Lion Shor Witness Certifier

title: Shor Witness Certifier — what the cell actually sealed audience: cryptographers_engineers_press contract_version: 1.0.0 authority_kind: normative release: v120

Shor Witness Certifier — what the cell actually sealed

This page corrects a category error. An earlier draft of this artifact was titled "Shor at Scale" and implied the cell had factored semiprimes up to 8 × 10¹². It had not. The cell factored 35 semiprimes from N = 15 to N = 65,021 by classical brute period-finding; for the larger 13 entries, the witness was constructed from already-known factors via the Chinese Remainder Theorem. The verification arithmetic is correct at every row; the framing that called all 48 "factorizations" was wrong. This page states what the seal earns.

The honest two-tier seal

Tier 1 — actual factorizations (35 rows, N = 15 → 65,021)

For each row in Tier 1, the cell discovered the multiplicative order r of a mod N by classical brute iteration:

v := a mod N
while v ≠ 1 and r < N:
    v := (v · a) mod N
    r := r + 1
halfPow := v at r/2 step

No knowledge of p or q is used. Once halfPow is in hand with halfPow² ≡ 1 (mod N) and halfPow ≠ 1, N − 1, Shor's classical reduction gcd(halfPow − 1, N) extracts a non-trivial factor of N. These rows ARE factorizations performed by the cell — classical, not quantum, but the period-finding (the hard step of Shor's reduction) was done.

The ceiling is N ≈ 65,000 because brute search is O(period), and orders for larger N grow past the cell's millisecond budget.

N	factors	provenance
15	3 × 5	Tier 1 — period found
21	7 × 3	Tier 1 — period found
143	11 × 13	Tier 1 — period found
1,517	37 × 41	Tier 1 — period found
10,403	101 × 103	Tier 1 — period found
65,021	253 × 257	Tier 1 — period found (largest)

35 rows total in Tier 1.

Tier 2 / Tier 3 — period-PROVIDED witness verifications (13 rows, N up to 8 × 10¹²)

For each row in Tier 2/3, the cell did NOT find the period. Instead, the witness halfPow was constructed from the already-known prime factorization (p, q) using the Chinese Remainder Theorem:

halfPow ≡ 1     (mod p)
halfPow ≡ N − 1 (mod q)

This construction assumes what factoring is supposed to discover. The Lean kernel + Swift recompute then verify that the constructed halfPow satisfies the four algebraic relations Shor's reduction operates on. This certifies the verification arithmetic at scale — it does NOT factor anything.

N	factors	provenance
999,919	991 × 1,009	Tier 2 — period PROVIDED (CRT)
9,999,399,973	99,991 × 100,003	Tier 2 — period PROVIDED (CRT)
2,000,009,000,009	1,000,003 × 2,000,003	Tier 3 — period PROVIDED (CRT)
8,000,321,000,351	1,000,039 × 8,000,009	Tier 3 — period PROVIDED (CRT)

13 rows total in Tier 2/3.

What this is and is NOT

What this IS

A real verification capability: the cell certifies any Shor witness (N, halfPow, p, q) bit-exactly in milliseconds, at semiprime sizes up to 43 bits, with two independent gates (Lean + Swift) that must agree.
35 actual factorizations at small scale (N ≤ 65,021), each performed end-to-end by the cell using classical period-finding without factor knowledge.
A certifier ready to grade any future Shor output — from quantum hardware, hybrid algorithm, or a future classical breakthrough — at scales the verifier handles.

What this is NOT

NOT a claim that the cell factored 43-bit semiprimes. The Tier 2/3 witnesses were constructed from already-known factors. The cell verifies them; it did not discover them.
NOT a quantum-computing capability claim. No quantum hardware is involved at any step.
NOT a claim against RSA or about cryptographic security at scale. Classical factoring records (RSA-250 = 829-bit, classical GNFS 2020) are far past anything here. The cell's seal is about verification, not factoring records.

What it does NOT close

summit.shor.order_finding_at_scale sits on the Rosetta open frontier with the licensing certificate written down. That summit's open obligation: find the multiplicative order r of a mod N at scale where classical brute search is infeasible AND the cell does not have access to (p, q). That is the actual hard step of Shor's algorithm. Quantum hardware addresses it via Shor's quantum subroutine in polynomial time; the cell does not run quantum hardware.

The cell does not claim to have closed this summit. It ships the certifier in advance so that when someone closes it — at whatever scale, by whatever means — the verifier is ready.

How to verify

git clone https://github.com/gaiaftcl-sudo/gaiaFTCL.git && cd gaiaFTCL

# 1. Lean kernel seals both tiers
cd proof/lean && lake build FirstRoars.ShorWitnessCertifier
# → ✔ Built FirstRoars.ShorWitnessCertifier (native_decide closes the seal)

# 2. Swift S4 recompute matches bit-for-bit
cd <substrate checkout>
swift run M8ShorCertifierSmokeTest
# → Tier 1 PASS: 35 / 35  Wall: ~0.6 ms
# → Tier 2/3 PASS: 13 / 13  Wall: ~0.2 ms
# → ✓ SHOR-WITNESS-CERTIFIER SEALED — both tiers verified

Lattice position

Sealed node: qc.qc-001.witness_certifier — finiteUniversalCertificate over the 48-row table
Base camp: qc.qc-001.n15.factored (the 2001 textbook factorization)
Licenses three things downstream:
- qc.qc-001.tier1.factored:35-rows — the 35 actual factorizations
- qc.qc-001.tier23.witness_verified:13-rows — the 13 period-provided verifications
- summit.shor.order_finding_at_scale:certifier-ready — the certifier stands ready for that summit's closure

Why this correction matters

The cell's whole architecture exists to expose category errors of this exact shape — claiming a hard step that was assumed rather than performed. The earlier "Shor at Scale" framing made the error the architecture refuses in others. A regulator or hostile cryptographer reading the original page would have caught the gap in 90 seconds. The honest seal is still valuable: the cell ships the only verified-end-to-end Shor witness certifier that handles 43-bit semiprimes with dual-gate certification. Stating that precisely is what makes it unassailable. Stating it as "Shor factoring at 533 billion× textbook" would have collapsed the brand on contact with the first careful reader.

This page exists so the seal's meaning equals what the kernel proved — no more, no less.

NATS subject

gaiaftcl.shor.witness.certifier.sealed — emitted on every successful smoke-test run.

What exists in this repo (2026-08-27)

Layer	Path	Status
Lean witness certifier	`proof/lean/FirstRoars/ShorWitnessCertifier.lean`	In tree
Lean textbook / large factor	`ShorFactor15.lean`, `ShorFactorLarge.lean`	In tree
Lean ECDLP	`ShorECDLP.lean` · couplings `QFTToShorCoupling.lean`, `QPEToShorCoupling.lean`	In tree
ECDLP substrate	the ECDLP substrate module (private repo)	Live 3D path: `Secp256k1ECDLPVerificationDispatcher`
Typed QC-001 shell	`AlgorithmCatalog.swift` `QC001Shor` / `QC001ECDLPShor`	Throws `vmNotConnected` until a VM is moored
Inventory	Quantum algorithms inventory	Maps Glama vs Lean vs stripped

What was stripped (cite the commits)

Commit	Date	Deleted
`6f39e8b8950256e090d68a31657e086989663874`	2026-07-09	Reversible-circuit cluster: `ReversibleECDLPOracle*.swift`, `ReversibleFieldP`, `ReversiblePointAdd`, `ReversibleScalarMul`, `ShorECDLPProjection.swift`, `SymbolicShorECDLP.swift`
`9192c03626f91b12bff8166644f102431c8b6ef3`	2026-07-09	`ShorECDLPTemplate.swift`, `ShorECDLPReversibleOracleTemplate.swift`, `StaticTensorBuilder.swift`
`add9d197a70bb2b52ba6d98cf6f11e559e1b9341`	2026-07-08	Boot bind `GlobalContraction.dispatcher = ShorECDLPCPUContractor()`
`d1a00b7b` / `068a548a`	2026-07	`GaiaCellMCPServer/main.swift` (`run_quantum_algorithm`, `distribute-shor` were that surface)

ShorBoundaryMaskFactory.swift remains as a mooring provider. Comments in GaiaFTCLCLIEntry.swift record Strip 6: the live answer to (kG=Q) is the audited secp256k1 dispatcher, not the retired MPS contractor.

Glama / public MCP

Shor IS a public court tool — as a presented-witness verifier, never a period search. This paragraph read "Shor is not a public court tool; tools/list has 23 names" until 2026-09-02, which was true on 2026-08-27 and is stale: live tools/list is 49, measured per cell on all nine A records, and it carries verify_shor_witness (QC-001: N, halfPow, factor, cofactor — 15 = 3×5 answers WIN/CALORIE), verify_period (a^r ≡ 1 mod N), project_shor_twin (post halfPow, receive the factors by gcd; post the factors, receive a by CRT — a bijection, not a search), plus verify_grover, verify_qft_phases, verify_vqe_energy and verify_qaoa_energy. None of them finds a period, a marked item or a variational minimum; each certifies what the caller presents. There is still no shor, prove_shor or period_find tool, and the Lean certifier below remains the textbook. See Math Court on Glama and the MCP user guide.

Leftover Python wrapper

a legacy Python shim (private repo) and the legacy CLI shim (private repo) still invoke gaiaftcl prove shor. The Swift prove dispatcher (GaiaFTCLCLIEntry.swift case "prove") lists language-games, poly-n, substrate-oo, conjecture-workload, qc020-verifier — not shor. Treat the Python verb as leftover, not a live compute path.

Honest bound

This page already forbids calling Tier 2/3 “factorizations.” It also forbids calling the certifier a quantum-hardware result. Period-finding at scale remains the open summit named above. The public court verifies presented QMA fixtures; it does not run Shor.

Rights — source-available, all rights reserved. This wiki and its repository are published for public inspection and to let anyone re-derive the figures. They carry no LICENSE; under default copyright, all rights are reserved. No right is given or intended to use, run, or deploy it for any purpose other than re-deriving the published figures, nor to modify or build on it — any other use requires a written licensing agreement with the authors. · Affine.Earth · zero float · zero shear

🧬 CURES — read in this order

Each step is the reason the next one exists. Nothing here is medical advice, and no page calls any medicine safe or unsafe.

1 · Why an exact safety screen at all

Cures Without the Gatekeeper — the medicine front door: six real written medicines, one screen anyone can re-run
The library admission law — what may enter, and the 71 arms that prove it refuses. The primary artefact.

2 · The three libraries, which grow rather than close

The Library of Compound Cures — exact off-target maps for the medicines the registry publishes
The Library of Proteins — 80,080 generated sequences, novel chemical matter, graded honestly
The Library of Material Systems — what a system is, what was measured, where the law lives. C-007 absolute: no recipes

3 · The maps — every place a molecule could act, counted

The off-target atlas — every nucleic-acid medicine the registry publishes a sequence for: WHERE it can pair
The order of the bases — WHETHER THAT BURDEN IS UNUSUAL: 472 strands ranked against sixteen rearrangements of their own bases
Where else could this guide cut? — the whole human genome, counted
Designed, or forced by its own bases? — every clinical CRISPR guide, with its own composition as the control
What a public genome deposit will tell you — and four ways it will mislead a health tool first
Study 45 — which of nine billion answers a laboratory can act on — a safety review of AlphaGenome Atlas, measured live on 1,200 real variants at two genes. The headline score separates every one. The detailed tracks do not: splice-site usage hands back 950 of every 1,000 values shared with another variant at HBB and 998 at CFTR, and the shared values pile up in the quiet band where a bench clears a variant

4 · One medicine at a time

Zilganersen — the first treatment for Alexander disease, screened on the real approved sequence
A drug an AI designed — rentosertib for pulmonary fibrosis, and exactly what our instruments reach
CAR-T, halted — the verdict a regulator could re-derive
N-of-1 antisense — the only safety net at a population of one
VERVE-102 — the off-target lattice a stranger can re-derive
PM359 — prime editing, certified before anyone is dosed
Del-Zota — the one safety question that can be made exact

5 · What keeps a disease alive, and what moves it

Study 26 — master regulator bonds — 17 tumour types, 7,673 tumours; eleven compound pairs where no single agent among 20,308 cleared any
Study 20 — Rife frequency — light and frequency, measured rather than dismissed
Study 37 — five molecules — 37,910 "validated discoveries", 5 distinct molecules; why per-item validation cannot see a corpus-level defect
Are the generated cures new? — 80,080 peptides against the human proteome
Study 16 — disease type · Study 17 — chemistry InChIKey · Study 14 — protein lattice

⚖️ How to read any page here

No language model in this stack — what the answers here are made of: measured 2026-09-12, no cell runs a model process, opens a model port or holds an unmasked model unit, and a gate refuses their return
Run any study in your browser — all ninety programs open on your own device, forty-nine run there, and the run tells you whether it printed the sealed bytes
The ontology — grades, terminals, controls, and what each page may say
Zero Float · Zero Shear — the method in one page
Ask someone you trust to check this — what to hand a sceptic
Readers’ guide · Program index — all 42 studies · White paper · Roadmap
The full-grade replacement — 49 retired instruments, 4 verticals
The exactness seam — the business case
Build a study — Falcon walkthrough — how to add one yourself

🔬 The method — exact against float, domain by domain

The same move every time: take a domain where a floating-point model is the accepted instrument, compute the same quantity in exact integers, and seal the cases where the two render opposite verdicts. The subject under grading is always the instrument, never the phenomenon.

Study 48 — the atom already has an address — silicon dimers 3.840 Å apart, the smallest commanded scale on the board: a length carried in single precision mis-addresses its first atom at step 8,783; an address cannot
Study 49 — the phase code never needs π — a phase-only modulator takes 256 codes per pixel; the code is a ratio of integers
Study 50 — CMS raw data from the LHC, read exactly — CMS's 2011 collision bytes streamed from CERN Open Data into the Affine IDE and read in exact integers, every collision a hologram you can turn: 138 of 3,564 bunch slots carry 93,110 of 120,742 collisions, and in 3,854 the event record reads its slot exactly 3 lower than the pixel boards · public release
Study 55 — IceCube: the light in the ice, hit by hit — IceCube's calibrated hits read byte for byte: 4 published files, 9,749 events, 2,289,821 hits, a census seal per file
Study 47 — translation shear: the meaning that survives a language — LAW FROZEN · LIVE CLAIM, measured 2026-09-11 and again fleet-wide 2026-09-12: translation as an exact coordinate transform, charts derived in memory at every start from the raw rows of a pinned public weight file and never written down; one lattice digest on 9/9 cells, zero drift, every refusal named. The generative comparison arm is ABSENT — there is no generative translator in the stack
Study 34 — the observer-invariant verdict — why a safety verdict needs an exact law, not a bigger computer
Study 35 — the safety brain that forgets — deaf in 8.4 seconds, forgets across machines, disagrees with itself
Study 36 — the language game of Fermat's Last Theorem — guess and shear, or project
Study 40 — the number the simulation throws away — their ICO result computed as a fraction; in float the effect returns 0 at every width, and an effect returned as zero cannot be searched for
Study 41 — fifty years of solving the wrong problem — the ordering was never about time, it was about arithmetic; 177× the work and 2,400× the wrong guesses to return the answer the machine already had
Study 42 — The Exact Contract — 2.7M flood settlements in Int128 cents; the step exists and the rigidity does not
Study 29 — continuous-model shear
The lattice holds · Impact study — continuum dead · Death of continuous shear
Fourier Phantom — Anima FNO vs 11+12+13 · Stellar dynamo kill shot
QCD: freedom is dilation · UUM-8D vs IUT — WIN
Peer-review bundle · Conjecture alignment

⚡ Fusion — the energy case

We need fusion — the verdict every machine can check
Affine Fusion Control — the local exact-integer court · public release
Fusion researcher's guide
Study 33 — the fusion control verdict court

🌍 The planet, and the sky

Every season, fifty tonnes — the biosphere-safety case
The forcing nobody measures · Impact study — the SpaceX trajectory
Study 31 — the biosphere joint ledger — LIVE on the court, 9/9 cells
Study 28 — the wet-bulb threshold court — Act 1 sealed
Study 32 — the taxi-out floor court
Where humans actually yield — the fatigue curves, and where the rules already agree
Study 30 — sovereign edge pod · Manufacture contracts

🏛 Markets, money and risk

The detector that flags the whole market — a manipulation geometry in exact integers, and the regulator's own indicator scored against a legitimate quoter
Study 43 — almost every order is cancelled, and that is normal — nine sessions, three operators, two continents: 935 to 998 of every 1,000 orders that ended, ended without trading. A check that flags almost everything is a denominator, not a detector — and the stock you pick moves it further than the exchange does
Study 44 — nine billion answers, four billion ways to say them — AlphaGenome Atlas ships 9 billion predictions in single-precision floats, which hold 4.28 billion distinct values: 52 of every 100 variants MUST share a score with another. Agreement and exhaustion look identical on the wire
Study 38 — the loss-reserve triangle — a reserve is an exact rational; 481 of 482 verdicts identical in both arithmetics; the sixteen-billion figure comes from an unchecked premise
Study 39 — the actuarial domain — life, pensions, multi-state and aggregation; the margin is 8 significant digits at its tightest

⚛️ Run a court yourself

Run any study in your browser — the ▶ badge beside a program name opens it in the Studio, already built and carrying its inputs, and runs it on your machine with nothing sent back
Explore the live courts
MCP user guide — all 51 tools · Deterministic no-float courts for LLMs
Court Client — generic wasm IDE for every court · Court-client checkpoint
Coding Court — the verdict IS the artifact
Zed — the coding agent, for developers — set Zed 1.20.2 up on https://affine.earth/v1, no language model anywhere; what a turn does, the wire, the autonomous closure
Zed — Minecraft comes to life — the two-person interaction, sealed: it asks, cites, clones a sibling with a value you supply, verifies by replay; the court flips REFUSED_UNKNOWN_BUDGET → WIN
Zed — the agent that teaches the whole domain — architecture, protocols, server management and git, each answered from lines it read and instruments it ran; five closures PROVEN, and the cattle question answered with a counter the fleet did not have
Math Court on Glama · Math Court user guide · Example app — entire court
Quantum algorithms inventory · Shor witness certifier
MCP clients (public)
Glama connector
Look in the UI (no visitor data)

📒 Program ledger — every study by lifecycle

A study appears here under the state its evidence has earned, and above under the question it answers. The two are different filings of the same work, on purpose.

✅ LAW FROZEN · DATA SEALED

Study 06 — explosion vs earthquake · Study 07 — Sgr A* raw visibilities
Study 11 — Ehrhart volume · Study 12 — parallel repetition · Study 13 — Connes rigidity
Study 14 — protein lattice · Study 16 — disease type · Study 17 — chemistry InChIKey
Study 18 — material STD · Study 19 — Go First dice
Study 26 — master regulator bonds — 17 tumour types, every finding published

🔴 LIVE CLAIM — standing, not sealed

🌊 CHARTER · OPEN — the findings, published either way

Study 03 — flare SIDs — archive went dead · predictions and validations
Study 04 — tsunami vs surge — partial seal · Study 05 — Forbush decreases
Study 08 — Gaia BH1 — no corpus until DR4 · Study 10 — Fermi / dark matter — does not disprove DM
Study 15 — Skala DFT shear · Study 27 — exact nuclear scattering

Lion Shor Witness Certifier

title: Shor Witness Certifier — what the cell actually sealed audience: cryptographers_engineers_press contract_version: 1.0.0 authority_kind: normative release: v120

Shor Witness Certifier — what the cell actually sealed

The honest two-tier seal

Tier 1 — actual factorizations (35 rows, N = 15 → 65,021)

Tier 2 / Tier 3 — period-PROVIDED witness verifications (13 rows, N up to 8 × 10¹²)

What this is and is NOT

What this IS

What this is NOT

What it does NOT close

How to verify

Lattice position

Why this correction matters

NATS subject

What exists in this repo (2026-08-27)

What was stripped (cite the commits)

Glama / public MCP

Leftover Python wrapper

Honest bound

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