a1cb1f0e202ef01810170a052e39606a88ed0d32d5f420
Python 3.14.6
python-flint 0.9.0
FLINT 3.6.0
Julia 1.12.6
Nemo 0.56.1
```

## Verification scope

The primary verifier proves every source threshold condition
permanently from the exact integer digit length, including the new
one-sided C13 floor envelope. The Nemo checker independently retypes
the binding C11, C12, C13, \(Y_{47}\), major, minor, and ceiling
calculations. The author-code path is corroborative only.

## Replay

From the repository root:

```sh
uv run --frozen python \
  canon/witnesses/C-0092/verify_all.py
```

The wrapper rejects optimized Python, pins every local executable
input and transcript, and compares all five replay outputs byte for
byte.
