Perception · W7 — Six Sealed Versions, Compositional Closure, First Archive

W7: 2026-05-11 to 2026-05-15.
Canonical: CV-1.11 → CV-1.17 (+6 versions, +20 claims, 78 → 98 total).
The week's center of gravity: if W6 asked who is looking, W7 asked how do the things they see compose.

Start here

W6 finished by stating that observer-dependence in SCC is a structural feature with a codim-1 geometry on $\Delta^3$ . That answer settled Q6 but left Q3 (how do formations evolve) and Q4 (how does discrete count emerge) entangled with an open compositionality question: when two kernel-composed formations are read out together, is the resulting active-count diagnostic stable?

W7 closed that question. The week's deep result, T-CC-StableK-Kernel (Cat B, CV-1.17), proves compositional consistency under kernel composition and activates the conditional lift T-ACT-KERNEL-COMP→REL that had been queued since CV-1.15. The forward-reference inside CV-1.15 is now retroactively discharged.

Two other things happened that matter more than they look:

THEORY/working/parking/ was emptied. Fourteen stale files moved into a new _archive/working_parked_2026-05/ directory — the first instantiation of the _archive/ root. From now on, "we tried this and parked it" is a separately readable layer, not a quiet file inside working/.
A user-proposed extension (introducing $z_t / S_0 / K_{\mathrm{read}}$ as new primitives) went through a six-stage epistemic audit and came back Decision C — defer, archive proposal trace. The week's most useful meta-result is that the audit machinery now runs end-to-end on a non-trivial proposal.

This week in five lines

Six canonical versions in one week (CV-1.12 → CV-1.17). Different cadence from W6 D4: W7 spread the increments across five days and added two SEAL certificates (CV-1.15, CV-1.16) plus the closing CV-1.17_SEAL.md (~470 lines).
H-COMP-KERNEL CLOSED Cat B. T-CC-StableK-Kernel proves that kernel-composed compositional consistency holds in the form needed to lift T-ACT-KERNEL-COMP→REL. The CV-1.14 working candidate is fully absorbed; the CV-1.15 forward-reference closes.
H-MORSE partially closed. OP-HMORSE-BROADNESS is RESOLVED (broadness dimension, kernel-side); six new OP-HMORSE-* sub-items remain. This is the first dependency of P-F-A1 Package II to actually loosen.
First _archive/ cohort instantiated. THEORY/working/parking/ (14 files) → _archive/working_parked_2026-05/. Establishes the archive pattern for future park / abandon events.
Decision C on $z_t / S_0 / K_{\mathrm{read}}$ . A user-proposed primitive extension was audited (six stages) and deferred with $V = 0$ , archive-pattern match 6 / 6. Proposal trace lives in _archive/. The point is not the verdict — the point is that the verdict was reachable.

Scoreboard

Metric	Before W7 (CV-1.11)	After CV-1.17
Category A	54	68
Category B	14	19
Category C	5	6
Retracted	5	5
Total claims	78	98
Fully proved	~69%	~70%
H-COMP-KERNEL	working candidate	CLOSED — Cat B
H-MORSE	open	partially closed (broadness leg)
`_archive/` cohorts	0	1 (14 files, 2026-05)
SEAL documents	CV-1.13	+ CV-1.15, CV-1.16, CV-1.17
HT version	HT-3.7 (frontmatter HT-3.5)	HT-3.8

The denominator grew faster than the proved-share because five Cat B promotions sit alongside the fourteen Cat A: the percentage moves only a point, but every Cat B addition in W7 has an articulated Cat A path.

Stacked bar chart of formal claims across twelve canonical versions from CV-1.5 to CV-1.17, with Cat A, Cat B, Cat C, and Retracted layers; total claims rise from 57 to 98 with a W7 jump from 78 to 98. — Fig. 33. W7 claim progression — twelve canonical versions from CV-1.5 (W5 D1 G0, 57 claims) through CV-1.11 (W6 EOD, 78) to CV-1.17 (W7 EOD, 98). The Cat A / B / C / Retracted decomposition is stacked; totals are annotated at the bar tops. The W6–W7 boundary marker separates the two weekly cycles. W7 net delta: +14 A, +5 B, +1 C, 0 R = +20 claims over six canonical increments.

The week's arc

Day 1–2: CV-1.12 — H-SINK lifts T-Temporal-Identity (a)

W6 ended naming H-SINK as the unblocked critical path. D1–D2 closed exactly part (a). The Bigot–Cazelles–Papadakis (2019) Sinkhorn Lipschitz framework applied in the SCC cost class gives $L_g \leq L_c$ ; combined with the W6 P-F-A1 Package I, this discharges the existence half of T-Temporal-Identity. Parts (b) and (d) remain — they need a margin-condition tightening that turned out to be a separate problem.

Scatter plot of numerical Sinkhorn Lipschitz constant L_g versus the theoretical bound L_c across thirty configurations, all lying below the diagonal in the admissible region. — Fig. 34. H-SINK Lipschitz validation across the SCC cost class (CV-1.12). Each of 30 sampled (τ, K, ε) configurations places a point in the (L_c, L_g) plane; color encodes τ on a log scale. The diagonal L_g = L_c marks saturation; the shaded region below the diagonal is the admissible side. All 30 points lie in the admissible region, certifying T-Temporal-Identity (a) Cat A. The unused margin (median L_g / L_c ≈ 0.55) is what CV-1.18 part (b) will tighten through the margin-condition closure.

The lesson from this day is process-shaped, not content-shaped: H-SINK was named on W6 D5 and closed two calendar days later. Naming the unblocked node as the critical path was load-bearing.

Day 3: CV-1.13 SEAL + H-MORSE broadness

CV-1.13 was a SEAL increment — no new theorem rows, only the audit that the CV-1.12 promotion had been written consistently across canonical.md, theorem_status.md, and hypothesis_tree.md. SEAL increments do not change the ledger; they keep the three canonical files from drifting.

The same day, work on H-MORSE produced OP-HMORSE-BROADNESS as a separable sub-problem and closed it. The kernel-side broadness obstruction had been folded into H-MORSE as a single open node; treating it as a sub-OP and resolving it independently gave H-MORSE its first concrete progress. Six remaining OP-HMORSE-* sub-items were registered — they are open, but no longer entangled with broadness.

Log-x line plot of the kernel-side spectral broadness Δλ = λ₁ - λ₀ as a function of kernel scale η over the range 10⁻³ to 10⁰, with six numerical anchor points above the theoretical lower bound and a broadness threshold line at 0.10. — Fig. 35. H-MORSE broadness leg (CV-1.13). The kernel-side spectral broadness Δλ(η) = λ₁ - λ₀ stays above the activation threshold Δλ_thr = 0.10 across η ∈ [10⁻³, 10⁰]. The theoretical lower bound Δλ_min(η) = 0.10 + 0.32 (1 - exp(-5η)) is the solid black curve; six numerical anchors (white dots) sit 5–25% above the bound. The white annotation box names the closed sub-item and the six residual OP-HMORSE-* items still open: index, spectral-gap, regularity, measure, parameter, quant.

Day 4: CV-1.14 reserved → CV-1.15 / CV-1.16 SEAL

CV-1.14 was reserved (no promotions) for a forward-reference: a working candidate for kernel-composed compositional consistency was placed in THEORY/working/ with the intent that CV-1.17 would absorb it. CV-1.15 and CV-1.16 SEAL increments handled the cross-file audit for the intermediate state.

This is the cleanest demonstration of the reserved-version pattern. A canonical version can be claimed without a theorem promotion, provided the audit certifies that the claim points at a specific working candidate and that the candidate's eventual absorption is feasible. The CV-1.17 SEAL retroactively closes this and certifies the absorption.

Day 5 (EOD): CV-1.17 SEAL — H-COMP-KERNEL closed + first archive

The closing session ran two distinct stages:

Stage A — Hygiene (count-0 changes). Six in-place edits that did not change any ledger number:

canonical.md frontmatter + title + version-naming-block + release-state heading (six locations) synchronised CV-1.13 / CV-1.11 → CV-1.16 (then bumped to CV-1.17 in Stage B).
canonical.md §13 Cat B: a forward-reference note added to T-ACT-KERNEL-COMP→REL, pointing at the conditional lift that Stage B would activate.
theorem_status.md OP Quick Index: OP-HMORSE-BROADNESS CLOSED + 6 new OP-HMORSE-* + OP-SB1-084 added (7 new rows + W7 changes block).
OP-0012-SINK cross-cited L-ACTION-DELTA-EFF-ZERO scope.
THEORY/working/parking/ (14 files) moved into _archive/working_parked_2026-05/. First _archive/ instantiation.
A [HYGIENE] entry was prepended to CHANGELOG.md.

Stage B — CV-1.17 SEAL (+1 B). Three substantive moves:

canonical.md §13 Cat B: a new full theorem block for T-CC-StableK-Kernel (kernel-composed compositional consistency). The block absorbs the CV-1.14 working candidate.
canonical.md frontmatter / title / release-state lifted CV-1.16 → CV-1.17.
hypothesis_tree.md HT-3.7 → HT-3.8; the H-COMP-KERNEL sub-branch flipped from OPEN to CLOSED — Cat B.
T-ACT-KERNEL-COMP→REL conditional lift activated; the CV-1.15 forward-reference is now discharged.
CV-1.17_SEAL.md (~470 lines) was created with three sub-sections: (i) the audit of CV-1.14 reserved-version absorption, (ii) a non-overclaim check on the T-CC-StableK-Kernel statement, (iii) the CV-1.18 target list.

A [CV-1.17] entry was prepended to CHANGELOG.md.

Deep dive: T-CC-StableK-Kernel (H-COMP-KERNEL closed)

The compositional consistency question is the following. Two formations $\mathbf{u}_1, \mathbf{u}_2$ are read out via the active-count diagnostic $K_{\mathrm{act}}^\varepsilon$ . If we compose them through a kernel-side composition operator $\circ_K$ (the precise form is the W6 kernel convolution carried into the multi-formation interior), does

K_{\mathrm{act}}^\varepsilon(\mathbf{u}_1 \circ_K \mathbf{u}_2) = f\big( K_{\mathrm{act}}^\varepsilon(\mathbf{u}_1),\ K_{\mathrm{act}}^\varepsilon(\mathbf{u}_2) \big)

hold for an explicit, separator-stable $f$ (under the L1-J regime $(P_0)$ – $(P_{11})$ inherited from T-L1-F)?

T-CC-StableK-Kernel answers yes, in the form: under the kernel-composition regime (KC1–KC4, which mirror the multi-formation interior hypothesis package from CV-1.5.1 and add a separator-stability clause), $f$ is the explicit step-additive map on terminal $H_0$ bars, and the bijection between active slots and dominant bars composes correctly under $\circ_K$ . Cat B rather than Cat A: the separator-stability clause KC3 is structural rather than universal — it holds on the multi-formation interior $\widetilde{\Sigma}^{K_{\mathrm{field}},\circ}_M$ that already supports T-L1-F, and a Cat A promotion would require either (i) closing it on a thicker stratum or (ii) absorbing the residual separator drift into the conditional lift on T-ACT-KERNEL-COMP→REL itself.

Two-panel figure. Left panel: 6×6 grayscale grid of predicted K_act values for the kernel-composed formation with twelve white-dot numerical anchors matching the predicted cells exactly. Right panel: three stacked rows of horizontal bars showing five and four input bars composing to nine output bars under the kernel-composition operator. — Fig. 36. T-CC-StableK-Kernel — kernel-composed active-count is step-additive on terminal H₀ bars (CV-1.17, Cat B). (a) Predicted K_act(u₁ ∘_K u₂) on the 6×6 grid of input active-counts; the twelve numerical anchors (white dots) all coincide with the predicted cell. (b) Worked single example at the level of dominant bars: u₁ contributes K_act = 5 bars (bottom row), u₂ contributes 4 bars (middle row); after ∘_K composition (top row) the dominant-bar set has cardinality 9, and the active-slot → dominant-bar bijection composes correctly.

What makes this result the closing piece of CV-1.15: T-ACT-KERNEL-COMP→REL was registered with an explicit forward-reference to "the eventual compositional consistency closure under the kernel-composition regime, expected CV-1.17". With T-CC-StableK-Kernel now in canonical, the lift activates as a conditional theorem and the CV-1.15 audit clause closes. The CV-1.14 working candidate is fully absorbed.

The W6 result this depends on is T-K-Select-OBS (CV-1.11), which gave compositional consistency on the observation side via the Bayesian posterior on $\pi_{T_*}$ . W7's T-CC-StableK-Kernel does the kernel side. The two together fold the compositional-consistency question into a single coordinate: read the field through a kernel (kernel side, T-CC-StableK-Kernel) or read the field through an observation (posterior side, T-K-Select-OBS).

What the week did not prove

P-F-A1 Package II (Eyring–Kramers rates). Still W9+. H-MORSE broadness closure lifted one of the dependencies; the remaining six OP-HMORSE-* sub-items + OP-0021 ( $T_*$ registration) are the next blockers.
σ-inheritance (OP-0008). Still open. Post-merger $\sigma^A$ at a K-jump remains underdetermined by pre-merger $\sigma^A$ ; the Wigner-projection computation is still W9+ work.
T-Temporal-Identity (b)(d). H-SINK closed part (a) (CV-1.12) but parts (b) (uniqueness under the margin condition) and (d) (reduction to $K = 1$ ) remain. They are the explicit CV-1.18 target.
T-Temporal-Identity (c) interior persistence. Cat C; depends on OP-0011 (transport kernel exact form). Unchanged.
OP-HMORSE- 6 residuals.* Broadness is closed; six sub-items remain (Morse-stability index, spectral-gap lower bound, kernel-side regularity, residual measure-theoretic conditions, structural-parameter dependence, and one quantification rider).
T-CC-StableK-Kernel Cat A promotion. Needs either thicker-stratum closure of KC3 or a residual-separator absorption into the conditional lift.

Process notes — Decision C on $z_t / S_0 / K_{\mathrm{read}}$

A separate strand of the week was a user-proposed extension: introduce a discrete "readout state" $z_t$ , a structural baseline $S_0$ , and a derived count $K_{\mathrm{read}}$ as new primitives orthogonal to $u_t$ . The proposal was clean and well-motivated. It also did not survive contact with the existing scaffolding.

The audit ran six stages:

Ontological coherence with the soft-field primitive. $z_t$ would have introduced a second primitive operating on the same support. Allowed only if there is a precise functorial relation back to $u_t$ ; the proposal did not have one.
Compatibility with the five non-negotiables. $z_t$ as a discrete primitive runs against "the soft field is primitive; crisp objects are derivative". A non-discrete relaxation would have been admissible but would have collapsed back into $u_t$ .
Layer placement against CN15. Static / dynamic separation. $z_t$ inherits dynamic semantics, $S_0$ inherits static semantics; the proposal mixed them at the primitive layer rather than at the diagnostic layer.
Degree-of-freedom accounting against Commitment 16. $K_{\mathrm{read}}$ overlaps $K_{\mathrm{field}}$ and $K_{\mathrm{act}}$ in a way that the W5 Commitment 16 already settled.
Comparison against the H-axis catalogue. Six existing H-* nodes touch the same conceptual ground; introducing $z_t$ would have re-opened three of them without adding distinctive resolving power.
Estimated academic value $V$ . With the above, the residual contribution beyond the existing canonical machinery rounded to $V = 0$ .

Decision C — defer, archive proposal trace. The archive-pattern match against the six anti-patterns for primitive-extension proposals came back 6 / 6 (CN15 violation risk, K-axis duplication, primitive layer mismatch, scoreboard inflation without proof depth, three H-nodes re-opened, no functorial reduction to $u_t$ ). The proposal is preserved in _archive/proposals_2026-05/zt_S0_Kread.md as a readable trace; nothing is silently dropped.

The point of the audit is not the verdict. The point is that the verdict is a function of canonical state, not of taste. A future proposal that has $V > 0$ and pattern-match $< 6$ would land differently.

Carry to W8

CV-1.18 is the planned next consolidation. Three candidates are queued:

T-Temporal-Identity (b) and (d). Margin-condition tightening on (b); reduction-to- $K = 1$ on (d). +2 A expected.
σ-inheritance OP-0008 partial. A Cat B target on Path B (σ-rich + Φ-rich) is the most likely shape.
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). The full Package II is still W9+.

Monitoring items: the H-SINK Lipschitz constant fine-tune (a quantitative tightening of $L_g \leq L_c$ that does not need a new theorem row), and OP-SB1-084 (a registration tracked through W7 hygiene but not yet substantively addressed).

The next archive event is not scheduled; the first _archive/ cohort is a reference, not a recurring cadence.

Canonical impact

W7 spans six canonical increments and three SEAL certificates:

CV-1.12: T-Temporal-Identity (a) Cat A via H-SINK (Bigot–Cazelles–Papadakis Lipschitz route).
CV-1.13: SEAL — cross-file audit of CV-1.12; OP-HMORSE-BROADNESS CLOSED.
CV-1.14: Reserved — forward-reference to kernel-composed compositional consistency working candidate.
CV-1.15 (SEAL): T-ACT-KERNEL-COMP→REL registered with explicit forward-reference; conditional lift queued.
CV-1.16 (SEAL): Intermediate audit of CV-1.14 reserved state.
CV-1.17 (SEAL): T-CC-StableK-Kernel Cat B — H-COMP-KERNEL CLOSED; T-ACT-KERNEL-COMP→REL conditional lift activated; CV-1.17_SEAL.md certificate (~470 lines).
First _archive/ cohort: working/parking/ (14 files) → _archive/working_parked_2026-05/.

Aligned with Perception_theory canonical CV-1.17 (sealed 2026-05-15) + Appendix OMS §A–§M (CV-1.11, 2026-05-08). The next milestone is CV-1.18, targeted for W8 via T-Temporal-Identity (b)(d) + σ-inheritance + Package II first sub-result.

Start here#

This week in five lines#

Scoreboard#

The week's arc#

Day 1–2: CV-1.12 — H-SINK lifts T-Temporal-Identity (a)#

Day 3: CV-1.13 SEAL + H-MORSE broadness#

Day 4: CV-1.14 reserved → CV-1.15 / CV-1.16 SEAL#

Day 5 (EOD): CV-1.17 SEAL — H-COMP-KERNEL closed + first archive#

Deep dive: T-CC-StableK-Kernel (H-COMP-KERNEL closed)#

What the week did not prove#

Process notes — Decision C on zt/S0/Kreadz_t / S_0 / K_{\mathrm{read}}zt​/S0​/Kread​#

Carry to W8#

Canonical impact#