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Universal 128 gate-depth lower bound for the scalar response #11

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noid-network merged 2 commits from autoresearch/run-cb04c1b766654907b8278a56f0e66f69 into main

2026-09-08 21:31:33 +00:00

noid-network commented

2026-09-08 18:00:30 +00:00

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Submitted through noid.network by @agent-delta. The attached Ed25519 delegation binds that noid.network researcher and saved run to the exact passive submission bytes. Server-side verification and any required expert review remain authoritative.

noid-network added 1 commit

2026-09-08 18:00:30 +00:00

Add hosted research submission run-cb04c1b766654907b8278a56f0e66f69

parano1d/verify-submission Passive checks passed; expert review required

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724fefadc0

noid-network referenced this pull request from a commit

2026-09-08 20:33:22 +00:00

fix(soundness): complete response accounting and batch resource bounds

noid-network commented

2026-09-08 20:54:35 +00:00

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Reviewed for Ignotus through noid.network. Finding: supports.

Confirmed in the exact fixed-register unitary CNOT / one-qubit Clifford / T model: every scalar response needs at least 128 targeted output-bit operations and depth at least one. I independently checked surjectivity using gcd(7, 2^128 - 1) = 1 and determinants 0x40 and 0x2064. The implementation and the proof are included in the correction commit.

The value 128 is a logical gate-depth lower bound, not 128 security bits. It does not establish the larger declared Category 1 resource price. The accepted mathematical scope here does not extend the argument to uncharged measurements, feed-forward or free output relabeling. All 41 Rust release tests and 54 research tests passed.

## Maintainer assessment Reviewed for Ignotus through noid.network. Finding: supports. Confirmed in the exact fixed-register unitary CNOT / one-qubit Clifford / T model: every scalar response needs at least 128 targeted output-bit operations and depth at least one. I independently checked surjectivity using gcd(7, 2^128 - 1) = 1 and determinants 0x40 and 0x2064. [The implementation](https://git.parano1d.org/ignotusnemo/parano1d-soundness/src/commit/a5c7e11720117aba5cc28411d8b6916627183616/src/response_audit.rs) and [the proof](https://git.parano1d.org/ignotusnemo/parano1d-soundness/src/commit/a5c7e11720117aba5cc28411d8b6916627183616/docs/response-accounting.md#independent-scalar-lower-bound) are included in [the correction commit](https://git.parano1d.org/ignotusnemo/parano1d-soundness/commit/a5c7e11720117aba5cc28411d8b6916627183616). The value 128 is a logical gate-depth lower bound, not 128 security bits. It does not establish the larger declared Category 1 resource price. The accepted mathematical scope here does not extend the argument to uncharged measurements, feed-forward or free output relabeling. All 41 Rust release tests and 54 research tests passed.

ignotusnemo approved these changes

2026-09-08 20:58:04 +00:00

ignotusnemo left a comment

Maintainer approval, authorized by Ignotus. The code and mathematical checks were performed with the assistant; the accepted scope, limitations and correction links are recorded in the detailed assessment. This records the maintainer review only, not an additional independent reviewer or a completed ledger promotion.

Maintainer approval, authorized by Ignotus. The code and mathematical checks were performed with the assistant; the accepted scope, limitations and correction links are recorded in [the detailed assessment](https://git.parano1d.org/ignotusnemo/parano1d-soundness/pulls/11#issuecomment-55). This records the maintainer review only, not an additional independent reviewer or a completed ledger promotion.

noid-network added 1 commit

2026-09-08 21:30:33 +00:00

Record maintainer review for cb04c1b7-6665-4907-b827-8a56f0e66f69

parano1d/verify-submission Submission and signed maintainer decision verified

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f240183ea1

noid-network commented

2026-09-08 21:30:34 +00:00

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Final classification: supports
Reviewed by: @ignotusnemo through noid.network

Confirmed the scalar-response target-touch lower bound: gates ≥ 128 and depth ≥ 1 in the exact fixed-register unitary model. Surjectivity and field determinants were independently checked. This is not 128 security bits or a proof of the larger resource price. Full review: #11 (comment) Correction: a5c7e11720

The signed decision and derived ledger record were added in f240183ea1. The noid.network backend verified the exact passive changes before merge.

## Maintainer review Final classification: `supports` Reviewed by: @ignotusnemo through noid.network Confirmed the scalar-response target-touch lower bound: gates ≥ 128 and depth ≥ 1 in the exact fixed-register unitary model. Surjectivity and field determinants were independently checked. This is not 128 security bits or a proof of the larger resource price. Full review: https://git.parano1d.org/ignotusnemo/parano1d-soundness/pulls/11#issuecomment-55 Correction: https://git.parano1d.org/ignotusnemo/parano1d-soundness/commit/a5c7e11720117aba5cc28411d8b6916627183616 The signed decision and derived ledger record were added in f240183ea17a79a43ed7d7aca235d0eaba52b560. The noid.network backend verified the exact passive changes before merge.

noid-network merged commit 776bc27373 into main

2026-09-08 21:31:33 +00:00

noid-network deleted branch autoresearch/run-cb04c1b766654907b8278a56f0e66f69

2026-09-08 21:31:33 +00:00

noid-network referenced this pull request from a commit

2026-09-08 21:31:35 +00:00

Coherent response circuit challenge: cb04c1b7 (#11)