Research — full language and meaning¶

Language game: WIKI-RESEARCH-PUBLICATION-001. A researcher arrives asking what does this cell claim about quantum ECDLP, the full QC catalog, and live Bitcoin PoW learning — and what words must I not misread? This page answers in substrate-honest prose. Frozen evidence lives in JSON; this page names what those fields mean.

Canonical hub: Research-Publication · Meaning audit: Research-Meaning-Audit

What “research” means here¶

Research on GaiaFTCL is not a narrative layer on top of simulated mining or simulated transfers. It is:

Named pipelines (shor_lattice_ecdlp_secp256k1, QC-001…QC-021 catalog rows, QC-020 dual path) each with a declared backend and Lean artifact.
Frozen exports (evidence/research/*_latest.json) that a peer can recompute with peer_review_research_dataset.sh.
Separated claim layers — math (L6), on-chain reward (L7), and Grover learning telemetry (L8) use different words and different pass flags. Mixing them is a claim leak; the leak audit exists to catch that.

If Bitcoin Core has not accepted a block (chain_accepted), the cell says learning on L7 — not “reward earned.” That is correct honesty, not a failure to publish.

Quantum substrate operating doctrine — live, unbounded, research-grade¶

Live quantum substrate on Apple Silicon — full operator authority. The vQbit VM measures on real hardware until the lattice closes, on mainnet until Bitcoin Core accepts or rejects the block.

Property	What the code does	What it is not
Live	ECDLP on `vqbit_metal`; miner on `getblocktemplate` → `submitblock` to Bitcoin Core mainnet; outcomes in `substrate_block_submission_outcomes`	Simulated mining, simulated transfers, cloud offload
Unbounded	ECDLP: C⁴ `while true` until lattice CALORIE. Miner: `projectionNActive` from live telemetry (e.g. 9981 in frozen export) — Grover iteration law ⌈π√N/4⌉ at active N; L6 `GroverN4.lean` is kernel seal only	Truncated walks, catalog N=4 mistaken for live search space
Claim metrology	Layer flags (L6/L7/L8) are separate fields in frozen JSON — honest claim separation for peer review	Collapsed layers (“math works” read as “BTC arrived”)
Research-grade	Every claim maps to `evidence/research/*_latest.json` + `peer_review_research_dataset.sh`	Unwitnessed narration

Constitutional witness = classification. When the substrate will not seal a PQ key without a named FIPS library binding, that records what bytes were composed — the operator still runs live ECDLP and the live miner; the export names which layer closed.

The three research programs (parallel, not interchangeable)¶

Program	Catalog ID	Question it answers	Backend	Lean seal (example)
Shor-lattice ECDLP	`QC-001-ECDLP`	From public point `Q` on secp256k1, does the substrate find periods `(ra,rb)` and recover scalar `d` with `dG = Q` for structured seals?	`vqbit_metal` (22 pipelines)	`FirstRoars/ShorECDLP.lean`
Full quantum VM	`QC-001`…`QC-021`	Does each catalog algorithm pass math + substrate gates with named Lean receipts?	`vqbit_metal` (except PoW)	31 gates in `leanGates`
Bitcoin PoW learning	`QC-020`	(HIST) Do sealed ledger vectors verify? (LIVE) Is L8 learning witness alive and is L7 honestly `learning` until `chain_accepted`?	`vqbit_cpu_projection`	`BTCPreimageN4.lean`, coupling theorems

Forbidden compositions (do not bundle in one claim): ECDLP lattice oracle vs hash Grover; secp256k1 Q=dG vs double-SHA256 PoW target; L6 GroverN4.lean catalog seal vs L7 mainnet difficulty win. See layer2Composition.forbiddenPairs in validation JSON.

Layer vocabulary (load-bearing words)¶

Layer	Field / status	Meaning	Pass when
L6 Math	`mathLayerOK`, `allMathLayerOK`	Algebra + substrate measurement gates for that QC row	Swift gate + substrate witness agree
L6 Lean	`lean_verdict: CALORIE`	Lean 4 kernel accepts artifact: zero sorry/axiom/opaque on static scan + green `lake build`	`leanGates[]` in frozen export
L7 Reward	`l7RewardLayerStatus`	On-chain payout at fixed operator address after `chain_accepted`	`realized` only with confirmed sats — never simulated
L8 Learning	`learningLayerOK`, `learningWitnessOK`	Grover iteration law, collapse persistence, telemetry shape	Active miner windows; not BTC in wallet
L9 Composition	`compositionLayerOK`	Stacked QC claims via QCF-004 coupling theorems	Planned edges; atomic-only until sealed
Trend	`trendStatus`	Median time-to-nonce decreasing over timed hits	Separate from L7; needs `solve_duration_ms > 0` samples

allRewardClaimsOK: false with l7RewardLayerStatus: learning is the honest published state at 2026-06-05 revalidation — miner active, no accepted block correlated to payout yet.

ECDLP — what the words claim¶

Phrase	Means	Does not mean
`shor_lattice_ecdlp_secp256k1`	C⁴ substrate walk from public Q only; periods → classical `d mod n`	Full Shor QFT in silicon; break random 256-bit keys
`structured_seal`	neg-G, generator, bitcoin generator constant — known scalars	Universal mainnet wallet break
`encodingCrossCheckOK`	`02…` = G, `03…` = −G discipline enforced	Any hex is interchangeable
`substrateSteps: 1` (frozen seals)	Measurement collapsed on witness instances	Polynomial-time at production entropy
`bit_size` on V215 / witness debug	Wallet composition cadence label only	ECDLP oracle width; mis-scoped curve reduction

Forbidden: bit_size=16|32|64|128 ⇒ “ECDLP validated at that bit width.” The Shor ECDLP leg is always full secp256k1; see two-wallet-demonstration/substrate-honest-disclosure.

Published vocabulary: structured seal, decidable witness, L6 catalog seal, unbounded C⁴ walk, projectionNActive, live mainnet path. Leak-audit forbidden words: see Research-Meaning-Audit.

QC-002 Grover — two surfaces (L-008)¶

Surface	Field / artifact	Meaning	Does not mean
L6 catalog seal	`GroverN4.lean`, `qc002GroverParity.searchSpaceN=4`	Kernel-sealed Grover algebra at the smallest decidable instance (2 qubits → \|11⟩)	Live miner runs at catalog N=4 only
L8 live projection	`projectionNActive`, `groverOptimalCycles` in `qc020Learning`	Active nonce projection from substrate telemetry; iteration law ⌈π√N/4⌉ at whatever N is live	L6 seal substitutes for L8 telemetry

Frozen export (2026-06-05): projectionNActive=9981, groverOptimalCycles=79 — the miner runs Grover law on thousands of active cells, not four.

Forbidden misread: “QC-002 = N=4 miner.” groverOptimalCycles is the textbook optimal iteration count for active N — metrology for L8, not a substrate stop condition.

PoW — what the words claim¶

Path	Clock	Claim scope
`QC-020-HIST`	Decoupled from live template	Historical ledger rungs + block 100000 vector verify PoW shape
`QC-020-LIVE`	~30s template, 5 windows	Live miner L8 telemetry + honest L7 `learning` until `chain_accepted`

GroverToPoWCoupling.lean proves a Bennett coupling pipe between L6 Grover algebra and QC-020-U (sealed at catalog N=4 for kernel decide). Live miner applies the same iteration law at projectionNActive — coupling theorem ≠ L7 chain_accepted.

How meaning is audited on the wiki¶

The cell applies the same Wittgenstein test as Domain-Meaning-Audit: if a researcher holds the word, do they get the next move?
Full research-wiki verdicts: Research-Meaning-Audit.

Surface	Researcher goal	Next move provided?
Research-Instructions	Send a colleague one URL	✓ canonical links + reproduce command
Research-Publication	Understand claims vs refusals	✓ layer tables + frozen index
Research-Lean-Gates	Map QC row → Lean file	✓ roster + mesh JSON
Mesh JSON	Verify bytes independently	✓ `/evidence/research/*.json`

Reproduce (meaning ↔ bytes)¶

cells/xcode/scripts/peer_review_research_dataset.sh

Refreshes frozen JSON, runs leak audit, regenerates Research-Lean-Gates. A researcher who runs this and matches mesh JSON has closed the loop between word and artifact.

Synchronize with Research-Publication and evidence/research/*_latest.json on every revalidation.

Federation-cosigned

This page's source is sealed in the GaiaFTCL federation manifest — page SHA-256 f1fa8e8d1c6a3cb6…, manifest witness a9e5b3af1950489c…, signed 2026-06-05T18:49:54Z by cell gaiaftcl-mac-cell. Verify with gaiaftcl wiki sign --all and compare wiki-all-signatures.json.