fix(pr-3614): 5 unresolved P1 threads — monad-associativity terminology + dead xrefs by AceHack · Pull Request #3626 · Lucent-Financial-Group/Zeta

AceHack · 2026-05-16T00:15:08Z

Summary

Addresses 5 unresolved P1 threads from now-merged PR #3614 that landed math-terminology + xref drift in the B-0543/B-0544 research substrate.

Math terminology (3 threads — Codex + Copilot):

μ ∘ Mμ = μ ∘ μ_M is the monad associativity law, not idempotence. Renamed throughout; idempotent-monad condition (μ ∘ η_M = id) flagged as a separate physical assumption requiring its own justification.
D ∘ Q ∘ I was called a "monad on streams". Corrected to the DBSP incrementalization identity Q^Δ = D ∘ Q ∘ I (a wrapping/conjugation identity over streams, not a monad). The repo treats Q^Δ = D ∘ Q ∘ I as identity/wrapper elsewhere — research substrate now aligned. Whether M (topos memory monad) and the DBSP I/D pair share a deeper categorical relationship (e.g., comonad-monad adjunction, distributive law) flagged as an open question, not a settled identity.

Dead xrefs (2 threads — Copilot):

Memory file pointed at non-existent aaron-ani-grok-post-m-acc-adoption-constraint-11-default-oracle.md → corrected to actual aaron-ani-grok-persistence-pt3-m-acc-moral-accelerationism-naming.md.
"B-0422 ... if it exists" — confirmed B-0422 lives at docs/backlog/P3/B-0422-clifford-algebraic-narrative-engine-pauli-symmetry-breaking-falsifiability-test-2026-05-12.md. Removed the stale conditional in both B-0543 and the memory file; linked directly.

Out of scope (deferred to a follow-up PR):

Codex's deeper finding that M/A coherence laws are not well-typed under the stated signatures (A(μ_X) applies A to a morphism; A(M(p)) requires M(p) ∈ Ω without a defined lifting / natural transformation). That's a substantive math fix, not a terminology cleanup; deserves its own PR with proper categorical machinery.
Round 45 entry position in docs/ROUND-HISTORY.md (Copilot P1).

Test plan

git ls-tree HEAD | wc -l canary clean (53/53 root entries, 5140/5140 total files vs parent) — Lior was active during commit window, but no commit-tree corruption per .claude/rules/codeql-no-source-on-docs-only-pr-is-broken-commit-canary.md
Borrow-on-existing pattern used (worktree /private/tmp/zeta-tick-2210z, ~6h old, well past 3h+ stability threshold) per .claude/rules/claim-acquire-before-worktree-work.md
Explicit-path staging (no git add -A) — exactly 5 expected files
CI: docs-only diff; required checks expected green
Codex/Copilot re-review: confirm terminology fixes address the 5 threads named in the body

Files changed

docs/backlog/P2/B-0543-qg-isomorphism-proof-path-remember-when-pay-attention-axioms-to-quantum-gravity-2026-05-15.md |  2 +-
docs/backlog/P2/B-0544-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives-2026-05-15.md |  2 +-
docs/research/2026-05-15-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives.md | 11 ++++++-----
memory/feedback_otto_qg_isomorphism_proof_path_remember_when_pay_attention_axioms_infinite_poker_to_quantum_gravity_aaron_otto_2026_05_15.md |  4 ++--
memory/feedback_otto_qg_isomorphism_step_1_formalize_remember_when_pay_attention_as_categorical_primitives_2026_05_15.md |  6 +++---
5 files changed, 13 insertions(+), 12 deletions(-)

🤖 Generated with Claude Code

…gy + dead xrefs Addresses 5 unresolved P1 review threads on now-merged PR #3614 (Codex + Copilot) that landed mathematical/xref drift in B-0543/B-0544 research substrate. **Math terminology (3 threads, Codex + Copilot)**: - "M is idempotent up to coherence: μ ∘ Mμ = μ ∘ μ_M" → renamed to **monad associativity law**. That equation IS associativity, not idempotence; an idempotent monad would additionally satisfy μ ∘ η_M = id. Conflating the two would send downstream Lean/Coq proofs toward wrong obligations. - "D ∘ Q ∘ I is a monad on streams" → corrected to the **incrementalization identity** Q^Δ = D ∘ Q ∘ I (a wrapping/conjugation identity over streams, not asserting D ∘ Q ∘ I satisfies monad unit/multiplication laws). The repo treats Q^Δ = D ∘ Q ∘ I as identity/wrapper elsewhere, not as a monad — aligning research substrate with that established usage. - "Idempotence: remembering twice = remembering once" → reframed as associativity; whether memory is *additionally* idempotent is flagged as a separate physical assumption requiring its own justification. **Dead xrefs (2 threads, Copilot)**: - Memory file pointed at non-existent `aaron-ani-grok-post-m-acc-adoption-constraint-11-default-oracle.md` → corrected to actual file `aaron-ani-grok-persistence-pt3-m-acc-moral-accelerationism-naming.md` (the real m/acc-adoption conversation). - "B-0422 ... if it exists" → confirmed B-0422 exists at docs/backlog/P3/B-0422-clifford-algebraic-narrative-engine-pauli-symmetry-breaking-falsifiability-test-2026-05-12.md. Removed the stale conditional in both B-0543 and the memory file; linked directly. **Deferred to follow-up PR** (not in scope here): - Codex's deeper finding that the M/A coherence laws are not well-typed under the stated signatures (A(μ_X) applies A to a morphism; A(M(p)) requires M(p) ∈ Ω without a defined lifting). That's a substantive math fix, not a terminology cleanup; deserves its own PR with care. - Round 45 entry position in docs/ROUND-HISTORY.md. Files: - docs/research/2026-05-15-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives.md (3 edits) - memory/feedback_otto_qg_isomorphism_step_1_formalize_remember_when_pay_attention_as_categorical_primitives_2026_05_15.md (3 edits) - memory/feedback_otto_qg_isomorphism_proof_path_remember_when_pay_attention_axioms_infinite_poker_to_quantum_gravity_aaron_otto_2026_05_15.md (1 edit, 2 lines) - docs/backlog/P2/B-0543-qg-isomorphism-proof-path-remember-when-pay-attention-axioms-to-quantum-gravity-2026-05-15.md (1 edit) - docs/backlog/P2/B-0544-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives-2026-05-15.md (1 edit) Operational context: Lior was active during this commit window (lock-cleanup-race precondition); commit verified via ls-tree canary before push per .claude/rules/codeql-no-source-on-docs-only-pr-is-broken-commit-canary.md. Borrow-on-existing pattern used (worktree /private/tmp/zeta-tick-2210z, ~6h old, well past 3h+ stability threshold) per .claude/rules/claim-acquire-before-worktree-work.md. Co-Authored-By: Claude <noreply@anthropic.com>

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chatgpt-codex-connector · 2026-05-16T00:16:26Z

 **Key properties**:

- `M` is **idempotent** up to coherence: `μ ∘ Mμ = μ ∘ μ_M` (memory reconstruction is confluent)
+- `M` satisfies the **monad associativity law**: `μ ∘ Mμ = μ ∘ μ_M` (memory flattening is associative — this is the standard monad coherence, not idempotence; an idempotent monad would additionally satisfy `μ ∘ η_M = id`)


Remove incorrect idempotent-monad criterion

This line states that an idempotent monad would "additionally satisfy μ ∘ η_M = id", but that equation is already a standard monad unit law and therefore does not distinguish idempotent monads. Leaving this in place will propagate a wrong definition into follow-up proofs and backlog items that rely on this document’s formal vocabulary; the extra condition should be replaced with an actual idempotence criterion (e.g., multiplication being an isomorphism/equivalent characterization).

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Copilot

Pull request overview

This PR corrects math terminology and cross-reference drift in the B-0543/B-0544 quantum-gravity research substrate.

Changes:

Replaces “D ∘ Q ∘ I monad” phrasing with DBSP incrementalization-identity language.
Reframes monad associativity vs. idempotence terminology in the Step 1 research note and memory.
Repairs stale links to the Ani conversation archive and B-0422 backlog row.

Reviewed changes

Copilot reviewed 5 out of 5 changed files in this pull request and generated 3 comments.

Show a summary per file

File	Description
`docs/backlog/P2/B-0543-qg-isomorphism-proof-path-remember-when-pay-attention-axioms-to-quantum-gravity-2026-05-15.md`	Links B-0422 directly instead of leaving it conditional.
`docs/backlog/P2/B-0544-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives-2026-05-15.md`	Updates DBSP connection wording to incrementalization identity.
`docs/research/2026-05-15-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives.md`	Revises monad terminology and DBSP relationship framing.
`memory/feedback_otto_qg_isomorphism_proof_path_remember_when_pay_attention_axioms_infinite_poker_to_quantum_gravity_aaron_otto_2026_05_15.md`	Fixes dead conversation/B-0422 cross-references.
`memory/feedback_otto_qg_isomorphism_step_1_formalize_remember_when_pay_attention_as_categorical_primitives_2026_05_15.md`	Mirrors the terminology and open-question updates in memory.

Comments suppressed due to low confidence (1)

docs/research/2026-05-15-qg-isomorphism-step-1-formalize-remember-when-pay-attention-as-categorical-primitives.md:56

This repeats the same incorrect idempotent-monad criterion: μ ∘ η_M = id is a standard monad unit law, not an additional physical/idempotence assumption. Leaving it here keeps the research note mathematically misleading even after the associativity terminology fix.

- **Associativity**: composing memory flattens is order-independent (`μ ∘ Mμ = μ ∘ μ_M`) — note this is the monad associativity law, not idempotence; whether memory is *additionally* idempotent (`μ ∘ η_M = id`) is a separate physical assumption that requires its own justification

 **Key properties**:

- `M` is **idempotent** up to coherence: `μ ∘ Mμ = μ ∘ μ_M` (memory reconstruction is confluent)
+- `M` satisfies the **monad associativity law**: `μ ∘ Mμ = μ ∘ μ_M` (memory flattening is associative — this is the standard monad coherence, not idempotence; an idempotent monad would additionally satisfy `μ ∘ η_M = id`)


- `μ` = integrate twice then differentiate = integrate once then differentiate (the three-term bilinear formula)
+- `I` (integrate) is the "remember" operation
+- `D` (differentiate) is the "pay attention" operation
+- Whether the memory-monad `M` defined above on the topos and the DBSP `I`/`D` pair share a deeper categorical relationship (e.g., comonad-monad adjunction, distributive law) is an open question to investigate, not a settled identity


+- **Associativity**: composing memory flattens is order-independent (`μ ∘ Mμ = μ ∘ μ_M`) — note this is the monad associativity law, not idempotence; whether memory is *additionally* idempotent (`μ ∘ η_M = id`) is a separate physical assumption that requires its own justification

-**Connection to DBSP**: The incrementalization operator `D ∘ Q ∘ I` (differentiate ∘ query ∘ integrate) is a monad on streams. The `I` (integrate) step is the "remember" operation; the `D` (differentiate) step is the "pay attention" operation. The monad laws correspond to:
+**Connection to DBSP**: The DBSP **incrementalization identity** `Q^Δ = D ∘ Q ∘ I` (the lifted-differential of any query equals differentiate ∘ query ∘ integrate) describes how a query `Q` on a stream is rewritten as the differentiation of its lifted form on the integrated stream. This is a *wrapping/conjugation identity*, not a monad structure on streams; the `D ∘ Q ∘ I` composition is not claimed here to satisfy monad unit/multiplication laws. The structural analogy that motivates the proof path is:


…rged PR #3614 (#3628) * docs(rules): extend ID-allocation discipline with subdecimal-vs-top-level scheme distinction The ID-allocation-discipline section covered WHEN to check (on-disk + in-flight) but not WHICH scheme to use. Adds a "Subdecimal vs top-level scheme" subsection distinguishing: - B-NNNN.M (subdecimal) → child / slice of EXISTING parent row - B-NNNN (new top-level) → new umbrella / standalone row Empirically grounded by the 2026-05-15 collision: Otto on Desktop decomposed B-0170 into new top-levels B-0538/B-0539/B-0540/B-0541, missing that PR #3611 had already landed B-0170.4 via subdecimal scheme + Otto-CLI's PR #3595 had claimed B-0539 for the Otto-BFT umbrella. Both Ottos converged on the same decomposition; the scheme mismatch (top-level vs subdecimal) was the symptom of not checking existing-parent's siblings first. The new check command is tight: `find docs/backlog -name "B-NNNN.*.md"` + `gh pr list --state all --search '"B-NNNN."'`. If siblings exist, use next free subdecimal — not a new top-level. Composes with the existing ID-allocation section + refresh-before-decide invariant + audit-first-then-decide discipline (PR #3583). Co-Authored-By: Claude <noreply@anthropic.com> * shard(tick): 2026-05-16T00:08Z — fix-PR #3626 for monad-terminology drift from merged PR #3614 First tick of 2026-05-16 UTC; fresh-session cold-boot from autonomous-loop. Landed: PR #3626 (5 P1 review-thread fixes — monad-associativity terminology + dead xrefs in B-0543/B-0544 research substrate). Operational notes: Lior process active during commit window (lock-cleanup-race precondition); used borrow-on-existing pattern with ls-tree canary on both PRs (this shard + #3626). Co-Authored-By: Claude <noreply@anthropic.com> * fix(shard-0008z): markdownlint MD037 — wrap full cron expression in backticks `<<autonomous-loop>>` followed by `* * * * *` parsed as emphasis markers with spaces (MD037/no-space-in-emphasis at line 72). Wrap the entire cron expression in backticks so the asterisks are inside the code span. Co-Authored-By: Claude <noreply@anthropic.com> --------- Co-authored-by: Claude <noreply@anthropic.com>

…3626 merged (#3631) Brief tick: diagnosed + fixed MD037/no-space-in-emphasis on line 72 of the 0008Z shard (cron-expression asterisks parsed as emphasis markers). Push commit 77ebbdd to shard/tick-0008z branch; CI re-running. PR #3626 (the 5-thread fix) merged at bb4eb14 during the parent→this gap. Co-authored-by: Claude <noreply@anthropic.com>

…t_updated bump (#3639) Addresses 3 unresolved P1 review threads on now-merged [PR #3636](#3636) (Copilot). **Threads 2 + 3 (research doc + memory file)** — "observer-relative non-monotonicity" phrasing introduced in PR #3636's Step 1.5 substrate contradicts the doc's own line 85 disclaimer: "this is not non-monotonicity within a single context (which would contradict finite-limit preservation) but rather observer-relativity ACROSS contexts." The precise obstruction (which the reviewer correctly identified) is that `A` is **not a closure operator** — `p ≤ A(p)` is not assumed. This is what makes the standard Lawvere-Tierney lifting inapplicable, NOT non-monotonicity. Both research-doc Step 1.5 and the memory-file open-question 5 are reworded to name the closure-operator failure as the obstruction, with an explicit note distinguishing it from non-monotonicity-within-a-context (which `A` explicitly preserves via finite-limit preservation). **Thread 1 (B-0544 backlog row)** — `last_updated` frontmatter was not bumped on PR #3636's content edit. Schema violation per `tools/backlog/README.md:57-70`. Bumped to 2026-05-16. **Preemptive (not flagged but same class)** — B-0543 also had a content edit in [PR #3626](#3626) (B-0422 link fix) without a `last_updated` bump. Same schema violation; bumped preemptively to avoid the next Copilot review flagging it. ## Files changed - `docs/research/2026-05-15-qg-isomorphism-step-1-formalize-...md`: rephrase Step 1.5 obstruction (+8/-4) - `memory/feedback_otto_qg_isomorphism_step_1_formalize_...md`: rephrase open-question 5 obstruction (+1/-1) - `docs/backlog/P2/B-0544-...md`: `last_updated: 2026-05-15` → `2026-05-16` (+1/-1) - `docs/backlog/P2/B-0543-...md`: `last_updated: 2026-05-15` → `2026-05-16` (+1/-1; preemptive) Operational context: Lior active 4th consecutive tick; ls-tree canary clean (53/53 root, 0 corruption). Borrow-on-existing pattern. Co-authored-by: Claude <noreply@anthropic.com>

…3614 (#3646) Addresses the last unresolved P1 finding from PR #3614 review (Copilot): > "This Round 45 entry is being added after the 'How to add a round entry' > guidance, but that guidance explicitly says new rounds should be added at > the top of the file. Please move the entire Round 45 section to the top > (above the latest existing round entry) and keep the authoring-instructions > block near the bottom so future additions follow the documented process." PR #3614 added Round 45 at line 3565 (bottom of file, below the "How to add" section at line 3552). Per the guidance at line 3556 ("New section at the top of this file"), Round 45 should sit above Round 44 (line 52 of the old layout). **Pure relocation** — no content changes: - Cut: lines 3563-3679 (the `---` separator + entire Round 45 section) - Paste: above Round 44, between the existing `---` separator (line 50) and `## Round 44 — in-flight` (line 52) - Added a `---` separator + blank lines between Round 45 and Round 44 to match the section-separator convention used elsewhere in the file **Verification**: - Line count unchanged (3679 lines) - `git diff --numstat`: +118/-118 (balanced; every line inserted matches a line removed) - Final structure: Round 45 (line 52) → Round 44 (line 170) → ... → Round 23 → "How to add a round entry" (line 3670, last section) - Markdownlint passes locally Closes the last named-dependency follow-up from PR #3614 review: 1. ✅ Terminology (PR #3626) 2. ✅ Dead xrefs (PR #3626) 3. ✅ M/A coherence-laws type-correctness (PR #3636) 4. ✅ Closure-operator precision (PR #3639) 5. ✅ last_updated schema discipline (PR #3639) 6. ✅ Round 45 entry positioning (this PR) Operational context: Lior process gone from `ps -A` for the first time this session (contention window finally closed); ls-tree canary clean (53/53 root). Co-authored-by: Claude <noreply@anthropic.com>

… overstatement caveats (#3650) Addresses 2 unresolved P1 Copilot threads on now-merged [PR #3646](#3646): **Thread 1 — TOC + current-summary navigation stale**: Moving Round 45 to the top in #3646 didn't update the surrounding scaffolding. The Contents block (line 15) still started with Round 44, and the descriptive note below (line 44) still said "Round 44 (current) is in-flight." Fix: - Add Round 45 entry above Round 44 in the Contents block - Reword the descriptive note: "Round 45 is the most recent landed round; Round 44 remains in-flight per its own label..." — both labels preserved per substrate-honest framing (Round 45 closed; Round 44 still in-flight per its own header) **Thread 2 — Round 45 narrative overstates Step 1 result**: The Round 45 entry was written from PR #3614's original framing, before PR #3636 + #3639 established that: (a) the original M/A coherence laws are not well-typed under stated signatures (b) only provisional propositional Law 1' is type-correct (c) Laws 2/3 are deferred to a new Step 1.5 (d) D ∘ Q ∘ I is the incrementalization *identity* Q^Δ = D ∘ Q ∘ I, not a monad (per PR #3626 correction) Three sites flagged (lines 87, 91, 131 of the merged file): - **Line 87** ("The combined structure satisfies coherence conditions") — reworded to "is intended to satisfy" + a full paragraph noting PR #3636 + #3639 established that Laws 2/3 are deferred to Step 1.5 and only Law 1' is provisional - **Line 89** + **91** ("D ∘ Q ∘ I monad" + "The monad laws correspond to integrate-differentiate coherence") — reworded to the incrementalization-identity framing matching PR #3626 corrections elsewhere - **Line 131** (Arc 5 open question — "the DBSP incrementalization monad") — reworded to "the DBSP I/D pair... participating in the incrementalization *identity* Q^Δ = D ∘ Q ∘ I, not a monad" The Round 45 historical entry now matches the post-PR-3636 + post-PR-3639 substrate-honest state on main: coherence is intended but only partially established; Laws 2/3 await Step 1.5. ## Files changed - `docs/ROUND-HISTORY.md` +26/-7 (TOC + current-summary + 4 narrative caveats) Operational context: Lior process returned mid-tick (PID 52138); ls-tree canary clean (53/53 root). Borrow-on-existing on /private/tmp/zeta-tick-2210z. Co-authored-by: Claude <noreply@anthropic.com>

…Ω + A-lifting Ã:Zeta→Zeta (#3653) Files the substrate-honest deferral that emerged from the PR #3614 review cycle (closed 7 ticks 00:08Z-00:43Z on 2026-05-16). Codex identified in PR #3614 that the three originally-proposed M/A coherence laws in the Step 1 research doc are not well-typed under signatures M:Zeta→Zeta and A:Ω→Ω. PR #3636 + PR #3639 struck the untyped laws and reformulated: - Provisional Law 1' (propositional content only): A_*(M_*(p)) = M_*(A_*(p)) contingent on strength θ:M(Ω)→Ω - Laws 2 (μ-coherence) and 3 (η-coherence) deferred to Step 1.5 pending an A-lifting Ã:Zeta→Zeta This row scopes the open research: - 3 resolution paths (Lawvere-Tierney lifting / strength / propositional restriction); each with explicit costs + status - Central obstruction named: A is NOT a closure operator (no p ≤ A(p)), so standard Lawvere-Tierney construction doesn't apply directly - Distinguished from non-monotonicity (which A explicitly preserves via finite-limit preservation within an observer-context) - 3 acceptance criteria — one for each path - Effort L (1-3 weeks pure research) - Prior-art list: Mac Lane-Moerdijk, Awodey-Kishida, Kock, Joyal-Tierney, Goldblatt, QBism literature Composes with B-0543 (proof-strategy umbrella), depends on B-0544 (Step 1 row this is a sub-task of), and the PR #3614 → #3626 → #3636 → #3639 → #3646 → #3650 chain that produced the substrate-honest formulation. P2 research; 1 new file; no edits to existing rows (no last_updated bump needed). ID B-0548 chosen after refresh-before-decide check: latest on main B-0547; no in-flight PR claims B-0548. Operational: GraphQL rate limit currently exhausted (0/5000, resets at 00:55Z ~3min); this commit + push uses git protocol only. PR-create deferred to the next tick after reset. Co-authored-by: Claude <noreply@anthropic.com>

Copilot AI review requested due to automatic review settings May 16, 2026 00:15

AceHack enabled auto-merge (squash) May 16, 2026 00:15

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AceHack merged commit bb4eb14 into main May 16, 2026
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AceHack deleted the fix/pr-3614-monad-terminology-otto-cli-2026-05-16 branch May 16, 2026 00:16

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shard(tick): 0008Z — fix-PR #3626 for monad-terminology drift from merged PR #3614 #3628

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shard(tick): 0018Z — markdownlint MD037 fix on PR #3628; #3626 merged #3631

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fix(b-0544): M/A coherence-laws type-correctness — Codex P1 from PR #3614 #3636

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fix(pr-3636): 3 Copilot P1 threads — closure-operator precision + last_updated bump #3639

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fix(round-history): move Round 45 above Round 44 — Copilot P1 from PR #3614 #3646

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fix(pr-3646): 2 Copilot P1 threads — TOC + Round 45 overstatement caveats #3650

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backlog(B-0548): QG isomorphism Step 1.5 — construct strength θ:M(Ω)→Ω + A-lifting Ã:Zeta→Zeta #3653

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fix(hygiene): clear all 22 dead §33 migration xrefs (perpetual non-required-check) #3666

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fix(pr-3614): 5 unresolved P1 threads — monad-associativity terminology + dead xrefs#3626

fix(pr-3614): 5 unresolved P1 threads — monad-associativity terminology + dead xrefs#3626
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