Optimize cyclic-deferred frames and phase-aware role compilation (kappa = 1.11513943837e-4)

[Th0rgal]

Summary

Extends the research/cyclic-deferred package on top of eumemic's PR #117 complex DAG (inputs/complex-dag.json.gz, retained byte-for-byte with SHA-256 3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b) and PR #114's saturated-frame / literal reflection audit package, advancing the conditional exponent saving from PR #114's $\kappa = 1.09281094468 \times 10^{-4}$ (109281094468 / 10^15) to:

$$\kappa = 1.11513943837 \times 10^{-4} = \frac{111513943837}{10^{15}} > 2^{-14}$$

with complex saving:

$$a_{\text{complex}} = \frac{111538935}{10^{12}} = 1.11538935 \times 10^{-4}$$

(+2,233,838 grid points on $a_{\text{complex}}$ over PR #114's 109305097 / 10^12, and +6.72% over PR #117's $\kappa = 1.044939 \times 10^{-4}$). Supersedes PR #114, PR #117, PR #118, and PR #120 while preserving all physical ledgers, literal forward/reflected scalar-charge audits, and upstream attributions.

Also fixes a bug in PR #114's research/cyclic-deferred/complex_deferred.py (line 557 wrote json.dumps(out, indent=1) instead of indent=2, causing verify.py to fail in test_controls.py with Source hash mismatch: complex-profile.json after regeneration).

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Technical Contributions

All four improvements operate purely on the $\mathbb{F}_2$ frame assignment, role-compilation schedule, and deferred readout selection on the unchanged PR #117 graph ($h = 24, v = 2024, c = 91770, q = 8120, \text{links} = 71185, R = 28705, W = 124390992, \text{total_rank} = 71647349312$):

1. Radical-Complement Initial Frame Lifting (U2):

   • In PR Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114, whenever the top-down orthogonal kernel intersection $W_x = \ker(K_x) \cap \bigcap_{t \in \text{succ}(x)} U_t$ at an addition node $x$ had a non-zero symplectic radical, U[x] was dropped all the way down to the elementary label envelope $E_x = \text{envelope}(x)$ (dropping 51,781 of the 91,770 addition nodes).
   • Because $E_x \subseteq W_x$ is always nondegenerate over $\mathbb{F}_2$, we decompose $W_x = E_x \oplus (W_x \cap E_x^\perp)$ and extract a maximal nondegenerate direct complement $C_x = \text{sat_nonsingular_part}(W_x \cap E_x^\perp)$, setting $U_x = E_x \oplus C_x$. This keeps $E_x \subseteq U_x \subseteq W_x$ nondegenerate and nested while lifting 69,450 addition nodes prior to placement and expanding initial copy-role candidate subspaces.

2. Phase-Aware Role Compilation & Target-Reach Sacrifice Ordering:

   • In the role compiler, a copy role $f$ created by ('copy', piv, f, x) at node $x$ is dragged into Phase 1 (touched) whenever piv is subsequently touched by a Phase-1 operation (either via a later copy at $x$ or via free[0] at a descendant of $x$).
   • Partitioning free(x) into centre-reaching uses (yes_c) and non-centre-reaching uses (non_c), assigning k0 = non_c[0] (chosen as the use in non_c with the largest target reach $|\text{u_reach}|$) to piv, emitting yes_c copies first, and emitting non_c[1:] copies last (after all Phase-1 operations on piv at $x$):
     • Reduces phase_one_ops from 18,844 to 16,353 (-2,491),
     • Reduces phase_one_roles (touched) from 13,555 to 11,064 (-2,491),
     • Expands copy-role deferral candidates from 6,385 to 8,876 (+39.0%), and
     • Cuts the mean target reach of copy-role candidates in half from 8.67 to 4.36.

3. Lazy Effective-Target Placement & Exact-Moment Local Search:

   • Replaces static one-shot candidate ordering with a lazy priority queue weighted by $2^{\dim(X)} / (r \cdot r_{\text{eff}})$, where $r_{\text{eff}}(s, X) = |{t \in \text{reach}(s) : X \notin \text{byT_set}[t]}|$ counts targets not already carrying the exact subspace $X$, re-inserting candidates whenever intersection shrinks $\dim(X)$ or $r_{\text{eff}}$.
   • Follows placement with cached steepest-ascent local search under the exact moment objective, pruning or snapping down net-negative singleton and small-cluster target-front levels (4,464 deferred roles retained with total dimension 59,912).

4. Bidirectional & Plateau-Peeling Frame Sweeps (optimize_U_for_placed):

   • For any role $s$, the internal steps along holds[s] partition $h - \dim(\sigma_s)$ into positive increments $\Delta_i$. Since $t \mapsto t \ln(m/t)$ is strictly concave (subadditive), intermediate steps strictly between adjacent frames split one larger step into smaller steps and increase the moment.
   • Alternating bottom-up and top-down sweeps over $U_x \in [L_x, W_x]$ with directional $\Delta c = 0$ tie-breaking and connected-component plateau peeling collapses redundant intermediate role-chain steps while maintaining all $\mathbb{F}_2$ nondegeneracy and nesting invariants.

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Comparison Across Cyclic / Deferred Witnesses

Witness	Additions $c$	Links	Roles $R$	Phase-1 Roles	Deferred Roles	Complex Saving $a_{\text{complex}}$	Certified $\kappa$
PR #117 (eumemic)	91,770	71,185	28,705	13,555	2,000	104,515,000 / 10^12	1.044939e-4
PR #114 (eumemic)	91,770	71,185	28,705	13,555	4,706	109,305,097 / 10^12	1.09281094468e-4
This PR	91,770	71,185	28,705	11,064	4,464	111,538,935 / 10^12	1.11513943837e-4

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Verification

python3 -B research/cyclic-deferred/verify.py
python3 -B research/cyclic-deferred/test_controls.py
python3 -B research/cyclic-deferred/certificate.py

All 16 negative controls in test_controls.py, the isolated full regeneration in verify.py, the $\mathbb{Z}/(2^{61}-1)$ arbitrary-scratch replay, and the literal forward/reflected scalar-charge audit in reflection_audit.py pass with assertions enabled.

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Attribution & Provenance

• eumemic (with Anthropic Claude and OpenAI Codex assistance): PR Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional κ = 1.044939e-4 #117 complex DAG (inputs/complex-dag.json.gz, unchanged) and PR Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114 saturated-frame integration and literal reflection audit (research/cyclic-deferred/).
• Avi Eisenberg / ikeboy (with Anthropic Claude assistance): PR Interval strips and core-aware pair assembly: conditional κ = 4986133/10^11 (5101691/10^11 stacked with #57) #62 and PR Deferred readouts on both stopped networks: conditional κ = 8.58478e-5 #110 complex role compiler and frame-lifting machinery.
• Rohan Arun (with Anthropic Claude assistance): PR Cyclic interval strips on both axes: conditional κ = 8.578151200855e-5 #111 / PR Deferred readouts on the cyclic-strip complex network: conditional κ = 9.39074e-5 #113 cyclic strip formulation.
• Swapnil Jain: Round-seven bit word (inputs/witness_23.json.gz, inputs/deferred_23.json.gz, unchanged), lifted frames, $V$ leaves, and deferred readouts.
• icekylinx: PR Stopped product-ring interchange and rational centers for conditional kappa = 7.79476e-5 #104 stopped-product and copied-center interfaces.
• Zhihao Chen (jacklightChen), Aurel Prosz (Paureel), and RaD / hipotures: Two-stage topology, reflected bit integration, and exact bulk assembly.
• Thomas Marchand (Th0rgal) (with Google Antigravity assistance): Radical-complement initial frame lifting, phase-aware role compilation with target-reach sacrifice ordering, lazy effective-target placement, exact-moment local search, and bidirectional/plateau-peeling frame sweeps.

[Mister-Meeseeks]

Thank you @Th0rgal. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Radical complements, phase-aware roles, lazy deferral and plateau pricing.

Review and limits: Exact-head CI evidence; whole-profile accounting, not additive local savings.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 2c97e8ab1578d05d0aacf03903f458b088c7dd50. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.