Skip to content

SC-42 (PR-B): operational completion within complex matrix kinematics - #976

Closed
amaybaum wants to merge 5 commits into
mainfrom
corpus/sc42-operational-kinematics
Closed

SC-42 (PR-B): operational completion within complex matrix kinematics#976
amaybaum wants to merge 5 commits into
mainfrom
corpus/sc42-operational-kinematics

Conversation

@amaybaum

@amaybaum amaybaum commented Oct 28, 2026

Copy link
Copy Markdown
Owner

This is a source-correction unit for #946 (the gate) and #918 (the Introduction). It comes from the full-corpus audit of #918 at 60c976fe: PR-B (CON-15) and B-B8.

  • Base: main at 0d917665.
  • Head: 756073ac.
  • Review: the independent review returned ACCEPT at this exact head, after four fix rounds. The owner agreed with the round-2 findings, and SC-42's verified wording takes precedence at reconciliation.

Finding

The operational-completion characterization (GR §3.3, Main §3.4) was restated in many places as if the five completion conditions derive the quantum kinematics, local tomography or the tensor-product composite, and as if they characterize the fixed-basis representation. The kernel does neither:

  • the complex matrix kinematics, the composite A × Fin n and with it local tomography are fixed by the types and taken as given;
  • the five conditions characterize when an operational theory's available instruments on a finite carrier and its composites are exactly the quantum instruments.

GR's condition (i) was also stated without "at every ancilla level", which the kernel definition (CompositeOperationalValidity) quantifies over.

Corrections

  • GR:216, condition (i): "at every ancilla level, every available family sends positive states to positive states and its outcomes' traces sum to the input trace". A setting sentence covers the OI⁺, primitive-source, substratum-source, layer-flow and typed forms (GR:240–278).
  • Every restatement of the characterization now carries "on a finite carrier, within complex matrix kinematics taken as given", with both §A.34 witnesses: exactAll_of_physical_general (conditions ⇒ exact) and physical_of_exactAll (exact ⇒ conditions). The sites are:
    • Main:210, :212, :580, :638 and :648;
    • GR:70 and :330;
    • glossary:21;
    • preface:5;
    • Explainer:375, :950 and :962;
    • Structure:1119;
    • ch02:12 and :20, ch03:186, ch04:92, ch14:76, ch19:264;
    • the FULL mirrors.
  • Main:212: the characterization takes the kinematics as given, "the tensor-product composite and with it local tomography included". Deriving that kinematics is open.
  • Main:580: each per-principle equivalence is stated with its kernel hypotheses. Observational independence ⟺ inert spectators is unconditional. The converse of reversible richness needs well-formed theories on a nonempty carrier. The converse of observer recursion needs identity and relative-readout availability at every level, which control and inert spectators supply.
  • The "lifting" framing is replaced corpus-wide by the five completion conditions, with the substratum's supply of them open. Four uses of "lifting" remain; each is legitimate (a negation, or the dilation sense).
  • Coverage: MAIN:T-statement is re-affirmed at SUM. No level changed.
  • Lean: no change.

Checks (reviewer, independently, under python3 -I)

  • check_sc42.py passes, and its output replays byte for byte. Four countercontrols fail as they should, one each against the base, round 2, round 3 and round 4. The script also checks each witness's hypotheses against the Lean source.
  • coverage_check (128), the census, edge_rigidity_probe and staleness_check all pass.
  • release_gate passes every step except lean-axioms, which runs in CI.
  • The rebuilt .tex files are byte-identical.

Reconciliation

The per-claim record is in verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC42-operational-kinematics/README.md.

No merge is authorized. Merging needs owner approval at an exact SHA, as a normal merge commit.

Generated by Claude Code

claude added 5 commits October 28, 2026 04:22
@claude
SC-42: state Theorem 4's matrix kinematics and its full operational s…
44a1eeb 
…etting

GR §3.3 now states the complex matrix kinematics that the operational-completion
characterization takes as given (operations on M_A(C), and on M_A(C) ⊗ M_n(C) at
ancilla level n), with its derivation from operational premises open (ROADMAP P1),
and states the setting as the thirteen fields of FiniteOperationalTheory: identity,
coarse-graining, feed-forward composition at the ancilla levels only, uniform
preparation with single-outcome closure, the spectator-independent readout, and
discard (CON-15, CON-48, B-B8, B-O6). The theorem statement is unchanged.

The restatements in Main (§3.2, §3.4, conclusion), Methodology, the Explainer,
book ch01/ch19 and FULL carry the kinematics clause; Main's restatements say
"every positive ancilla level" as the kernel does. GR:330 no longer says Part I
delivers QM (CON-09). Main's "open"/"operational-lifting problem" framing at
:99, :210, :348, :550, :594, :770 and the book's at ch09:42, ch19:10 and
glossary:107 states the characterization, with substratum sourcing and the
kinematics derivation open (CON-14).

Track README and field-by-field check under
verification/audits/manuscript/intro-corpus-audit-20261026/tracks/SC42-operational-kinematics/.
GR, Main, Methodology, Explainer and the book rebuilt.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
@claude
SC-42 review: condition (i) at ancilla levels; remaining lifting-prob…
b83bbcf 
…lem framing

Condition (i) in GR §3.3 now quantifies over the ancilla levels, as
CompositeOperationalValidity does. The system-level form was failed by the
(ii)-witness systemLoose (system amplifier X -> 2X), so five_way_minimality did
not establish (ii)'s independence as stated. "No external premise" becomes "no
premise beyond its stated setting" (GR:216, Main:352). Main:210 keeps the
w < kappa criterion for the lattice coherence result.

The "operational lifting" framing is replaced by the operational-completion
characterization, with the substratum's supply of the conditions open, at
Main:82, :212, :550, :594, :618, :650, GR:70, Methodology:399, Structure:1119,
Substratum:14, :323, Explainer:707, :916, :950, :962, preface:5, ch00:55,
ch01:185, :197, ch02:12, :20, ch03:168, :174, :186, ch04:92, ch14:76, :78 and
glossary:21, with their FULL mirrors. MAIN:T-statement's ledger fingerprint
re-affirmed (SUM, unchanged). Track README and check updated; GR, Main,
Methodology, Explainer, Structure, Substratum and the book rebuilt.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
@claude
SC-42 round 3: kinematics fixes the composite; theorem is about avail…
20da13c 
…able instruments

Main:212 now says the characterization takes the complex matrix kinematics as
given, the tensor-product composite and local tomography included, and
characterizes within it whether the available interventions are exactly the
quantum instruments. glossary:21 (and FULL) states the theorem for an
operational theory's available instruments, not the fixed-basis
representation; witnesses exactAll_of_physical_general and physical_of_exactAll
recorded. The same correction at GR:330, Explainer:375, :962, Structure:1119 and
preface:5. "within complex matrix kinematics taken as given" added at ch02:12,
:20, ch03:186, ch04:92, ch14:76, GR:70 and Explainer:950, with FULL mirrors.
check_sc42.py pins the new texts and fails on the old; README updated with the
reconciliation note for sc17, sc33 and sc40. GR, Main, Explainer, Structure and
the book rebuilt.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
@claude
SC-42 round 4: Explainer:375 scope; kinematics clause at Main:638 and…
07d8b0e 
… remaining restatements

Explainer:375 now says the characterization gives, within the kinematics, when
the available instruments are exactly the quantum instruments. Main:638, :648,
:580 and ch19:264 (with FULL) carry the kinematics clause where they restate
the characterization as "exactly when/under"; GR §3.3's setting states that the
OI+, primitive-source, substratum-source, layer-flow and typed forms use the
same kinematics. check_sc42.py pins the new texts and fails on the old; README
updated. GR, Main, Explainer and the book rebuilt.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
@claude
SC-42 round 5: state the OI+ converses with their kernel hypotheses
756073a 
Main:580 replaces "on the relevant class" with the hypotheses the kernel
converses carry: observational independence is equivalent to inert spectators
on every finite carrier; reversible richness implies control, and conversely
for well-formed theories on a nonempty carrier; observer recursion implies
iterated composition, and conversely given the identity and relative readout
at every level, which control and inert spectators supply. The README records
the per-direction witnesses and which script produced each countercontrol;
check_sc42.py pins the new text and checks the hypotheses in the Lean source.
Main rebuilt.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01Y87wExth9RoUb3dtbumhTb
@amaybaum Claude

amaybaum commented Oct 28, 2026

Copy link
Copy Markdown
Owner Author

Lean kernel check failed on 756073ac (run 40636274376) in its install step, before any check ran. It could not download the Lean toolchain (lean-4.35.0-linux.tar.zst from releases.lean-lang.org) because of an SSL connect error.

This PR changes no Lean file and no workflow file. The same download error hit #974 at 04:45 UTC. The Lean check on #973 (04:42) and #975 (04:52) passed.

Once this run finishes, I will re-run the failed job once. If it fails a second time, I'll treat that as a real failure and investigate.

Generated by Claude Code

This was referenced Oct 28, 2026
Closed
Closed
Closed
Closed
Merged
@amaybaum Claude

amaybaum commented Oct 31, 2026

Copy link
Copy Markdown
Owner Author

Closing without merge: fully absorbed into main. The owner approved this closure in the Workstream D survival audit, checked against main c596904a.

All 52 changed SC-42 lines are on main: 43 identical, the rest more tightly scoped through #1000 and #997. Examples:

  • Book: ch01:185 = FULL:529 (operational boundary); chapters 02, 03, 04, 09, 14, 19; glossary; preface.
  • Main: :82, :99, :210, :212, :348, :352, :550, :558, :578–650, :770.
  • GR: :70, :216, :330.
  • Methodology: :45, :399.
  • Structure: :1117.
  • Substratum: :14, :373.
  • Explainer: :375–381, :707, :916, :950, :962.

The SC-42 successor checker on main verifies them. The branch and history are kept.

Generated by Claude Code

@amaybaum amaybaum closed this Oct 31, 2026
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Reviewers

No reviews

Assignees

No one assigned

Labels

None yet

Projects

None yet

Milestone

No milestone

Development

Successfully merging this pull request may close these issues.

2 participants

@amaybaum @claude