Research publication — papers, datasets, and frozen findings¶

Canonical URL for external reviewers

https://gaiaftcl.com/Research-Publication/ · short link https://gaiaftcl.com/research/
Copy-paste brief for email/chat: Research-Instructions

Primary paper (code-indexed): cells/xcode/docs/SHOR_ECDLP_RESEARCH_PAPER.md — document ID gaiaftcl.shor.ecdlp.research.paper.v3

Operational guides:

Doc	Role
`cells/xcode/docs/SHOR_ECDLP_RESEARCH.md`	ECDLP pipeline commands
`cells/xcode/docs/QC020_DUAL_PATH_QUALIFICATION.md`	Historical OQ/PQ vs live miner
`cells/xcode/docs/QC21_QUANTUM_VM_VALIDATION_REVIEW.md`	Full QC-001…QC-021 matrix
`cells/xcode/docs/RESEARCH_VALIDATION_LEAK_AUDIT.md`	Claim-leak guards (Pass 6 dual-path)
BTC-Mining-Circuit-Narrative	Human ↔ circuit map for PoW

Frozen datasets (2026-06-05 revalidation): evidence/research/*_latest.json

Operating doctrine (research-grade)

Live — Metal ECDLP + Bitcoin Core miner RPC. Unbounded — ECDLP C⁴ while true; miner Grover law at projectionNActive (L6 GroverN4.lean is kernel seal only). Claim metrology — L6/L7/L8 are separate frozen flags. See Research-Meaning § Operating doctrine and QC-002 two surfaces.

Lean proofs (research publication):

Surface	Role
Research-Lean-Gates	QC-001…QC-021 ↔ `FirstRoars/*.lean` gate roster (frozen `leanGates`)
Lion-Math-Artifacts	Full FirstRoars catalog — sorry/opaque/CALORIE per file
Swift-Gate-Trust	Swift checker ↔ Lean kernel agreement history
Mesh JSON	`https://gaiaftcl.com/evidence/research/qc_vm_validation_latest.json` (includes `leanGates`)

Research docs (full text on mesh wiki research section): SHOR ECDLP paper v3, QC-021 validation review, dual-path qualification, leak audit.

What the paper claims (and does not)¶

Shor-lattice ECDLP (QC-001-ECDLP)¶

Layer	Claim	Backend
Substrate measurement	Find `(ra, rb)` from public `Q` only; unbounded C⁴ walk	`vqbit_metal` (22 pipelines)
Classical recovery	`d ≡ −ra·rb⁻¹ (mod n)` on secp256k1	Swift `BigInt` + P256K
Lean post-processing	Small-modulus seals only	`FirstRoars/ShorECDLP.lean` CALORIE

Does not claim: polynomial-time break of random 256-bit mainnet keys; full QFT/QPE in silicon; Lean proof at full secp256k1 order.

Structured seals (evaluation.v1): neg-G (d = n−1), generator (d = 1), bitcoin generator constant — all witnessOK on vqbit_metal, encodingCrossCheckOK=true, typical substrateSteps=1.

Full quantum VM (QC-001…QC-021)¶

Schema: gaiaftcl.qc_vm.research.v4 — embeds per-row mathLayerOK / learningLayerOK / rewardLayerOK, circuit graphs, Lean gate NDJSON, L7/L8 witnesses.

Flag (frozen row)	Value	Meaning
`allMathLayerOK`	`true`	Algebra + substrate gates pass
`allLearningClaimsOK`	`true`	L8 Grover learning / collapse persistence
`qaLayerClosed`	`true`	Claim leaks closed (L6+L8+QCF-004)
`leakAuditPass`	`true`	L7 operational (`learning` or `realized`)
`allRewardClaimsOK`	`false`	Correct — no `chain_accepted` block yet
`l7RewardLayerStatus`	`learning`	Miner active; L7 not realized
`metalPipelineCount`	`22`	Metal-only for catalog QC (except PoW projection)

Substrate backend honesty:

Family	Backend
QC-001…QC-021 (except PoW)	`vqbit_metal`
QC-001-ECDLP	`vqbit_metal`
QC-020 PoW	`vqbit_cpu_projection` (`M8MeasurementComposer`)

QC-020 PoW findings (dual path + learning trend)¶

Bitcoin PoW qualification runs on two parallel paths — neither implies the other (gaiaftcl.qc020.dual_path.v1).

Path	ID	Clock	Claim	Frozen status
Historical OQ/PQ	`QC-020-HIST`	Decoupled	`pow_ledger_oq_pq`	`qualificationOK=true`
Live miner	`QC-020-LIVE`	Template ~30s, 5 windows	`pow_live_miner_l7_l8`	`qualificationOK=true`

Historical vectors: ledger rung 1 (synthetic 2²³⁶) + block 100000 (nonce=274148111, nBits=0x1b04864c).

Live L8 (learning): qc020_substrate_research_telemetry — frozen snapshot ~2999 rows, ~168 rows in last 5 min, learningWitnessOK=true, groverOptimalCycles=79.

Live L7 (reward): onChainRewardOK only when chain_accepted + confirmed sats at payout — never simulated. acceptedSubmissionCount=0 at revalidation is honest.

Time-to-nonce improvement trend (separate from L7)¶

Schema: gaiaftcl.qc020.improvement_trend.v1 — measures whether nonce discovery is getting faster, not whether BTC landed.

Field (frozen)	Value
`trendStatus`	`insufficient_hits`
`totalHitSamples`	`0`
`captureHitCount`	`211` (ledger bootstrap; `solve_duration_ms=0` pre-V155)
`improvingOK`	`false`

Trend flips to improving when ≥3 timed CALORIE/capture rows accumulate with decreasing median time_to_hit_ms. Weekend mining research (app boot) is wired to grow this dataset.

Frozen artifact index¶

File	Schema	Mesh URL
`evidence/research/ecdlp_research_20260605T134447Z.json`	`gaiaftcl.shor.ecdlp.research.v2`	git only (timestamped snapshot)
`evidence/research/ecdlp_evaluation_latest.json`	`gaiaftcl.shor.ecdlp.evaluation.v1`	/evidence/research/ecdlp_evaluation_latest.json
`evidence/research/qc_vm_validation_latest.json`	`gaiaftcl.qc_vm.research.v4` (+ `leanGates`)	/evidence/research/qc_vm_validation_latest.json
`evidence/research/qc020_dual_path_latest.json`	`gaiaftcl.qc020.dual_path.v1`	/evidence/research/qc020_dual_path_latest.json
`evidence/research/qc020_improvement_trend_latest.json`	`gaiaftcl.qc020.improvement_trend.v1`	/evidence/research/qc020_improvement_trend_latest.json

Reproduce (peer review)¶

# Metal shaders (required before substrate QC)
cells/xcode/scripts/build_metal_shaders.sh

# ECDLP witness + evaluation
cells/xcode/scripts/export_ecdlp_research_dataset.sh

# Full QC catalog + leak audit + research.v4
cells/xcode/scripts/peer_review_research_dataset.sh

# QC-020 dual path + improvement trend
cells/xcode/scripts/export_qc020_dual_path_research.sh
cells/xcode/scripts/export_qc020_improvement_trend.sh

# CLI neg-G seal (no wallet file)
cd cells/xcode && swift run GaiaFTCLCLI shor break-classical \
  --neg-generator-seal --witness-out 2>/dev/null | tail -1

Strict CI gates:

Env	Enforces
`STRICT_REWARD=1`	L7 `chain_accepted` only
`STRICT_LEARNING=1`	`allLearningClaimsOK`
`STRICT_IMPROVING=1`	Decreasing time-to-nonce trend

Weekend mining research (operator)¶

On Franklin.app boot, after sovereign stack .ready:

M8BTCSubstrateMiner + M8BTCArrivalWatcher spawn (mainnet PoW)
FranklinSubstrateResearchMonitor observes window summaries (5 min)
Improvement trend snapshots at boot + every 6 hours → evidence/research/

Prerequisites: destination_address in ~/.gaiaftcl/qc021_payout.toml; ~/.gaiaftcl/btc_node.toml (substrate writes default if absent). Keep the app running — quit tears down the miner.

tail -f ~/Library/Logs/GaiaFTCL/M8BTCSubstrateMiner.log
cd cells/xcode && swift run M8QC020LedgerTail   # live hit stream

Skip: GAIAFTCL_SKIP_QC020_MINER=1

Peer-review response log (summary)¶

ID	Issue	Resolution
M1	Name implied full Shor QFT	Pipeline renamed `shor_lattice_ecdlp_secp256k1`
M4	G vs −G hex confusion	`ShorECDLPEncodingCrossCheck` mandatory
M7	QC Lean IDs mislabeled	`QCQuantumVMValidationRegistry`
M10	QC-020 conflated ledger + live	Dual-path `QC-020-HIST` / `QC-020-LIVE`
M11	No learning-improvement visibility	`qc020.improvement_trend.v1`
M12	Global `vqbit_metal` misread for PoW	`substrateComputeBackendNote`; PoW uses CPU projection

Full table: paper §14.

Honest open items (not hidden)¶

L7 realization — chain_accepted block + confirmed payout sats
Timed hit accumulation — improvement trend needs CALORIE rows with solve_duration_ms > 0
Lean at full 256-bit curve — deferred; Swift/P256K is verifier-of-record at scale
Universal ECDLP break — not claimed; demonstration wallets ≠ arbitrary mainnet break

→ two-wallet-demonstration/substrate-honest-disclosure — bit-size and wallet honesty

Synchronize with paper v3 and evidence/research/*_latest.json on every revalidation run.

Federation-cosigned

This page's source is sealed in the GaiaFTCL federation manifest — page SHA-256 9e2b73687c0a8e98…, 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.