SCC — Current Research Status (May 2026, CV-1.17)

This is a living page. It documents the state of Soft Cognitive Cohesion — the research thread I am currently most active on — at the level of granularity that lets a collaborator (or future me) pick up where things stand without re-reading a year of notes.

Last updated: 2026-05-15 (W7 EOD close).   Canonical version: CV-1.17 (sealed 2026-05-15, W7 Day 5 EOD).   Full specification: see the Canonical Spec note.

What SCC is, in one breath#

A mathematical theory of how coherent formations emerge prior to discrete objecthood. The primitive is a soft cohesion field

over a relational support space. Objects are a distinguished limit of the formation space, not its starting point. Four independent energy terms govern closure, separation, boundary, and transport; a diagnostic vector $\mathbf{d}=(\mathrm{Bind},\mathrm{Sep},\mathrm{Inside},\mathrm{Persist})$ reads off formation state.

Theorem ledger (CV-1.17)#

68 Category A + 19 Category B + 6 Category C + 5 Retracted = 98 claims, ~70% fully proved.

Category A — Fully proved (68)#

The Cat A roster carries forward the CV-1.5 set (existence T1, closure fixed point T6a/T6b, axiom monotonicity T-A2, phase transition core T8-Core, axiom consistency T20, gradient flow T14, stability duo T3 / T6-Stability, enhanced metastability T7 with $p=0.037$, $\Gamma$-convergence T11, the four QM results QM1–4, the Predicate–Energy Bridge, Deep Core Dominance 2b, T-Bind-Proj / T-Bind-Full (both Cat A for all ${\tau }_{\mathrm{cl}}\in (0,1)$ per the Phase 13 upgrade — confirmed by the 2026-05-04 W6 G2 audit which caught a stale Cat B / Cat C shadow in theorem_status.md), Propositions 1.1 / 1.2 and Theorem 3.1, Persistence Threshold Equation, the W4 Pre-Objective Mechanism cluster T-PreObj-1 / T-PreObj-1G / Lemma 4 / F-1 Resolution Corollary, the W4-extended Goldstone result T-V5b-T, and the W5 Day 1 G0 σ-framework supporting structures T-σ-Lemma-1/2/3 + T-σ-Theorem-3) and adds, since 2026-04-27:

• CV-1.5.1 D-6a Multi-Static (3 Cat A definitional) — T-Commitment-14-Multi-Static, T-σ-multi-A-Static, T-σ-multi-D-Static. Defined on the multi-formation interior ${\tilde{\Sigma }}_M^{K_{\mathrm{field}},\circ }$ (Option A pragmatic; corners deferred to NQ-248 W7+); ${\sigma }_{\mathrm{multi}}=({\sigma }^A,{\sigma }^D)$ is a joint invariant under the wreath product $\mathrm{Aut}(G)\wr S_{K_{\mathrm{act}}}$. The within-formation σ-tuple multi-set is invariant under $S_{K_{\mathrm{act}}}$ permutation in the well-separated regime, and the between-formation cohomology pull-back is a conjugacy-class label in $H^1(\mathrm{Aut}(G)\wr S_{K_{\mathrm{act}}};\mathrm{Stab}({\mathbf{u}}^{\ast }))$.
• CV-1.5.1 V5b-T-zero (sub-statement, Cat A def) — Sub-spinodal translation-invariant regime: ${\mu }_{\mathrm{Gold}}^{V5b-\mathrm{T}-\mathrm{zero}}=0$ exactly (discrete translation orbit on ${\mathbb{Z}}_L^d$). Replaces the V5b-T' WITHDRAWN entry. Empirical anchor NQ-198f $T_{20}^2/T_{28}^2$ with $|\mu |\le 0.028$ within FD numerical noise.
• CV-1.5.2 T-L1-F (Hard-Bar / Active-Count Bridge) — Cat A conditional under the L1-J regime hypothesis package $(P0)$–$(P11)$. First multi-formation canonical Cat A theorem. On a finite graph $G=(X,E)$ and a shared-pool multi-formation state $\mathbf{u}\in {\tilde{\Sigma }}_M^{K_{\mathrm{field}}}(G)$, $K_{\mathrm{bar}}^{{\ell }_{\min }}(U(\mathbf{u});G)=K_{\mathrm{act}}^{\epsilon }(\mathbf{u})$, and the map ${\mathcal{A}}_{\mathrm{bar}}:A^{\epsilon }\to {\mathrm{Bars}}_0^{\mathrm{term}}(U;G)$ is a bijection from active slots to dominant terminal $H_0$ bars. NOT a global identity — T-L1-F does NOT solve OP-0005 or OP-0008, and does NOT establish $K_{\mathrm{soft}}^{\varphi }=K_{\mathrm{act}}$.
• CV-1.6 T-ST-5a (Hard-Depth Topological Locking) — Cat A (W6 D4 Session E, 2026-05-06). A depth-disconnected stereo graph forces $K=2$ topologically: $\Delta E=+\infty$ (state-space disconnection). No P-F flag. Gaps G1–G4 closed (Session E): graph topology alone suffices (Lemma 3 not required); merger/decay distinction, A-STRICT assumption, and threshold convention addressed.
• CV-1.7 T-OP6-B (PersRidge Boundary Equivalence, Phase-Sep Regime) — Cat A conditional under H1–H5 (W6 D4 Session K, 2026-05-06). OP-0006 RESOLVED. Under the phase-separation regime on a connected finite graph: $d_H(\mathrm{PersRidge}(u^{\ast }),\partial {\Omega }^{\ast })\le 2(\alpha /\beta {)}^{1/2}$. B1 topological separator, B2 curved Hausdorff ($C<1.37$ under H4), B3 stereo conditioning (hard-cut D-ST-1), and B4 ${\rho }_{\mathrm{bd}}=1/(4\xi )$ all closed. exp06: shadow 5/5 ratio 4.09, blur 5/5 ratio 50.8.
• CV-1.7 T-P-F-ε0 (Gibbs Measure Continuity at $\epsilon =0$) — Cat A (Session I, 2026-05-06). ${\mu }_{\epsilon }\Rightarrow {\mu }_0$ weakly as $\epsilon \to 0$ under H1–H4. NOT P-F-A1 — does not prove spectral gap, Eyring-Kramers, $T_{\ast }$ existence, or Lions-Sznitman construction.
• CV-1.8–CV-1.9 P-F-A1 Package I (T-PF-A1-AR / T-PF-A1-SDE / T-PF-A1-GI / T-PF-A1-PE) — all Cat A (Sessions O + P, 2026-05-06). P-F-A1 Package I fully Cat A. (AR) Affine reduction proves ${\tilde{\Sigma }}_M$ is a bounded convex polytope — polytope SDE well-posed. (SDE) Lions-Sznitman Theorem 1 (convex domain) + Tanaka uniqueness establishes the reflected Langevin SDE on ${\tilde{\Sigma }}_M$. (GI) Unique Gibbs invariant measure ${\pi }_{T_{\ast }}$ via zero-current + L²(π) kernel argument. (PE) Poincaré inequality ${\lambda }_1\ge ({\pi }^2/n)\exp (-\mathrm{osc}(\tilde{\mathcal{E}})/T_{\ast })$ + exponential ergodicity via Payne-Weinberger + Holley-Stroock. NOT Eyring-Kramers — Package II (explicit rates) remains open (OP-0021, W9+).
• CV-1.12 T-Temporal-Identity (a) — Existence — Cat A (W7 D1–D2, 2026-05-11/12). Closed via H-SINK: the Bigot–Cazelles–Papadakis (2019) Sinkhorn Lipschitz framework applied in the SCC cost class gives $L_g\le L_c$; combined with P-F-A1 Package I, this discharges the existence half of T-Temporal-Identity. Parts (b) (uniqueness under the margin condition) and (d) (reduction to $K=1$) remain, planned for CV-1.18. Part (c) (interior persistence) remains Cat C (OP-0011).
• CV-1.13 through CV-1.17 — additional Cat A registrations (W7, 2026-05-12 → 2026-05-15). Sub-theorem promotions accompanying the SEAL increments (H-MORSE broadness closure ancillary results, T-Temporal-Identity supporting lemmas, kernel-side regularity riders). Authoritative row-by-row list lives in CV-1.17_SEAL.md (~470 lines) §"Cat A increment audit"; the net W7 Cat A delta is +14.

Category B — Proved with structural parameter (19)#

Original 5 (pre-W6):

• Barrier exponent ${\gamma }_{\mathrm{eff}}\approx 0.89$ — empirical fit, branch / path / manifold conditioned.
• T-Birth-Parametric (general non-$D_4$ graphs) — supercriticality on $D_4$-symmetric graphs is Cat A; general graphs remain Cat B.
• T-d_min-Formula — branch-conditioned regression fit.
• T-Beyond-Weyl — structured spectral perturbation bound; the quantitative 33× factor is config-specific.
• T-σ-Theorem-4 — Retroactive Cat A → Cat B at CV-1.5.1 per Critic 7-agent verdict. Continuum-vs-discrete caveat: canonical statement (ii) (${\mu }_0={\mu }_1$ from $A_2/A_1=4$) is a continuum-limit prediction not realised on finite discrete grids $L\le 16$ (NQ-187: ${\mu }_1/{\mu }_0\approx 2$, $p\approx 1.03$). Cat A re-promotion deferred post γ/β/α path closure.

W6 additions (2026-05-06):

• T-ST-5b (Smooth-Depth Barrier Raising) — Cat B (Session G). Full SCC with $E_{\mathrm{cl}}+E_{\mathrm{sep}}$ active raises the merge barrier ~25% over GL-only in the intermediate-β regime (exp02e 6/6 SUPPORTED). GL alone: NULL. Monotone-in-Δz NOT confirmed. Cat A path: monotonicity proof + analytical lower bound on barrier gap.
• T-P-F-ε0-K (Kramers Exponent Stability under Bernoulli Regularization) — Cat B (Session I). Conditional on H5 (Morse stability): $\Delta E_{\epsilon }=\Delta E_0+\epsilon \cdot \Delta R$; ${\Gamma }_B/{\Gamma }_A=\exp (O(\delta ))$ at phase-separated endpoints. NOT P-F-A1. Cat A path: H5 proof + spectral gap.
• T-K-Select-PF (Equilibrium K-Selection under P-F-A1 Package I) — Cat B (CV-1.10, Session R). Pushforward of ${\pi }_{T_{\ast }}$ under $K_{\mathrm{act}}$ defines sector probabilities $\{p_K\}$; $K^{\ast }=\arg {\max }_K{p}_K$. OP-0005-EQ partially resolved. Does NOT resolve OP-0005-DYN (Kramers) or OP-0005-OBS.
• T-K-Select-OBS (Observation-Conditioned K-Selection) — Cat B (CV-1.11, Session Y). Bayesian posterior ${\pi }_{T_{\ast }}(\cdot \mid \mathcal{O})$ over observation-compatible states selects $K_{\mathrm{obs}}^{\ast }$. exp85 ALL PASSED. OP-0005-OBS partially resolved.
• D-ST-1/2/3/4/5 (Stereo-SCC definitions) — B candidates (CV-1.6, in canonical.md §3.9–§3.11, §16; formal canonical-row promotion pending). Stereo adjacency (hard/smooth), field space ${\mathcal{F}}_M(P)$, $K_{\mathrm{act}}$ as PersComp observable, topological sector / partition function / Kramers rate, backprojection / pullback / prior-likelihood separation.

W7 additions (2026-05-11 → 2026-05-15):

• T-ACT-KERNEL-COMP→REL (Kernel-Composed Active-Count → Relational Reading, conditional lift) — Cat B (CV-1.15 registered; conditional lift activated at CV-1.17, 2026-05-15). The active-count diagnostic composed through the kernel-side composition operator ${\circ }_K$ lifts to a relational reading via the explicit step-additive bijection inherited from T-L1-F. Activated by T-CC-StableK-Kernel; the CV-1.15 forward-reference is now discharged. Cat A path: closing the conditional lift on a thicker stratum than the W7 separator-stability clause.
• T-CC-StableK-Kernel (Kernel-Composed Compositional Consistency) — Cat B (CV-1.17 SEAL, W7 D5 EOD, 2026-05-15). H-COMP-KERNEL CLOSED. Under the kernel-composition regime (KC1–KC4, mirroring the L1-J multi-formation interior package plus a separator-stability clause), $K_{\mathrm{act}}^{\epsilon }({\mathbf{u}}_1{\circ }_K{\mathbf{u}}_2)$ is given by the explicit step-additive map on terminal $H_0$ bars, and the active-slot → dominant-bar bijection composes correctly under ${\circ }_K$. Absorbs the CV-1.14 working candidate. Cat A path: thicker-stratum closure of KC3 or residual-separator absorption into the conditional lift on T-ACT-KERNEL-COMP→REL. Authoritative theorem block: canonical.md §13 Cat B (CV-1.17).
• CV-1.13 through CV-1.17 ancillary Cat B promotions — three additional Cat B rows registered alongside the SEAL increments (H-MORSE broadness leg ancillary results + T-Temporal-Identity supporting Cat B target on the margin-condition direction + a kernel-side regularity rider). Row-by-row list lives in CV-1.17_SEAL.md §"Cat B increment audit". Net W7 Cat B delta: +5.

In addition, T-σ-Multi-1 (Multi-Formation Goldstone-Pair Instability) is a CV-1.5.1 Cat B target (sketch only; Cat A pending NQ-242 anchor). V5b-F-empirical is a Cat B sub-statement target (NQ-198a; quantified $C(\beta =4,{\xi }_0=0.5)\approx 13.2\pm 0.4$).

Category C — Conditional (6 + Cat C riders + new finding)#

• T-Persist-1(d) — exact-threshold preservation under structural condition $\beta >7\alpha$.
• T-Persist-Full — composition through (d).
• T-Persist-K-Sep — well-separated regime conditions (WS, SR). (Per the canonical Erratum 2026-04-07 the Cat-C example list contains T-Persist-K-Sep; cross-file C-vs-B placement is acknowledged drift deferred to a future audit pass per the 2026-05-04 W6 G2 audit note.)
• T-Persist-K-Weak — weakly-interacting regime conditions (WI, SR, NB-K).
• T-Persist-K-Unified — parametric (PS, ND, BC′-K, TC-K, SR-Λ), 100% geometric-Lambda agreement on exp46–47.
• V5b-F (W4-extended new finding, 2026-04-26) — Partial Goldstone on boundary-modified graphs; quantified at CV-1.5.1 as (V5b-F-empirical) Cat B target sub-statement: ${\mu }_{\mathrm{Gold}}^{V5b-\mathrm{F}}\approx C(\beta )\cdot \Vert \partial S\Vert /n$ with $C(\beta =4,{\xi }_0=0.5)\approx 13.2\pm 0.4$ (NQ-198a 6 corner-saturated, SNR 35). Refutes the Phase 3 heuristic and the Day 3 §4 derivation. Full $C(\beta ,{\xi }_0)$ is open via NQ-198k W6+.
• T-σ-Lemma-2 sub-statement riders — sub-statements (v) Courant upper bound and (vi) $G_u$-orbit divisibility are Cat C riders within the Cat A entry.
• T-Temporal-Identity (c) — Interior persistence (W7 D1–D2, CV-1.12) — Cat C, conditional on OP-0011 (transport kernel exact form). Existence half (a) was lifted to Cat A at CV-1.12 via H-SINK; (c) remains the interior-persistence statement that needs an exact-form transport kernel before it can promote.

Retracted (5)#

• Theorem 3.3 (general $\tau$ form of ${\bar{r}}_0$) — falsified.
• T-Merge (c) / T-Merge (d) / T-Merge (e) — merge path manifold error.
• K-Saddle Conjecture — pre-v2.1 retraction.

A 5/5 clean sweep on the five single-formation predictions (historical record):

Open Problems Catalog (post-W5 + 2026-05-04 unified)#

Note on the catalog file. Until 2026-05-04 the project carried two files: THEORY/canonical/theorem_status.md (theorem index) and THEORY/canonical/open_problems.md (OP catalog). They had drifted into using two incompatible OP-ID systems. On 2026-05-04 the OP catalog was merged into theorem_status.md as a unified Open Problems Catalog section, and open_problems.md was deleted. Do not reference open_problems.md — it no longer exists. All OP body content (Statement, Evidence, Resolution mechanism, Sub-item tables, References, Statistics, Critical Path) now lives under theorem_status.md §Open Problems Catalog.

The W4 close (2026-04-24) reduced the Critical count from 3 to 0 by SPLIT-RESOLVING OP-0001 (F-1 K=2 vacuity), LAYER-CLARIFYING OP-0002 (M-1 K=1 preference), and SIDESTEPPING OP-0003 (MO-1 Morse inapplicability). Those resolutions are unchanged. The post-W5 active catalog is:

Net post-W7 active count: 3 High + 9 Medium + 4 Low = 16 active OPs (plus 6 closed/resolved entries OP-0001 / OP-0002 / OP-0003 / OP-0004 / OP-0006 / OP-HMORSE-BROADNESS retained for traceability). The W7 medium count grew because the H-MORSE umbrella was deliberately decomposed into seven separable sub-items (1 closed, 5 medium open, 1 low open) — a finer registration that lets each sub-item move independently, at the cost of a higher catalog count. OMS sub-OPs OP-OMS-032b / 033b / 034b / 034c are non-blocking formalities tracked in THEORY/working/observer_moduli/open_problems.md.

Most recent canonical edits (CV-1.5.2 → CV-1.17)#

• 2026-05-02 (W5 Day 6): T-L1-F merged Cat A conditional. CV-1.5.1 → CV-1.5.2. 45A → 46A. 61 claims.
• 2026-05-04 (W6 Day 1): T-Bind Cat A confirmed; T-σ-Theorem-4 continuum caveat added; open_problems.md merged into theorem_status.md (deleted). Strategic plan redesigned.
• 2026-05-06 (W6 Day 4, Sessions A–Y): CV-1.5.2 → CV-1.6 → … → CV-1.11 in a single work session. Net: +8A +9B = +17 claims. Key promotions: T-ST-5a Cat A (CV-1.6); T-OP6-B Cat A + T-P-F-ε0 Cat A (CV-1.7, OP-0006 RESOLVED); P-F-A1 Package I fully Cat A (CV-1.8–CV-1.9); T-K-Select-PF Cat B (CV-1.10, OP-0005-EQ partial); T-K-Select-OBS Cat B (CV-1.11, OP-0005-OBS partial).
• 2026-05-07 (W6 Day 5): DECLARATION.md DECL-1.0 (6 epistemological commitments) + hypothesis_tree.md HT-3.0 (dependency graph, critical path for CV-1.12) created.
• 2026-05-08 (W6 Day 6, Sessions 7–8): OMS-2.0 promoted from Conditional Accepted → Accepted — Full. OP-OMS-034 CLOSED (temporal $G_{\mathrm{cw}}^{\mathrm{temp}}=\{e\}$ confirmed; 19-branch Δ³ map). Appendix OMS §A–§M (Static + Temporal) added to canonical.md.
• 2026-05-08 (W6 EOD): theorem_status.md header + canonical.md DEVELOPMENT NOTICE updated to CV-1.11 state. Weekly summary written. Targeted CV-1.12 via H-SINK (T-Temporal-Identity a/b/d, +3A, Bigot–Cazelles–Papadakis route).
• 2026-05-11/12 (W7 D1–D2): CV-1.12 — H-SINK closed via Bigot–Cazelles–Papadakis Sinkhorn Lipschitz framework ($L_g\le L_c$ in SCC cost class). T-Temporal-Identity (a) Cat A. Parts (b)(d) deferred to CV-1.18.
• 2026-05-12 (W7 D3): CV-1.13 SEAL — cross-file audit of CV-1.12. OP-HMORSE-BROADNESS CLOSED (H-MORSE partially closed via the kernel-side broadness leg); six new OP-HMORSE-* sub-items registered.
• 2026-05-13/14 (W7 D4): CV-1.14 reserved (forward-reference to kernel-composed compositional consistency working candidate). CV-1.15 SEAL + CV-1.16 SEAL — intermediate audits; T-ACT-KERNEL-COMP→REL registered with explicit forward-reference (conditional lift queued).
• 2026-05-15 (W7 D5 EOD): CV-1.17 SEAL — T-CC-StableK-Kernel Cat B absorbed the CV-1.14 working candidate; H-COMP-KERNEL CLOSED; T-ACT-KERNEL-COMP→REL conditional lift activated; CV-1.15 forward-reference discharged. Stage A Hygiene (6 in-place edits) + Stage B SEAL. CV-1.17_SEAL.md (~470 lines) certifies CV-1.14 reserved-version absorption, non-overclaim audit, and CV-1.18 target list. First _archive/ cohort (working/parking/ → _archive/working_parked_2026-05/, 14 files). HT-3.7 → HT-3.8. Net W7: +14A +5B +1C = +20 claims. CV-1.11 → CV-1.17. 78 → 98 claims.
• 2026-05-15 (W7 EOD): theorem_status.md header + canonical.md frontmatter + release-state heading synchronized to CV-1.17 state. Weekly summary written at THEORY/logs/weekly/2026-05-W2/weekly_summary.md. Next target: CV-1.18 via T-Temporal-Identity (b)(d) + σ-inheritance OP-0008 partial + P-F-A1 Package II first sub-result.

Implementation#

scc/ package — 215 passed + 1 xfailed (216 collected)#

The 175 → 215 jump came from test modules added on 2026-04-28 (test_outside_spinodal_override.py) and 2026-04-30 (test_aut_g_stabilizer.py, test_sigma_rich.py, test_sigma_rich_integration.py); earlier CHANGELOG entries that say "196/196" were corrected by the 2026-05-04 audit. The authoritative measurement is 215 passed, 1 xfailed in 231.57s.

The pipeline is canonical: graph → params → operators → energy → optimizer → diagnostics.

Experiments — exp1 through exp97 + W4-extended + W5 numerical#

The numbered experiment series runs exp1 through exp97, plus the W4-extended E-0090 through E-0097 cluster anchoring T-PreObj / T-V5b-T / σ supporting structures, plus the W5 numerical work that does not consume an expN slot:

• NQ-141 R23 32×32 — single-graph σ empirical Cat A anchor for T-σ-Lemma-2 / Theorem-3 (W4-04-25).
• NQ-170c 2D torus L = 20 ζ = 0.5 overlap 0.97 — anchors T-σ-Lemma-3 Goldstone–ℓ=1 saturation (W4-04-26).
• NQ-187 σ-Theorem-4 scaling test — $L\in \{4,8,16\}$, $ϵ\in \{\mathrm{0.001..0.1}\}$ on discrete $D_4$ free-BC grids; falsified the continuum $A_2/A_1=4$ degeneracy on finite grids (W6 audit, 2026-05-04).
• NQ-198a V5b-F empirical scaling — 6 corner-saturated configurations; quantified $C(\beta =4,{\xi }_0=0.5)\approx 13.2\pm 0.4$ at SNR 35.
• NQ-198f — V5b-T'-WITHDRAWN (phantom on torus; $|\mu |\le 0.028$ within FD numerical noise).
• L1-I 439 / 1920 = 22.9% feasible on $T_{20}^2$ — empirical anchor for the T-L1-F hypothesis package; best case ${\sigma }_b=0.5$, $\delta =0.02$, $r=0$, ${\ell }_{\min }=0.10$ raw_gaussian.
• L1-H2 stress 5/5 + L1-J PO-1 6/6 — additional T-L1-F anchors.

Promotion pipeline (3-stage, unified 2026-05-04)#

THEORY/logs/daily/YYYY-MM-DD/         (raw chronological record)
                ↓ reorganize by topic
THEORY/working/<topic>.md             (active theory development)
                ↓ proof + review + tests
THEORY/canonical/canonical.md         (authoritative — one-way only)

The earlier 4-stage weekly rotation pipeline (working / topic.md → logs/weekly/YYYY-MM-W<n>/weekly_draft_storming.md → weekly_summary.md → canonical.md) was retired on 2026-05-04 as part of the Pass 2 audit — THEORY/canonical/README.md and THEORY/logs/README.md were rewritten to describe the 3-stage pipeline that the rest of the meta-docs (CLAUDE.md, CONVENTIONS.md, working/README.md, MAIN_PROMPT.md) already used. Weekly summaries are now retained as retrospective synthesis only and are no longer a promotion-pipeline stage.

Repository structure (2026-04-20 reorganisation, 2026-05-04 canonical contents)#

The current repository structure is a clean CODE / THEORY split:

• CODE/ — executable assets: the scc/ package (12 modules), pytest suite (215 passed + 1 xfailed), experiments/ (exp1–exp97 plus W4-extended E-0090–E-0097), papers/ (currently IEEEtran.cls + figures/ + generate_figures.py; the two paper drafts were deleted on 2026-05-04 and will be rewritten from scratch later), and scripts/.
• THEORY/ — theory documents with strict three-way separation:
  • canonical/ — authoritative; canonical.md + theorem_status.md + figures/ + README.md (the previously-separate open_problems.md was merged into theorem_status.md on 2026-05-04 and deleted). Promoted content only.
  • working/ — in-progress development; one file per topic. Notable current resident: the L-M Soft-Count Corollary working draft at THEORY/working/MF/ksoft_kact_bridge_L1M_soft_count_corollary.md (Cat B sketched, R-1 / R-2 / R-3 audit items pending; CV-1.6 promotion target via the L1-M-AUDIT cycle).
  • logs/ — chronological journal; daily/ + weekly/ + monthly/.

The 2026-04-12 "Research OS" reboot — an 8-layer structure with numbered 00_meta/ … 07_archive/ directories and 5-role daily logs — was tried for four days, collapsed under its own scaffolding on 2026-04-16, and was archived on 2026-04-18. The current CLAUDE.md policy explicitly forbids re-introducing the numbered-directory / 5-role / per-item registry structure. The honest "tried and abandoned" record lives in _archive/research_os_2026-04-12/.

W7 outcomes + next session plan#

W7 is closed (2026-05-11 → 2026-05-15). W7 carried three workstreams; all are resolved or audited:

• G1 — H-SINK closure (CV-1.12 target) — DONE (2026-05-11/12). Bigot–Cazelles–Papadakis Sinkhorn Lipschitz framework discharged in the SCC cost class; T-Temporal-Identity (a) Cat A. Parts (b)(d) deferred to CV-1.18.
• G2 — H-COMP-KERNEL closure (compositional consistency) — DONE (2026-05-15, CV-1.17 SEAL). T-CC-StableK-Kernel Cat B; T-ACT-KERNEL-COMP→REL conditional lift activated; CV-1.15 forward-reference discharged.
• G3 — working/parking/ inventory and archive — DONE (2026-05-15). 14 files moved into _archive/working_parked_2026-05/; first instantiation of the _archive/ root.

A fourth workstream — auditing a user-proposed primitive extension ($z_t/S_0/K_{\mathrm{read}}$) — was carried through six audit stages and resolved as Decision C (defer, archive proposal trace): $V=0$, archive-pattern match 6 / 6. The proposal lives in _archive/proposals_2026-05/zt_S0_Kread.md; no canonical change.

Net W7 result (entry → exit):

Next session — CV-1.18 (three queued candidates):

1. T-Temporal-Identity (b) and (d). Margin-condition tightening on (b); reduction-to-$K=1$ on (d). +2 A expected.
2. σ-inheritance OP-0008 partial. A Cat B target on Path B (σ-rich + Φ-rich) is the most likely shape.
3. Eyring–Kramers Package II first sub-result. With H-MORSE broadness closed, the next-easiest dependency is the spectral-gap lower bound (Cat B path); full Package II remains W9+.

Monitoring items: H-SINK Lipschitz constant fine-tune (quantitative tightening of $L_g\le L_c$, no new theorem row) and OP-SB1-084 (registered in W7 hygiene, not yet substantively addressed). Entry point: THEORY/canonical/hypothesis_tree.md (HT-3.8) §CV-1.18 targets + CV-1.17_SEAL.md §"CV-1.18 target list".

Twelve iterations of method (historical)#

The path from brainstorming to the current spec can be read as twelve distinct iterations (this list is unchanged from the 2026-04-27 snapshot — it is a historical retrospective, not a live count):

The W4 / W4-extended / W5 / W6 work since 2026-04-19 is best read off the weekly summaries in THEORY/logs/weekly/ rather than as a thirteenth iteration; the iteration numbering froze at I12.

Papers on this track#

Dedicated SCC manuscripts are currently not in the working tree — the two earlier drafts (paper1_math.tex, paper2_cogsci.tex) were deleted from CODE/papers/ on 2026-05-04 and will be rewritten from scratch. When they reappear, they will appear in the papers index. In the meantime, the closest published-side work is the Axiomatic Framework for Understanding Relations via Gauge-Invariant Cohomology, which establishes the relational substrate underpinning SCC.

Related#

• SCC status, April 2026 (W5 Day 1 G0 close, CV-1.5) — historical snapshot.
• Canonical Specification — the full formal text of SCC (mirrors canonical.md, sealed CV-1.17; includes Appendix OMS §A–§M from CV-1.11 W6 D6).
• Part I — RelationWorld Foundations — the discrete-gauge substrate SCC operates over.
• Perception research track — the public-facing overview page.
• Week 6 weekly (2026-05-08) — Observer Moduli Space, OMS-2.0 Accepted — Full.
• Week 7 weekly (2026-05-15) — six sealed versions, H-COMP-KERNEL closed, first _archive/ cohort.