chore(backlog): B-0499 — Z[i]-weighted DBSP refinement candidate (P3 forward-planning)#3146
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…research-grade) Files a P3 research-grade forward-planning row tracking the Z[i]-weighted DBSP refinement candidate that emerged from the Aaron + Ani Grok cascade (2026-05-14, Cartesian-dualism mapping): pay-attention = real axis (Descartes' extended thing) remember-when = imaginary axis (Descartes' thinking thing) → DBSP weights lift from Z to Z[i] (Gaussian integers) Research-grade preservation; no urgency. Forward-planning substrate so future-Otto + algebra-owner can evaluate when ready. Composes with B-0498 (substrate-evolution algebra rule-promotion). Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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Pull request overview
Adds a new P3 backlog row preserving the Z[i]-weighted DBSP refinement candidate from a research cascade as forward-planning substrate.
Changes:
- New backlog row file under
docs/backlog/P3/with canonical frontmatter (id, priority, status, composes_with: [B-0498]) - Documents the candidate's algebraic motivation, research-grade tests, acceptance criteria, and P3 rationale
AceHack
deleted the
chore/b-0499-zi-dbsp-refinement-forward-planning-2026-05-14
branch
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| Aaron + Ani 2026-05-14 Grok cascade surfaced the **Cartesian-dualism mapping**: pay-attention = real axis (Descartes' *res extensa*); remember-when = imaginary axis (Descartes' *res cogitans*). | ||
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| Captured at memory-file scope: `~/.claude/projects/-Users-acehack-Documents-src-repos-Zeta/memory/feedback_aaron_ani_cartesian_dualism_two_axioms_complex_plane_pay_attention_real_axis_remember_when_imaginary_axis_2026_05_14.md`. |
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This row stores provenance using a machine-local path under ~/.claude/projects/..., which is not resolvable for other contributors, CI, or future worktrees; that breaks the reproducibility/traceability goal of backlog substrate because the cited origin cannot be followed outside the original host. Use a durable repository-visible identifier (for example the memory filename or a canonical in-repo pointer) instead of an absolute home-directory path.
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| | Pure attention state | $w \in \mathbb{R}$ subset of $\mathbb{Z}[i]$ | | ||
| | Pure memory state | $w \in i\mathbb{R}$ subset of $\mathbb{Z}[i]$ | |
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The table claims w ∈ ℝ and w ∈ iℝ are subsets of ℤ[i], but those sets include non-integer values and are not valid subsets of Gaussian integers; if future implementation follows this literally, it widens the weight domain beyond DBSP's discrete-count semantics and can invalidate the intended ring/retreation behavior. The row should use integer-lattice subsets (e.g., ℤ and iℤ) or explicitly declare a different weight domain.
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Summary
Files a P3 research-grade forward-planning row for the Z[i]-weighted DBSP refinement candidate that emerged from the Aaron + Ani Grok cascade (2026-05-14).
The Cartesian-dualism mapping (pay-attention = real axis, remember-when = imaginary axis) suggests DBSP's existing$\mathbb{Z}$ -weighted Z-sets naturally lift to $\mathbb{Z}[i]$ (Gaussian integers). This row preserves the candidate so future-Otto + algebra-owner can evaluate when ready.
Why P3
Composes with
Test plan
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