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title: Research publication — ECDLP + QC VM + PoW learning (v3)

audience: researchers_and_auditors

game: WIKI-RESEARCH-PUBLICATION-001

updated: 2026-06-05

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Research publication — papers, datasets, and frozen findings

!!! success "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:

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

!!! info "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):

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

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What the paper claims (and does not)

Shor-lattice ECDLP (QC-001-ECDLP)

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.

Substrate backend honesty:

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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).

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.

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.

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Frozen artifact index

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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:

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Weekend mining research (operator)

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

1. M8BTCSubstrateMiner + M8BTCArrivalWatcher spawn (mainnet PoW)

2. FranklinSubstrateResearchMonitor observes window summaries (5 min)

3. 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

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Peer-review response log (summary)

Full table: paper §14.

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Honest open items (not hidden)

1. L7 realization — chain_accepted block + confirmed payout sats

2. Timed hit accumulation — improvement trend needs CALORIE rows with solve_duration_ms > 0

3. Lean at full 256-bit curve — deferred; Swift/P256K is verifier-of-record at scale

4. Universal ECDLP break — not claimed; demonstration wallets ≠ arbitrary mainnet break

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

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