Read and recompute
The core tier uses exact standard-library integer arithmetic. A changed relation causes a nonzero exit; a changed generated ledger fails byte-for-byte synchronization.
Exact Reader · public recomputation surface
Recompute Kernel
v0.2
One atom registry. Ten core exact-integer atoms. One reproducible table.
The stated inputs, executable checks, Markdown ledger, machine record, and result fingerprints travel in one packet. The core run uses only Python’s standard library; SymPy is optional for S01.
input → atom registry → executable result → ledger → manifest → SHA-256
Run one command
The shortest path is the calculation.
Unzip the packet, verify its contents, and run the same registry that generated the readable ledger and JSON record.
1 · verify the packet
sha256sum -c SHA256SUMS
2 · run all core atoms
python3 -I run_all.py
3 · verify the ledger sync
python3 -I run_all.py --check-ledger ledger.md
Core table SHA-256d8a27ca8e1344ab2e3583b300b505ef1d0536aebfa6df3e7cc415529509daa4b
Ledger SHA-256101b97c8c71e5246cbfb91a339d0fca1eadc8e45615c375420dcf37b8ddbdf00
Packet SHA-256f83943f6399226366cb63cff7494dbd17703d2cde9738415fd97335a90205c60
A01–A10 · declared atoms
The core table.
Every line below is generated from the same registry used by the runner, ledger, and manifest.
| Atom | Declared result | Check kind |
|---|---|---|
| A01 | G = [Q, Ω] = [C1, Q] = [[−2, 1], [1, 2]] | Exact integer |
| A02 | G² = 5I and det G = −5 | Exact integer |
| A03 | C1² = −I, C1⁴ = I, Ω = −C1 | Exact integer |
| A04 | Q² = Q + I and det Q = −1 | Exact integer |
| A05 | Qⁿ = FₙQ + Fₙ₋₁I for n = 1…40 | Exact finite range |
| A06 | Cassini identity for n = 1…40 | Exact finite range |
| A07 | T = GC1 is symmetric; T² = 5I; S = T/√5 has S² = I | Exact integer |
| A08 | TG + GT = 0 and GTG = −5T | Exact integer |
| A09 | ⟨C1, Π⟩ is an 8-element dihedral matrix realization | Exhaustive closure |
| A10 | m = 4 is unique on 1…3000 for both stated 137 identities | Exact finite range |
Controls: K01 and K02 carry deliberately false relations and must print EXPECTED_FALSE. S01 is an optional symbolic check of L(s)ᵀGL(s) = G and HL(s)H = L(−s); it reports SKIP only when SymPy is unavailable.
One released object
The statement stays with its record.
The source bundle exposes its runner, generated ledger, manifest, and SHA-256 file map as direct public files.
Keep the interval visible.
A05 and A06 name n = 1…40; A10 names m = 1…3000. The packet preserves those finite domains in the statement rather than enlarging them in prose.
Claim scope. This packet recomputes the stated matrix identities, finite searches, and optional symbolic identities from its declared inputs. Each subsequent field construction carries its own equations, parameters, and receipt.